9th Jan, 2019

retired from Technion Israeli Institute of Technology

Question

Asked 20th Nov, 2018

There are different proofs that the quantum nechanics (QM), more exactly the quantum formalism (that was NEVER contradicted by experiment), does not admit a substructure of particles following **continuous** trajectories. As two rigorous proofs I recommend my article

and section 5, "Does a quantum objecthave a 'particle' ? ", in my article

Deleted research item The research item mentioned here has been deleted

However, with all my efforts until now, I didn't succeed to prove a stronger statement: that the quantum object, which travels in our apparatus(es) does not possess a **weird 'particle'** which jumps accross disjoints regions, separated by a space in which the wave-function is null. This problem arises very strongly when we have to do with a wave-function consisting in two or more wave-packets traveling through isolated regions, e.g. : |ψ> = |a> + |b>.

In my last article mentioned above, I used as assumption the idea that a particle cannot do such a jump. i.e. cannot jump from the wave-packet |a> to the wave-packet |b>. The motivation is that an instant jump between two disjoint regions would mean, in a suitable frame of coordinates in movement with respect to the lab, that the particle disappears for a while from the universe. That would contradict the energy conservation, which has to be respected in any frame of coordinates.

Could there be a NO-GO here? Could it be that it is impossible to prove that there is no such weird particle? Could it be that it though exists?

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Ilja,

The time of measurement is not a parameter in my calculi. All the detectors in the picture are are the same distance from the central beam-splitter BS that produces the wave-packets |u_{1}> and |u_{2}>. The rationale would be the same if a pair of detectors would be more distant than the other pair.

Moreover, I have full right to do the experiment dynamically, i.e. to place the beam splitters BS_{1} and BS_{2}, with the accompanying detectors, when I want. The particle does not know my intentions.

Thus, the bottom line of my proof is that if we keep the idea of a particle, then, for obtaining a detection of type F1 = F2 = 1, the particle should have gone, compulsorily, to BS_{1}, but, also, it should have gone, compulsorily, to BS_{2}. It's not a personal interpretation of QM - **I have no interpretation** - it's a **PROOF** according to the QM formalism.

The Schrodinger equation simply assumes energy is conserved, it is built from this.

conservation of matter is derived from it.

It does not contemplate inelastic stuff, which does take place.

In my opinion the uncertainty principle can be interpreted that you can violate conservation of energy for short time periods.

In the interference of quantum waves, you have places where there are no particles, this means going somewhere else where there is a bright fringe.

So overall you may have conservation laws, but locally there need not be.

Then you have to add my other remarks, that there can be a lot of noisy stuff going on.

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Dear **Sofia****,**

let me separate the problem in two parts:

non-relativist quantum mechanics and relativist quantum mechanics

for non-relativist quantum mechanics:

The Schrodinger equation describes all that quantum mechanics know about the sub-atomic level, I prefer to use the path integral formulation (that is equivalent to the Schrodinger equation), as you know the path integral formulation gives us the probability to catch particle in position p2 and time t2 that starting from position p1 and time t1, so (and that what I want to say) any theory or ideas (that respect the particle existence probability distribution) about what happened between time t1 and time t2 we can't approve it or disapprove it via path integral formulation (or Schrodinger equation), because path integral formulation (or Schrodinger equation) didn't have any explanation beyond the probability existing picture.

so if you have for example any theory that postulates that the particle stay sometimes in position p1 and move instantly at time t2 to p2 so you didn't have

any violation of conservation energy because any other frame will see exactly what you see (instantly motion between p1 and p2) because you work now in non-relativist quantum mechanics! and the special relativity theory is not applicable in Schrodinger equation because the time in this equation is absolute ...

It is clear that the problem, in fact, starts only in relativist quantum mechanics!

With best regards.

Dear Juan,

Let's leave aside noise. Usually, as you know, we make our considerations on noiseless (ideal) experiments, and leave to the experimenters to find methods to eliminate noise as well as possible.

Now, my problem does not involve scattering. And when the wave-function is a quantum superposition, |ψ> = |a> + |b>, the two wave-packets are far from one another.

The problem with the two wave-packets is that when passing through fields, e.g. electric, magnetic, etc., they behave as if each one of the wave-packets contains an electric charge (or magnetic dipole), even if the wave-function is of a single charge.

This is the issue! If we believe that a quantum object consists, besides the wave, in a "particle", which encapsulates the charge or the magnetic dipole, we have to admit that each one of |a> and |b> contains such a particle. Indeed, the experiment shows that the behavior of each one of |a> and |b> through different fields is so, as if each one of the wave-packets contains the electric/magnetic property. HOWEVER, our wave-function is a SINGLE PARTICLE wave-function. Therefore, if we believe in the existence of a "particle" we get a contradiction, unless we admit that the particle jumps over distances inside which the wave-function is null.

Well, such jumps contradict the relativity, as I explained in the question. But, I am not enough pleased with this argument. I look for an argument provided by the formalism of the QM, without using relativity.

With kind regards,

Sofia

Dear and lovely Mazen,

The issue is not simple. To jump instantly from the position **p**_{1} to **p**_{2}, the particle needs infinite velocity. That contradicts relativity. One cannot say that he prefers to work with the non-relativistic QM, as one cannot say that he assumes that all the population of the earth is males and there are no femails. An assumption has to cope with all the physics not only with part of it.

I also explained in the question that jumping from the wave-packet |a> to the wave-packet |b> when the two wave-packets are far away from one another, means, in another frame of coordinates, i.e. another time axis, that the particle disappeared from |a> at time *t*_{1} and appeared at |b> at time *t*_{2}. If *t*_{2} > *t*_{1}, in the interval between them the particle disappeared from the universe. If *t*_{2} < *t*_{1}, in the interval between them the particle was present in both regions, despite the fact that we have only one particle.

With kind regards!

Dear and lovely **Sofia** ,

You said:" One cannot say that he prefers to work with the non-relativistic QM, as one cannot say that he assumes that all the population of the earth is males and there are no femails. An assumption has to cope with all the physics not only with part of it. "

Yes, sure I agree with you, this is obvious :), just I mean that we didn't have any problem with Schrodinger formalism.

I want to say that the problem exists when we want to integrate the special relativity into quantum mechanics, for example the first problem is we didn't have a real position operator for massive relativistic quantum particles, and many people doubt with any attempt to build one like for example Newton–Wigner localization.

With best regards.

Dont know. I suppose the single particle is in both state a and state b.

with the respective amplitudes, until you force the system to decide in which it is.

Just like the double slit, the particle passes through both, until you determine

through which it passes, which spoils the interference pattern.

Dear Sofia,

So because we didn't have a real position operator in relativistic quantum theory, we can't measure the position of a particle with less than the Compton wavelength of the particle: h /(mc), and to catch a particle over a distance of order h /(mc) need an energy (for photon by example) in order of mc^2, then the localization process will therefore generally create particle-antiparticle pairs, so the particles thus produced are indistinguishable from the original particle.

Then in relativistic quantum theory we didn't have the simple picture that particle jumps from p1 to p2 so we have a lot of problems here to be understand ...

With best regards.

Sophia

Now I adhere to my last answer.

I think you are still trying to trick the quantum into rationality

by having the entity declare itself a particle or wave.

That a single particle to behave essentially the same as if it were a whole number

as far as statistics goes is indeed mind boggling, but at some stage you have to accept the facts.

Juan,

You said such a high phylosophy that I understood nothing. What's that "*to trick the quantum into rationality*"? Everything is rational. We do science, not mistics.

Could it be that you didn't understand my question? It's a sure fact that the quantum objects, the "thing" traveling in our apparatus, is a wave, because it is able to produce interference. But inside this wave, should there be a "particle" floating?

By "particle" people mean a reality that triggers a detector. That is, if the wave-function has the form, say, |ψ> = |a> + |b> + |c> + . . . , at a given time the particle is in only one of these wave-packets. Though, for imposing a correct passing through fields and devices, the particle has to jump from one wave-packet to another, so as to be present in all the wave-packets. That would imply jumps *forward and backward in time*. Worse than that, one can always find a sphere passing through four points, therefore one can find a frame of coordinates by which the particle should be at once in as much as four wave-packets. Thus, if the wave-function consists in 4 or more wave-packets, the number of particles may be in fact as much as 4, despite the fact that he wave-function is what we name "single -particle wave-function".

