Foundations of Physics - Science topic

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How to Ground Science and Philosophy Together Axiomatically?

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1 Jul 2023

HOW TO GROUND SCIENCE AND PHILOSOPHY TOGETHER AXIOMATICALLY?

Raphael Neelamkavil, Ph.D., Dr. phil.

We see many theories in physics, mathematics, etc. becoming extremely axiomatic and rigorous. They call themselves or attempt to be as quantitative as possible. But are adequate comparisons between mathematics, physical sciences, biological sciences, human sciences, and philosophy, and adequate adaptation of the axiomatic method possible by creating a system of all exact, physical, and human sciences that depend only on the quantitively qualitative proportionalities and call them invariables?

They cannot do well enough to explain Reality-in-total, because Reality-in-total primarily involves all sorts of ontological universals that are purely qualitative, and some of them are the most fundamental, proportionality-type, quantitative invariables of all physical existents in their specificity and totality in their natural kinds. But as the inquiry comes to Reality-in-total, ontological qualitative universals must come into the picture. Hence, merely quantitative (mathematical) explanations do not exhaust the explanation of Reality-in-total.

Existence as individuals and existence in groups are not differentiable and systematizable in terms of quantitatively qualitative universals alone. Both qualitative and quantitatively qualitative universals are necessary for this. Both together are general qualities pertaining to existents in their processual aspect, not merely in their separation from each other. Therefore, the primitive notions (called traditionally as Categories) of Reality-in-total must be ontological qualitative universals involving both the qualitative and quantitative aspects. The most basic of universals that pertain properly to Reality-in-total are now to be found.

Can the primitive notions (Categories) and axioms of the said sciences converge so that the axioms of a system of Reality take shape from a set of the highest possible ontological Categories as simple sentential formulations of the Categories which directly imply existents? This must be deemed necessary for philosophy, natural sciences, and human sciences, because these deal with existents, unlike the formal sciences that deal only with the qualitatively quantitative form of arguments.

Thus, in the case of mathematics and logic there can be various sorts of quantitative and qualitative primitive notions (categories) and then axioms that use the primitive notions in a manner that adds some essential, pre-defined, operations. But the sciences and philosophy need also the existence of their object-processes. For this reason, the primitive axioms can be simple sentential formulations involving the Categories and nothing else. This is in order to avoid indirect existence statements and to involve existence in terms exclusively of the Categories.

Further, the sciences together could possess just one set of sufficiently common primitive notions of all knowledge, from which also the respective primitive notions and axioms of mathematics, logic, physical and human sciences, and philosophy may be derived. I support this view because the physical-ontological Categories involving the existence of Reality and realities, in my opinion, must be most general and fully exhaustive of the notion of To Be (existence) in a qualitatively universal manner that is applicable to all existents in their individual processual and total processual senses.

Today the nexus or the interface of the sciences and philosophies is in a crisis of dichotomy between truth versus reality. Most scientists, philosophers, and common people rush after “truths”. But who, in scientific and philosophical practice, wants to draw unto the possible limits the consequences of the fact that we can at the most have ever better truths, and not final truths as such?

Finalized truths as such may be concluded to in cases where there is natural and inevitable availability of an absolute right to use the logical Laws of Identity, Contradiction, and Excluded Middle, especially in order to decide between concepts related to the existence and non-existence of anything out there.

Practically very few may be seen generalizing upon and extrapolating from this metaphysical and logical state of affairs beyond its epistemological consequences. In the name of practicality, ever less academicians want today to connect ever broader truths compatible to Reality-in-total by drawing from the available and imaginable commonalities of both.

The only thinkable way to accentuate the process of access to ever broader truths compatible to Reality-in-total is to look for the truest possible of all truths with foundations on existence (nominal) / existing (gerund) / To Be (verbal). The truest are those propositions where the Laws of Identity, Contradiction, and Excluded Middle can be applied best. The truest are not generalizable and extendable merely epistemologically, but also metaphysically, physical-ontologically, mathematically, biologically, human-scientifically, etc.

The agents that permit generalization and extrapolation are the axioms that are the tautologically sentential formulations of the most fundamental of all notions (Categories) and imply nothing but the Categories of all that exist – that too with respect to the existence of Realit-in-total. These purely physical-ontological implications of existence are what I analyze further in the present work. One may wonder how these purely metaphysical, physical-ontological axioms and their Categories can be applicable to sciences other than physics and philosophy.

My justification is as follows: Take for example the case of the commonality of foundations of mathematics, logic, the sciences, philosophy, and language. The notions that may be taken as the primitive notions of mathematics were born not from a non-existent virtual world but instead from the human capacity of spatial, temporal, quantitatively qualitative, and purely qualitative imagination.

I have already been working so as to show qualitative (having to do with the ontological universals of existents, expressed in terms of adjectives) quantitativeness (notions based on spatial and temporal imagination, where, it should be kept in mind, that space-time are epistemically measuremental) may be seen to be present in their elements in mathematics, logic, the sciences, philosophy, and language.

The agents I use for this are: ‘ontological universals’, ‘connotative universals’, and ‘denotative universals’. In my opinion, the physical-ontological basis of these must and can be established in terms merely of the Categories of Extension-Change, which you find being discussed briefly here.

Pitiably, most scientists and philosophers forget that following the exhaustively physical-ontological implications of To Be in the foundations of science and philosophy is the best way to approach Reality well enough in order to derive the best possible of truths and their probable derivatives. Most of them forget that we need to rush after Reality, not merely after truths and truths about specific processes.

Bibliography

(1) Gravitational Coalescence Paradox and Cosmogenetic Causality in Quantum Astrophysical Cosmology, 647 pp., Berlin, 2018.

(2) Physics without Metaphysics? Categories of Second Generation Scientific Ontology, 386 pp., Frankfurt, 2015.

(3) Causal Ubiquity in Quantum Physics: A Superluminal and Local-Causal Physical Ontology, 361 pp., Frankfurt, 2014.

(4) Essential Cosmology and Philosophy for All: Gravitational Coalescence Cosmology, 92 pp., KDP Amazon, 2022, 2nd Edition.

(5) Essenzielle Kosmologie und Philosophie für alle: Gravitational-Koaleszenz-Kosmologie, 104 pp., KDP Amazon, 2022, 1st Edition.

Relevant answer

6 Apr 2024

Answer

Preprint GRAVITATIONAL COALESCENCE COSMOLOGY (22 pp.) Part II

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Physical and Exact Sciences and Axiomatic Philosophy: Introducing Grounding (long text)

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6 Jul 2023

PHYSICAL AND EXACT SCIENCES AND AXIOMATIC PHILOSOPHY:

INTODUCING GROUNDING

Raphael Neelamkavil, Ph.D., Dr. phil.

1. WHY SHOULD PHYSICS AND COSMOLOGY BE GROUNDED?

I get surprised each time when some physicists tell me that either the electromagnetic (EM) or the gravitational (G) or both the forms of energy do not exist – that EM and G are, are "existent" neither like nor unlike material bodies – but that EM and G are to be treated or expressed as mathematical waves or particles propagated from material objects that of course exist for all sciences.

Some of them put in all their energies to show that both EM and G are mere mathematical objects, fields, etc., and not physically existent objects or fields of energy emissions that then become propagations from material bodies. If propagation from material bodies, then their nature too would have to be similar to that of material bodies!!! This is something that the mathematical realists of theoretical physics and cosmology cannot bear!!!

This is similar in effect to Newton and his followers thinking honestly and religiously that at least gravitation and perhaps also other energies are just miraculously non-bodily actions at a distance without any propagation particles / wavicles. But I admit that I explained certain things in the first paragraph above as if I myself were a Newtonian. This has been on purpose.

Even in the 21st century, we must be sharply aware that from the past more than 120 years the General Theory of Relativity with its various versions and especially its merely mathematical interpretations have succeeded in casting and maintaining the power of a terrifying veil of mathematical miracles on the minds of many scientists – miracles such as the mere spacetime curvature being the meaning of gravitation and all other sorts of fields. The mathematics did not need existence, and hence gravitation did not exist! But the same persons did not create a theory whereby the mathematics does not need the existence of the material world and hence the material world does not exist!!

A similar veil has been installed by quantum physics on the minds of many physicists and their audience too. We do not discuss it here. Hence, I have constructed in four published books a systemic manner of understanding these problems in cosmology and quantum physics. I do not claim perfection in any of my attempts. Hence, I keep perfecting my efforts in the course of time, and hope to achieve some improvement. The following is a very short attempt to summarize in this effort one important point in physics, cosmology, and the philosophy of physics and of cosmology.

There exists the tradition of lapping up whatever physicists may say about their observable and unobservable constructs, based on their own manner of using mathematics. The mathematics used are never transparent. Hence, the reader or the audience may not have the ability to makes judgements based on the minimum physical ontology expected of physicists. I believe that this should stop forever at least in the minds of physicists. Moreover, physicists are not to behave like magicians. Their readers and audience should not practice religious faithfulness to them. Nor should physicists expect it from them.

2. ONTOLOGICALLY QUALITATIVE NATURE OF INVARIANTS

When the search is for the foundations of any science, it is in fact for the invariant aspects of all the realities of that science, and not merely for the invariant aspects of some parts of the realities (object-set/s), methods, conclusions, etc. This does not suffice for science for maximizing success. This is because, any exclusive search for the foundations of the specific object-set or of the discourse of the specific object-set will further require foundations upon the totality of all specific object-sets and their discourse.

We find ourselves in a tradition that believes that proportionality quantities are to be taken as the invariables in physics. But I used to reduce into universal qualities the quantitative-structural aspect of all sciences, that are represented in mathematics as the ontological quantities dealt with in science. The real invariants of physics are not the ontological quantities or proportionalities of certain quantities being treated in physics.

The latter, being only the constant quantities, are one kind of ontological qualities, namely, (1) the quantitatively expressible qualities of processes, e.g., ‘quantity’, ‘one’, ‘addition’, etc. are explicable, respectively, as the qualities: ‘being a specific quantity’, ‘being a unity’, ‘togetherness of two or more units’, etc. The other kind is (2) the ontological qualities of processes in general (say, malleability, toughness, colour, redness, etc.) which cannot directly be expressed as ontological quantities of processes. This shows that pure ontological qualities are a more general notion than ontological quantities and includes the latter.

Explaining ontological qualities in terms of physical quantities cannot be done directly by fundamental physical quantities, but by physical properties that involve fundamental physical quantities. Properties are a mix mainly of ontological qualities and of course includes ontological quantities, of which some are the fundamental physical quantities. Hence, the invariants must be qualities that are generative of and apply to both quantities and non-quantities. These invariants then are fully qualitative.

If the invariants apply to all physical processes, these invariants are qualities ontologically universal to all of them in the specified group. Out of them are constructed properties by mixing many qualitative and quantitatively qualitative universals. Clearly, universals applying to all existents are the real invariants of all Reality – which is a matter to be discussed later.

Since universals are all qualitative and some of them are quantitative as qualities, ontological qualities are broader than mathematical in scope, because, the moment mathematics uses quantities, the use is not of quantities devoid of qualities, but instead, of the quantitative variety of general / universal qualities.

Qualities can also behave as some of the primitive notions that underlie all of physics and other sciences – but this will not exhaust the most necessary foundations of physics and other sciences, because these sciences require the general qualities of all existents, and not merely those of mathematics. These are the axiomatically formulable Categorial notions of philosophy, which latter is thus a general science.

In short, quantitative proportionalities as invariants are very partial with respect to existent processes and their totality. Naturally, philosophy too needs general qualities and not merely quantitative qualities to base the discipline.

3. DIFFERENCES IN FOUNDATIONS: EXACT AND NATURAL SCIENCES AND PHILOSOPHY

The agents that permit generalization and extrapolation are the axioms that are the tautologically sentential formulations of the most fundamental of all notions (Categories) and imply nothing but the Categories of all that exist – that too with respect to the existence of Reality-in-total. These purely physical-ontological implications of existence are what I analyze further in the present work. One may wonder how these purely metaphysical, physical-ontological axioms and their Categories can be applicable to sciences other than physics and philosophy.

4. SYSTEMIC FOUNDATIONS VS. EXISTENCE/TS, NON-EXISTENCE/TS

4.1. Basis of Axiomatizing Science and Philosophy

The problem of axiomatizing philosophy, and/or philosophy of science, and/or all the sciences together is that we need to somehow bring in the elemental aspects of existence and existents, and absorb the elemental aspects of non-existence and non-existent objects that pertain to existents. Here it should be mentioned that axiomatizing mathematics and logic does not serve the axiomatization of philosophy, and/or philosophy of science, and/or all the sciences together. So far in the history of philosophy and science we have done just this, plus attempts to axiomatize the sciences separately or together by ignoring the elemental aspects of non-existence and non-existent objects that pertain to existents.

Existence (To Be) is not a condition for the possibility of existence of Reality-in-total or specific processual objects, but instead, To Be is the primary condition for all thought, feeling, sensation, dreaming, etc. All other conditions are secondary to this. If To Be is necessary as the condition for the possibility of any philosophy and science as discourse, we need to be axiomatic in philosophy and science about (1) existence (To Be, which is of all that exist) and/or (2) the direct and exhaustive implications of existence.

It is impossible to define existence without using words that involve existence. But it is possible to discover the exhaustive implications of To Be in order to use them in all discourse. Therefore, towards the end of this short document, I shall name what could be the inevitable primitive notions that are exhaustive of To Be and that may be used to create axioms for both philosophy and science together.

To put it differently, I attempt here to base all philosophy and science on the concept of existence of Reality-in-total as whatever it is, by deriving from the concept of the existence of all that exist the only possible (i.e., the exhaustive) implications of To Be.

Of course, the basic logical notions of identity and contradiction will have to be used here without as much danger as when we use them in statements on other less fundamental notions. I would justify their use here as the rational inevitabilities in the foundations – not as inevitabilities in the details that issue later. The inevitabilities in the later details need never to be realized as inevitabilities, because To Be implies some fundamental notions which will take case of this.

That is, the various ways in which the principles of identity and contradiction should be seen as inexact and inappropriate may be discovered in the in fields of derivation beyond the provinces of the fundamental Categorial implications of To Be. This latter part of the claims is not to be discussed here, because it involves much more than logic – in fact, a new conception of logic, which I would term as systemic logic.

Let me come to the matter that I promise in the name of the foundations of ‘Axiomatic Philosophy and Science’. First of all, to exist is not to be merely nothing. In this statement I have taken access to the Laws of Identity, Non-Contradiction, and Excluded Middle at one go in that whatever is, must be whatever it is, and not its opposite which is nothing but nothing, nor a middle point between the two extremes.

Therefore, existence must always be non-vacuous. That is, the primary logical implication of To Be is the non-non-being of whatever exists. But such a logical implication is insufficient for the sciences and philosophy, because we deal there with existents. Hence, let us ignore the logical implication as a truism. The existential implications of To Be are what we need.

I have so far not found any philosopher or scientist who derived these implications. But let us try, even if the result that obtained may be claimed by many ancients and others as theirs. In fact, theirs were not metaphysical / physical-ontological versions. Their epistemic versions of the same have been very useful, but have served a lot to misguide both philosophy and science into give “truth/s” undue importance in place of “Reality”. My claim about the exhaustive physical(-ontological) implications of To Be that I derive here is that they do not incur this fallacy.

To Be is not a thing. It is, as agreed at the start, the very condition for the possibility of discourse: philosophy, science, literature, art … and, in general, of experience. The To Be of existents is thus not a pre-condition for To Be – instead, it is itself the source of all conditions of discourse, not of existence.

4.2. Extension, Change, Universal Causality

If To Be is non-vacuous, it means that all existents are something non-vacuously real. Something-s need not be what we stipulate them to be, both by name and qualifications. But the purely general implication is that existents are something-s. This is already part of philosophical activity, but not of the sciences. We need to concretize this implication at the first tire of concrete implications. Only thereafter are sciences possible.

To be something is to be non-vacuous, i.e., to be in non-vacuous extendedness. However much you may attempt to show that Extension does not follow from the notions of To Be, something, etc., the more will be extent of your failure. You will go on using the Laws of Identity, Contradiction, and Excluded Middle, and never reach any conclusion useful for the sciences. Then you will have to keep your mouth and mind shut. I prefer for myself meaningful discourse in science and philosophy – when I meditate I shall attempt to keep my mind and lips as “shut” as possible.

As said above, Extension is one of the primary physical-ontological implications of To Be. Nothing exists without being extended, without being in Extension. Extended something-s are not just there in Extension. If in Extension, everything has parts. Thus, having parts is one of the primary implications of being something in existence. I term it alternatively also as Compositionality.

It is the very implication of being something that something-s are in Change. The deepest and most inevitable form of implication of Change is this: nothing that is in existence with parts can have the status of being something existent without the parts impacting at least a few others. This is the meaning of Change: impact-formation by extended parts. Any existent has parts existing in the state of impact formation in other parts and in themselves.

Hence, Change is the only other implication of To Be, not second to but equally important as Extension. I call it differently also as Impact-Formation. The notion of motion or mobility does not carry the full weight of the meaning of Change.

There cannot be any other implication equally directly derivable from To Be as Extension and Change can be. In other words, all other implications can be found to be sub-implications of Extension-Change, i.e., involving only Extension-Change. Showing them as involving only Extension-Change would suffice to show their sub-implications status with respect to Extension-Change.

Existence in Extension-Change belongs to anything existent, hence ubiquitous – to be met with in any existent. This is nothing but existence in the ubiquitously (to be met with in any existent) extended form of continuance in ubiquitous (to be met with in any existent) impact formation. What else is this but Universal Causality?

If you say that causation is a mere principle of science – as most philosophers and scientists have so far thought – I reject this view. From the above paragraphs I conclude that Causation is metaphysically (physical-ontologically) secondary only to existence. Everybody admits today that we and the universe exist. But we all admit that every part of our body-mind and every existent in the world must be causal because we are non-vacuously existent in Extension-Change.

This means that something has been fundamentally wrong about Causality in philosophy and science. We need to begin doing philosophy and science based fully on To Be and its implications, namely, Extension-Change-wise continuance, which is nothing but being in Universal Causation. It is universal because everything is existent. Universal Causality is the combined shape of Extension-Change. Causation the process of happening of Extension-Change-wise continuance in existence. Causality is the state of being in Extension-Change-wise continuance in existence.

4.3. Now, What Are Space and Time?

Note that what we measurementally and thus epistemically call as space is metaphysically to be termed as Extension. Space is the measuremental aspect of the primary quality of all existents, namely, of Extension. That is, space is the quantity of measurement of Extension, of measurements of the extended nature of existents. In this sense, space is an epistemic quality.

Further, note also that what we call time is the measuremental aspect of the primary quality of all existents, namely, of Change. If there is no impact-formation by parts of existents, there is no measurement called time. Hence, time is the epistemic quality of measurements of Change, which is the impact-formation tendency of all existents.

Immanuel Kant termed space as the condition for the possibility of sensibility, and Edmund Husserl called it as one of the fundamental essences of thought. Space and time in Kant are epistemic since they are just epistemic conditions of possibility; and essences in Husserl are epistemic, clearly as they are based on the continuous act of epochḗ.

Nothing can exist in epistemic space-time. That is, language and mind tend to falsely convert space and time into something that together condition existents. Thus, humans tend to believe that our measuremental concepts and derivative results are all really and exactly very essential to existent something-s, and not merely to our manner of knowing, feeling, sensing, etc.

This is the source of scientific and philosophical misconceptions that have resulted in the reification of the conclusions and concepts of thought and feeling. Thus, this is also the source of conceptual insufficiencies in philosophical and scientific theories. Scientism and scientific and mathematical instrumentalism justify these human tendencies in the name of pragmatism about science and thought.