Finally, my question is whether the idea of such a (weird) particle and such jumps cannot be excluded (a NO-GO).

I understood your question.

You say:

the (single) particle is in just one of these wave packets....

Thats where your wrong. If it is a superposition its in all (here both) with respective amplitudes. (already said in previous post) The charged deviation plates on both sides not enough to determine on which side the electron is.

The one particle behaves like many in a sense, as if there were many.

Regards, juan

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Dear Juan,

When someone said that "the single particle exists in all trajectories and interfere with itself to achieve the superposition ", in fact, this is only a metaphor!

We have only one particle here not two or more.

I think that the particle did a real jump by disappearing from one location and appearing in another location (and obey statistically the Schrodinger equation).

with best regards.

What you need to do in any quantum problem is decide what is the universe of possible available states.

Then the total wave function is a superposition of these states multiplied by amplitudes, and in the time dependent case also by a time dependent phase factor.

If for some reason a give state is very separatade spatially from the rest, perhaps it does not need to be included in this universe. or perhaps it can be done.

This always depends only on the creteria of the investigator, we cannot do anything else.

All this need involve just one particle.

That is quantum theory, what do you want me to say?

Deleted profile

Dear Sofia Wechsler,

Have you thought about the possibility that the concept of the dynamical properties of a rest mass carrying particle is incomplete? There is a search for a united field theory for nearly a century so maybe there are foundational problems.

With kind regards, Sydney

Juan,

What kind of a statement is this

"*The one particle behaves like many in a sense, as if there were many.*"

Would you accept your employer to tell you that he pays you only part of the salary, but take that "*in a sense*" as if it were much more?

You see, when I think over this problem, what comes in my mind is the fullerenes, the dinosaurs of the microscopic world - see picture. I suppose you know that interference was done also with fullerenes. How shall I imagine that a fullerene passing through gratings becomes a handful of fullerenes? If I would reason with particles from the standard model, electrons, or others, I could think that it is the vacuum that supplies additional particles, for endowing each wave-packet with a particle. But for fullerenes we do not have such a vacuum, able to generate such dinosaurs.

On the other side, imagine yourself the fullerene jumping instantly from the wave-packet |a> which travels, say, through Worcester, to the wave-packet |b> which travels, say, through Kyryat Motzkin. Does it seem realistic to you?

By the way, are you good at QFT? In particular, do you know Wich theorem? The probability of such a jump should be given by the 2nd order correlation

G^{(2)}(**r**, *t*; **r', ***t*') = <*ψ*̂ ^{†}(**r**, *t*) *ψ*̂ (**r**, *t*) *ψ*̂ ^{†}(**r'**, *t*') *ψ*̂ (**r'**, *t*')> = *ρ*(**r**, *t*) *ρ*(**r**′, *t*') + |G^{(1)}(**r**, *t*; **r′**, *t*')|^{2} + *ρ*(**r**, *t*)δ(**r** − **r′**)δ(*t* − *t*′).

You see, for the case that at the time t the particle is in the wave-packet |a>, and at the time t' the particle is in the wave-packet |b>, with |a>_{t} and |b>_{t'} disjoint, I get G^{(2)}(**r**, *t*; **r', ***t*') = 0. So, no chance for such a jump.

What you say?

- 9.33 KBFluorofullerene.gif

Hi, Sydney,

I sent you a reply yesterday, and it seems to have disappeared.

What shall I do with a united field theory? If QM is at odds with the concept of "particle" then the QM formalism should be able to provide a rigorous proof against this concept. Otherwise, it should admit this concept.

Would you read my reply to Juan, just above? The most important is the 2nd order correlation G(2)(**r**, *t*; **r',** *t*').

With kind regards

Well, they say QM is a statistical theory, pedicts probabilities, and sometimes using only one particle. Dont you think this is strange?

Ill take a bit of time to see the rest.

Juan, my friend,

Please see my calculus of the 2nd order correlation. The calculus should be trivial, but the conclusion is not.

Dear Sofia,

I want to say too that with the jump model of motion we should interpret that the wave collapse is the appearing of the particle in any location, so after any appearing event, the wave function (that specify the existence probability distribution) start again, and we can not preserve the old state (the original wave function).

With best regards.

Obviously thr fullerenes do not multiply. All that happens is that the amplitude (or wave function) splits.

The fullerenes do not turn up unless detected. No need for jump.

Give me more time on the rest of your remarks.

Dear Sofia,

One of your main assumptions that you do is that:

But that is very difficult to understand for me within Quantum Mechanics (QM). In QM the two disjunt functions must be included inside of a Hamiltonian and the main part would be the potentials, thus it is necessary to define a potential with discontinuities or other physical condition. Spacetime is not possible because it is assumed to be simply connected or provided with a trivial topology for QM.

On the other hand, taking two disjoint regions existing for a given particle, how can we know it just defining |ψ> = |a> + |b>? ψ> is a vector in 2-D Hilbert functional space with two components? Where is the mathematical and physical information containing the condition of the two disjoint regions?

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Dear Sofia Wechsler,

If you don’t mind I keep it simple. Your question is about the nearly instantaneous “pop up” and disappearance of a rest mass carrying particle at distinct positions that are separated from each other because the distinct positions represent 2 different trajectories that lie behind a beam splitter. At the end of each trajectory is a detector and each trajectory is curved by an electrostatic device.

So there are 2 questions:

- does the phenomenon exist like proposed,
- if it exist, can QM predict the phenomenon?

The answer for both questions is “yes”. The answer to question 2 is simple: you haven’t done the experiment but it was the outcome with the help of QM formalism. Question 1 was answered in a question of you about the experiment. I suppose you didn’t like my comment because it seemed it had nothing to do with QM.

So I presume that your real question is about the “magic” behind the experiment because you have the opinion the results don’t confirm some known concepts in phenomenological physics. That is why I asked you in my last comment if you are sure about the reliability of your concepts because if we struggle for nearly a century to find a unified field theory, our present concepts must be incomplete, even QM.

Does my “translation” describes it all or is there something essential missing?

With kind regards, Sydney

@ Sofia: "There are different proofs that the quantum nechanics (QM), more exactly the quantum formalism (that was NEVER contradicted by experiment), does not admit a substructure of particles following **continuous** trajectories. "

There is no such proof. Bohmian mechanics is equivalent to non-relativistic quantum mechanics and it has a substructure of particles even following **differentiable** trajectories. And Bohmian mechanics can without problem be generalized to relativistic speeds as long as no particle creation or annihilation can take place (i.e., it will describe electrons with kinetic energies up to almost 0.5 MeV, i.e., a speed of 0.7 c).

"By the way, are you good at QFT? In particular, do you know Wick theorem? The probability of such a jump should be given by the 2nd order correlation

G(2)(**r**, *t*; **r', ***t*') = <*ψ*̂ †(**r**, *t*) *ψ*̂ (**r**, *t*) *ψ*̂ †(**r'**, *t*') *ψ*̂ (**r'**, *t*')> = *ρ*(**r**, *t*) *ρ*(**r**′, *t*') + |G(1)(**r**, *t*; **r′**, *t*')|2 + *ρ*(**r**, *t*)δ(**r** − **r′**)δ(*t* − *t*′)."

This correlation function describes two-particle correlations (there are two creation operators in it). It is not compatible with your one-particle example.

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Klaus,

I won't get into our old dispute about Bohm's mechanics as long as I can't offer you a proof that would convince you.

So, you say that the G^{(2)} that I speak of is for two particles . . . Hmmm! Can't it be for two MODES, and not particles? Are you sure?

I checked in the past Wick's theorem, but to say that I can handle it easily, I can't say.

Now it's very late in my country. I would like to continue this dialogue.

With thanks, and kind regards!

Dear Klaus,

I appologize for the delayed reaction. I am asking again, the 2nd order correlation is only for two particles? can't it be for two MODES of one and a same particle? What it's known to you?

Klaus

You afirm that Quantum Mechanics is consistent with a substructure particles following

differentiable trajectories? Do I understand well?

Or is it just Bohmian Mechanics?

(If so, I think you are in a most absolute minority, just consider uncertainty principle phenomenon) as illustrated in many sources of modern physics.

The usuall is that there is no trajectory, wheather continuous or differentiable.

Best regards, Juan

Dear Juan,

Don't forget the Feynman's formalism where you have not one unique trajectory but many depending of how big the action is respect to h.

Given that there exists interpretations of QM which has continuous trajectories, like de Broglie-Bohm theory or Nelsonian stochastics, there can be no no-go theorem about this.

Klaus Kassner, these interpretaions can be generalized to relativistic field theories even without any problems with particle creation. One simply has to use a field ontology. See http://ilja-schmelzer.de/quantum/QFT.php

Juan Weisz, do you really think that physics and mathematics is democracy where majority rules? The question discussed here is essentially mathematical, namely a no-go theorem. And dBB is proven to be equivalent where it is applicable.

Yes, Feyman theory has trajectories but certainly not unique. In any case it is only supposed trajectoriies within this theory.

But I claim that due to the uncertainty principle there cannot be

Newtonian trajectories.(ie. usual calculus based trajectories)

Is it possible that Bohmian mechanics gets around the uncetainty principle,

the later having an empiric basis?

In any case my understanding of Bohm indicates a force pulling to where the modulus of wave function is greatest,

on top of a very noisy and short distance effects which keeps electrons rattling around inside the wave function. So at most it cannot be a differentiable trajectory everywhere.

My remarks were based on Klauss answer.

regards to all, juan

Dear Juan, de Broglie-Bohm circumvents the uncertainty relation because the trajectory is in the configuration space only, q(t), not in the phase space (q(t),p(t)). The trajectory q(t) is smooth, but the relation p = mv does not hold.

Dear Sofia,

you wrote in the article "Berndl et al. showed that from Hardy’s article results that Bohmian trajectories are non Lorentz-invariant, therefore, Bohm’s mechanics requires a preferred frame". This answers the question, but has always been well-known.

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somehow researchgate had me as recommending the last answer. I was simply reading and cannot undo the recommendation

Non the less, there is the formula p= grad (S) for momentum.

I have been re reading J. Bell, who supports the Bohm vision, but he seems to avoid the subject of the uncertainty principle like the plague.

The relation for momentum is a classical one. The momentum is a property of the wave function, not of the trajectory. The measurement result of a momentum measurement depends on the initial state of the measurement device too, it is not defined by the Bohmian trajectory alone.

In the quantum equilibrium, the uncertainty relations hold, without any problem. So there is nothing to talk about, no need to avoid it.

Ilja

Based on your comments and the different definition of momentum in

Bohmian theory, the mechanics seems quite unintuitive. Then why speak of a trajectory at all.? If you define q(t) you can also define dq/dt, wheather you like it or not. Then maybe you discover ( or not) that it coincides with the Bohmian p ?

Not sure what you mean by quantum equilibrium.

Regards, Juan

Juan, in quantum equlibrium the configuration q is distributed following the probability distribution rho(q) = |psi(q)|^2.

In dBB, you have, of course, dq/dt. But it is not what you will get if you measure momentum. Momentum measurement is well-defined in quantum theory, so that there is no "Bohmian momentum". So, for example, in one-dimensional energy eigenstates you have dq/dt = 0 but momentum may be as large as you like, say with probability 0.5 around some p_0 =/=0 and with probability 0.5 around -p_0.

This is the simplest example where Bohmian trajectories have been named "surrealistic" because they do not fit into classical ideas how particles behave. Classical intuitions work better with other realistic interpretations like Nelsonian stochastics. In this case, the Bohmian velocity is the same, but interpreted only as an average velocity. The particle itself moves stochastically, something similar to Brownian motion or random walk, so that you have a continuous trajectory but it is not smooth. And, again, the trajectory itself does not give you information about momentum, now because it does not give you even a velocity. But in this case one can imagine that with probablity 0.5 the velocity is around p_0/m and with 0.5 around -p_0/m.

I see, there is a sort of drift current, quantum current found from the wave function?

Though my idea of bound state is that there is no quantum current either.

Of course you can always have an open quantum system.

Thanks, Juan

The continuity equation for the probability distribution in the configuration space

d_t(rho(q,t)) + d_i (rho(q,t) v^i(q,t)) = 0

follows directly from the Schroedinger equation (it is essentially the imaginary part of it), and the velocity v^i in this equation is the Bohmian velocity. In this sense, the quantum current as well as the Bohmian velocity itself is found already in the wave function. So, indeed, in a one-dimensional bound state this current, and, therefore, also the Bohmian velocity is zero.

Yes, maybe because of this copenhagen is still a bit more favorable to me, even though it is also absurd. As I say Im still the dualist....till I hear better.

If the electron really rattles inside a wave function, maybe there would be evidence

like radiation being emitted, or some detectable noise. Or better still detect the electron as it flies between two split beams.?

Juan,

I had to withdraw my solution that a particle cannot jump between two distant places. There was a mistake there and it's long discourse to explain that mistake. Thus, my question remains open.

I can say with 99% probability that if the charge jumps, it wouldn't radiate, and would make no noise. Radiation means loss of energy, and these jumps, occurring all the time, would decrease the energy of the electron. It would be experimentally noticeable.

With kindest regards

OK Sofia

If everything you say checks out, you have pretty much already buried the Bohm model.

You start off from a wave packet, and then you split it. The original wave packet

just had one electron. So one of the two split packets is empty. They dont share the last electron?

Yes, Juan,

I think that the section 5 of my article

Deleted research item The research item mentioned here has been deleted

buries completely Bohm's mechanics. Not only there are no continuous trajectories for particles, as a substructure of QM, but also there are no possibility that a particle be at the same time in two places.

About your question

"*The original wave packet just had one electron. So one of the two split packets is empty. They don't share the last electron?*"

for the moment I am able to give only an incomplete answer. Both wave-packets, when passed through an electric field, **bend**. That would be impossible if one of them would not contain an electron, or if each wave-packet would contain the electron only part of the time (in case the electron jumps).

However, as I said, I had to withdraw my solution which concludes that the particle does not jump. My question remains open.

Dear Sofia D. Wechsler

I disagree, you come not even close to bury de Broglie-Bohm theory.

Let's start with the point that you claim "For photons, even Bohm’s mechanics acknowledged that particles and trajectories cannot exist [26]." What is written in [26] is essentially a Bohmian field theory for bosons. Such a field theory preserves the main points of dBB theory, namely continuous trajectories for the classical objects, namely, in case of the EM field, for the fields, thus, A^m(x,t). So this not at all buries dBB theory for bosonic fields.

Hardy's experiment does not do it too. He discusses this explicitly, pointing out that the contradiction appears only if one ignores non-locality. dBB theory is non-local, thus, no contradiction appears.

You essentially acknowledge that you only reinterpret the same math, using the same experiment except for using the word "electron" instead of "photon". But let's see how the non-locality appears in your variant of interpretation. Essentially, dBB trajectories look quite local as long as what is measured is the position (configuration). But you consider the experiment where on both ends it is not the position which is measured. In this case, the Bohmian trajectories depend on which experiment is done first, and the first non-position experiment modifies the Bohmian trajectory of the measurement devices which defines the result of the second experiment.

"The partial phenomenological answer is that both wave-packets, when passed through an electric field, **bend**. That would be impossible if one of them would not contain an electron"

This is plainly wrong. The wave function follows the Schroedinger equation independent of the question if it contains an electron or not.

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Dear Sofia,

Please let me give you my objections to your solution:

1- You can't use a "relativistic reason" and at the same time use "the conservation of the number of particles" because in relativistic quantum mechanics the number of particles is not conserved.

And worse than that in relativistic quantum mechanics you didn't have a real position operator.

2- And for the "non-relativistic reason":

We have a one wave-function for the two particles, so when the particle 1 jumps at a time t from the region A to the region B, the wave was collapsed, and absolutely the particle 2 has also jumped at the same time from the region C to the region D regardless someone measures it (the particle 2) or not.

With best regards.

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Dear Ilja Schmelzer,

Thanks for your comment. Although I disagree with it, it's a good comment.

Now, I did not draw by myself the conclusion that the photons don't have particles following trajectories. It's Hiley who claimed that, calling my attention on that in an exchange of letters. Let me ask you straightly: **would you send Hiley a letter** and tell your claim about their Bohmian field for bosons?

"*Such a field theory preserves the main points of dBB theory, namely continuous trajectories for the classical objects, namely, in case of the EM field, for the fields, thus, A^m(x,t).*"

Hiley is a kind person, I think he would answer you. You see, the photons cannot obey the Bohmian velocity, which comprises mass, so, it's a problem. But I encourage you to ask Hiley and tell us what he answered you. I won't argue with him because I am not particularly interested in photons, as long as I can show that particles possessing rest-mass do not obey dBB.