Reification of certain statistical conclusions as probabilities and the metaphysicization of probable events as the only possible events are not merely due to the above sort of reification. It is also by reason of the equivocation of probability with possibility and the reification of our scientific and statistical conclusions of probabilities as real possibilities. Humans tend to forget that a certain amount of probability is exactly and properly the measure of the extent of human capacity (and by implication, of human incapacity), at a given instance and at a given measuremental moment of history, to use instruments to get at all the existents that are the causes of a given process.

As we know, To Be is not a Category / Quality. It is the very condition that is the same as the existence of something-s as whatever they are. This is a tautology: To Be is To Be. If To Be is a metaphysical notion, the physical-ontologically and scientifically relevant metaphysical implications of To Be are Extension-Change. These are the highest and only highest Categories of all philosophy and science. Universal Causality is the notion of combination of Extension-Change. It is not an indirectly derived notion.

If scientists tend to relegate such notions as philosophical, they are trying to be practical in a silly manner. Even scientific results need the hand of proper and best possible formulations of notions and theoretical principles. Theoretical principles (say, of causation, conservation, gravitation, matter, mass, energy, etc., which may clearly be formulated in terms of Extension-Change-wise existence and existents) must be formulated in the most systemic manner possible.

I would call Extension, Change, and the combination-term Universal Causality not merely as the highest metaphysical Categories. They are the very primitive terms in addition to terms like ‘existent’, ‘matter-energy’, etc., which are necessary for an axiomatic formulation of the foundations of the sciences. Hence, we need to formulate axiomatically both philosophy and science.

Universal Causality may hereafter also be taken as an axiom in philosophy and the sciences. An axiom is a formulated basic principle. In that case, why not formulate also the primitive notions (Categories) of Extension and Change as axioms? In short, the difference between mathematical-logical axiomatic foundations and physical-philosophical axiomatic foundations is that in the former set primitive notions are not axioms, and in the latter primitive notions may be formulated as axioms.

In the light of the above discussion, it becomes clear that Einstein’s postulation of gravitation and matter-energy as space-time curvatures is at the most a formulation of these notions in terms of the mathematical necessity to use space-time (epistemic) measurements and theorize based on them in theoretical physics.

Einstein was immersed in the neo-positivism and logical positivism of his time. Hence, he could not reason beyond the use, by mathematics, of quantitative notions as concrete measurements. Scientists and philosophers who still follow Einstein on this sort of a misguided reification of epistemic space and time are taking refuge not on Einstein but on his theoretical frailties. Even today most scientists and philosophers are unaware that quantities are in fact quantitatively characterized pure qualities – and not properties that are combinations of qualitative and quantitatively qualitative notions.

Minkowski formulated the mathematics of space-time and thus reduced space-time into a sort of ether in which physical processes take place gravitationally. Einstein put gravitation into this language and mistook this language (the language of mathematical space-time) to be the very matter-energy processes that curve according to gravitational processes. For the mathematics this is no too great error, because it worked. This is why some physicists even today consider gravitation and/or all energy forms as ether, as if without this stuff in the background material bodies would not be able to move around in the cosmos! A part of the cosmos is thus being converted into a background conditioner!

Only formal functioning has so far been found necessary in mathematics. Derivation from the metaphysical sources of existents and non-existents has not so far been found necessary in mathematics. But, note here also this: for more than 100 years physicists and philosophers of physics lapped up this substitution of the language of mathematics for the actual, physically existent, processes, which otherwise should have been treated also metaphysically, and if possible, in a manner that is systemically comprehensive of the sources of all sciences.

The implications of existence, non-existence, existents, and non-existents too can help to make the mathematical adaptations work pragmatically. Hence, clearly it does not suffice that only the mathematical formalism attained so far be used in physics and the sciences. The project of science, philosophy, mathematics, and logic must grow out of their limits and become parts of a systemic science with foundations in the implications of existence, non-existence, existents, and non-existents.

I have been attempting to explain in these pages a limited realm of what I otherwise have been attempting to realize. I show only that there are two physical-ontological Categories and some derived axioms (out of these many axioms, only one is discussed here, i.e., Universal Causality), using which we need to formulate not merely philosophy but also physics and other sciences.

But I suggest also that the existence-related and non-existents-related mathematical objects too must be formulated using some primitive terms and axioms that are compatible with the philosophical and physical primitive terms and axioms that may facilitate a systemic approach to all sciences.

4.4. Why Then Is Science Successful?

The awarding of the Nobel Prize 2023 for quantum informatics to Alain Aspect, John F. Clauser, and Anton Zeilinger does not, therefore, mean that all of quantum physics and their assumptions and results are ‘the realities’ behind the ‘truths’ formulated. Instead, it means only that the truths they have formulated are relatively more technology-productive within the context of the other truths and technologies that surround them in physics. Quantum informatics works at a level of effects where we involve only those movements and processes that result in the resulting discoveries, general truths, and the derivative technology.

Similarly, the successes of engineering, informatics, medical processing technology, and the medical science that (as of today) are based on these need not be a proof for the alleged “absolute truth status” of the theories based on Newtonian physics, of molecular and atomic level chemistry and biology, etc. These sciences use only certain contextual levels of interaction in the physical world.

Recollect here the ways in which occidental philosophers dating at least from Parmenides and Heraclitus and extending up until today have been mistaking space and time as (1) two metaphysical categories, or (2) as mere existents, or (3) as illusions.

Oriental philosophies, especially Hindu and Buddhist, have been the best examples of rejecting space-time as metaphysical and as equivalent to permanent substances in a manner that made some Occidental thinkers to look down on them or to reject all of them. In the course of conceptualization that is typical of humans, having to create further theoretical impasses is necessarily to be avoided as best as we can. Such an ideal requires the help of Extension, Change, and Universal Causality.

In the foregoing paragraphs I have only hinted at the necessity of axiomatic philosophy and science. I have only suggested some basic notions in this systemic science. I do also use these notions and some axioms developed from them to formulate a new philosophy of mathematics. I have already published some books based on these and have been developing other such works. I hope to get feedbacks from earnest minds that do not avoid directly facing the questions and the risk of attempting a reply to the questions themselves.

Bibliography

(1) Gravitational Coalescence Paradox and Cosmogenetic Causality in Quantum Astrophysical Cosmology, 647 pp., Berlin, 2018.

(2) Physics without Metaphysics? Categories of Second Generation Scientific Ontology, 386 pp., Frankfurt, 2015.

(3) Causal Ubiquity in Quantum Physics: A Superluminal and Local-Causal Physical Ontology, 361 pp., Frankfurt, 2014.

(4) Essential Cosmology and Philosophy for All: Gravitational Coalescence Cosmology, 92 pp., KDP Amazon, 2022, 2nd Edition.

(5) Essenzielle Kosmologie und Philosophie für alle: Gravitational-Koaleszenz-Kosmologie, 104 pp., KDP Amazon, 2022, 1st Edition.

Relevant answer

6 Apr 2024

Answer

Preprint GRAVITATIONAL COALESCENCE COSMOLOGY (22 pp.) Part II

9 Recommendations

【NO.29】The Relation Between Mathematics and Physics (5) - If the quantization of nature is inevitable, what are its mathematical determinants?

asked a question related to Foundations of Physics

Question

19 answers

30 Jan 2024

The concept of quantization in physics begins with the expression E=hν, P=h/λ obtained from the blackbody radiation law, where h is the minimum amount of action [1]. Since there is a mass-energy relation E=mc^2 [2], all matter particles (with mass) can and must be equally capable of being expressed ‡ in terms of E=hν, which leads to the fact that the structure and interactions of all matter must be finite, integer multiples of the quantity hν. While the fact that ν can be continuous* does not prevent the fulfillment of occasions where there is a requirement for energy continuity, the discrete nature of the energy levels dictates that the choice of ν is finite.

In quantum mechanics, the state of a particle can be described by its wave function Ψ(r), or there can be described by the momentum representation φ(p). In fact, we can regard Ψ(r) as a time-domain energy packet and φ(p) as a frequency-domain momentum packet; momentum φ(p) and energy Ψ(r) are a pair of Fourier transformations. If the fundamental composition of matter is a variety of quanta E=hνi (i=1,2,3), then the momentum pi implied in all matter is also a variety. The Fourier transform of a continuous function in the time domain produces an infinite multitude in the frequency domain, and vice versa. Physics really cannot express infinite multinomials. Only the Fourier transform DFT of a finitely discrete time-domain function corresponds to a finite number of discrete terms in the frequency domain, which can express the physical reality under certain conditions. The Fourier transform is related in quantum mechanics to wave-particle duality, superposition, the uncertainty principle, measurement, etc. Therefore, we ask:

1) Is the discrete Fourier transformation the only inevitable choice for the quantization of physics?

2) Since everything is expressed by the photon's E=hν, should fermions (electrons, quarks), W bosons, gluons also be expressed by photons?

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Notes

‡ including all fermions, electrons, quarks, etc. Do we then need to find a direct compositional relation between fermions and E=hν? Since, the composition of quarks is associated with E=hν, why is the interaction not it, but changed to gluons?

* We need to think about the question, what must be the physical meaning of ν in E=hν?

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References

[1] Planck, M. (1900). The theory of heat radiation (1914 (Translation) ed., Vol. 144).

[2] Einstein, A. (1905). Does the inertia of a body depend upon its energy-content. Annalen der Physik, 18(13), 639-641.

[3]

Preprint The Relationship Between the Theory of Everything and the Co...

[4]

Preprint Convergent and Disperse Cyclic Multiverse Model (CDCMM)

Relevant answer

6 Feb 2024

Answer

Best wishes for a speedy recovery!

Once more: Quantization means constructing the quantum theory, whose classical limit is a given classical theory. If the classical theory is a relativistic field theory, the classical equations of motion describe nonlinear waves. In the quantum theory their states can be understood as multiparticle states that can be massless or massive. For the free theory, the dispersion relation can be shown to be hω=h|k| <=> E = |p|c for massless particles and

(hω)² = (hk)² + m²c⁴ <=> E²=|p|²c² + m²c⁴for massive particles.

So a massless particle doesn't display dispersion, since the phase velocity is equal to the group velocity of the wave, which is described by the coherent superposition of one-particle states, whereas the massive particle does display dispersion, since the phase velocity isn't equal to the group velocity.

The quantities that are relevant for describing a quantum field theory are the transition probabilities from any state of n particles, with given properties (energy, momentum, angular momentum, internal charges) to any state of n' particles with given properties. How to compute these is what quantization is about.

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Does 4 dimensional spacetime have a physical time component?

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43 answers

21 Sept 2023

An event in 4 dimensional spacetime is designated by coordinates x, y, z and t. Spacetime physically has the three spatial coordinates (x, y and z). Does spacetime also have a physical property that gives it a temporal coordinate? For example, the rate of time depends on the gravitational potential. Clocks run slower in the 4D space close to a large mass compared to the 4D space far from a large mass. Is this just an effect on physical objects such as clocks and atoms or does the space itself have a temporal property that is slowed by the effect of gravity?

This is a discussion question. Therefore, I will express my opinion. I believe in John Wheeler’s spacetime foam representation of spacetime. He said “Empty space is not empty. It is the seat of the most violent physics.” He then described spacetime on the scale of Planck length as having Planck length oscillations at Planck frequency. If spacetime has oscillations at a frequency that can be affected by gravity, then spacetime has an internal clock and a physical time component. Even the physical constants G, c, and ħ each have time components. It is not possible to define any of these three physical constants without introducing a local rate of time.

I think that spacetime must incorporate Planck frequency oscillations to achieve the temporal properties (the 4^th dimension) of spacetime. Do you agree or disagree? If you believe spacetime does not have an internal clock (oscillations), then what determines the local rate of time?

Relevant answer

Erhan Güler

4 Jan 2024

Answer

While providing a definitive answer is challenging, I can share my perspective on whether spacetime has an internal clock. Considering John Wheeler's spacetime foam theory, the idea that spacetime oscillates at Planck frequency seems intriguing and reasonable. If this oscillation frequency can be influenced by gravity, we might argue that spacetime possesses an internal clock.

However, this topic is complex, and the nature of spacetime's internal properties remains not fully understood. Further research is crucial to comprehending the intricacies of spacetime. If spacetime lacks an internal clock, there could be other factors determining the local rate of time—potentially tied to the topological or geometric features of spacetime.

In conclusion, the question of whether spacetime has an internal clock is still a subject of scientific debate, necessitating additional research for a more comprehensive understanding.

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【NO.25】The Relation Between Mathematics and Physics (1) - What Are the Fundamental Quantities in Physics?

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7 answers

28 Dec 2023

From the earliest Pythagorean (~570BCE-~490BCE) view that "everything is number" [1], to the founder of modern physics, Galileo (1564-1642), who said "the book of nature is written in the language of mathematics" [2], to attempts by Hilbert (1862-1943) to mathematically "axiomatize" physics [3]，and to the symmetry principle [9], which today is considered fundamental by physics, Physics has never been separated from mathematics, but there has never been a definite answer as to the relationship between them. Thus Wigner (1902-1995) exclaimed [4]: "The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. gift which we neither understand nor deserve."

CN Yang, commenting on Einstein's "On the method of theoretical physics" [5], said, "Was Einstein saying that fundamental theoretical physics is a part of mathematics? Was he saying that fundamental theoretical physics should have the tradition and style of mathematics? The answers to these questions are no "[6]. So what is the real relationship between mathematics and physics? Is mathematics merely a tool that physics cannot do without? We can interpret mathematics as a description of physical behavior, or physics as operating according to mathematical principles, or they are completely equivalent, but one thing is unchangeable, all physics must ultimately be concretely embodied in its physical parameters, regardless of who dominates whom. We need to remember the essential question, "That is, we don't invent mathematical structures - we discover them, and invent only the notation for describing them"[7]. Mathematics is abstract existence, physics is reality. We cannot completely replace physical explanations with mathematical ones. For example, ask "How do light and particles know that they are choosing the shortest path [8]. The answer is that it is determined by the principle of least action. This is the correct mathematical answer, but not the final physical answer. The final physical answer should be, "Light and particles are not searching for shortest paths, they are creating and defining shortest paths". Why this can be so is because they are energy-momentum themselves. The ultimate explanation is just math*，if we can't boil it down to specific, well-defined, measurable physical parameters. Following Pythagoras' inspiring vision that the world can be built up from concepts, algorithms, and numbers [9]. When we discuss the relationship between math and physics, do we need first ask:

1) What are numbers? Shouldn't we first attribute numbers to "fundamental quantities" in mathematics and physics? Are scalars, vectors, and spinors complete expressions of such fundamental quantities? All other quantities are composites of these fundamental quantities, e.g., tensor.

2) Do mathematics and physics have to have these fundamental quantities in common before we can further discuss the consistency between their theorems? That is, the unification of mathematics and physics must begin with the unification of fundamental quantities.

3) Where do these fundamental quantities come from in physics? In what way are they represented?

--------------------------------

Notes：

* And then what do imaginary numbers in physics correspond to? [10][11]

--------------------------------

References：

[1] McDonnell, J. (2017). The Pythagorean World: Why Mathematics Is Unreasonably Effective In Physics Springer.

[2] Kosmann-Schwarzbach, Y. (2011). The Noether Theorems. The Noether Theorems: Invariance and Conservation Laws in the Twentieth Century. Y. Kosmann-Schwarzbach and B. E. Schwarzbach. New York, NY, Springer New York: 55-64.

Einstein, A. (1934). "On the method of theoretical physics." Philosophy of science 1(2): 163-169.

[3] Corry, L. (2004). David Hilbert and the axiomatization of physics (1898-1918): From Grundlagen der Geometrie to Grundlagen der Physik, Springer.

[4] Wigner, E. P. (1990). The unreasonable effectiveness of mathematics in the natural sciences（1960）. Mathematics and Science, World Scientific: 291-306. 【这个说法本身可能是存在问题的，不是数学在物理学中的有效性，而是不能够区分物理学准则和数学算法。】

[5] Einstein, A. (1934). "On the method of theoretical physics." Philosophy of science 1(2): 163-169.

[6] Yang, C. N. (1980). "Einstein's impact on theoretical physics." Physics Today 33(6): 42-49.

[7] Russell, B. (2010). Principles of mathematics （1903）, Routledge.

[8] https://www.researchgate.net/post/NO4_How_do_light_and_particles_know_that_they_are_choosing_the_shortest_path

[9] Wilczek, F. (2006). "The origin of mass." Modern Physics Letters A 21(9): 701-712.

[10] Chian Fan, e. a. (2023). "How to understand imaginary numbers (complex numbers) in physics." from https://www.researchgate.net/post/NO6_How_to_understand_imaginary_numbers_complex_numbers_in_physics.

[11] Baylis, W. E., J. Huschilt and J. Wei (1992). "Why i?" American Journal of Physics 60(9): 788-797. 【复数、虚数、波函数】

Relevant answer

29 Dec 2023

Answer

They're determined by the symmetries; and the symmetries are discovered by the hints provided by experiment, which are completed by mathematical analysis.

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【NO.21】 Symmetry, Invariance and Conservation (2)-Can Noether's theorem be extended naturally if spacetime is not curved but inhomogeneous?

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12 answers

8 Dec 2023

Noether's theorem is a fundamental result in physics stating that every symmetry of the dynamics implies a conservation law. It is, however, deficient in several respects: for one, it is not applicable to dynamics wherein the system interacts with an environment; furthermore, even in the case where the system is isolated, if the quantum state is mixed then the Noether conservation laws do not capture all of the consequences of the symmetries[1].

In SR, force-free motion in an inertial frame of reference takes place along a straight-line path with constant velocity. Viewed from a non-inertial frame, on the other hand, this path of motion will be a geodesic curve in a flat spacetime. Einstein made the plausible assumption that this geodesic motion also holds in the non-flat case, i.e. in a spacetime region for which it is impossible to find a coordinate system that leads to the Minkowski metric in SR[2].

All spacetime models can be expressed in terms of the gμν = {4x4} matrix, differing only in the distribution of matrix elements. The gμν of Minkowski spacetime is the unit diagonal matrix {1 -1 -1 -1}; the gμν of Riemann spacetime is { X }. If a new spacetime model is introduced gμν={a0,-a1,-a2,-a3}, which is a non-unit diagonal matrix. (ds)^2=(a0)^2+(a1)^2+(a2)^2+(a3)^2, always holds, interpreting it as a non-uniformly flat spacetime, generalised Minkowski spacetime, and no longer a curved spacetime. Should Noether's theorem maintain its validity in this case.

----------------------------------

References

[1] Marvian, I., & Spekkens, R. W. (2014). Extending Noether's theorem by quantifying the asymmetry of quantum states. Nature Communications, 5(1), 3821. https://doi.org/10.1038/ncomms4821 ;

[2] Rowe, D. E. (2019). Emmy Noether on energy conservation in general relativity. arXiv preprint arXiv:1912.03269.

Relevant answer

12 Dec 2023

Answer

Every-continuous-symmetry implies a conservation law and vice versa. Noether's theorem isn't valid for discrete symmetries.

There's no ``forcing'' of Noether's theorem, regarding general relativity. I, already, recalled what happens for general relativity, where the symmetry group is a gauge group: The conservation laws are defined in terms of covariant derivatives and conserved charges depend on the observer, since, in general, they can only be defined locally (and observers are local). If the spacetime is asymptotically flat, then conserved charges can be defined at infinity.

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Would laws of physics be broken if entanglement could transfer information faster than light?

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32 answers

6 Oct 2023

If momentum could be transferred faster than the speed of light, then a mass could be accelerated without an opposite momentum (energy) being transferred to a local mass. This would be a violation of the conservation of energy and the conservation of momentum. However, suppose it was possible to slightly modulate the quantum fluctuations of entangled electrons or entangled photons. No energy would be transferred faster than the speed of light, but it appears that a superluminal message could be sent. Therefore, is there any fundamental reason that a superluminal message cannot be sent between two points in space?