You also say

"*Hardy's experiment does not do it too. He discusses this explicitly, pointing out that the contradiction appears only if one ignores non-locality. dBB theory is non-local, thus, no contradiction appears.*"

I suppose that my article

shows clearly continuous trajectories that the hypothesis of particles following continuous trajectories, is impossible.

Then you say

"*But you consider the experiment where on both ends it is not the position which is measured. In this case, the Bohmian trajectories depend on which experiment is done first, and the first non-position experiment modifies the Bohmian trajectory of the measurement devices which defines the result of the second experiment.*"*" *

How it is not position what is measured? The detectors C_{j} and D_{j} locate the particle. And how the Bohmian trajectories depend on which experiment is done first? Also, how the *first non-position experiment modifies the Bohmian trajectory of the measurement devices? *It makes no sense to me.* *To the contrary, the measurement result depends on the Bohmian trajectory, as to measurement devices, they have no Bohmian trajectories, they are fixed in space. *You are trying to say something, but it is not clear to me. *So, please, make it more clear.

Maybe it would be of help if I'd add that I don't ask in my proof which measurement is done first. No time-order interests me. The detection in a detector behind the beam-splitter BS_{1} is simultaneous with the detection in a detector behind the beam-splitter BS_{2}. I only assume that a particle doesn't jump from the BS_{1} to BS_{2}, and vice-versa. That means, a particle detected by the detector D_{1} (D_{2}) was previously at the input u_{1} of BS_{1} (u_{2} of BS_{2}) - i.e. it has a continuous trajectory. That brings a contradiction: any joint detection in D_{1} and D_{2} was produced by the electron that previously was at the input u_{1} of BS_{1}, however, also, any such joint detection was produced by the electron that was previously at the input u_{2} of BS_{2}. This is impossible, a particle has a position, it is either at BS_{1}, or at BS_{2}.

Please tell me whether I made myself clear.

Kind regards

Lovely Mazen,

Your comment is **splendid**, I like it very much.

It already was suggested by a smart fellow, Stefano Quattrini, saying that while in one wave-packet, e.g. |a>, travels the initial particle, while in |b> travels a virtual particle.

About my argument with entanglements, it is wrong, a measurement collapses the wave-function, s.t. **I withdrew my solution**. A measurement collapses indeed the wave-function, and my solution fails.

For position operator, I do have the creation operator â_{r} which creates a particle at the position **r**.

But, please tell me, are you aware of the experiments with interference of fullerenes? See in attach how a fullerene looks like. Each dark-green circle represents an atom of carbon, and each light-blue circle, an atom of fluor. In the microscopic world the fullerene is like a dinosaur in comparison with particles as electrons, protons, etc. How can the number of fullerenes be undefined? There are no virtual fullerenes.

So, I have a problem.

With kindest regards

- 9.33 KBFluorofullerene.gif

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Dear Sofia D. Wechsler

"Let me ask you straightly: **would you send Hiley a letter** and tell your claim about their Bohmian field for bosons?"

There is no need for this, because this is what they have presented in the paper - the field ontology instead of a particle ontology for bosons. See eq. (13) for the "field velocity", which is simply the Bohmian velocity of the field configuration phi(x,t).

What Duerr et al have understood is something I have never questioned, namely that dBB theory needs a preferred frame. You can, of course, choose any frame you like, and prefer it, but for different frames the Bohmian trajectories will be different too. (Or, if you formulate this from the other end, closer to the language of the paper, if you use a particular set of Bohmian trajectories from one such frame, this set will not give in another frame quantum equilibrium.) So, it is not an argument against quantum equilibrium, but against the idea that it could be made Lorentz-invariant.

"And how the Bohmian trajectories depend on which experiment is done first?"

Look at the equation for the Bohmian velocity. The position of the measurement device influences during the interaction the whole configuration, on both sides. The experiment done first influences the whole wave function and the whole trajectory (which becomes surrealistic).

"shows clearly continuous trajectories that the hypothesis of particles following continuous trajectories, is impossible."

No. You exclude the Bohmian solution, which defines such trajectories in the preferred frame, with:

"Admitting “collapse at a distance”, i.e. that the measurement of one particle collapses the description of the other particle to a certain state, is at odds with the relativity theory."

As well in the article itself, you write:

"Berndl et al. showed that from Hardy’s article results that Bohmian trajectories are non Lorentz-invariant, therefore, Bohm’s mechanics requires a preferred frame [2]. Though, not only Bohmian trajectories but any continuous trajectories appear to be impossible."

The first statement is completely correct, but then you slip from "needs a preferred frame" to "impossible".

It is well-known that dBB is at odds with fundamentalist relativity (but not with the Lorentz ether). If this is sufficient for you to reject dBB, so be it. But it has nothing to do with any impossibility.

You assume that somehow the velocity of the labs somehow matters: "assume now that Alice’s and Bob’s labs are in movement". So what? In the Lorentz ether, it does not change anything, what defines the collapse is the absolute preferred frame (thus, plausibly the CMBR frame).

"That means, a particle detected by the detector D1 (D2) was previously at the input u1of BS1 (u2 of BS2) - i.e. it has a continuous trajectory. "

In this case, read the Hardy article again. The outcome he cares about, F_1, is not the one which tells the outcome of U_1. It tells that U_2 = 1, that means, the particle is on the other side. The detector D1 clicks, but the particle is at U2.

In the experiment, you have two particles which possibly reach the detector, one from u direction, the other possibly from some other coherent source. See the formulas below (8). There is a |0>_a|1>_u contribution and also a |1>_a|0>_u contribution, and both interfere: "This means that the two possibilities contributing to the |0>_C|1>_D, term as can be seen from (9) will interfere destructively". So, you see a particle has reached D1, but it may be from U1, but also from A1. You cannot know, given that they interfere. Both trajectories may be continuous - from A1 to D1 as well as from U1 to D1.

So, if the 1 experiment is first, then it is the A1 which arrives at D1 and U1 is not present. And even more is known, U2 is present.

If you measure 2 first, and measure U there, the same happens. Position measurements are harmless in dBB. But if you don't measure U2, but the superposition of |0>_a2|1>_u2 and |1>_a2|0>_u2 then this influences the final measurement at 1. And it may be the particle U1 which arrives at D1.

"How it is not position what is measured?"

D2 as well as C2 measure superpositions of |0>_a2|1>_u2 and |1>_a2|0>_u2. So, they do not measure the Bohmian positions of the particles u and a.

Ilya

Well, there are two different attitudes. One is to say that the entity is only one, sometimes it can be a wave, sometimes a particle. I think this is more Copenhagen.

The next is Bohm, that there is a real particle and a real wave which guides it. Here there is not one entity but two.

So I think the difference is fairly clear.

So as soon as someone mentions a wave with one particle, or a one particle wave function, the person is unconsciously perhaps siding with Bohm. This was the de Broglie vision, a particle accompanied by a wave.

Maybe Sofia is guilty of this, language is tricky.

There comes contradictions from Bohm point of view.

ie. that a wave splits(the one particle wave function) so that only one branch is left with the particle and the other is empty.

This is not too credible, so I prefer the first point of view, even though I will be screamed at that the entity cannot be both.

So I perhaps understand someone who claims jumps between the two branches (sharing the electron) but this is rather stange.

Not so strange, as there really are quantum transition in the atom between different stationary states, but motivated by a photon.

What I prefer is no jumps, but that there are only waves in the branches. Which in turn creates problems about charge.

The only real conclusion is that nothing works out that well yet.

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My dear Sofia,

big thank for your reply.

Yes, I know in general about the interference that happened with big particles like atoms, but I think this is only a problem of complexity, I mean that the secret of quantum foundations exists simply in the tiny particles like electron, so if we can understand what happened with the electron during the interference experiment we can understand the whole game, I suggest to split the problem with two steps, the first step is a non-relativist step:

1- can we build a model of motion with quantum jumps that is compatible with the Schrodinger equation?

If we can, so we have a new theory equivalent to the Schrodinger equation and path integral formulation, etc...

The second step :

2- What we need to make this theory to be compatible with the special relativity theory etc...

I claim that I did the first step (in my theory of disappearance and appearance) and a very tiny part of the second step ...

With best regards.

My dear Mazen,

We do not understand what happens even with the electron. We make assumptions and try hard to find experiments to test the assumptions. But, while some assumptions are satisfactory with the elementary particles from the Standard Model, with dinosaurs like the fullerenes they don't work.

"*1- can we build a model of motion with quantum jumps that is compatible with the Schrodinger equation?*

2- *What we need to make this theory to be compatible with the special relativity theory etc...*

My lovely friend, on the paper we can write whatever we want. You can build on paper what you want, but the question is whether you can prove EXPERIMENTALLY the truth of your model. If you can do that, it's worth of the Nobel prize.

I do not discourage you from building models, we MUST do such things. But people won't consider those models important unless you can suggest experiments to test them. Worse than that, you have to convince experimenters to perform those tests, and that is not a simple task. Also, keep in mind that your model should NOT contradict the formalism of the quantum theory.

With kindest regards

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Dear Ilja,

I appologize for reacting to your comment with such a delay.

To put it in short, in those articles that Hiley recommended I saw no explanation of how the photon field leaves a single spot on a photographic plate. And, you see, I consider** the duty of those who present a theory, to solve its problems**. One cannot tell me "read my article" and solve by yourself the problems remained open.

Bottom line, if it is left to me to complete the ellimination of the collapse from the field ontology you talk about, my reply may be only "NO, thank you!"

2. ". . . . *for different frames the Bohmian trajectories will be different too*. . . . . *it is not an argument against quantum equilibrium, but against the idea that it could be made Lorentz-invariant.*"

Ilja, let's stay focused. Did you see a rocket that passes above Prague, but in fact it passes above Congo? This is exactly what gives us the dBB interpretation, and it's unacceptable. I suppose that you read my article

and you saw the proof. Sorry, if the Bohmian particle exists, its trajectory has to be well defined.

"*And how the Bohmian trajectories depend on which experiment is done first*?"

In continuation you discuss my proof against continuous trajectories. **I am very glad that you read seriously these articles of mine.** In short, I can say that you did not understand properly my statement. But I want, at this step, to make a pause and wait for your reactions to my comments above. My proof based on Hardy's schema in "Nonlocality of a single photon revisited", may be a bit difficult and let's discuss it separately.

With kind regards,

Sofia

My dear Juan,

Now, I want again to speak of my last article, which tries to test the collapse. You say "*The only real conclusion is that nothing works out that well yet.*" If indeed, the experiment would confirm the collapse, **we have to be prepared for MUCH WORSE! **At present, people don't realize in full how much illogical is the collapse.

With my best wishes!

Dear Sofia D. Wechsler

You wrote: "Sorry, if the Bohmian particle exists, its trajectory has to be well defined."

It is well-defined, in a theory which has a preferred frame. In dBB theory there is one, as in its particle variants as in its relativistic field theory version. The Dürr group tries to get rid of it, and therefore tries to present it as relativistic as possible. I don't. There exists a preferred frame, it is roughly the one defined by CMBR, with possible local corrections defined by the preferred coordinates being harmonic. The trajectories defined by dBB in this preferred frame are the well-defined trajectories you want.

I have no objections at all against the thesis that dBB theory needs a preferred frame. But once this is clarified (and essentially this has been clarified already by Bell's theorem), further criticism of dBB theory cannot be based on this necessity of a preferred frame. This is already known, and further criticism requires that one accepts, even if only for the sake of the argument, that dBB has a preferred frame. And once it has a preferred frame, it has also well-defined trajectories for the configurations.

"**Each experiment is done first,** you have only to choose the appropriate frame of coordinates. And, according to the relativity **there is no preferred frame**. Please tell me, **why should I sacrifice the relativity, so well verified, for Bohm?"**

Feel free to sacrifice realism, causality (even the logic of plausible reasoning, the Bayesian interpretation of probablity following Jaynes, see ) to preserve the spacetime interpretation of relativity. Even if all this is compatible with another interpretation of relativity, the Lorentz ether.

A dBB theory is useful to show that the alternative exists, and that the alternative theory has a very simple and natural math apparatus. It is already part of the Schroedinger equation.

"Bohm's mechanics has imprinted on its flag the removing of the collapse postulate. If it does not do that, it looses any value. If we have to admit the collapse, the standard quantum theory is good enough."

Relativity sais no frame better than another, but you can always select a given one, and work in it alone.

If ddB uses the same Schrodinger eq. (my understanding?)it is non relativistic anyway.

Therefore of course you may select a given frame.

Maybe in ddB the wave function (or knowledge) does not collapse or change because it is thought to be physically real.

Relativity is not questioned one way or the other by ddB

Dear Juan Weisz

You wrote "If ddB uses the same Schrodinger eq. (my understanding?)it is non relativistic anyway."

This is wrong for field theory. The Schroedinger equation works once the energy operator has the form p^2 + V(q), quadratic in the momentum variables. But this is also the form of the energy in relativistic field theory.

Field theory is problematic because the number of degrees of freedom is infinite. But this is a technical problem, and one can use a lattice approximation to circumvent it.

The reference to a paper where the case of relativistic field theory is considered:

D. Bohm, B. J. Hiley and P. N. Kaloyerou, “An Ontological Basis for the Quantum Theory”, Physics Reports (Review Section of Physics Letters) 144, no. 6, page 321, (1987).

"Maybe in ddB the wave function (or knowledge) does not collapse or change because it is thought to be physically real."

In dBB the wave function is real, and does not collapse. But what we know about the wave function? All what we see, and what we are, is not the wave function but the configuration. But we can gain knowledge about some part of the wave function of some quantum subsystem, using some preparation procedure and when using the classical, visible configuration of the measurement devices q_device(t):

psi_subsystem(q_subsystem,t) = psi_full(q_subsystem, q_device(t),t).

It is only the effective wave function of the subsystem which collapses if the subsystem interacts with the environment. The full wave function does not collapse.

"Relativity is not questioned one way or the other by ddB"

It is not relativity itself which is questioned, but only a particular interpretation of relativity, which is questioned. Even if this interpretation, the spacetime interpretation, is the only one which is tought today. The Lorentz ether is as well a viable interpretation of relativity, and it is indeed not questioned by dBB.

Ilja,

I owe you an answer for a couple of days already. I appologize!

Now, if there exists a preferred frame, there means that there exists a preferred wave-function, and the other wave-functions, written according to the other frames, are false. Gisin did many experiments with moving frames. He considered frames attached to beam-splitters, frames attached to detectors, frames attached to a fixed aether around the Earth, with respect to which the Earth moves. For none of these frames he found that the wave-function is violated.

So, if a preferred frames exists, the wave-function should be usually violated, because inall the other frames than the preferred one, the wave-function should be violated. But we did a lot of tests, typically with the polarization singlet of photons, even tests in space (Zeilinger's group). No violation of the wave-function.

Now, I'll refer to the 2nd part of a comment of yours from 4 days ago (the comment begins by quoting my question, "*Would you send Hiley a letter* . . .?") You also discuss there the proof against continuous trajectories in the section 5 of my

Deleted research item The research item mentioned here has been deleted

By the way, I am glad that you read the proof. I acknowledge that it is a bit difficult proof. So, you say

"*read the Hardy article again. The outcome he cares about, F_1, is not the one which tells the outcome of U_1. It tells that U_2 = 1, that means, the particle is on the other side. The detector D1 clicks, but the particle is at U2.*"

Yes, Hardy proved that. But, my proof follows another line. So, please follow me. I have suspicion against continuous trajectories. The stategy I use to rule them out, is to prove that assuming continuous trajectories I get a contradiction. Therefore, I do this assumption.

Now, look please at the formula (22). You see that the probability of getting F_{1} = F_{2} = 1 (i.e. both D_{1} and D_{2} click, while both C_{1} and C_{2} remain silent) is

(22) Prob[F_{1} = F_{2} = 1] = *q*^{2}*M*^{2} |α|^{4}/4.

I also prove that the probability of the initial electron to impinge on BS_{1} and an electron from the coherent wave to impinge on BS_{2}, is *q*^{2}*M*^{2} |α|^{4}. Thus, **according to the hypothesis of continuous trajectories**, the initial electron will cross in continuation BS_{1} and the electron from the coherent wave will cross BS_{2}. None of them would jump from the lefthand end of the apparatus to the rigthhand end and vice-versa.