Relevant answer

John Hodge

26 Oct 2023

Answer

The Alain Aspect (1982) experiment showed information was transmitted faster than light. This could be entanglement. But information is not matter. So, read Special Relativity and the Lorentz Ether Theory to say no matter can travel faster than light. This would change physics theory. So, it depends on where the inertia is accounted in a theory. In General Relativity, energy-momentum (matter things) warp spacetime (an aether?) which then directs matter.

Entanglement (now demonstrated by Aspect experiment) requires new physics for all standard models.

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【NO.20】Symmetry, Invariance and Conservation (1) - Who is the Primary?

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26 answers

25 Oct 2023

Do we need to find a motivation for symmetry: {?} → {invariance} → {conservation} → {symmetry} →

Should there be an ultimate symmetry that is identical to the conservation, structure invariance, and interaction invariance of the energy-momentum primitives and that determines all other symmetries?

Symmetry, invariance, and conservation are, in a sense, the same concept [1][2][3] and will generally be described in this order, as if symmetry were dominant.

As commonly understood, energy-momentum conservation was the first physics concept to be developed. It exists as a matter of course in mechanics, thermodynamics, and electricity. However, after physics entered the twentieth century, from quantum mechanics to general relativity, the conservation of energy-momentum has been repeatedly encountered with doubts [5][6][7][8][9][10], and so far it still can't be determined as a universal law by physics. Some of the new physics is insisting on "something out of nothing"[11][12][13][14] or spontaneous vacuum fluctuations[15], which equals to the rejection of energy-momentum conservation. The important reasons for this may be: First, Energy-momentum conservation cannot be proved† . Second, energy-momentum in physics has never been able to correspond to a specific thing, expressed by a unified mathematical formula‡, and it can only be the "equivalence" of various physical forms that are converted and transferred to each other [16]. Third, we have a biased understanding of the status of energy-momentum conservation, such as "These symmetries implied conservation laws. Although these conservation laws, especially those of momentum and energy, were regarded to be the most important of all. Although these conservation laws, especially those of momentum and energy, were regarded to be of fundamental importance, these were regarded as consequences of the dynamical laws of nature rather than as consequences of the symmetries that underlay these laws."[17]. Conservation of energy-momentum was relegated to a subordinate position. Fourth, it is believed that the Uncertainty Principle can be manifested as a " dynamics ", which can cause various field quantum fluctuations in the microscopic domain, and does not have to strictly obey the energy-momentum conservation.

"Symmetry" refers to the "invariance under a specified group of transformations" of the analyzed object [4]. Symmetry is always accompanied by some kind of conservation, but conservation does not only refer to the conservation of energy-momentum, but also, under different conditions, to the conservation of other physical quantities, such as charge, spin, or the conservation of other quantum numbers. Thus, "conservation" is usually the constant invariance of something at some level, and Wigner divided symmetries into classical geometrical symmetries and dynamical symmetries, which are associated with specific types of interactions, every interaction has a dynamical invariance group. "It may be useful to discuss first the relation of phenomena, laws of nature, and invariance principles to each other. This relation is not quite the same for the classical invariance principles, which will be called geometrical, and the new ones, which will be called dynamical."[1]. According to Wigner, we can define the "geometric invariance" of everything as the manifestation of interactions filtered through the absoluteness of the spatio-temporal background. This interaction exhibits itself whenever you assume an observer*. displacement invariance, Lorentz invariance are typical. We can define all "dynamical invariance" as manifestation when the background absolutes of the potential field are filtered out. gauge invariance, the diffeomorphism invariance are typical manifestations." from a passive role in which symmetry is the property of interactions, to an active role in which symmetry serves to determine the interactions themselves --a role that I have called symmetry dictates interaction." "Einstein's general relativity was the first example where symmetry was used" actively to determine gravitational interaction" [2]. This expresses the same idea, that the role of symmetry is elevated to the status of "force". Gross says that the secret of nature is symmetry. The most advanced form of symmetries we have understood are local symmetries-general coordinate invariance and gauge symmetry. The most advanced form of symmetries we have understood are local symmetries-general coordinate invariance and gauge symmetry. unified theory that contains both as a consequence of a greater and deeper symmetry of which these are the low energy remnants [18]. He regards the unification of general relativity and quantum field theory as a unification of symmetries. He regards the unification of general relativity and quantum field theory as a unification of symmetries. If we define generalized invariance as the completeness of the structure, properties, and laws of interaction of the analyzed objects when they interact, i.e., the undecomposability of the whole as a whole, the conservation of the properties (charge, spin, other quantum numbers, etc.), and the consistency of the interaction relations (laws), it is clear that the invariance in this case is special invariance, which means only the invariance of the laws of interaction.

While symmetry, conservation, and invariance are almost equivalent expressions at the same level, there are subtle but important differences. If unbounded, it is the order in which the three are expressed, who actually determines whom, and who ultimately determines the laws of physics. In any case, when we currently speak of symmetry, it must correspond to specific invariance and conservation, not to broad invariance and conservation. This in fact greatly limits the claim that "symmetry dictates interaction", since interaction is much more general. There is no such thing as a failure of interaction, but there is often a failure of symmetry, unless we decide that there will be an ultimate symmetry that determines all other symmetries.

"A symmetry can be exact, approximate, or broken. Exact means unconditionally valid; approximate means valid under certain conditions; broken can mean different things, depending on the object considered and its context. different things, depending on the object considered and its context."[19] "It is not clear how rigorous conservation laws could follow from approximate symmetries"[1]. This reflects the uncertainty of the relationship between conservation currents ( charges) and symmetries, and if we know that conservation currents can still be maintained even with approximate symmetries, it should be understood that this must be a function of the fact that conservation currents have a more universal character. From a reductionist point of view, the conservation charge at all levels will gradually decompose with the decomposition of matter, until finally it becomes something that cannot be decomposed. Such a thing can only be the most universal energy-momentum and at the same time be the ultimate expression that maintains its conservation as well as the invariance of interactions. Otherwise, we will pursue the questions:

1) If energy-momentum conservation is not first, where does the power to move from one symmetry to another, symmetry breaking [11] [12], come from? How can symmetry violations [13] in physics be explained?

2) If symmetry fully expresses interactions, how do we evaluate "symmetry implies asymmetry", "imperfect symmetry", " approximate symmetry", " hidden symmetry"? hidden symmetry"?

3) One of the implications of energy-momentum conservation is that they have no origin, are a natural existence, and do not change with scale and energy level or temperature; symmetry has an origin, and is related to scale, temperature and energy level. How are they equivalent to each other?

4) Must there be an ultimate symmetry which will determine everything and be consistent with conservation and invariance?

--------------------------------------------------------------------------------------------

Notes

† We will analyze this separately, which is its most important physical feature [20].

‡ Can different forms of energy be unified?[16]

* We can define the actual observer to be the object of action and the abstract observer to be the object of action for analysis. For example, when we analyze the Doppler effect, we are analyzing it in the abstract; if you don't actually detect it, no Doppler effect occurs in the object of analysis.

--------------------------------------------------------------------------------------------

References

[1] Wigner, E. P. (1964). "Symmetry and conservation laws." Proceedings of the National Academy of Sciences 51(5): 956-965.

[2] Yang, C. N. (1996). "Symmetry and physics." Proceedings of the American Philosophical Society 140(3): 267-288.

[3] Yang, C. N. (1980). "Einstein's impact on theoretical physics." Physics Today 33(6): 42-49.

[4] Brading, K., E. Castellani and N. Teh (2003). "Symmetry and symmetry breaking."

[5] Bohr, N., H. A. Kramers and J. C. Slater (1924). "LXXVI. The quantum theory of radiation." The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 47(281): 785-802.

[6] Dirac, P. A. M. (1927). "The quantum theory of dispersion." Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character 114(769): 710-728.

[7] Carroll, S. M. and J. Lodman (2021). "Energy non-conservation in quantum mechanics." Foundations of Physics 51(4): 83.

[8] Bondi, H. (1990). "Conservation and non-conservation in general relativity." Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 427(1873): 249-258.

[9] Maudlin, T., E. Okon and D. Sudarsky (2020). "On the status of conservation laws in physics: Implications for semiclassical gravity." Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 69: 67-81.

[10] Pitts, J. B. (2022). "General Relativity, Mental Causation, and Energy Conservation." Erkenntnis 87.

[11] Hoyle, F. (1948). "A new model for the expanding universe." Monthly Notices of the Royal Astronomical Society, Vol. 108, p. 372 108: 372.

[12] Vilenkin, A. (1982). "Creation of universes from nothing." Physics Letters B 117(1): 25-28.

[13] Josset, T., A. Perez and D. Sudarsky (2017). "Dark energy from violation of energy conservation." Physical review letters 118(2): 021102.

[14] Singh Kohli, I. (2014). "Comments On: A Universe From Nothing." arXiv e-prints: arXiv: 1405.6091.

[15] Tryon, E. P. (1973). "Is the Universe a Vacuum Fluctuation?" Nature 246(5433): 396-397.

[16] Chian Fan, https://www.researchgate.net/post/NO10_Can_different_forms_of_energy_be_unified

[17] Gross, D. J. (1996). "The role of symmetry in fundamental physics." Proceedings of the National Academy of Sciences 93(25): 14256-14259.

[18] Gross, D. J. (1992). "Gauge theory-past, present, and future?" Chinese Journal of Physics 30(7): 955-972.

[19] Castellani, E. (2003). "On the meaning of symmetry breaking." Symmetries in physics: Philosophical reflections: 321-334.

[20] https://www.researchgate.net/publication/369890893_Summary_Table_of_Light_String_and_Light_Ring_Properties_Supersymmetry

Relevant answer

26 Oct 2023

Answer

All questions like “what comes first” - and first of all the so-called “fundamental question of philosophy” (forgive me, Lord!) - do not give rise to anything other than many years of empty word debate. And then - conflicts of varying intensity, up to revolutionary wars. There is nothing new under the Moon: let us remember Hegel, for whom Being through Nothing (through singularity) gives rise to Otherness. And vice versa. And so it is with all other questions of this kind. We need to look for connections, and not the mythical “primacy”, which does not exist according to definition.

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【NO.18】How the View of Space-Time is Unified (4) - Is Space-Time Expansion a Space-Time Creation?

asked a question related to Foundations of Physics

Question

28 answers

25 Sept 2023

If it is true that space-time is expanding, how does the measure of space-time change?

The shape of space-time is the shape of the universe; how can expansion without a boundary be called expansion? If the boundary of spacetime is the boundary of the universe, can spacetime expansion with a boundary have no background? How is the boundary maintained? If the boundary of spacetime is infinite, how does it expand?

We will use these paired terms to describe spacetime: infinite/finite, absolute/relative*, flat/curved, continuous/discrete, four-dimensional†/higher-dimensional, and so on. Normally we think of these properties as opposites ‡ and only one or the other can be chosen. But the full range of properties of spacetime will be combinations between these different properties. For example, spacetime has infinite, absolute, continuous, flat, four-dimensional properties, or spacetime has finite, discrete properties, etc. In any case, none of us thinks that there is a concept of "multiple spacetimes", or that spacetime should have its own background, or that spacetime can overlap, although physics suggests that there may be local "warps" in spacetime.

Astronomical observations show that the universe is in a process of accelerated expansion [1][2][3], with all stars moving away at an accelerated rate and possibly never returning. Physics attributes the expansion of space-time to the presence of dark energy with negative pressure [4]. Dark energy has been hypothesized in various ways (including non-existence), one of which is the cosmological constant Λ in Einstein's field equations (the zero-point radiation of space [5], the energy of the vacuum, the zero-point energy [6]).

Physics has not exactly explained the exact relationship between spacetime and the various fields assumed by the Standard Model [7], but only assumes the existence of vacuum energy [8][6], and is not sure which field's vacuum energy it is, whether it is the electromagnetic field, the electron field, the muon field, or the up-quark field, the charm-quark field, the Higgs field [9], or just the sum of their respective vacuum energies. So when it is assumed that space-time is expanding, and vacuum energy is expanding, are they created in it, or are they diffused across the boundary? Are they the driving force or the result? How do they manifest within microscopic particles when expanding at high speeds on the macroscopic scale?

Physics does not explain the origin of the dynamics of the Big Bang, nor does it explain when and how all the various fields in the Standard Model were formed, how they were formed, how they were maintained in existence, and how they evolved along with, or determined, the evolution of the Universe throughout the entire evolution of the Universe from the Big Bang onward. It is not clear how the various particles were excited initially from their own fields, but the explanation of nucleosynthesis [10] to the current period is relatively clear.

Usually we think of the universe as a set of space-time and matter-energy. There are many different models of the universe, and in addition to the Standard Model, there are many cyclic universes and multiverse views [11][15]. Then, when we haven't confirmed the model of the universe, there is no confirmed goal of the evolution of the universe, and there is no confirmed shape and boundary of the universe.

Both Einstein and Hawking say that the universe is "finite and unbounded" [12]. They believe that the universe is a finite three-dimensional sphere with a finite volume but no boundary. Topological theory says, "The boundary of a region has no boundary itself. "** [13]. Wheeler's statement is, "The boundary of a boundary is zero" [14]. What is the result of the infinite extension of the three orthogonal coordinate axes for a finite three-dimensional spherical universe?

Mathematically, there are four combinations between measures and boundaries: finite bounded, infinite unbounded, finite unbounded, and infinite bounded. The first two concepts are clear, but the latter two need to be recognized carefully when translated to physics. The "singularity" is a typical example of an "infinite bounded". Usually in physics, when time or space shrinks to zero, the corresponding physical quantity tends to infinity. For example, E=hν, when ν→0; F=q1*q2/r^2, when r→0. However, we believe that this is only a trend and that there can be no state that reaches a singularity. Therefore, "infinitely bounded" is not real. The Koch Curve, often thought of as a fractal geometry expressing "finite unbounded", is one of the nth iterations of the Koch snowflake that can be implemented in the Wolfram Language as KochCurve[n]¶. The difference between physical reality and mathematics can be shown here, as n cannot be chosen to be infinite, so the Koch Curve will always be in a definite state in reality, and although it can evolve, "finite and unbounded" is a tendency, not a state. The formulation of the Mobius strip††, the irrational numbers, is another way of saying "finite unbounded". In physics, a typical example of "finite unbounded" is the electron. The electron has a fixed charge e, but the boundary of the electric field E of the charge extends infinitely (the field strength is convergent). Of course, the concept of zero-dimensional "point particles" is also a kind of abstract "finite unbounded". In short, in physical terms, finite must have boundaries.

General relativity is the basis for modeling the universe, but is there any good reason why we should be able to determine the evolutionary goals of the universe, its shape, and its boundaries through general relativity alone? Shouldn't such boundaries be "boundary conditions" of GR?

There should not be any boundary conditions, which are the conditions necessary for the model of the universe to hold correctly.

------------------------------------------------------

Notes

* cf, https://www.researchgate.net/publication/373877548_Convergent_and_Disperse_Cyclic_Multiverse_Model_CDCMM.

† cf, https://www.researchgate.net/post/NO1_Can_This_Be_an_Argument_for_3-D_Space;

‡ As long as we do not have a precise definition of spacetime, viewing these properties as opposites can only be taken for granted. As with the wave-particle duality of particles, which property is presented depends on the observer's perspective; the structure of the particle itself does not change. Further characterizations of spacetime include whether it is inherently existent or generative, whether the vacuum contains energy, and so on.

¶ https:// mathworld.wolfram.com/KochSnowflake.html; Stephen Wolfram, Founder of Wolfram Language, is very interested in the question of the evolution of the universe, and is the author of the book "a new kind of science", which has been trying to find out how the universe evolves using metacellular automata.

** e.g. the two-dimensional region has as its boundary a one-dimensional loop; the loop has no end, that is, it has no boundary itself.

†† The Möbius strip is bounded as long as one does not confuse metrics with boundaries.

------------------------------------------------------

References

[1] Linder, E.V., Exploring the expansion history of the universe. Physical Review Letters, 2003. 90(9): p. 091301.

[2] Riess, A.G., The expansion of the Universe is faster than expected. Nature Reviews Physics, 2020. 2(1): p. 10-12.

[3] Freedman, W.L., The Hubble constant and the expansion age of the Universe. Physics Reports, 2000. 333: p. 13-31.

[4] "Dark Energy Survey, Collaboration." from https://www.darkenergysurvey.org/the-des-project/overview/.

[5] Oks, E. (2021). "Brief review of recent advances in understanding dark matter and dark energy." New Astronomy Reviews 93: 101632.

[6] Carroll, S. M., W. H. Press and E. L. Turner (1992). "The cosmological constant." Annual review of astronomy and astrophysics 30: 499-542.

[7] Group, P. D., P. Zyla, R. Barnett, J. Beringer, O. Dahl, D. Dwyer, D. Groom, C.-J. Lin, K. Lugovsky and E. Pianori (2020). "Review of particle physics." Progress of Theoretical and Experimental Physics 2020(8): 083C001.

[8] Jaffe, R. L. (2005). "Casimir effect and the quantum vacuum." Physical Review D 72(2): 021301.

[9] Springer (2020). 100 Years of Fundamental Theoretical Physics in the Palm of Your Hand: Integrated Technical Treatment.

[10] Cyburt, R. H., B. D. Fields, K. A. Olive and T.-H. Yeh (2016). "Big bang nucleosynthesis: Present status." Reviews of Modern Physics 88(1): 015004.

[11] Carr, B. and G. Ellis (2008). "Universe or multiverse?" Astronomy & Geophysics 49(2): 2.29-22.33.

[12] Hawking, S. W. and M. Jackson (2001). A brief history of time, Bantam Books New York.

[13] Yang, C. N. (1980). "Einstein's impact on theoretical physics." Physics Today 33(6): 42-49.

[14] Misner, C. W., K. S. Thorne and J. A. Wheeler (2017). GRAVITATION, Princoten University Press.

[15] https://www.researchgate.net/publication/373877548_Convergent_and_Disperse_Cyclic_Multiverse_Model_CDCMM.

Relevant answer

29 Sept 2023

Answer

Dear Chian Fan

There's no such notion as ``mainstream physics''-there's only physics, which is the mathematically consistent description of natural phenomena.

Regarding energy and momentum: In curved spacetime energy and momentum aren't well-defined notions, because translations in time and space-which is what lead to the definition of energy and momentum-aren't globally defined. So the answers to your questions are all, in fact, No.

Regarding Einstein's equations-of course boundary conditions must be imposed and they are imposed. For describing cosmology the boundary conditions are, typically, radiative. It is possible to impose different boundary conditions and compare the results with observations.

While it was thought that including the cosmological constant was optional, it turns out that it is mandatory-the only question is its sign and its value. For a long time it was thought to vanish and a lot of effort went into trying to describe this. In 1998 it was finally possible to measure its value that turned out to be non-zero and positive. What matters is that the cosmological constant is the only term, besides the Ricci scalar, that it is possible to include in the Einstein-Hilbert action.

26 Recommendations

【NO.13】Does Born's statistical interpretation of the wave function conflict with “the Uncertainty Principle”?

asked a question related to Foundations of Physics

Question

26 answers

22 Aug 2023

There are many kinds of certainty in the world, but there is only one kind of uncertainty.

I: We can think of all mathematical arguments as "causal" arguments, where everything behaves deterministically*. Mathematical causality can be divided into two categories**: The first type, structural causality - is determined by static types of relations such as logical, geometrical, algebraic, etc. For example, "∵ A>B, B>C; ∴ A>C"; "∵ radius is R; ∴ perimeter = 2πR"; ∵ x^2=1; ∴ x1=1, x2=√-1; .......The second category, behavioral causality - the process of motion of a system described by differential equations. Such as the wave equation ∂^2/ ∂t^2-a^2Δu=0 ...

II: In the physical world, physics is mathematics, and defined mathematical relationships determine physical causality. Any "physical process" must be a parameter of time and space, which is the essential difference between physical and mathematical causality. Equations such as Coulomb's law F=q1*q2/r^2 cannot be a description of a microscopic interaction process because they do not contain differential terms. Abstracted "forces" are not fundamental quantities describing the interaction. Equations such as the blackbody radiation law and Ohm's law are statistical laws and do not describe microscopic processes.

The objects analyzed by physics, no matter how microscopic†, are definite systems of energy-momentum, are interactions between systems of energy-momentum, and can be analyzed in terms of energy-momentum. The process of maintaining conservation of energy-momentum is equal to the process of maintaining causality.

III: Mathematically a probabilistic event can be any distribution, depending on the mandatory definitions and derivations. However, there can only be one true probabilistic event in physics that exists theoretically, i.e., an equal probability distribution with complete randomness. If unequal probabilities exist, then we need to ask what causes them. This introduces the problem of causality and negates randomness. Bohr said "The probability function obeys an equation of motion as did the co-ordinates in Newtonian mechanics "[1]. So, Weinberg said of the Copenhagen rules, "The real difficulty is that it is also deterministic, or more precisely, that it combines a probabilistic interpretation with deterministic dynamics" [2].

IV: The wave function in quantum mechanics describes a deterministic evolution energy-momentum system [3]. The behavior of the wave function follows the Hamiltonian principle [4] and is strictly an energy-momentum evolution process***. However, the Copenhagen School interpreted the wave function as "probabilistic" nature [23]. Bohr rejected Einstein's insistence on causality by replacing the term "complementarity" with his own invention, "complementarity". Bohr rejects Einstein's insistence on causality, replacing it with his own invention of "complementarity" [5].

Schrödinger ascribed a reality of the same kind that light waves possessed to the waves that he regards as the carriers of atomic processes by using the de Broglie procedure; he attempts "to construct wave packets (wave parcels) that have relatively small dimensions in all directions," and which can obviously represent the moving " and which can obviously represent the moving corpuscle directly [4][6].

Born and Heisenberg believe that an exact representation of processes in space and time is quite impossible and that one must then content oneself with presenting the relations between the observed quantities, which can only be interpreted as properties of the motions in the limiting classical cases [6]. Heisenberg, in contrast to Bohr, believed that the wave equation gave a causal, albeit probabilistic description of the free electron in configuration space [1].

The wave function itself is a function of time and space, and if the "wave-function collapse" at the time of measurement is probabilistic evolution, with instantaneous nature, [3], neither time (Δt=0) nor spatial transition is required. then it is in conflict not only with the Special Relativity, but also with the Uncertainty Principle. Because the wave function represents some definite energy and momentum, which appear to be infinite when required to follow the Uncertainty Principle [7], ΔE*Δt>h and ΔP*Δx>h.

V: We must also be mindful of the fact that the amount of information about a completely random event. From a quantum measurement point of view, it is infinite, since the true probability event of going from a completely unknown state A before the measurement to a completely determined state B after the measurement is completely without any information to base it on‡.

VI: The Uncertainty Principle originated in Heisenberg's analysis of x-ray microscopy [8] and its mathematical derivation comes from the Fourier Transform [8][10]. E and t, P and x, are two pairs of commuting quantities [11]. While the interpretation of the Uncertainty Principle has been long debated [7][9], "Either the color of the light is measured precisely or the time of arrival of the light is measured precisely." This choice also puzzled Einstein [12], but because of its great convenience as an explanatory "tool", physics has extended it to the "generalized uncertainty principle " [13].

Is this tool not misused? Take for example a time-domain pulsed signal of width τ, which has a Stretch (Scaling Theorem) property with the frequency-domain Fourier transform [14], and a bandwidth in the frequency domain B ≈ 1/τ. This is the equivalent of the uncertainty relation¶, where the width in the time domain is inversely proportional to the width in the frequency domain. However, this relation is fixed for a definite pulse object, i.e., both τ and B are constant, and there is no problem of inaccuracy.

In physics, the uncertainty principle is usually explained in terms of single-slit diffraction [15]. Assuming that the width of the single slit is d, the distribution width (range) of the interference fringes can be analyzed when d is different. Describing the relationship between P and d in this way is equivalent to analyzing the forced interaction that occurs between the incident particle and d. The analysis of such experimental results is consistent with the Fourier transform. But for a fixed d, the distribution does not have any uncertainty. This situation is confirmed experimentally, "We are not free to trade off accuracy in the one at the expense of the other."[16].

The usual doubt lies in the diffraction distribution that appears when a single photon or a single electron is diffracted. This does look like a probabilistic event. But the probabilistic interpretation actually negates the Fourier transform process. If we consider a single particle as a wave packet with a phase parameter, and the phase is statistical when it encounters a single slit, then we can explain the "randomness" of the position of a single photon or a single electron on the screen without violating the Fourier transform at any time. This interpretation is similar to de Broglie's interpretation [17], which is in fact equivalent to Bohr's interpretation [18][19]. Considering the causal conflict of the probabilistic interpretation, the phase interpretation is more rational.

VII. The uncertainty principle is a "passive" principle, not an "active" principle. As long as the object is certain, it has a determinate expression. Everything is where it is expected to be, not this time in this place, but next time in another place.

Our problems are:

1) At observable level, energy-momentum conservation (that is, causality) is never broken. So, is it an active norm, or just a phenomenon?

2) Why is there a "probability" in the measurement process (wave packet collapse) [3]?

3) Does the probabilistic interpretation of the wave function conflict with the uncertainty principle? How can this be resolved?

4) Is the Uncertainty Principle indeed uncertain?

------------------------------------------------------------------------------

Notes:

* Determinism here is a narrow sense of determinism, only for localized events. My personal attitude towards determinism in the broad sense (without distinguishing predictability, Fatalism, see [20] for a specialized analysis) is negative. Because, 1) we must note that complete prediction of all states is dependent on complete boundary conditions and initial conditions. Since all things are correlated, as soon as any kind of infinity exists, such as the spacetime scale of the universe, then the possibility of obtaining all boundary conditions is completely lost. 2) The physical equations of the upper levels can collapse by entering a singularity (undergoing a phase transition), which can lead to unpredictability results.

** Personal, non-professional opinion.

*** Energy conservation of independent wave functions is unquestionable, and it is debatable whether the interactions at the time of measurement obey local energy conservation [21].

† This is precisely the meaning of the Planck Constant h, the smallest unit of action. h itself is a constant of magnitude Js. For the photon, when h is coupled to time (frequency) and space (wavelength), there is energy E = hν,momentum P = h/λ.

‡ Thus, if a theory is to be based on "information", then it must completely reject the probabilistic interpretation of the wave function.

¶ In the field of signal analysis, this is also referred to by some as "The Uncertainty Principle", ΔxΔk=4π [22].

------------------------------------------------------------------------------

References：

[1] Faye, J. (2019). "Copenhagen Interpretation of Quantum Mechanics." The Stanford Encyclopedia of Philosophy from <https://plato.stanford.edu/archives/win2019/entries/qm-copenhagen/>.

[2] Weinberg, S. (2020). Dreams of a Final Theory, Hunan Science and Technology Press.

[3] Bassi, A., K. Lochan, S. Satin, T. P. Singh and H. Ulbricht (2013). "Models of wave-function collapse, underlying theories, and experimental tests." Reviews of Modern Physics 85(2): 471.

[4] Schrödinger, E. (1926). "An Undulatory Theory of the Mechanics of Atoms and Molecules." Physical Review 28(6): 1049-1070.

[5] Bohr, N. (1937). "Causality and complementarity." Philosophy of Science 4(3): 289-298.

[6] Born, M. (1926). "Quantum mechanics of collision processes." Uspekhi Fizich.

[7] Busch, P., T. Heinonen and P. Lahti (2007). "Heisenberg's uncertainty principle." Physics Reports 452(6): 155-176.

[8] Heisenberg, W. (1927). "Principle of indeterminacy." Z. Physik 43: 172-198. “不确定性原理”源论文。

[9] https://plato.stanford.edu/archives/sum2023/entries/qt-uncertainty/; 对不确定性原理更详细的历史介绍，其中包括了各种代表性的观点。

[10] Brown, L. M., A. Pais and B. Poppard (1995). Twentieth Centure Physics（I）, Science Press.

[11] Dirac, P. A. M. (2017). The Principles of Quantum Mechanics, China Machine Press.

[12] Pais, A. (1982). The Science and Life of Albert Einstein I

[13] Tawfik, A. N. and A. M. Diab (2015). "A review of the generalized uncertainty principle." Reports on Progress in Physics 78(12): 126001.

[14] https://www.princeton.edu/~cuff/ele301/files/lecture8_2.pdf;

[15] 曾谨言 (2013). 量子力学（QM）, Science Press.

[16] Williams, B. G. (1984). "Compton scattering and Heisenberg's microscope revisited." American Journal of Physics 52(5): 425-430.

Hofer, W. A. (2012). "Heisenberg, uncertainty, and the scanning tunneling microscope." Frontiers of Physics 7(2): 218-222.

Prasad, N. and C. Roychoudhuri (2011). "Microscope and spectroscope results are not limited by Heisenberg's Uncertainty Principle!" Proceedings of SPIE-The International Society for Optical Engineering 8121.

[17] De Broglie, L. and J. A. E. Silva (1968). "Interpretation of a Recent Experiment on Interference of Photon Beams." Physical Review 172(5): 1284-1285.

[18] Cushing, J. T. (1994). Quantum mechanics: historical contingency and the Copenhagen hegemony, University of Chicago Press.

[19] Saunders, S. (2005). "Complementarity and scientific rationality." Foundations of Physics 35: 417-447.

[20] https://plato.stanford.edu/entries/determinism-causal/;

[21] Carroll, S. M. and J. Lodman (2021). "Energy non-conservation in quantum mechanics." Foundations of Physics 51(4): 83.

[22] https://math.libretexts.org/Bookshelves/Differential_Equations/Introduction_to_Partial_Differential_Equations_(Herman)/09%3A_Transform_Techniques_in_Physics/9.05%3A_Properties_of_the_Fourier_Transform;

[23] Born, M. (1955). "Statistical Interpretation of Quantum Mechanics." Science 122(3172): 675-679.

=========================================================

Relevant answer

André Michaud

25 Aug 2023

Answer

Dear Chian Fan

Thank you for your answer. However, when so many certainties as you state are already established in someone's worldview, I know of no way that they can be reconsidered. So I will not try to explain or argue.

The available alternate possibilities and possible solutions that electromagnetism put at our disposal all are available anyway for anybody interested in my articles, with direct references to all historical formal sources, all available on the internet, given that they all are now in the public domain.

You wrote: "The main purpose of this discussion is to have the Copenhagen Interpretation revisited. It gave quantum mechanics a grounding in the last century, but not a solid foundation, and may have hindered, restricted, or even misled physics today."

I completely agree that the Copenhagen interpretation must be gotten rid of.

This is what I have been working at for the past 25 years.

The Copenhagen interpretation has been the scourge of the past hundred years in physics, and it contributed absolutely nothing other than endless arguments and waste of time for mainstream in lieu of fundamental research, combined with general disregard and disappearing of any referencing to the historical foundational discoveries that underlie real physics.

I observed that the equations of QM always were fine as they were initially conceived and owe absolutely nothing to the Copenhagen interpretation. The only issue is that they have been disconnected from their historical classical formal grounding foundations by the Copenhagen interpretation, thus preventing further progress from their states established 100 years ago.

I expect that this will be remedied by the upcoming generation. My contribution is the set of historical formal references that I located over the past decades that they can lean on for the purpose.

Best Regards, André

30 Recommendations

【NO.12】Should an Object at rest have Rest Momentum?

asked a question related to Foundations of Physics

Question

18 answers

14 Aug 2023

A body at rest has rest Energy, so it should also have rest Momentum.

Lao Tzu said, “Gravity is the root of lightness; stillness, the ruler of movement”(重为轻根，静为躁君)*. The meaning of this statement can be extended in physics to mean that "big-G determines how light or heavy an object is, and rest-m determines how easy or difficult it is to move".

According to the mass-energy equation** [1], E=mc^2, any object with mass m has "rest energy" [1], regardless of its inertial frame†. Note that E here is meant to be the energy lost when radiating the photon γ, which is absolute and unchangeable in any inertial frame. The mass-energy equation has been experimentally verified [2] as the correct relation.

According to special relativity [3], the mass of the same object is different in different inertial frames, m' = βm. Therefore, the energy of conversion of m of an object into photon γ is different in different inertial frames. This issue has been discussed in [4], but there is no consensus. Our view is that the "rest energy" is theoretically not Lorentz invariant, and the existence of a minimum value is a reasonable result. The most rational explanation for this is that the minimum corresponds to an absolutely static spacetime, i.e., absolute spacetime(Later we will show that absolute space-time and relative space-time are not in conflict). Analytically, this is one of the reasons why absolute spacetime should exist. The constant speed of light is another reason.

In all cases in physics, energy and momentum coexist and have a fixed relationship, not independent metrics. The energy-momentum ‡ of a photon, E=hν[5], P=h/λ[6]; the energy-momentum relation of Newtonian mechanics, E=P^2/2m; and the relativistic energy-momentum relation, E^2=c^2p^2+m^2c^4. Therefore, it is assumed that if there is a body of mass m that has "rest energy", then it should also have "rest momentum". There is a "rest momentum", and the rest momentum cannot be zero. The rest energy is not intuitive, and the rest momentum should not be intuitive too. The calculation of the rest momentum is the same as the calculation of the rest energy. The nature of mass looks more like momentum; after all, energy is a sign of time, while momentum is a sign of movement. Therefore, instead of calling it the principle of equivalence of inertial mass and rest-energy[1], it should be called the principle of equivalence of inertial mass and rest-momentum.

When positive and negative electrons meet and annihilate [7], -e+e→γ+γ, radiating two photons in opposite directions. Their energy is conserved and so is their momentum. Energy is a scalar sum, while momentum is a vector sum. It seems that the "rest momentum" inside the object should be zero. However, one could argue that it is actually the momentum of the two photons that is being carried away, but in opposite directions. The momentum of the two photons should not come out of nothing, but rather there should be momentum of the two photons, also in some balanced way, and probably playing a very important role, such as the binding force.

Our questions are:

1) Since energy and momentum cannot be separated, should an object with "rest energy" necessarily have "rest momentum".

2) Elementary particles can be equated to a " energy packet ", and energy is time dependent. If an elementary particle is also equivalent to a "momentum packet", the momentum in the packet must be related to space. Does this determine the spatio-temporal nature of the elementary particles? And since momentum is related to force, is it the force that keeps the "energy packet" from dissipating?

------------------------------------------------------------------------------

Notes：

* Lao Tzu，Tao-Te-Ching，~500 BCE. This quote is a translation of someone else's. There are some excesses that I don't entirely agree with. Translating classical Chinese into modern Chinese is just as difficult as translating classical Chinese into English.

** There is a historical debate about the process of discovery of the mass-energy equation, and digging into the history shows that there were discoverers and revisers both before and after Einstein, see literature [8][9]. Important contributions came from Poincaré, F. Hasenöhrl, Planck et al. Their derivations do not have the approximation of Einstein's mass-energy equation. And there is also a debate about the interpretation of the mass-energy equation. Notable debates can be found in the literature[10].

† There is a question here, i.e., is the rest mass Lorentz invariant? That is, is the rest mass the same in different inertial systems? Why?

‡ Einstein questioningly emphasized that energy and momentum seem to be inseparable, but did not explain it.

------------------------------------------------------------------------------

References：

[1] Einstein, A. (1905). "Does the inertia of a body depend upon its energy-content." Annalen der physik 18(13): 639-641.

Einstein, A. (1935). "Elementary derivation of the equivalence of mass and energy." Bulletin of the American mathematical society 41(4): 223-230.

[2] Rainville, S., J. K. Thompson, E. G. Myers, J. M. Brown, M. S. Dewey, E. G. Kessler, R. D. Deslattes, H. G. Börner, M. Jentschel, P. Mutti and D. E. Pritchard (2005). "A direct test of E=mc2." Nature 438(7071): 1096-1097.

[3] Einstein, A. (1905). "On the electrodynamics of moving bodies." Annalen der physik 17(10): 891-921.

[4] Is there a minimum value of m in the mass-energy equation E=mc^2? https://www.researchgate.net/post/NO7_Is_there_a_minimum_value_of_m_in_the_mass-energy_equation_Emc2；

[5] Planck, M. (1900). " " Verh. Deutsh. Phys. Ges 2: 237.

[6] Einstein, A. (1917). Physikalisehe Zeitschrift xviii: p.121

[7] Li, B. A. and C. N. Yang (1989). "CY Chao, Pair creation and Pair Annihilation." International Journal of Modern Physics A 4(17): 4325-4335.

[8] Ives, H. E. (1952). "Derivation of the mass-energy relation." JOSA 42(8): 540-543.

[9] Sharma, A. (0000). "The past present and future of the Mass Energy Equation DE =Dmc2." http://www.mrelativity.net/Papers/8/Sharma4.htm.

[10] Peierls, R., J. Warren and M. Nelkon (1987). "Mass and energy." Physics Bulletin 38(4): 127.

Relevant answer

László Attila Horváth

22 Aug 2023

Answer

Dear Chian Fan ,

The next conclusion is connected to your previous comment:

Research Proposal Physico-metaphysical proof of the existence of graviton (Fiz...

So far, two people with PhDs have made veiled, arrogant criticisms... somewhat suggesting my stupidity. So far, there are four opinions. : one is a normal honestly worded opponent opinion. What's your opinion?

Regards,

Laszlo

P.S.: there is a thought that relates to your topic...

42 Recommendations

Is spacetime an elastic medium that propagates waves?

asked a question related to Foundations of Physics

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6758 answers

2 Aug 2023

The fallacy of the aether was that its only function was to propagate light waves. This question goes much further and probes whether space (the vacuum) is an elastic medium that propagates waves at the speed of light. For example, do gravitational waves propagate in the elastic fabric of space? If space is assumed to be an elastic wave propagation medium, then gravitational wave equations imply this medium has enormous impedance of c³/G = 4 x 10³⁵kg/s.

This is a discussion question, and I am going to take the position that spacetime is an elastic medium with “spacetime foam” properties first proposed by John Wheeler. He determined that the uncertainty principle and vacuum zero-point energy implied space has Planck length oscillations at Planck frequency. This would make spacetime a physical medium that propagates waves at the speed of light with impedance of c³/G. This impedance is so enormous that a rotating wave with Planck length amplitude and an electron’s Compton radius would have an electron’s energy.

I am taking the position that the quantum vacuum is a sonic medium that propagates waves at the speed of light. This medium gives the vacuum its “intrinsic” properties such as vacuum permittivity ε_o, vacuum permeability μ_o, impedance of free space Z_o, virtual particle formation, etc. If spacetime is not a physical medium, why does it have finite values for ε_o, μ_o and Z_o? The following link has more information about my opinion and model. What is your opinion?

Article Oscillating Spacetime: The Foundation of the Universe

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4 Aug 2023

Answer

Of course, the proposed opus does not answer all the questions posed here. But I think it can be useful when looking for answers.

Research Proposal ВАКУУМ ДИРАКА: ФЕРМИОНЫ МАЙОРАНЫ В ВИРТУАЛЬНОМ МЕТАЛЛИЧЕСКОМ...

Where is the boundary of space-time?