Therefore, it's trivial to get from *q*^{2}*M*^{2} |α|^{4} that the probability of obtaining F_{1} = F_{2} = 1 from the initial electron impinging on BS_{1} and an electron from the coherent wave impinging on BS_{2}, is again (22).

Well, I also prove that the probability of the initial electron and an electron from the coherent wave **to impinge vice-versa**, i.e. the initial electron on BS_{2} and an electron from the coherent wave on BS_{1}, is again *q*^{2}*M*^{2} |α|^{4}. Therefore, *according to the hypothesis of continuous trajectories*, we get that the probability of obtaining F_{1} = F_{2} = 1 from the initial electron impinging on BS_{2} and an electron from the coherent wave impinging on BS_{1}, is again (22).

Bottom line, F_{1} = F_{2} = 1 is obtained from the initial electron going to BS_{1}. But, F_{1} = F_{2} = 1 is obtained from the initial electron going to BS_{2}. **Where goes the initial electron, PLEASE TELL ME!**

I stop here again, my reply is very long. I'll let you read it and after that I'll go on.

With kind regards.

Dear Sofia D. Wechsler

I will give you an immediate answer to the first argument and look at the problem with your proof later. You write:

"Now, if there exists a preferred frame, there means that there exists a preferred wave-function, and the other wave-functions, written according to the other frames, are false. Gisin did many experiments with moving frames. He considered frames attached to beam-splitters, frames attached to detectors, frames attached to a fixed aether around the Earth, with respect to which the Earth moves. For none of these frames he found that the wave-function is violated."

How do you know that the wave-function is violated? Do you see it? You don't.

Then, you use here a quite sloppy language: Gisin did not make experiments with moving frames, he did experiments with moving devices. Then, he possibly described them using corresponding moving frames. But experiments with moving devices can be described also using the CMBR frame. The experiments do not have frames.

Then, you know, he cannot measure trajectories. What he can measure are only the predictions of quantum theory. But the empirical predictions of quantum theory do not depend on the decision which frame has been used to define the wave function. This independence of the choice of the frame is a proven result in QFT.

Then, the next use of sloppy language: "For none of these frames he found that the wave-function is violated." This suggests that he measured the wave function. He did not, because he cannot measure it. He has data from the preparation procedure, which allows, assuming the Schroedinger equation holds in this frame, to conclude that the wave function is the one he uses in his computations.

You can argue that this is all a big conspiracy theory: If you use the wrong frame, you start with a wrong initial wave function, use a wrong Schroedinger equation to compute how it evolves, with wrong Bohmian trajectories, and nonetheless the final measurement result is the same - such a conspiracy needs explanation. Fine. But this is the same conspiracy argument which is already present 1905 in the classical situation. If you use the wrong frame, you use wrong time, wrong spatial distances, a wrong ether model, a wrong notion of contemporaneity, but finally obtain the correct result.

But this can be explained and has been explained. It is a mathematical artefact, the equations are mathematically equivalent to equations for some completely different mathematical objects (namely some traces of some operators localized in some four-dimensional space following some operator equation). And these other strange mathematical objects do not depend on a choice of some frame. So, this is nothing but a consequence of the fact that the same math can be applied to very different things. The same math being applicable to very different things starts with the applicability of natural numbers to counting whatever you like. 3^{2 }+ 4^{2} = 5^{2 }holds for every application of natural numbers, like for counting apples, even if they have no relation at all to right-angled triangles.

Dear Sofia!

As you say: The quantum formalism is a theory which is developed in accordance with serendipitous discoveries (Bequerel) and subsequent experimental results under the assumption that particles are mechanical objects. Therefore it is not even wrong but it is wrong to say: QM is the right way to declare the world of particles.

A particle within a certain system (for example atomic shells or atomic nuclei) takes an accurately defined place. The rules of the distribution of particles are given by geometrical conditions. The assumption of material waves ( → wave functions) within particle structures is more than questionable. It was the only and the the most elegant way in the 1930s to describe the becoming visible order within atomic shells and atomic nuclei too.

My Best Wishes! Hans

Dear Sofia D. Wechsler

Now the answer about your proof. We already have an agreement about the fact that the Bohmian trajectories depend on the choice of the preferred frame. The same experiment, described based on different assumptions which frame is the preferred one, gives different trajectories. So, every statement made about Bohmian trajectories makes sense only if one adds information about the particular preferred frame used to compute the trajectory. This information is missed in your proof. So, it cannot be a valid proof about dBB theory in this form.

Let's try to correct this flaw. Say, we assume that the statements hold for the trajectories computed for the CMBR frame. But in this case, we find that one cannot prove the claims without additional information being given.

The necessary additional information is which of the two final measurements is the first one in the CMBR frame.

If experiment 1 is the first one, we can prove that F1 -> U2. But if experiment 2 is the first one, we cannot make this conclusion. In this case, F2->U1. But this cannot be proven if experiment 1 is the first one.

The answer to your question "**Where goes the initial electron, PLEASE TELL ME!**" is, therefore, quite simple: If the experiment 1 is done first, and F1=F2=1, then there was a particle and it was in BS2. If the experiment 2 is done first, and F1=F2=1, then there was a particle and it was in BS1.

We have here two different experiments (one with measurement 1 before 2, one in the reverse order). So, even if the final outcomes seem identical, it is certainly possible that the initial conditions to reach these final outcomes have to be different.

But in both scenarios all trajectories are continuous.

Ilya

Would like further opinions about your answer, that it is relativistic in field theory.

With the discovery that the Dirac equation does not support many particle solutions, people went the way of Schrodinger form

in field theory.

In QED, with the second quantization of the Mawell equations in vacuum, they found a relativistic case where the form of the Hamiltonian looks like Schrodinger, but where the meaning of the terms is clearly different. The "momentum" is in effect the dual of the magnetic vector potential.

Then if you are clever enough, you could go from Boson statistics to Fermi statistics, and juggle your way into something like Schrodinger which is relativistic. But is it really?

@Schmelzer:

" **dBB does not have a collapse at its fundamental, ontological level**."

This is true for standard qm as well, as the wave function is not ontological there.

"It reappears as a derived concept, once you distinguish, on a purely pragmatical level, that there are parts of the universe where you see the trajectory yourself, and other parts, where you cannot see them yourself, but have to rely on the equations of the whole theory to make some conclusions about what happens based on the trajectories you see in the environment of the process."

For standard qm this would roughly read: "It appears as a derived concept, once you distinguish, on a purely pragmatical level, that there are parts of the universe that are considered 'system' and parts that are considered 'the outside universe', containing the 'observer'."

The collapse is, in standard qm, a consequence of the necessity of separating quantum object and observer. Give up that separation and you have no collapse. (E.g. the many-worlds interpretation.)

" **Relativity does not say that there is no preferred frame**. All it says is that it is not defined by the equations of classical relativity."

No. Relativity says a preferred frame is not detectable by any experiment. And it says that before any equations. It then takes the view that one should not assign reality to anything that cannot be detected. In fact, the reason to prefer relativity over Lorentzian ether theory does not have anything to do with empirical results, which are the same for both. The reason is essentially Occam's razor: don't invoke entities that are not necessary. And that same reason can of course be brought up against Bohmian mechanics.

Of course, I agree with you that Bohmian mechanics has continuous, even differentiable trajectories, and hence, something must be wrong with Sofia's proof, because we have a working counterexample.

K. Kassner and Ilja Schmelzer,

There is a total **mathematical separation** between the **macro**scopic objects and **micro**scopic objects. The latter are described by a wave-function and admit states which are superposition of several eigenstates of some operator. The former do not admit a wave-function, they follow a trajectory described, at each time, by parameters - for example position and linear momentum - which are incompatible in the quantum theory. **Macroscopic object don't admit superposition of states, e.g. |dead cat> + |living cat>.**

People speak of entanglement between microscopic systems and macroscopic objects, e.g. |S_{1}>|living cat> + |S_{2}>|dead cat>, where S1 and S2 are states of the microscopic system. Such a superposition is impossible. It remains impossible when we replace the cat by another macroscopic system.

Klaus says "*The collapes is, in standard qm, a consequence of the necessity of separating quantum object and observer*." **Wording does not help!!!!!** The mathematics of QM gives us a wave-function which is a superposition of eigenstates, while the result of the macroscopic measurement leaves us with only one of those eigenstates. **About "many worlds" I wonder when did Klaus visit those worlds, for relying on their existence? **We would be pleased to understand what happens in OUR WORLD.