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Dolce Donatello

asked a question related to Foundations of Physics

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32 answers

14 May 2014

Quantum mechanics can answer this question. Relativity defines the differential structure of space-time (metric) without giving any indications about the boundary. This suggests that relativity is a correct but not a complete theory (a well-formulated mathematical problem, i.e. Dirichlet problem, needs differential equations and boundary conditions). Is it possible that quantum mechanics is the manifestation of microscopic boundary conditions of space-time? Recent papers, e.g. see attached "Elementary space-time cycles" , absolutely confirm the viability of this unified description of quantum and relativistic mechanics.

Article Elementary spacetime cycles

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Sergey Shevchenko

10 Jun 2023

Answer

Again – see the SS post on page 3 – any spacetime of any informational pattern/system is by scientific definition infinite empty container, in which some “bounded” pattren/system is placed.

Including the Matter’s fundamentally absolute, fundamentally flat, and fundamentally “Cartesian”, [4+4+1]4D spacetime with metrics (cτ,X,Y,Z,g,w,e,s,ct) is fundamentally infinite in all dimensions.

That is another thing that Matter with a well non-zero probability is, though huge but finite, system, which exists, and everything in Matter happens, only in the finite Matter’s ultimate base - the [4+4+1]4D dense lattice of [4+4+1]4D binary reversible fundamental logical elements [FLE] that occupies a finite [4+4+1]4D volume,

- however, at that at Matter creation and evolution this volume has the topology that isn’t known now.

Cheers

Spaces with Same Geodesics/Projectively Related Systems: exsaustive list and study?

7 Recommendations

Kishin Mariwalla

asked a question related to Foundations of Physics

Question

2 answers

26 Oct 2016

In my paper in Phys. Letts..vol 68A (1978)409-411, I have discussed a metric

projectively related to Friedman/R-W metric with identical geodesics.Questions:

Are there other such solutions for this case or for other conformaly flat

spaces? One such solution defines an infinite succession. Is there a computer

program to find infinite succession of (covariant)Einstein tensors.; the

change represents the erruption of matter-energy in assumed spontaneous

projective change. on approach to a singularity. Physically the change is

caused by intervention of Gauge fields to avoid gravity-induced collapse.

The point is that addition to Christofell connection of a term (Identity tensor

times Vector) leaves a system of geodesics unchanged,and is in accord

with equivalence principle. This way one can relate both gauge field and

Q.M. with G .R..Details on request.See also Matsience Report no92(1978)/

paper 9,14pp (www.imsc.res.in/Library)-Black Body Structure of a Black

Hole. And Lie Structure of Quasiconformal Maps in R*(*=N). And Physics of

String Theory in Quantum Field Theory. QM,& Optics- Ed VV Dodonov &

V I Manko , Moscow (1990) Nova Publishers (N,Y)vol 187 of Proc 0f Lebedev Phy. Inst.Acad. 0f Sciences 0f the USSR./pp113-116..

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Kishin Mariwalla

10 Jun 2023

Answer

Define the meaning of global constant differnt from that used. in Relativigy.

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Does a fermion’s energy density imply it also has tremendous internal pressure?

asked a question related to Foundations of Physics

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27 answers

18 Jan 2023

If an electron and a positron interact, they release over a million eV of energy. If this energy is in the form of photons confined in a reflecting box, this energy density generates pressure on the box’s walls. The equation is U = 3P where U is the energy density of the confined photons and P is photon pressure on the reflecting walls of the box. Energy density and pressure have units of (J/m³) and (N/m²) respectively. These intuitively seem very different, but they both have the same dimensional units of M/T²L.

If an electron is assumed to be smaller than 10^-18 m in radius, then this energy density exceeds 10⁴⁰ J/m³. This assumption implies an internal pressure exceeding 10⁴⁰ N/m². If an electron is assumed to be a point particle, then this would generate infinite internal pressure.

Does this conversion between energy density and pressure apply to fermions? If so, what offsets the fermion’s internal pressure to stabilize a fermion?

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Christian G. Wolf

1 Apr 2023

Answer

T. H. Ray You stated:

“I'm not sure I agree with the equations in your first paragraph. I know they're standard, but I think you are going to need to show N=M to give them the same dimensional units.“

John is completely right about this, which is most easy to see in iSpace theory, and within the unit systems iSpace-SI (using SI identical metric values but only Volt, Ampere, Meter and Second as base units) and iSpace-IQ units (first of its kind able to get away without human artifacts whatsoever, but only iSpaceVolt, iSpaceAmpere, iSpaceMeter and iSpaceSecond).

So (J/m^3) = (N/m^2) are indeed also unit and not only metric value wise identical, because (J:=VAs) and (N:=VAs/m) which naturally results in (VAs/m^3).

Other than that, iSpace is able to *exactly* predict constants of nature in two completely different unit systems, one of which having no need for any human artifact, yet being 100% forward and backward compatible. An as all iSpace math is simple purely first order multiplicative (plain *integer geometry* !!) it cannot be related to anything „infinity“ and hence proves, John‘s question is more than a valid one (esp. with respect to do called „Standard Model“).

As QM is how imho a physically completely correct model of our world, it leaves us with the conclusion the „just“ the mathematical (continuum) model of R and C (complex numbers, i^2=-1 and so on) is completely on the wrong track or otherwise said - only a nice approximation up up exactly Bohr radius devided by FSC alpha (10*-13m about) so all physical activity below that distance is governed strictly by discrete iSpace (LEGO style) rules with so called „changed distance definition„ Pi3=3 (6 around 1 cell) base geometry.

An this is solves the problem stated in Johns question - hence there is of course no infinite pressure or energy density. So please also note this does not at all contradict a so far experimentally verified point particle model (in some hypothised 4D continuum spacetime). as iSpace states 10D=6D+3D+1D spacetime and 6D subspaces are Calabi-Yau d style rolled-in giving an entity with only inside (in 6D) and no outside (in 4D) so no length in 4D gives naturally a point particle - which solves the case.

5 Recommendations

Are fields independent of the vacuum or a property of the vacuum?

asked a question related to Foundations of Physics

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27 answers

17 Nov 2022

The standard model has 17 named fundamental particles and each of these particles are derived from a corresponding field. Do you visualize these fields as additions to the properties of the vacuum or part of a single quantum vacuum? For example, virtual electron/positron pairs are continuously forming and annihilating. Are the virtual electrons/positrons distinct additions to the vacuum or is the electron/positron field and these virtual particles a fundamental part of the quantum vacuum?

If an expanded model of the quantum vacuum incorporates all fields, this implies that a grand unification of all particles and forces is possible. However, if all these fields are independent, then unification does not appear to be possible.

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8 Dec 2022

Answer

Until now, I have imagined any variant of the physical vacuum by analogy with the Dirac vacuum. That is, as a sea of virtual particles representing the quanta of the corresponding fields. May be, I was wrong?

18 Recommendations

How can the speed of light be constant in all frames of reference?

asked a question related to Foundations of Physics

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52 answers

13 Oct 2021

The constant speed of light is just the most obvious example of the covariance of all the physical laws. The physical laws do not change even when gravity produces different rates of time or motion gives different frames of reference. For example, energy, force, inertia, mass, etc. all must undergo coordinated changes in order to keep the physical laws (including the constant speed of light) the same in all frames of reference and all gravitational potentials. Do you have any insights or partial explanations into the constant speed of light and the covariance of the physical laws?

From 1916 until his death, Einstein believed that space was not an empty void. He also rejected the idea of the ether that had a specific frame of reference and propagated classical waves. Instead, he believed that space had physical content that achieved the relativistic covariance of the physical laws. He used words such as “new ether”, “physical space” and “relativistic ether” to convey this concept. This is documented in the book titled, Einstein and the Ether by L. Kostro. Einstein did not suggest how "relativistic ether" could achieve a constant speed of light and create covariance of the physical laws.

My answer to this question and other surprising physics predictions are contained in the preprint: www.researchgate.net/publication/353049276

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6 Apr 2022

Answer

Dear Sydney Ernest Grimm, thank you very much for your very interesting reply and preprints!

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Is the foundation of physical reality observable?

asked a question related to Foundations of Physics

Question

25 answers

24 Jul 2016

The foundation of physically reality is necessarily very simple and quite probably its structure cannot observed. But recently I came to the conclusion that the signature of this foundation can be observed in all aspects of the universe. All separated items in universe are either modules or modular systems.

Is modular configuration a fundamental characteristic of physical reality?

http://vixra.org/abs/1607.0146

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L Kurt Engelhart

15 Nov 2021

Answer

Reflect: what came first, consciousness or the brain? If consciousness, then the brain has been created in consciousness. If the brain? No that is ridiculous!

Primitive humans surely had no idea of the brain, (except to eat it!) but they were just as surely conscious.

The concept of the brain (and all other things) has accumulated through experience, shared by communication, as a phenomenon we now share as "reality."

Today, to understand reality in any other way is simply an attempt to pose one reality as superior (more real) than others. This is a game that has played out historically as a function of force or fraud, i.e., a function of power.

If we want reality to be any more than the result of power play, we must understand it as a phenomenon within consciousness. And deal with that reality!

Respectfully,

Kurt

Negative numbers, debt or rotation?

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Ed Gerck

asked a question related to Foundations of Physics

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16 answers

13 Jan 2017

Some say that negative numbers were introduced because of the commerce need to represent a debt. While that explanation could be true in some fashion, it seems to be lacking. For example, how could the product of two debts be positive? Alternatively, one could view negative numbers just as a 180 degree rotation of a positive number, where complex numbers in polar form, A • exp (i•angle), are then a better representation of the true natural numbers -- and humanity was not able to reach this understanding until quantum mechanics was developed and became our most successful description of Nature. If the angle = 0 degrees, then the number is A; if the angle = 180 degrees, the number is -A. The product of two negative numbers is thus positive because it stands for a 180 + 180 = 360 degree rotation in a QM view of numbers, which seems to be self-consistent whereas the debt concept seems not to be.

NOTE: within the bigger picture of finding meaningful hidden structures in mathematics, this thread is about whether negative numbers can be better viewed as a rotation.

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Ed Gerck

23 Mar 2021

Answer

All: the question here is whether nature and QM can be used as a better foundation for the concept of numbers than made up postulates from the last 4,000 years of quaint mathematics.

Where do these "hidden structures" in math come from? If we accept that QM is our most comprehensive theory of nature, then it is logical to look for an answer to this math problem in nature and using QM, not in made up concepts that deny such structures a priori. This is not a call for Platonism, or a return to the mathematical program proposed by David Hilbert in the 1920s.

Is there a peculiarity in the cooling of identical bodies in a special relativistic setting ?

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Demetrios Kalamidas

asked a question related to Foundations of Physics

Question

6 answers

9 Oct 2019

Hi all,

Consider the situation depicted in the illustration. Two identical 'square plates' are situated at rest, in frame S, as shown: Plate A has its thickness 'a' parallel to the x axis and its sides 'L' parallel to the y and z axes, while plate B has its thickness parallel to the y axis and its sides parallel to the x and z axes. They are heated to the same temperature and then are accelerated until they attain a velocity 'v' along the x axis with respect to an observer in frame S'. Now, in S', plate A will only have its thickness 'a' contracted while plate B will only have the side 'L' parallel to the x axis contracted. This means that, for the observer in S', plates A and B have different total surface areas and, if we presume that a<<L and that v is in the relativistic range, this difference in total surface area will be dramatic. For the observer at rest with plates A and B, in frame S, the two plates will display the same temperature for all times as they cool (assuming, in this thought experiment, that we are in the vacuum of outer space and that outer space is homogeneous and isotropic). The identically dropping temperature readings, at all times, are an objective fact.......how does the observer in S' explain this fact despite his perception of drastically different surface areas associated with plates A and B ??

Cheers,

Demetri

srtp.j
pg
186 kB

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22 Oct 2019

Answer

Invoking the Doppler effect amounts to defining a preferred frame, therefore of breaking Lorentz invariance.

Indeed, temperature, also, implies a preferred frame, that one, where the bath, with which the object under study is in equilibrium.

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Which fundamental questions about physical reality are still open?

asked a question related to Foundations of Physics

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25 answers

10 Oct 2019

The origin of gravitation, the origin of electric charge and the fundamental structure of physical reality are resolved, but these facts are not yet added to common knowledge. Also the structure of photons is resolved and the begin of the universe is explained. A proper definition of what a field is and how a field behaves have been given. These facts are explained in

Preprint A SELF-CREATING MODEL OF PHYSICAL REALITY

This model still leaves some open questions. The model does not explain the role of massive bosons. It does not explain the existence of generations of fermions. The HBM also does not provide an explanation for the fine details of the emission and absorption of photons. The model does not give a reason for the existence of the stochastic processes that generate the hopping paths of elementary particles. The model does not explain in detail how color confinement works. It also does not explain how neutral elementary particles can produce deformation. The referenced booklet treats many of its open questions in sections that carry this title.

The model suggests that we live in a purely mathematical model. This raises deep philosophical questions.

With other words, the Hilbert Book Model Project is far from complete. The target of the project was not to deliver a theory of everything. Its target was to dive deeper into the crypts of physical reality and to correct flaws that got adapted into accepted physical theories. Examples of these flaws are the Big Bang theory, the explanation of black holes, the description of the structure of photons, and the description of the binding of elementary particles into higher order modules.

The biggest discovery of the HBM project is the fact that it appears possible to generate a self-creating model of physical reality that after a series of steps shows astonishing resemblance to the structure and the behavior of observed physical reality.

A major result is also that all elementary particles and their conglomerates are recurrently regenerated at a very fast rate. This means that apart from black holes, all massive objects are continuously regenerated. This conclusion attacks the roots of all currently accepted physical theories. Another result is that the generation and binding of all massive particles are controlled by stochastic processes that own a characteristic function. Consequently the Hilbert Book Model does not rely on weak and strong forces that current field theories apply.

The HBM explains gravity at the level of quantum physics and thus bridges the gap between quantum theory and current gravitation theories.

The Hilbert Book Model shows that mathematicians can play a crucial role in the further development of theoretical physics. The HBM hardly affects applied physics. It does not change much in the way that observations of physical phenomena will be described.

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13 Oct 2019

Answer

The field that represents the universe exists always and everywhere. It acts as our living space. All objects in universe are constituted from field excitations of this field. The electric field depends on sources or sinks that occur at the geometric center of the platforms on which elementary particles reside. Fields exist as eigenspaces of normal operators that reside in a quaternionic Hilbert space. In separable Hilbert spaces these fields are sampled fields and are constituted by a countable number of samples these samples are archived in rational quaternions. In non-separable Hilbert spaces the fields are represented by continuum eigenspaces of normal operators.

Fields can be described by quaternionic functions and the dynamics of fields can be described by quaternionic differential calculus.

Thus, the field that represents our universe and the electric fields obey the same quaternionic field equations. They differ in their start and boundary conditions.

The creation of the underlying model also creates the fields. Elementary particles never die.

Quaternionic differential calculus applies the quaternionic nabla operator ∇. This calculus uses proper time τ, where Maxwell equations apply coordinate time t.

We use boldface to indicate vectors.

∇≡∇ᵣ+∇

∇≡{∂/∂x, ∂/∂y, ∂/∂z}

∇ᵣ≡∂/∂τ

In the quaternionic differential calculus differentiation is a multiplier operation.

Compare:

c=cᵣ+c=a b≡(aᵣ+a)(bᵣ+b)=aᵣbᵣ−〈a,b〉+abᵣ+aᵣb±a×b

and

ϕ=ϕᵣ+ϕ=∇ψ≡(∇ᵣ+∇)(ψᵣ+ψ)=∇ᵣψᵣ−〈∇,ψ〉+∇ψᵣ+∇ᵣψ±∇×ψ

∇ψ represents the change of field ψ. This change covers five terms. Part of these terms can compensate for other terms. For example, ∇ᵣ ψ can compensate ∇ψᵣ.

ϕᵣ=∇ᵣψᵣ−〈∇, ψ〉

Maxwell does not use the real part ϕᵣ of ϕ

ϕ=∇ψᵣ+∇ᵣ ψ ±∇×ψ

Double differentiation leads to the quaternionic second order differential equation:

ζ=∇*ϕ=(∇ᵣ−∇) (∇ᵣ+∇) (ψᵣ+ψ)= {∇ᵣ∇ᵣ+〈∇, ∇〉} (ψᵣ+ ψ)=ρᵣ+J

ζ={∇ᵣ∇ᵣ+〈∇, ∇〉} ψ

The equation can be split into two first-order partial differential equations ϕ=∇ψ and ζ=∇*ϕ

This equation offers no waves as its solutions. The quaternionic equivalent of the wave equation is:

φ= {∇ᵣ∇ᵣ−〈∇, ∇〉} ψ

The homogeneous version of this equation offers waves as its solution:

∇ᵣ∇ᵣ ψ=〈∇, ∇〉ψ =−ω² ψ

Corresponding Maxwell-like equations are:

E=−∇ψᵣ−∇ᵣψ

B=∇×ψ

ρᵣ=〈∇,E〉

J=∇×B−∇ᵣE

∇ᵣB=−∇×E

The corresponding second-order differential equations are:

{∇ᵣ∇ᵣ −〈∇,∇〉}ψ=J

{∇ᵣ∇ᵣ −〈∇, ∇〉}ψᵣ=ρᵣ

Solutions

The two second-order partial differential equations describe the behavior of dark objects.

φ=(∂²/∂τ²± 〈∇, ∇〉)ψ

A third equation skips the first term

φ= 〈∇, ∇〉ψ

This is the Poisson equation.

In fact, these equations are quaternionic differential equations. Thus, φ and ψ are quaternionic functions that own a scalar real part and an imaginary vector part. The solutions are quaternionic functions.

The equation using the − sign is the quaternionic equivalent of the wave equation. The equation using the + sign splits into two quaternionic first order partial differential equations. This second equation does not offer waves as solutions.

The homogeneous wave equation can be written as:

∂²ψ/∂τ²= 〈∇,∇〉ψ =-k² ψ

This delivers the quantized wave solutions of the Helmholtz equation

The dark objects behave as shock fronts and operate only as odd-dimensional field excitations. During travel, all shock fronts keep the shape of the front.

All solutions of a homogeneous second-order partial differential equation superpose in new solutions of that equation

One-dimensional shock fronts

The one-dimensional shock fronts also keep their amplitude. Consequently, the one-dimensional shock fronts can travel huge distances without losing their properties. Combined equidistantly in strings, they represent the functionality of photons. This means that the one-dimensional shock fronts are the tiniest possible packages of pure energy.

Depending on the PDE, the solutions can be described by different equations. The solution for the wave equation is

g(q ,τ)=f(c τ ± |q−qₒ|)

This solution cannot represent polarization.

The solution for the other equation is

g(q ,τ)=f(c τ ± |q−qₒ| i)

The vector i can indicate the polarization of the shock front.

A photon is a string of equidistant energy packages that obeys the Einstein-Planck relation

E = h ν.

Since photons possess polarization, they use the second solution for their energy packages. Thus, the constituents of photons are not solutions of the wave equation.

Green’s function

One of the solutions of the Poisson equation is the Green’s function

g(𝐪)=1/|𝐪−𝐪ₒ|

∇g(𝐪)=( 𝐪−𝐪ₒ)/|𝐪−𝐪ₒ|³

〈∇, ∇〉 g(𝐪)= 〈∇, ∇g(𝐪)〉=4πδ( 𝐪−𝐪ₒ)

Thus, the Green’s function is a static pulse response under purely isotropic conditions.

Three-dimensional shock front

The three-dimensional shock fronts require an isotropic trigger. These field excitations integrate over time into the Green's function of the field. That function has some volume, and the pulse response injects this volume into the field. Subsequently, the front spreads the volume over the field. The corresponding solution of the wave equation is

g(r ,τ)=f(c τ ± r)/r

The parameter r is the radius of the spherical front. The formula can also be written as

g(q ,τ)=f(c τ ± |q−qₒ|)/|q−qₒ|

The solution for the other PED is

g(q ,τ)=f(c τ ± |q−qₒ| i)/|q−qₒ|

In this solution, the vector i acts as a spin vector.

Thus, the initial deformation quickly fades away. but the expansion of the field stays. Having the capability to deform the carrier field corresponds to owning a corresponding amount of mass. This means that temporarily, the spherical pulse response owns some mass. This mass vanishes, but the expansion stays.

A huge coherent, recurrently regenerated swarm of spherical pulse responses can generate a significant and persistent deformation that moves with the swarm. This happens in the footprint of elementary particles. The spherical pulses are generated by the hop landing locations of the particle. The hopping path forms a hop landing location swarm that is described by a location density distribution. This distribution equals the square of the modulus of the wavefunction of the particle.

Pulse responses are a solution of {∇ᵣ∇ᵣ±〈∇, ∇〉} ψ((𝐪, τ)=4πδ( 𝐪−𝐪ₒ)θ(τ−τₒ)

A proposed QM interpretation - random jumps. But I have questions. E.g. is a picture of DIScontinuous motion compatible with Feynman's path integral?

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Sofia D. Wechsler

asked a question related to Foundations of Physics

Question

49 answers

26 Apr 2019

NOTE: In consequence of some answers of users due to whom part of the issues become clarified, I do from time to time MODIFICATIONS in this question stressing the remaining questions.

Shan Gao, the author of the book

Article The Meaning of the Wave Function: In Search of the Ontology ...

proposed a new interpretation for the QM: a substructurea of QM consisting in a moving particle. But instead of moving continuously, as in Bohm's mechanics, or as in the trajectories of all forms considered by Feynman in his path-integral theory, Gao's particle performs a random, discontinuous motion (RDM) - see section 6.3.2 and 6.3.3 in his book. In short, gao's particle jumps all the time from a position to another

"consider an electron in a superposition of two energy eigenstates in two boxes. In this case, even if the electron can move with infinite velocity, it cannot continuously move from one box to another due to the restriction of box walls. Therefore, any sort of continuous motion cannot generate the required charge distribution. . . .

I conclude that the ergodic motion of a particle cannot be continuous. . . .

. . .

a particle undergoing discontinuous motion can . . . “jump” from one region to another spatially separated region, whether there is an infinite potential wall between them or not.

. . . .

Furthermore, when the probability density that the particle appears in each position is equal to the modulus squared of its wave function there at every instant, the discontinuous motion will be ergodic and can generate the right charge distribution"

An important implication of the RDM interpretation is, as the author says, that the charge distribution of a single electron (for instance, in an atom) does not display self-interaction

"Visually speaking, the ergodic motion of a particle will form a particle “cloud” extending throughout space (during an infinitesimal time interval around a given instant), . . . . . . This picture . . . may explain . . . the non-existence of electrostatic self-interaction for the distribution.”

Part of the questions regarding this picture were already clarified by the posts of some users. The questions remained non-clarified are:

1) Is Gao's picture of a particle jumping from position to position, and visiting in this way all the volume occupied by the wave-function, fit for obtaining the Feynman path integral?

Feynman considered two points in tim and space (t₁, r₁) and (t₂, r₂). He also considered all the possible paths between these two points - the majority of the paths having crazy forms, though being continuous. The particle starting at (t₁, r₁) and traveling to (t₂, r₂), was supposed by Feynman to be totally non-classical - it was supposed to follow SIMULTANEOUSLY all the paths, not one path after another. This is was permitted him to do summation over the phases of the paths, and obtain the path integral.

The movement of Gao's particle is not only discontinuous and endowed with no phase, but it os also SERIAL, one point visited after another. What you think, if one would endow these discontinuous trajectories with phases, could we obtain Feynman's path integral despite the seriality of his particle's movement?

3) Gao author also says

"discontinuous motion has no problem of infinite velocity. The reason is that no classical velocity and acceleration can be defined for discontinuous motion, and energy and momentum will require new definitions and understandings as in quantum mechanics"

This statement seems to me in conflict with the QM, because the uncertainty principle says that if at a given time a particle has a definite position, the linear momentum (therefore also the velocity) would immediately become undetermined. QM doesn't say that the linear momentum does not exist.

Can somebody offer answer(s) to my questions/doubts?

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9 May 2019

Answer

We can only catch the quantum world in a model. Most aspects of that world cannot be perceived, not even when observation is aided by sophisticated equipment. Several scholars in the early decades of the twentieth century have tried to discover which model could fit. One of them was John von Neumann. He doubted long between Hilbert spaces and projective geometries and finally he selected Hilbert spaces. Many quantum physicists followed him in that choice. Then Schrodinger came with his equation that used a wavefunction. Apart from him Heisenberg came with his matrix theory. Then Dirac showed that both theories are principally identical and could be represented in a Hilbert space. The wavefunction is a hypothetical object. It is never observed. Quantum objects behave in ways that can be explained by similarity to wave behavior. Their detection patterns shoe interference behavior. Nobody ever saw a quantum object as a wave or as a wave package. In similar sense show quantum objects behavior that is similar to the behavior of point-like particles. However, no instrument can directly observe a point-like particle. So the model that must explain the behavior of quantum objects must offer an explanation of this wave-particle dualism.

A separable Hilbert space can archive the dynamic geometric data of a point-like particle when it applies quaternions for the eigenvalues of its operators. However, the eigenspaces of the operators in a separable Hilbert space are countable. These eigenspaces can only store an ongoing hopping path. The squared modulus of the wavefunction is a detection probability distribution. As a storage medium the separate Hilbert space can only implement the wavefunction or better its squared modulus as the descriptor of a coherent hop landing location swarm. The ongoing hopping path can recurrently regenerate such hop landing location swarm when the hopping object hops around in a stochastic manner such that after each cycle the path is closed. If the object can be characterized by its wavefunction, then each cycle must generate a coherent swarm that represents a closed hopping path, while each time the location density distribution of the hop landing location swarm is practically identical. This can only happen if a stochastic mechanism generates the hop landing location in a sufficiently controlled way. This means that the mechanism must be a stochastic process that owns a characteristic function, which is the Fourier transform of the location density distribution that describes the hop landing location swarm that the mechanism recurrently reproduces. Thus the separable Hilbert space, the stochastic proces and the operator that manages the storage of the dynamic geometric data of the hopping object are all private to the quantum object. Together, they form the platform on which the object lives. The eigenspace of the operator archives the complete life story of the quantum object.

In quantum physics many of such objects exist and each of these elementary particles owns it own platform.

A Hilbert space applies a private version of a quaternionic number system to define the inner products of pairs of vectors. It uses that same version for the specification of the eigenvalues of its operators. Further it applies a vector space from which the Hilbert space retrieves its vectors. Many separable Hilbert spaces can share the same vector space. The selected version of the quaternionic number system is also used as the private parameter space of the Hilbert space. A dedicated reference operator manages this parameter space in its eigenspace. However, in a separable Hilbert space, that eigenspace only stores the rational values.

One separable Hilbert space acts as a background platform. Its reference operator manages the background parameter space of the model. All other separable Hilbert spaces float with the geometric center of their private parameter space over the background parameter space. In this way will all elementary particles float over the background parameter space.

So where Dirac used only one Hilbert space, a better suited model will apply a myriad separable Hilbert spaces that all share the same underlying vector space.

The elementary particles act as elementary modules. Together they constitute all other modules that exist in the model. Some modules are modular systems.

This sketches the main structure of an applicable model.

The main message is that the hopping paths of the particles recurrently regenerate a similar coherent hop landing location swarm that show particle behavior and wave behavior. The particle lives on a platform that moves as one unit.

The map of the swarm on the background parameter space moves smoothly, while the image of the point-like particle hops violently.

How do we find/construct closed system needed to use Newtons laws?

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Anatoly A Khripov

asked a question related to Foundations of Physics

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4 answers

11 Mar 2019

Dear Sirs,

1, 2, 3 laws of Newtons need closed system (net force is zero). How do we practically realize, create such closed system?

One example. Let us look at a body motion. One can say If the body velocity is constant, e.g. zero then no forces act to it. Is it true? I think no. According to the 1st Newton law the velocity constance is the CONSEQUENCE of F=0.

So are there precise ways to construct closed system? Or all physical theory is just a mean to generate a hypothesis which has more higher probability to be true then other random thought?

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Bhavya Bhargava

17 Mar 2019

Answer

Dear Sir,

To the point how to construct.

Let us take component wise

Forces = Air frictional force if your relative velocity is high like 1m/s, frictional force from ground and touching surfaces, EM forces, Temperature gradients, Electrical Gradients, Gravitational forces.

Maintain constant Temperature that is generally room temperature- If temperature gradients exist then, source of it should be eliminated or considered in the system.

Use Glass material polished with talcum powder.

If any EM material Exist that is taken care by glass itself.

If high velocity Evacuate the chamber i.e. create vacuum.

Cover other surfaces also with talcum powder.

X & Z components are taken care by these.

Y component gravity is left that comes vey expensive.

So to eliminate gravity either use Archemedies Principle or do it simulation if real is not compulsory.

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Ilian Peruhov

asked a question related to Foundations of Physics

Double slit with a clock

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34 answers

24 Oct 2018

We have the simple arrangement of the double slit, but with the addition of a precise clock. The screen is also substituted by a CCD camera, so one can check when there is an event (hitting of the photon on a camera pixel).

Now we concentrate on the first minimum (say left side). If we don’t watch the clock we must get the normal interference pattern. (e.g. no events in this segment of the camera). But if we watch the clock we should know where the particles come from (left or right slit) because the distance from the left slit is slightly closer to this minimum. So we get which way information and the interference pattern is destroyed – so we must get events (and even many such) in this segment.

There are some paradoxes appearing. Without any efforts I can figure out at least 3. Surely there are many more.

1. How watching the clock on a distant spot is changing the physics on the slit panel (there seems to be no connection between them)?

2. If we use a less precise clock we would get interference. How can it be that the precision of the instruments can influence the events?

3. We could place a CCD camera above the first and not use clock with it. So on the first CCD there is 0 events and on the second CCD some events. The physics (on the slits) must be the same but it is not?

In order not to water up the discussion I would be thankful if your comments are concerned on the first item. Also please try to analyze this from the view of the orthodox interpretation of QM (Copenhagen or some variant).

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Jacques Lavau

8 Nov 2018

Answer

The 17th postulate practiced by the winning pack of the Solvay coup in 1927 is the arrogant Superiority-of-the-pack postulate:

We are the modern forever. The vile objectors and non-believers are just dimwitted, brain-damaged, and retired colonels of cavalry, who try to return to classical physics.

And after me, there will be no more prophets, as the new physics is complete!

All the sects and most of the packs sell prostheses of narcissism to their adherents

So, as an adherent, you dispensed yourself from studying optics, coherent and incoherent optics. You have forgotten that for interference through a device like the double slit, each photon must be several hundred wavelengths and periods long, and a hundred of thousands of periods is typical. When an emitter is not adamant on the frequency to emit (so are the Bremsstrahlung and the synchrotron radiation), the absorber may be spectral and monochromatizing for both. It is practiced daily at the ESRF and in any neutronic radiocrystallography. But we have NO antispectral absorbers, no way to impose the shortening of a photon at the arrival.

Even three or four generations later, the ideations in the Göttingen-København pack remain delirious.

If Schrödinger evolution equation is a scientific mistake, what else has to be discarded?

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Daniel Crespin

asked a question related to Foundations of Physics

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22 answers

25 Oct 2018

The Schrödinger self adjoint Hamiltonian operator H correctly predicts the stationary energies and stationary states of the bound electron in a hydrogen atom. To obtain such states and energies it suffices to calculate the eigenvalues and eigenfunctions of H. Since 1926 up to now, and for the foreseeable future of Physics, any theoretical description of the hydrogen atom has to assume this fact.

On the other hand the Schrödinger time dependent unitary evolution equation $\partial \Psi / \partial t = -iH(\Psi)$ is obviously mistaken. So much so that in order to explain transitions between stationary states the unitary law of movement has to be (momentarily?) suspended and then certain "intrinsically probabilistic quantum jumps" are supposed to rule over the process.

Transitions are physical phenomena that consist in the electron passing from an initial stationary state with an initial stationary energy, to another stationary state having a different stationary energy. Physically transitions always involve the respective emission/absorption of a photon. Whenever transitions occur the theoretical unitary evolution is violated.

It is absurd to accept as a law of nature an evolution equation that does not corresponds with the physical phenomena being considered. Electron transitions are not predicted, nor described by, nor deducible from the Schrödinger evolution equation. In fact Schrödinger evolution equation is physically useless. This is the reason for Schrödinger's "Diese verdammte quantenspringerei". Decades of belief in unitary evolution originated countless speculation, contradiction and confusion with enormous waste of human talent and time.

Assume then that physicists accept the mistaken nature of unitary evolution and proposes its replacement with a novel equation that a) is consistent with the predictive virtues of H b) deterministically describes transitions In principle a probability free, common sense, rational, deterministic, well constructed replacement of Quantism should be a welcome relief for physicists and chemists, and for philosophers of science as well. Then, among equations and theories currently accepted by mainstream Physics, which ones would be affected by the eventual replacement of unitary evolution? Here is a short list of prospective candidates that the reader can extend and refine Quantum chemistry Dirac equation Quantum field theories Quantum gravity Standard model Lists of physical theories are available at

https://en.wikipedia.org/wiki/Theoretical_physics https://en.wikipedia.org/wiki/Branches_of_physics could be relevant for this question.

For more on the inconsistencies of Quantism and details on a theory that could replace it see our Researchgate Contributions page

https://www.researchgate.net/profile/Daniel_Crespin/contributions

With most cordial regards, Daniel Crespin

Relevant answer

André Michaud

26 Oct 2018

Answer

Dear Christian,

You wrote: "There seems nothing wrong with Schrödinger's equations. Only Bohr and Heisenberg did not like it. They preferred the mystery."

And so did most in the community almost from the start.

De Broglie and Schrödinger already considered transitions as "not instantaneous" even as Schrödinger introduced the wave equation, and this was practically 100 years ago, not a few decades ago, and this is what they were attempting to address, but could interest nobody else.

At the beginning of the 1950's, Schrödinger himself very publicly and futilely protested again about the very idea of instantaneous quantum jumps. Unfortunately, nobody paid attention.

If you had even glanced at the paper I referred Daniel to in the first answer in this thread, you would have found the direct quotes from him and the actual references where you can find them.

It is to this 100 years disconnect that I have been trying to draw attention.

At long last, some research seems to be resuming in the right direction.

Best Regards

André

What is the dimensionality of spacetime?

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Ioannis Hadjidakis

asked a question related to Foundations of Physics

Question

62 answers

29 Aug 2018

Where from we have arrived to the conclusion that space of our Universe is 3D (and so the dimensionality of spacetime is 4D)?

I suppose this is the result of our sense of vision that is based on both of our eyes. However, the image we conceive is the result of mind manipulation (illusion) of the two “images” that each of our eyes send to our brain. This mind manipulation gives us the notion of depth that is translated as the third dimension of space. This is why one eye vision (or photography, cinema, TV, ...) is actually a 2D vision. In other words, when we see a 3D object and our eyes are (approx.) on a line perpendicular to the plane that form object's “height” and “long”, our mind concludes about object's “width”. Photons detectable by each of our eyes were, e.g. t(=10^-20sec) before, on the surface of a sphere with our eye as center and radius t*c. As the surface of a sphere is 2D (detectable space) and if we add the dimension of "time" (to form the spacetime) we should conclude that the dimensionality of our detectable Universe is 3D ((2+1) and NOT 4D(3+1)).

PS: (27/8/2018) Though, I am aware that this opinion will reveal an instinctive opposition as it contradicts our “common sense”… I will take the risk to open the issue.

Relevant answer

Sergey Shevchenko

9 Sept 2018

Answer

Thank heavens, a bottle with a good cognac has 3D+1 dimensionality…

Cheers

Would we call gluons, photons and the like "exchange particles" if Feynman diagrams had not been invented?

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Oliver Passon

asked a question related to Foundations of Physics

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16 answers

23 Aug 2018

According to common understanding the fundamental interactions of the standard model are mediated by the exchange of so-called gauge bosons (photon, gluon etc.). Now, the e.g. number of gauge bosons is related to the gauge group of the corresponding theory. But the wording "exchange particle" is apparently motivated by the graphical representation of Feynman diagrams. I wonder if we would talk and think differently if this tool of organizing your perturbative expansion would not have been invented.

By the way: the background of this question is the following: Since I believe that Feynman diagrams cannot be interpreted realistically, the notion of (virtual) exchange particles appears to me questionable (i.e. based on an artefact, like the specific solution technique of perturbation theory). But perhaps this “exchange” idea could be motivated also differently and independently.

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Walter Smilga

28 Aug 2018

Answer

Dear Oliver,

"...do physicists commit a fallacy in the Whitehead sense or are are we not in the arena of "logical reasoning"? "

That depends. Of course, we can argue logically with Feynman diagrams as long as we and our conversation partners know the mathematical terms symbolized by the lines and stick to the logic of the Feynman rules. Most physicists use Feynman diagrams in this way.

However, if the internal lines are "explained" as particles that are able to leave their mass shell, then this is a fallacy, because such explanations leave the logical arena of the Feynman rules.

Although well-intentioned, such pseudo-explanations are superfluous for the experts and give the laymen a false understanding of particle physics.

Walter

In reference to the cascaded Stern-Gerlach experiment, what right we have to consider spin as an intrinsic property?

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Mohammad Sayem Mahmood

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9 Jul 2018

In Stern-Gerlach system cascade we get electrons of two states (spin up and spin down) even after filtering out any of the one set. We know an intrinsic property is a property that an object or a thing has of itself, independently of other things, including its context. Then how it is legitimate to say that the spin is an intrinsic property of the electron?

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Shane Mansfield

11 Jul 2018

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I'd like to propose a different kind of answer. I think what you're referring to, Mohammad Sayem Mahmood, is an experiment in which Stern-Gerlach apparatuses are arranged in sequence. In this case the following is observed (see also the attached figure taken from wikipedia):

1.If we orient an SG device in the z direction we observe electrons as being deflected up or down.

2. Following that, we can filter out the electrons that have been deflected down. We can then pass the remaining electrons through a second SG device. With this second device also oriented in the z direction we only observe deflections up and never down, as expected. However, If the second SG device is oriented in the x direction then we observe that half of electrons are deflected left and half deflected right.

3. Now we can consider an arrangement with three SG devices. As before the first device is oriented in the z direction and we filter out those electrons that are deflected down. The second device is oriented in the x direction, and we can choose to filter out those that are deflected right, say. Then the third device is oriented in the z direction again.

What might be considered surprising here is that even though we have filtered out electrons that have z spin down, the act of using the second SG device to measure x spin means that when we check z spin once more using the third device half of those electrons passing through are deflected down!

As for an explanation of what is happening here, quantum mechanically the second device acts as a measurement which acts on the state of the system by collapsing it into a state oriented right or a state oriented left. So even though we had filtered to leave only z spin up electrons after the first device, we have now reset these electrons into a state that is unbiased relative to the third SG device; so accordingly we see half of the electrons being deflected up and half down. By invoking measurement invasiveness, via collapse of the wavefunction, we avoid difficulties with interpreting spin as an intrinsic property in this instance.