I repeat, there is no such superposition as |S_{1}>|one world> + |S_{2}>|another world> + |S_{3}>|a third world> + . . . A world is even more macroscopic than a cat.

With kind regards to both of you, and despite the difference of opinions, I am thankful for comments.

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Dear K. Kassner,

in standard QM (minimal interpretation) you cannot give up separating quantum object and observer. The split is part of the formalism, measurements (which presuppose observers) are defined by operators-valued measures and the states (which describe quantum objects) are defined by density operators.

I will not comment the value of the many wolds interpretation, given the restrictions by netiquette.

You write "No. Relativity says a preferred frame is not detectable by any experiment. And it says that before any equations. It then takes the view that one should not assign reality to anything that cannot be detected."

I agree with "not detectable". The point is that by "taking the view that" it makes a metaphysical assumption. So far we seem to agree.

"The reason is essentially Occam's razor: don't invoke entities that are not necessary. And that same reason can of course be brought up against Bohmian mechanics."

But, surprisingly, we end up with entities we would like to see if they would exist, but which we cannot see at all - our future. Instead of the common sense 3D world filled with matter which changes we get a whole four-dimensional manifold, which is claimed to exist in the same sense as what I see here before me now exists. A strange application of Occam's razor, there I'm forced to accept fatalism (the future exists already in the same way as the present) without any necessity and any empirical evidence for this.

A 3D world containing entities which change continuously is certainly necessary (it is, last but not least, also contained in the 4D spacetime). But everything beyond it is not necessary, given that there exist interpretations of the accepted theories which do not contain more than this.

I can present a similar proof for the existence of God. There are, clearly, theories which contain, together with humans, also angels and various Gods. If somebody who looks like a human (say, Jesus) is a God or not I cannot measure. So, the theory which distinguishs Gods from humans requires additional information which I cannot measure. So, using Occam's razor, it does not exist, and we should prefer the theory that Gods exist and are indistinguishable by observation from humans.

Dear Sofia D. Wechsler ,

while I agree with most of your reply to K. Kassner, let's note the difference to dBB theory.

|S1>|living cat> + |S2>|dead cat> is possible as a wave function, and unproblematic, because together with this wave function there is also the configuration, which is either a living cat or a dead cat. And the wave function

|S1>|living cat> + |S2>|dead cat> guides, say, the living cat (and together with the living cat also the rest of its universe) in the same way as |S1>|living cat>.

Dear Juan Weisz ,

In a field theory, with fields phi(x,t), the configuration variables will be **q**(t)= phi(x,t), and the momentum variables **p**(t)= pi(x,t)=d phi(x,t)/dt. The momentum has, indeed, nothing to do with the momentum of the corresponding particles in the particle picture. This is quite similar to condensed matter theory, where the momentum of the atoms in a lattice have nothing to do with the momentum variables of the phonons. I see no problem here.

The way to obtain Fermion statistics and the Dirac equation from a bosonic scalar field I have already found, the reference is I. Schmelzer, A Condensed Matter Interpretation of SM Fermions and Gauge Fields, Foundations of Physics, vol. 39, nr. 1, p. 73 (2009), resp. arxiv:0908.0591.

I start with a degenerated vacuum, so that the field theory reduces for low energies to a Z_{2}-valued theory. And I use a 3D lattice regularization, which is sufficient to get rid of the field-theoretic infinities. The theory appears equivalent to a 3D staggered discretization of the Dirac equation in the original form (with the alpha instead of the gamma), which, because the doubling happens only in 3 dimensions, reduces to 2 Dirac fermions instead of 4 in the standard 4D approach. The remaining doublers are unproblematic, given that we have, anyway, Dirac fermions in the SM only in electroweak doublets.

No, Ilja,

the superposition |S1>|living cat> + |S2>|dead cat> is NOT possible, as is not possible the superposition |living cat> + |dead cat>. Did somebody see the cat in the latter superposition?

The superposition |S1>|W1> + |S2>|W2>, where W1 and W2 are states of a macroscopic apparatus, are as impossible as |living cat> + |dead cat>. There is a fundamental difference between the description of a macroscopic object, and that of a microscopic object. As I said, the **micro**scopic object admits a wave-function, the **macro**scopic object admits a well defined trajectory. Did somebody see a superpositon of the type

|the aircraft flies to Moscow> + |the aircraft flies to New York> ?

The trajectory is not necessarily a trajectory in the physical space, it may be characterized by other observables. But there is no quantum superposition, it's EITHER one trajectory, OR the other.

With best regards

@Schmelzer:

"But, surprisingly, we end up with entities we would like to see if they would exist, but which we cannot see at all - our future. Instead of the common sense 3D world filled with matter which changes we get a whole four-dimensional manifold, which is claimed to exist in the same sense as what I see here before me now exists. "

No. That is only an impression implied by inaccurate use of the word "exist". Of course, four-dimensional spacetime "exists" in a mathematical sense. But that is precisely not the same sense of what I see here before me now exists. The number pi definitely exists, one can prove it does -- mathematically. And once you have described to aliens how it is defined and explained our decimal system to them, they can verify its existence by calculating the nth digit of it and finding that it agrees with our nth digit. So pi exists, contrary to, say, ghosts or dream entities but it does not exist in a physical sense. Nor do distant spacetime events exist in a physical sense. They do exist, but this is not the same way of existing as what you see before you now. (In fact, the word "existence" has as many different facets as, or more than, the word "real". And as Bohr taught us, in the light of quantum mechanics, we have to learn anew what the word "real" means -- it is not just a given and most certainly not just a matter of definition. The same goes for the word "existence". A certain level of language analysis à la Wittgenstein would do many of these would-be-philosophers of science good. And this is a point Bell did not really understand well, in spite of his other profound insights.)

Your example with God is far-fetched, even a bit nonsensical. What Occam's razor says about God is that his existence is not provable, so we should not use the entity God in our physical theories (contrary to what Newton did). Occam's razor is useful to distinguish between theories that have precisely the same empirical content, so it cannot be ridiculed by some silly arbitrary examples.

Of course, you may or may not believe in God, depending on your mental constitution, but you should not use God as a hypothesis in physical theories, just as you should not use ether unless you are forced to. The question is not whether an entity looks like a more plausible explanation. The question ist whether it is necessary in an explanation. Neither God nor ether are disproved, nor Bohmian trajectories. But none of these concepts is needed either. Moreover, some of them may impede progress.

"the superposition |S1>|living cat> + |S2>|dead cat> is NOT possible, as is not possible the superposition |living cat> + |dead cat>."

Of course, the first of these* is* possible. It is precisely the description Schrödinger gave of the situation. Quantum mechanics is not only applicable to the microscopic world but also to the macroscopic one.

"Did somebody see the cat in the latter superposition?"

No. And quantum mechanics explains why you do not ever see it in a superposition. But the explanation involves superpositions and they are a necessary part of quantum mechanics, so you cannot eliminate them by Occam's razor or a similar construction. You would have to make a whole new theory that still reproduces the results of quantum mechanics and gets by without superpositions. Then you can claim that the combined system of atom and cat cannot be in a superposition. But otherwise, you can't. Quantum mechanics says it is in a superposition and tells you why you do not observe it in one. That was part of Sid Coleman's lecture that you once mentioned here.

There is actually a very simple argument (but turns out bad) that a particle is not a wave. From fermi statistics two identical

electrons cannot be in the same exact state. But what happens if we superimpose two identical waves? What happens is that

we get a stronger wave, not no wave. Seems conclusive so far in favor of dBB, that waves live in Boseland, but particles like the electron live in Fermiland.

But the tricky part is that there can be an arbitrary phase factor in front of a wave in the quantum, and still have the same physical sense. In particular we could multiply a wave by -1 before adding it to the other, so then it seems to work.

However in any case there sould be an extra physical rule somewhere to make this possible, that we do not know about.

What do people think?

Deleted profile

Here is a link to Art Hobson's paper about "the cat" (measurement problem): https://arxiv.org/ftp/arxiv/papers/1711/1711.11082.pdf

Art Hobson doesn't say that he has solved the problem but he thinks he has come quite far.

Dear K. Kassner ,

First, quantum mechanics does not explain why we don't see such superpositions. (Last but not least, this failure to explain it makes such nonsense like the many worlds interpretation possible.)