From a foundational perspective, we might be suspicious of this measurement invasiveness via wavefunction collapse, however. For instance we could take something akin to the perspective of EPR (which in their case was in response to a different kind of experiment) and say that, we might be able to find a more complete theory than Quantum Mechanics, which would nevertheless agree with QMs empirical predictions, but which would describe the electrons passing through the SG devices in a non-invasive way.

A no-go theorem due to Leggett and Garg essentially says that there can be no deeper theory with this property. Another way to interpret the Leggett-Garg result would be that if we insist on describing SG devices as non-invasive then we have a problem with considering spin as an intrinsic non-contextual property of electrons.

(Incidentally, on the Leggett–Garg theorem, I personally found an article by Maroney and Timpson to give a clearer discussion of how to interpret it than the original.)

I find it interesting, too, that you make the link in your question with context. There is also a related feature that can be picked out in the empirical predictions of quantum mechanics, in other kinds of experiments, known as contextuality, which indeed poses problems for our understanding of observable properties being intrinsic to the system of study independent of context of which observables are being observed in conjunction. In fact, in some of my own research I have been looking particularly at the link between contextuality and Leggett–Garg-type results.

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Will anyone of the routine QM variants ever meet the experimental facts?

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Jacques Lavau

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16 Jun 2018

Will anyone of the routine QM variants ever meet the experimental facts?

Experimental fact 1:

The conduction electrons collide with the phonons. And they collide with the dislocations, too.

Though the electrons are routinely said to be “punctual”, dimensionless corpuscles.

And the phonons are sampled on many atoms, and cannot transmute into something small.

Experimental fact 2:

The plane polarized light exists, and is used by the bees. So the light is never corpuscular, and never transmutes into something corpuscular.

Experimental fact 3:

The Ramsauer-Townsend resonant transparency exists, and is largely documented for 1921.

First, the projectiles were electrons, next different projectiles were used, with the same principle results. This transparency works because [electron] = [electron wave]. It is green cabbage and green cabbage (in French it is funnier: chou vert et vert chou).

Experimental fact 4:

The anti-reflect coatings work well, and continue to have some efficiency when the incidence angle differs notably from the normal, though the optimal transparency shifts to longer wavelengths. This property is used in photography and microscopy. It proves that a visible light photon has a notable width, at least comparable to its wavelength at the optical dioptre.

Experimental fact 5:

The quarter-wave plates work well, for transforming a plane-polarized light into circular, and vice-versa.

So any intermediate between purely circular polarization and purely plane polarization is always a valid polarization for a photon.

Experimental fact 6:

The interferential colors are all around us, and change with the incidence. With a grazing incidence, the wing mirror of the teals is seen as magenta, instead of green. It again gives a minorant to the width of a photon.

Experimental fact 7:

The Goos-Hänchen effect in plane polarization and the Imbert-Fedorov effect in circular polarization exist, and again give minorants to the width of a photon.

Experimental fact 8:

Daily, the radiocrystallography works well, even with electrons (experiments with neutrons are less frequent, and largely more expensive). Incompatible with a corpuscular theory. Linus Pauling and E. Bright Wilson Jr gave the example of their miserable failure, postulating a quantification of the linear momenta. Radiocrystallography uses the 1819 theory of physical optics, by Augustin Fresnel. The Scherrer law, giving the enlargement of the diffraction reflex by the smallness of the crystallites is daily used by mineralogists, and soil or public-works engineers. Only with waves…

Experimental fact 9:

Even when your eyes are astigmatic, or myopic, or hyperopic, you still see the same colors and the same illumination. The photons still converge on ONE couple opsin-cis-retinal, each. Impossible without causality flowing from the absorber to the optical medium (air).

Experimental fact 10:

The interferential astronomy on long bases works well. Impossible without bosonic interactions on the incoming electrons: bunching. The width of the Fermat spindle for each photon is largely compatible with this interaction on astronomical distances. However, their limited length poses a real problem: about one meter for a visible photon emitted by a hot star surface. This makes really difficult to find mates of travel, with such a short length each. Unless of a retrocausality from the transmitting vacuum to the individual emitters, synchronizing them?

Experimental fact 11:

The industrial apparatus for detecting and measuring the presence of carbon monoxide in the air by spectrographic absorption work very well, even for surveying from planes. The CO molecule captures the photon of the resonant frequency of 65.05 THz (4.608 µm wavelength), with an astonishing cross-section. But how the photon knows it has to converge on such a tiny molecule, 0.47 nm of longer axis?

Experimental fact 12:

The same question for any dye molecule, or any F-center on the surface of a solid. The absorbing molecule or site are all thousands of times smaller than the wavelength of the converging photon.

Experimental fact 13:

The same question for any spectral absorption. And they are many!

Experimental fact 14:

The Dirac-Schrödinger intrinsic frequency of the electron, 2mc²/h, has been measured at the ALS.

http://aflb.ensmp.fr/AFLB-331/aflb331m625.pdf

Experimental fact 15:

You age: Each year, the probability that you die in the next year increases.

But the atoms and their nuclei do not age: A 232 thorium nucleus keeps the same probability to decay in the next year, as when synthesized in the implosion of a supernova. An excited cloud of electrons around a nucleus does not age either: if its environment does not change, it keeps the same probability to de-energize. Well used in the 21 cm radioastronomy.

It seems that our familiar macro-time is far too big to penetrate an atom.

Experimental fact 16:

When two correlated photons are sent from the same emitter to two different absorbers, the laws of this transaction between five partners (one emitter, two absorbers, two intermediate media of propagation) never bother of the timing of the anxious physicist, in his/her Newtonian macro-time of the laboratory.

Experimental fact 17:

Shahriar S. Afshar has proved in 2001 and 2003 that interfering photons never transmute into something corpuscular; they always remain individual waves.

Afshar S. Violation of Bohr’s complementarity: one slit or both? AIP Conference Proceedings, 2006 v. 810, 294-–299.

Afshar S., Flores E., McDonalds K. F., Knoesel E. Paradox in wave-particle duality. Foundations of Physics, 2007, v. 37, 295-–305.

My conclusion: any anti-transactional theory is doomed.

Many disagree.

Your reasons for disagreeing, please? A way to save the now-hegemonic ideations?

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25 Jun 2018

Answer

Please quarrel on Quora, but keep ResearchGate clean.

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What experimental evidence prevents us using non-unitary, non-Hermitian mathematics to represent pure quantum states?

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23 Apr 2018

What experimental evidence (or any other) contradicts the use of non-unitary, non-Hermitian mathematics to represent pure quantum states? This question relates to pure states, not mixed states. Note that rational matrices have rational (real) eigenvalues.

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James T. Wheeler

24 Apr 2018

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The mathematics used to describe quantum mechanics was chosen to correspond to the observed physical realities of experiment. The reason we use Hermitian operators is because they have real eigenvalues, corresponding to the fact that the numbers produced by measurements are real. While you could certainly claim to "measure" a complex or other sort of number, ultimately that could be seen as measuring a pair of real numbers (the real and imaginary parts), or four real numbers for a quaternion, so we don't lose any possibilities by requiring real numbers.

As a further example of this, measurements DID force us to use spinors rather than just the single complex wave function; again the predictions are collections of real numbers.

The need for unitarity is a consequence of our interpretation of quantum mechanics as probabilistic and evolving via the Schrodinger equation. The wave function is unchanged by an overall constant multiple. By interpreting the magnitude of the wave function to be one, we normalize probabilities in the usual way using the real part of this number. The phase that remains is arbitrary (*relative* phases are not, just an overall one).

If we were to transform a wave function by a non-unitary transformation, it is easy to show (try it!) that the Schrodinger equation does not preserve total probability. This, with the standard interpretation, means that there is not probability one that the particle is *somewhere*. The experimental observation you are asking for is that we do not see particles spontaneously vanish or come into being.

How can the Mach Zehnder interferometer results be consistent with an epistemic view on the wavefunction WF?

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Ilian Peruhov

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1 Feb 2018

I consider the epistemic view on WF as something happening in the mind of the observer (e.g. he observed something and then the WF changed for him). So I would like to know how this view is consistent with the results from Mach Zehnder interferometer (MZI) for just one particle, which are well known.

Namely: If one changes the phase in one leg (by increasing its length or by placing phase plates etc.) then this action changes the result on the output of MZI completely (one can extinguish the intensity (have no clicks at all) in one of the two detectors placed at the output of the second Beamsplitter (BS) of MZI and redirect it toward the other detector (have all clicks here)).

So the WF is changed as a consequence of the physical action (phase lag induction) and not on paper (in the head of the observer). One can even imagine that the observer on the second BS has no knowledge about the phase lag, which can be inducted by other experimentator or by a device. Of course the observer will see change in his results which are surely due to this event and not by some process in his mind.

So the epistemic view of the WF seems very improbable? Why do official physics stick to it? What do you think?

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Willem Marinus de Muynck

7 Feb 2018

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In my view the answer is simple: the wave function does not describe something that is in your mind, it just is a mathematical description of something happening in physical reality. What happens in physical reality is a physical process of preparation and measurement of the individual microscopic objects of a physical ensemble.

The connection with epistemology is analogous to the usual identification of a `relative frequency' and a `probability distribution' in a series of the above-mentioned individual measurements, which is unphysical because in relative frequencies we only can have a finite number of individual measurement results, whereas probability distributions often require an

infinite number. What happens in the mind of the observer is just `counting the relative frequencies' and `treating these relative frequencies as probability distributions'.

Should the processes of extracting data in the universe be regarded as inseparable from the subject about which the data is extracted?

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Matthew Brown

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3 Dec 2013

It is a logical conclusion that data is as much a part of the apparatus that produced it as it is a part of the system that is being studied. It is illogical to attribute all extracted data to the system being studied, without explicit regard for the contribution from the apparatus.

I was hoping for people to discuss their views on this to try and establish a measure of how much people are incorporating the role of apparatus into their theories of the universe. It seems so often that this is simply not fundamentally considered.

[Generally by apparatus I refer to any means by which a datum occurs or data accumulates (that includes laboratory apparatus,..., humans,..). Then I hope to discuss more intricate questions like: are deductions of `truth' about the universe heavily constrained by the evolutionary path of the apparatus? And how is our understanding of reality conditioned by the observations that we make?]

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Matthew Brown

15 Nov 2017

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*For anyone that should stumble upon this string of answers:

This was originally a back-and-forth discussion with another researcher/scientist. However, he has, for some reason unknown to me removed all of his contributions from the discussion.

I will not do the same as I think it is nice to see how one's own opinions change as time goes on.

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Does physical reality possess a mathematical foundation?

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11 Oct 2017

If reality owns a structure, then this structure will have one or more foundations. The foundations must have a rather simple and thus quite comprehensible structure. Quite probably humans will have made these simple structures part of their mathematical set of structures. Consequently it is sensible that physical reality possesses a foundation that is a structure, which is also known as a part of mathematics.

A foundation of physical reality has an extra property. It must automatically evolve into a more complicated structure that owns more features and shows more complicated phenomena. This will also happen to its mathematical equivalents. After a few evolution steps the mathematical model will evolve into a physical theory.

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Marek Wojciech Gutowski

12 Oct 2017

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Physical reality does not possess a mathematical foundation, rather it has a mathematical description. Often not perfect. Besides, my cat - certainly a part of physical reality - seems completely unaware of the very existence of mathematics.

Do Feynman diagrams have only a time but also a space-axis?

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Oliver Passon

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13 Sept 2017

Before all of you cry out "No, stupid, they live in momentum space" I would like to remark that (i) why, then, is there never a momentum-axis attached to them and (ii) the renowned physicist Sivan S. Schweber has included a space-axis in his "An introduction to relativistic quantum field theory" (p. 448). Such a smart guy should have some back thought...

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Herbert H H Homeier

14 Sept 2017

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Actually, there is quite a good discussion regarding the meaning and interpretation of Feynman diagrams on wikipedia, see the link below. Basically, they show particle paths in space time.

https://en.m.wikipedia.org/wiki/Feynman_diagram

Does the GHZ argument add something new to the question of non locality compared to what Bell's Theorem and Kochen-Specker theorem say?

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Federico Comparsi

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13 Jun 2017

Is the GHZ argument more useful than BKS theorem or is only a misinterpretation of EPR argument?

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Sofia D. Wechsler

31 Jul 2017

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The GHZ rationale is much better than Bell's inequalities. Bell's inequalities try to prove the nonlocality of quantum entanglements by a non-recommendable technique. Namely, the proof of the inequalities tries to substitute the type of calculus used in the quantum formalism - the calculus with complex amplitude - by a calculus with positive probabilities. No doubt that such a substitution is impossible.

What in fact Bell proved was not that quantum entanglements are nonlocal, but that a calculus with positive numbers cannot replace the calculus with complex numbers.

The GHZ proof of the nonlocality of the quatum entanglements doesn't suffer of such problems. It is a rigorous proof.

There exists also a proof due to L. Hardy showing that there cannot exist local hidden variables, but the proof is more complicated.

Is there any difference between the proper time interval of special relativity and the proper time interval of general relativity

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Ramesh Chandra

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12 May 2017

The metric tensor of general relativity reduces to the metric tensor of special relativity in the absence of gravity. Therefore, both possibilities may exists.

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Eric Lord

19 May 2017

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“A physical quantity is defined by the series of operations and calculations of which it is the result” - A S Eddington

Accepting that, we can say that the physical quantity we call “time” is defined as “that which is measured by a clock”.

Suppose we measure the time elapsed between an event A and an event B, by transporting a clock from A to B. In Newtonian physics it is assumed that the elapsed time will be independent of how the clock is transported from A to B (ie, independent the route taken by the clock - independent of the clock’s trajectory). In Einsteinian physics (Special or General Relativity - makes no conceptual difference) that assumption is not valid. The time elapsed is not merely a property of the pair of events A and B, it is a property of the chosen trajectory between A and B, and is calculable. It is the “proper time” of the trajectory. It is independent of the choice of coordinate system; it is an invariant.

https://www.researchgate.net/publication/281145037_NMR_Technique_for_Determining_the_Depth_of_Shallow_Nitrogen-Vacancy_Centers_in_Diamond/figures?lo=1

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Asif Javed

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What is quantum plasma

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8 Apr 2017

how prove mathematical form of Magnetic Quantization ?

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James F. Peters

10 Apr 2017

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This is a good question.

For a visualization of magnetic quantization, see

For a precise answer to this question, see

Feature-Rich Magnetic Quantization in Sliding Bilayer Graphenes

https://www.researchgate.net/publication/264862774_Feature-Rich_Magnetic_Quantization_in_Sliding_Bilayer_Graphenes

Energy Bands of Carbon Nanotubes in Magnetic Fields

https://www.researchgate.net/publication/234323160_Energy_Bands_of_Carbon_Nanotubes_in_Magnetic_Fields

Article NMR Technique for Determining the Depth of Shallow Nitrogen-...

Article Feature-Rich Magnetic Quantization in Sliding Bilayer Graphenes

Article Energy Bands of Carbon Nanotubes in Magnetic Fields

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Do founding structures exist that extend by default into a more complicated structure that covers many parts of mathematics?

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27 Mar 2017

For example, the orthomodular lattice extends into a separable Hilbert space because the set of closed subspaces of this Hilbert space is lattice isomorphic to the orthomodular lattice.

This question is important because if such founding structures exist, then it is possible to derive the structure of physical reality from one founding structure or a small set of founding structures.

This again is important because it becomes apparent that the lower levels of physical reality are inaccessible to investigation via experiments.

One of the problems with the example is that the Hilbert space applies a number system for the specification of its inner product. That number system must be a division ring.

If the answer is positive, then physical reality needs only to incorporate these founding structures to also incorporate many parts of mathematics.

https://docs.com/hans-van-leunen

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28 Mar 2017

Answer

Hilbert spaces require number systems that are division rings for the specifications of its inner products. This means that the choice is restricted to the real numbers, the complex numbers and the quaternions.

Each infinite dimensional quaternionic separable Hilbert space owns a non-separable companion Hilbert space that embeds the separable Hilbert space. This combination suits as a proper model in which the Hilbert spaces act as a repository for athe dynamic geometric data of all elementary particles. Elementary particles are elementary modules that constitute all other modules and modular systems.

By defining reference operators that use the rational elements of number systems as their eigenspace, these reference operators supply parameter spaces to functions and the function values define a new category of defined operators that supply sampled continuums as their eigenspaces. If a similar trick is done to the non-separable Hilbert space, then function theory is merged with Hilbert space operator technology. The purely mathematical Hilbert Book Model applies this approach.

https://doc.co/kQjP6b

Would you have any idea how to transform the wavefunction as such into an informational onservable in quantum algebraic sense?

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András Balázs

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4 Feb 2017

I am contemplating about such a formalism as regards to introduce the wave side of the dualism in a much more explicite way than is done in orthodox QM, in which the "informationally" interpretable wavefunction as such is introduced directly as an informational observable, but have less mathemetical skills than a physicist. Could you help?

The New Paradigm of the Univers
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Joseph Jean-Claude

9 Feb 2017

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Tony,

So you start from an ontology of two particles in electromagnetic interaction. I don’t quite understand your metric though, because the metric generally applies to the background spacetime. I gather that SFT metric applies to the interaction field instead, is this correct? That being the case, how do you treat background space in the theory? Also if you start out with two particles, you automatically are limiting the theory to the atomic realm up. Further if the basis ontology requires a particle duplet, how can the theory explain unsaturated orbitals in atoms?

I thank you for the offer of the courtesy copy of the publication, which I will take. I can certainly read the first chapter and the paper as well, if you have them readily available in pdf. The discussion here might perhaps contribute to even more improvements for the next edition in the works, if nothing else. I sure have a few more questions from your intro, but let’s do it one question at a time.

Joseph

Why it is accepted that there is no absolute relation in time between two events?

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Andrew Wutke

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11 Dec 2016

This conjecture has become a dogma since 1905 and it is simply not true.

There exists a class of events which have definite absolute temporal relation

of succession.

Given a motion of a line segment AB passing a point P, A first then B:

There is no inertial system in which the kinematic event of A passing P and B passing P could be "seen" it in a different order

Einstein's statement:

There is no absolute (independent of the space of reference) relation in space, and no absolute relation in time between two events, but there is an absolute (independent of the space of reference) relation in space and time,

If the point P is between A and B there is no coordinate system in space where it would be outside of A B .

Whatever that statement means it unnecessary disregards simple tempora and spatial reasoning valid without invoking the spacetime cluster.

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F. Leyvraz

12 Dec 2016

Answer

@ Andrew: Of course, you are quite right in saying that two events which are timelike separated can only occur in one temporal sequence, and cannot be observed under any circumstances to occur in the opposite sequence.

The fact that Einstein once made an unclear statement, as the one you quote would indicate, does not mean that this is what relativity is about. The issue that the sequence in which two events occur may be undefined *always* concerns spacelike separated events. Since, for such events, no observer can ever be there to witness both, their sequence cannot be witnessed by any single observer, and it is therefore not necessarily absurd to say that it can change according to the reference frame.

https://www.newscientist.com/article/mg23130890-900-metaphysics-special-is-time-an-illusion/?cmpid&utm_medium=EMP&utm_source=NSNS&utm_campaign=metaphysics_part6&utm_content=IsTimeAnIllusion

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Hossein Javadi

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Is time an illusion?

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5 Sept 2016

WE ARE born. We die. We call the span that separates these events time. Its passage is perhaps the most fundamental feature of our human experience, yet we are incapable of saying exactly what it is. Worse – the laws of physics don’t help. That time exists is undeniable, but the way we experience it makes no sense.

“There’s an old joke about time – it’s nature’s way of keeping everything from happening at once,” says physics Nobel laureate Steven Weinberg of the University of Texas, Austin. To us mortals, time is the passage of the sun and seasons, the progressive wrinkling of our skin as we age – irreversible markers of a present that is moving forwards, and a future that is ineluctably becoming the past. Unlike space, time has a natural order. If A influences B, then B is always later in time. This is the central feature of time as we perceive it: as a flowing entity that orders our lives.

There’s only one problem with this, says David Deutsch of the University of Oxford: it’s nonsensical. We see ourselves as living in a present that marches down an imaginary timeline at a set pace. The imagery implies the existence of some sort of universal ticking time setting the beat against which all else is measured. “But what is that other time?” says Deutsch. We’ve only succeeded in creating a new problem.

In classical mechanics, time is something that passes uniformly regardless of whatever happens in the world. For this reason Newton spoke of absolute space and absolute time. On the other hand, Einstein's Special Theory of Relativity predicted that time does not flow at a fixed rate: moving clocks appear to tick more slowly relative to their stationary counterparts. Quantum mechanics does not neglect the time either. In standard model, photon does not experience time. Some new theories suggest that time does not exist at the quantum level. The study of the quantum universe shows us that time does not exist. It shows us that time is a function of relativity only and exists relative to some arbitrary point of reference [1]. Whatever else may be said about time, one thing is certain. It defies definition. The best we can say is that we all know what time is, intuitively. The Seventh Edition of Webster's Collegiate Dictionary tells us that time is "the measured or measurable period during which an action, process, or condition exists or continues." Of course, what the lexicographer has done here is to tell us that time is defined by its measurement and that measurement is of a period during which something occurs. He has not told us what time really is [2]. In fact it is the definition of a clock. What is the nature of physical time, really? In this paper, I have tried to answer this question.

https://www.researchgate.net/publication/279531060_Graviton_physical_time_and_thermodynamics

Article Graviton: physical time and thermodynamics

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Albert Manfredi

6 Sept 2016

Answer

I would argue that any dimension could be called "an illusion," if we did not perceive it from a higher dimensional space.

Consider the first dimension. A dot in space. If that's all there was, there would be nothing, and we would perceive nothing.

Now you arrange many dots consecutively, and in the two dimensional space, the first dimension takes on meaning. At least now, the concept of a first dimension can be understood.

Three dimensional space expands on two dimensional space, allowing objects to be defined conceptually. But still nothing exists, because all matter is frozen. Nothing can even be formed.

Time allows three dimensional objects to be perceivable, as much as a flat two dimensional space allowed one dimensional dots to be conceptualized.

Mathematics has no problem at all defining multi-dimensional spaces, in which time would be just another dimension. Physics deals with what we can see and measure, so it doesn't delve in these higher dimensional spaces. But that doesn't mean they don't exist. So, once we figure out how to detect these higher dimensional realities, that's when we'll get a clear understanding of what time is.

Remember, you read it here first. :)

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Could the Physical Universe operate, devoid of Natural Mathematical Processes?

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12 May 2016

Are Natural Mathematical Processes a necessary component in the running of the Physical Universe? Could the Universe operate without them? For example, are mathematical processes essential in the addition of distances or displacements?

This question is an attempt at rewording of my earlier question asking whether mathematics is intrinsic in Nature. That ealier question was rather open to interpretational debate. I am hoping, this time, I more acutely address the point I intend.

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Jonathan Edwards

17 May 2016

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What exactly do you envisage as mathematical processes, Steve? If I add 2 and 2 and get 4 I doubt my brain even computes. It just remembers the answer. An ensemble of photons going through 2 slits instantiate a physical process that for us requires complex numbers to describe. But surely nobody suggests that the photons or God are doing any complex arithmetic on the back of a celestial envelope.. What would a 'mathematical process' be?

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If two false statements can combine to prove a statement that is true , is there something remarkable about this kind of proof?

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26 Apr 2016

The example I have in mind is a pair of integrals, over an inseparable domain, that do not exist unless weighted by functions in Banach space. But even if they are not, they can inter-substitute to imply existence of the Fourier transform and its inverse.

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Mihai Prunescu

27 Apr 2016

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I think that false physical models can combine and build together correct predictions. The big problem about this is that sometimes correct statements stay on false proofs. People find errors in the proofs, and then they claim that the statement itself is false. This is not always true. They proved only that this particular proof is false.

The situation is particularly embarassing as the last 150 years compose together the most active time in developping and concatenating physical theories.

Particularly, the statement E = mc^2 stays only on proofs which are literally false, but can still be correct. I don't know it to have been hardly fasified by experiments. Also "dark energy" and "dark matter" are almost sure inconsistent, but they build also some correct predictions together with other theories, which are not completely true. We need a fast and radical clean and clear action, or we run directly in a major crisis of science, faster than we believe.

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Could contradiction play a role in quantum systems, during measurement?

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27 Dec 2015

Could contradiction play a role in quantum systems, as part of the mechanism of measurement, forcing a single random outcome from the spectrum of possibilities?

All ideas are welcome, including outrageous ones.

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8 Jan 2016

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My idea is that contradiction may be the impetus that forces decision during quantum measurement. Again referring to the donkey dilemma -- the donkey that starved to death after being placed equidistant between two bails of hay. The donkey cannot feed because no preference is possible.

If the donkey was forced to move forward by some strict contradiction behind him, forcing a decision on him, the contradiction would be imperative while the non-preference is no imperative at all. What do you think about this kind of idea?

Steve.

How does my three-term system of formal logic compare to Steve Faulkner’s work?

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Victor J Aguilar

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6 Dec 2015

https://www.researchgate.net/publication/270687116_AXIOMATIC_THEORY_of_ECONOMICS

This paper provides a simplified exposition (no real analysis) of the economic theory presented in the second part of my 1999 book, Axiomatic Theory of Economics. It makes no mention of the first part of my book about the foundations of economics. In this question we will discuss my three-term system of formal logic, specifically with comparison to the attached paper by Steve Faulkner, which was posted in reply to another question that I recently asked.

http://www.researchgate.net/publication/282647562_Logical_independence_inherent_in_Elementary_Algebra_seen_in_context_of_quantum_randomness

In Section 4.3 of my 1999 book I write:

“The great crack in the foundation of mainstream logic where first-sense and third-sense truth are confused has been resolved. Whenever mainstream logic speaks of affirmation they refer to phenomena having been observed that conform to a definition (truth in the first sense) and whenever they speak of negation they refer to the impossibility of phenomena conforming to a definition (falsity in the third sense). The three senses of truth must be strictly separated…”

The three sense of truth are defined in an earlier section of my book, but suffice it to say that I was not bothered so much by the paradoxes that Gödel addressed but by the fact that, if p is impossible, the statement “some p are q” is false while the statement “all p are q” is true. This is absurd. If I told you that all red-headed Eskimos can foresee the future, a logician would have to admit that, within his science, this statement is true. But everybody else would denounce me as a lunatic: Eskimos do not have red hair and nobody – regardless of the color of their hair – can foresee the future. The logical truth value of my statement will not inspire anybody to travel to Alaska to find Sibyl the Eskimo with her flaming red hair.

“A new system of formal logic will now be introduced. The three terms of this system of logic are P for possible, I for impossible and M for maybe (similar to Zen Buddhism’s mu.) Following are eleven logical relations concerning the definitions p and q. These statements are followed by a truth table which shows, in each of the four situations with which one could be presented when observing phenomena’s conformance to p and q, whether the statement affirms its possibility, its impossibility, or says nothing about that situation.”

While I do not have space here to print the entire list of eleven logical relations, I will print the truth table for “p is possible unless q is possible” to give a taste of what I am doing:

Do phenomena conform to definition p? T T F F

Do phenomena conform to definition q? T F T F

p is possible unless q is possible I P M M

I then use an example from Willard Quine’s Methods of Logic (p. 196) to illustrate how my method works:

Premises:

1) The guard searched all who entered the building except those who were accompanied by members of the firm.

2) Some of Fiorecchio’s men entered the building unaccompanied by anyone else [unaccompanied by non-Fioreccio men].

3) The guard searched none of Fioreccio’s men.

Using my system, by filling in a truth table with P (possible), I (impossible) and M (maybe), we can quickly determine if the statement, “Some of Fioreccio’s men are members of the firm” is proven. There is no room to print this here, but it is a sixteen-column truth table with four rows of P, I or M for each of the three premises and the relation, “people who work for Fioreccio.” Below this is another row labeled “result.”

“Now, filling in an I wherever we see one, a P wherever we see one that is not dominated by an I, and an M only where no statement is made either way, we get the result.”

This is in contrast to Dr. Quine’s method (p. 199), which only proves or disproves one statement at a time. I write:

“From this result [the three-term truth table] one can test the truth of any conclusion one is interested in… If we were interested in knowing whether the statement ‘All of Fiorecchio’s men entered the building unaccompanied by non-Fiorecchio men’ is implied by the premises, we would need [elaborate what is needed that we do not know] so the conclusion is not proven; it is a maybe. This is a more insightful ‘maybe’ than we had before analysis, however, as we now know where our investigation must lead.”

REFERENCES

Quine, W.V. 1982. Methods of Logic. Cambridge, MA: Harvard University Press

Chapter Simplified Exposition of Axiomatic Economics

Article Logical independence inherent in Elementary Algebra seen in ...

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Marcia Ricci Pinheiro

19 Dec 2015

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Victor, I am both a mathematician and a philosopher, and I work a lot with Logic, which is my preferred part.

I have just studied Godel's proof of God and you can see the result of that in the book On Religion, which is found on my profile here.

I think that the aim of Logic is not confusing people, but making things easier and nicer instead.

Priest, like you, loved formalizing anything.

The problem with that is that you end up working in the abstraction, but you then want to come back to reality in the end and, whilst the first move could be acceptable, if things were ever done properly, the second move is usually impossible to to accept.

Basically, I have written a lot about this by now: We can fit a reduced universe into a large one, but there are lots of things that escape logic in human language/discourse and the reverse move is not usually OK.

The sentences you wrote are easily dealt with without us changing them into symbols and, therefore, the need to do that does not exist. We are not simplifying if doing that either, we are actually complicating and probably missing the point, so that that is also not advisable.

What Prof. Faulkner says is true and it actually occurred to me as I read your writing, but in a much more informal way.

If you read more of my work, you will understand why this concern you seem to be having is actually equivocated for Mathematics. Creating new systems of logic, as Priest does, is fun, but may also be completely useless activity.

Apart from learning the concepts involved in the modelling of the systems and applying those, there is nothing to it.

If you want them to be useful, you must make sure you find a situation for which we feel the necessity of coding things. In second place, as you have probably noticed, you should also check if the system already exists.

Remember that we must improve things with them, not confuse people even more or lead them to mistake in reasoning.

Priest has a book with almost all non-classical systems and you could actually use his book, since it works like an encyclopedia, to find out if a system already exists or not.

I think he finished this book in 2000, after he went through it with me.

Do the effects of mind on matter as demonstrated in the experiments of Radin et al (Physics essays 2012 & 2013) herald a new scientific paradigm ?

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Rajat Kumar Pradhan

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15 Jul 2015

This refers to the recent experiments of Radin et al :

1) D. Radin, L. Michel, K. Galdamez, P. Wendland, R Rickenbach and A. Delorme

Physics Essays, 25, 2, 157 (2012).

2) D. Radin, L. Michel, J. Johnston and A. Delorme, Physics Essays, 26, 4, 553 (2013).

These experiments show that observers can affect the outcome of a double slit experiments as evidenced by a definite change in the interference pattern.

It requires urgent attention from the scientific community, especially Physicists.

If these observed effects are real, then we must have a scientific theory that can account for them.

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Ulrich Mutze

19 Jul 2015

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@Rajat.

I don't know to which point of the debate the queer thoughts of your first paragraph are meant to be a contribution.

For science it is not a problem to be faced with empirical facts for which an explanation is presently out of reach. During most part of the ninetenth century astronomers knew that no chemical reaction could deliver the radiative power that was observed to originate in stars. One had to wait till the discovery of atomic nuclei and a preliminary understanding of their internal workings before the radiation of stars could be explained. If there are clear facts science will find an explanation, perhaps only after a few hundred years.

Pseudoscience is characterized by the missing of clear facts. Pseudoscientists have enough knowledge of science that they can impress uncritical people but are unable to arange experiments and observations in a manner that repetition by independent groups reproduces the original findings.

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What kind of imperative can force quantum randomness?

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28 Apr 2015

If the decision between two choices is to be made, but neither choice is preferred over the other, because there is perfect symmetry between the two, then no information separates the choices and the only decision that can be made is a random one.

What kind of imperative can force such a decision, and does such a decision resist the imperative?

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Igor Goliney

6 May 2015

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Bell inequalities compare two results obtained for the cases of probabilities (hidden variables, randomness) and amplitudes of probabilities (coherence). So far coherence wins over randomness,

Why electromagnetic field propagates via void vacuum?

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Zhiliang Cao

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11 Apr 2015

Water wave propagates via the water. Sound wave propagates via matters in solid, liquid or gas states. It is pretty logical.

"Electromagnetic field propagates via void vacuum" is commonly accepted. In this case, void vacuum is media for light. If vacuum is true void, why it can be a media for carrying electromagnetic wave? Can you provide a logical answer?

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Sofia D. Wechsler

14 Apr 2015

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Some history of the photon as an independent particle:

The concept of photon as an independent particle developed gradually due to the need to explain different experimental facts, among which the ultraviolet catastrophe (solved by Planck by introducing the quantum of e.m. energy), the photo-electric effect (solved by Einstein also by admitting the frequency dependence of light's energy), and others.

These experiments could have been alternatively explained by admitting that atoms and molecules can absorb or emit e.m. energy only in discrete amounts. However, Einstein proposed the idea that if Planck's formula is accepted, each quantum of energy should also carry a linear momentum p = h/λ, i.e. such a quantum has full particle behavior, linear momentum and energy.

Einstein's idea was confirmed by the results of scattering experiments of single photons by electrons, 1923 (for which H. A. Compton was awarded the Nobel Prize in 1927). Thereafter, the idea of photons as independent particles became widely accepted. (A attempt of reconciliation of the above results with the Maxwell continuous e.m. field, was done later by Bohr, Kramers, and Slater, but the attempt failed.)

Do you know of any case in which physicists accepted a basic theory based on a derivation from accepted theories, or its mathematical structure?

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Richard James Petti

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4 Mar 2015

Kuhn says leading physicists accepted Newton's theory of gravitation before astronomical measurements were accurate enough to decide the issue ["Structure of Scientific Revolutions" 1962]. Other than this aged example, is there any case in which physicists accepted a new or modified basic theory of physics based on a mathematical derivation from well-accepted theories, before direct empirical evidence was available? The Higgs boson and cosmic inflation have something of this flavor: these theories had substantial credibility before empirical evidence was available because they explained phenomena that were left unexplained by existing theories, but they were not fully accepted in the canon of physics.

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Claude Pierre Massé

11 Mar 2015

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Akira, all what you write is so off the mark and so surrealistic than we don't even know where to begin with to answer you. I already gave up for a long time. You have only read the books that reinforce your prejudices, and/or suitably misconstrued other ones. Your knowledge on the very matter, on the scientific community, on the methods, on the history must be very thin to utter such absurdities. Your motivation is only to put down the scholars, and not to seak the truth, so a discussion with you is pointless. You want to think that they are all mislead? All right, think so, it's your problem, not ours.

Quantum mechanics have been discovered independently by Schrödinger and Heisenberg, and in different forms. But Schrödinger has proved that they are mathematically equivalent. There was also an american physicist who discovered it even before De Broglie's thesis. But his paper has not been accepted for publication for deemed to be too abstract. It has been destroyed, but Schrödinger saw it, and said that it was the same thing as his own work. This story is very little know, I can't find the references again. So, three identical and independent copies of the same theory, in different settings, there is certainly something in it. Before the debate between Bohr and Einstein, and before the famous EPR paper, quantum mechanics was thought to be perfectly rational, even though not intuitive, not "anschaulich." It explained quite naturally the empirical rules of Bohr and Sommerfeld, without the irrational-magical tinge they carry. In only two or three years after its official birth, quantum mechanics has been applied succesfully to a wealth of problems. Since then, despite much efforts, and even despite the rationalist movement, no better theory could be found. The only rôle we could ascribe to the "anti-rational hysteria," is that these invaluable papers could be published, contrary to with the stringent and arbitrary policy of the American Physical Society. De Boglie who sparked this revolution was not in Germany.

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What is the energy density of the vacuum?

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4 Mar 2015

John Archibald Wheeler said: “Empty space is not empty.” However, there are many different models of the energy content of the vacuum. One extreme position is that the only energy density present in the vacuum is dark energy which is about 6x10^-10 J/m³. The standard model has 17 named particles and each particle has its own field which fills all of spacetime. For example, the Higgs field is one of these fields and the energy density of this field has been estimated at about 10⁴⁶ J/m³. Quantum chromodynamics also requires energy density at least this high. Field theory has zero point energy where the vacuum is assumed to have harmonic oscillators with energy E = ½ ħω where all frequencies up to Planck frequency are represented. This implies Planck energy density equal to about 10¹¹³ J/m³. This is often assumed to be impossible, but the argument can be made that general relativity implies that spacetime has impedance equal to c³/G ≈ 4x10³⁵ kg/s. This tremendously large impedance is consistent with the vacuum having Planck energy density. http://onlyspacetime.com/QM-Foundation.pdf

We do not interact directly with the energy of the vacuum, but something is giving the vacuum properties such as constants G, c, ε_o, µ_o, ħ, etc. Therefore, how do you view the energy density of the vacuum?

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8 Mar 2015

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The energy-momentum (or stress-energy) tensor is *a* source term: it can't be eliminated by fiat, any more than the cosmological constant term can. However, it doesn't contribute to the vacuum energy density, since then the matter fields take the values that make it vanish. So the only consistent contribution to the vacuum energy density is that of the cosmological constant-which experiment has shown doesn't vanish.

Can quantum entanglement be effectivelly simulated by using classical fields?

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Jian Fu

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3 Mar 2015

We discuss an effective simulation of quantum entanglement is presented using classical fields modulated with n pseudorandom phase sequences (PPSs) that constitute a n2^n-dimensional Hilbert space with a tensor product structure.

Is it reasonable？

If it is right, quantum entanglement is the unique property of quantum mechanics?

see http://arxiv.org/abs/1502.07002v2

http://arxiv.org/abs/1502.07002v2

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Andrea Aiello

4 Mar 2015

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Yes, quantum entanglement features can be present in classical fields, because the two mathematical properties underlying entanglement are the validity of the superposition principle and the existence of a bipartite (or multiparty) Hilbert space. These features are commonplace in classical electromagnetism where electric and magnetic fields obey the superposition principle and possess independent (e.g., polarization and spatial) degrees of freedom. For details see: http://arxiv.org/abs/1409.0213 "Classical entanglement: Oxymoron or resource?"

It is important, though, to make it clear that entanglement and nonlocality are different properties of a system, and only the latter seems to be an exclusive feature of the quantum world.

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In mathematics, there is no absolute truth. What kind of truths are we striving for in Physics?

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25 Feb 2015

In pure mathematics there is no absolute truth [Stabler]; we invent rules then see what they prove or see what is consistent with them. So in physics, what kind of truths are we looking for? Are we looking for absolute truths in physics?

(Note that the premise of my question immediately contradicts itself -- saying there is not absolute truth is an absolute statement. Maybe it is not a mathematical statement, I'm not sure. Apologies for this mess.)

Ref: Edward Russell Stabler, An introduction to mathematical thought, Addison-Wesley Publishing Company Inc., Reading Massachusetts USA, 1948.

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Clifford Chafin

2 Mar 2015

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Akira, Welcome to physics! ha ha! This is the reason we have made essentially no progress on fundamental problems in the last 60+ years. Low bars and big egos and the sensible people skulk out of the room before the sparks fly.