Only realistic interpretations, which include some physical reality beyond the wave function, like the Bohmian trajectories, explain in a simple way why we don't see such superpositions: Because what we see are the trajectories, not wave functions.

It is fine that you mention the differences in the notions of existence. Pi exists in a different sense that the cup of tea before me, fine. And that the 4D spacetime exists in the same sense as pi exists, is unproblematic too.

(BTW, the difference between pi and ghosts is much less clear than you think. Mathematics are rules of thinking. They are applicable to human thinking, as well as to alien thinking. We can define, say, real numbers, or groups, or ghosts. We give some axioms, and then one can apply logic to make conclusions. Nothing prevents us from making axioms about ghosts, say, that they can appear only during a ghost hour, and the application of logic to these axioms will lead to a similar agreement between humans and aliens about some theorems about ghosts.)

But about what type of existence Occam's razor is about? It is about the existence which is relevant in physical theories. A realistic theory has to describe what really exists, in the sense of the cup of tea before me. That means, it has to define its ontology. (There are also physical theories which don't give such a definition - like Bohr's version of quantum theory. For such theories, Occam's razor does not make sense, once we cannot even say how many entities exist in this theory. For realistic theories, Occam's razor makes sense, once the ontology is well-defined.)

The ontology of the spacetime interpretation is the 4D block world. With me somewhere inside moving along a predefined trajectory, (seeing it like a film, which also exists completely now). The ontology of the Lorentz ether contains only a 3D world, which changes. The fatalistic 4D world certainly contains much more than necessary. The entity "myself" is multiplied there an infinity of times, including my whole worldline, without necessity.

For you, a little bit Popper would do good, to prevent you from using the word "provable" in connection with theories of physics, SCNR. So, no, Occam's razor does not tell us we should not use things in our theories if their existence is not provable, simply because nothing about the physical world is provable. BTW, this interpretation of Occam's razor would be deadly for relativists, because the existence of the 4D spacetime is obviously not provable.

The point of my example with God was to show the absurdity of the "application" of Occam's razor by the relativists, which implicitly forces us to accept the whole 4D blockworld and then to consider the 3D part which really exists in the Lorentz ether to be defined by some additional entity together with the whole 4D blockworld. But the really existing entities used in the Lorentz ether are not 4D + a preference for some frame, but simply 3D. Which is much less.

Actually, the way to anwers my last question is the 2 particle wave function Psi(x1,x2) = -Psi(x2,x1)

Psi(x,x)=0 is a consequence.

This actually should limit one particle superpositions, that cannot just be anything.

Then the form Psi(x1,x2) = psi(x1)-psi(x2)

is good enough.

Macro rules are different. One same object (say cat) cannot be in two different states.

Ah, Klaus,

my mathematician! Shall I remind you what we learnt in school, that **physics is first of all an experimental science?** We stay with purely theoretical hypotheses only when we are unable to test them, but if we can test, it's our duty to test our theories. **The supreme judge is the experiment.**

And now, how cannot a smart person like you, see that ( |S_{1}>|living cat> + |S_{2}>|dead cat> ) is as impossible, as the simple superposition ( |living cat> + |dead cat>) ?

I suggest the following experiment: bring the state |S_{1}> your microscopic system to one side of a beam-splitter, and the state |S_{2}> to the other side, just placing a phase-shifter by π/2 on the path of |S_{2}>. At the beam-splitter you get the transformations

(1) |S_{1}> --> (1/√2) ( |a> + i|b>), i|S_{1}> --> (1/√2) ( -|a> + |b>),

where by |a> and |b> I labelled the two output states. With this manipulation we get

(2) (1/√2)( |S_{1}>|living cat> + |S_{2}>|dead cat> ) --> (1/2) { |a> ( |living cat> - |dead cat>) + i( |living cat> + |dead cat>).

Would you kindly check if you get the output |b> from the beam-splitter? Or, do you prefer the output |a>? In which state remains the cat in each case?

With wishes of health to the cat

Still to Klaus,

"*quantum mechanics explains why you do not ever see it in a superposition* (i.e. |living cat> + |dead cat>). *But the explanation involves superpositions and they are a necessary part of quantum mechanics, so you cannot eliminate them . . . *. You would have to make a whole new theory that still reproduces the results of quantum mechanics and gets by without superpositions."

The superposition principle is a fundamental principle of QM, but NOT superposition between **macro**scopic states. Only **quantum** objects may be in superposition of states. You know to perfection that a macroscopic object has a unique trajectory. The parameters of the trajectory don't have to be necessarily position and linear momentum, they may be temperature and volume, or spin projection along x and spin projection along y, but the trajectory is one and well defined. NO SUPERPOSITION.

Read also my question where I discuss exactly this issue:

Before an entanglement between a micro object and a macro object may appear, the COLLAPSE occurs and forbids whatever such entanglement.

With kind regards

(P.S. We speak of the superposition principle. Read my words: EVEN FOR MICROSCOPIC OBJECTS WE DO NOT UNDERSTAND THIS PRINCIPLE. It is a completely illogical abracadabra, things ARE, and ARE NOT, at the same time**.** We MUST do the effort to understand first of all the superposition principle in the micro-world.)

Hi, Sofia,

its no use getting incoherent...

"And now, how cannot a smart person like you, see that ( |S1>|living cat> + |S2>|dead cat> ) is as impossible, as the simple superposition ( |living cat> + |dead cat>) ?

I suggest the following experiment: bring the state |S1> your microscopic system to one side of a beam-splitter, and the state |S2> to the other side, just placing a phase-shifter by π/2 on the path of |S2>. At the beam-splitter you get the transformations"

I don't know anything about how to construct a *beam splitter for a cat*. But that is not necessary. Quantum mechanics simply predicts the state of the cat in Schrödinger's example to be a superposition. No point in arguing with that. You may believe that quantum mechanics is wrong, but you cannot argue with it making that particular prediction in the example chosen by Schrödinger. Even Bohmian mechanics makes this prediction regarding the wave function of the cat. (But it decides that the cat is always dead or alive according to which of the two wave packets describing dead and alive contains the "multidimensional" particle to which the cat corresponds. The property is decided by which wave packet is full and which is empty. Of course, there is still an ambiguity the moment the particle moves from one to the other.)

You might of course argue that it is impossible to separate the cat-atom system well enough from its environment, so the superposition cannot be achieved for practical reasons. But that does not make the theoretical prediction go away for the case that you somehow succeed with the separation.

Now, as to my statement that the superposition is unobservable. Let us for simplicity assume that it is always possible to decide whether a piece of matter is living or dead and that there are no intermediate situations (such as patients whose heart is not beating anymore but their brain neurons are still flashing or braindead people whose heart still beats, being supported by a machine). Then the property of being dead or alive is describable by a hermitian operator with just two eigenvalues, for which we might take one and minus one. Each time we determine for some object by a (possibly complicated) measurement, whether it is alive or dead, we will cast it into an eigenstate of the dead-alive operator, getting a definite answer, i.e. one or minus one, alive or dead. After the measurement, the object will be either dead or alive with certainty, even if it was in a superposition before. So there is no way to observe the superposition. But we know from theory that it is there, if the conditions of the experiment are met.

Now to put that into perspective, let us consider a simple microscopic experiment. We measure the z component of the spin of an electron. We will always get, in units of hbar/2, one or minus one. Should we therefore believe that an electron cannot be in a superposition of the two states? No. For we have a direct access to superpositions in this case, as we have other axes at our disposal, along which we can measure. And if we measure in the x direction, the only way to describe the result in the z basis is by a superposition.

So the difference between the z component of the spin and the cat is that in the case of the cat there is no other axis, no measurement available from which we can *prove* that there is a superposition. Which does not prevent it from being there, according to theory.

By the way, there are other operators having two eigenvalues which behave similar to my dead-alive example. The parity operator, for example. It has eigenvalues -1 and +1 for odd and even functions, and there seems to be no "other direction" along which you can measure in order to determine whether or not systems are in a superposition of odd and even parity states. But some are as the quantum mechanical formalism tells us.

Hi Ilja,

"First, quantum mechanics does not explain why we don't see such superpositions. "

Of course, it does. See my answer to Sofia.

"It is fine that you mention the differences in the notions of existence. Pi exists in a different sense that the cup of tea before me, fine. And that the 4D spacetime exists in the same sense as pi exists, is unproblematic too. "

It does not exist in the same sense as pi. It just exists in a different sense from "existing now". It exists in a similar sense as the whole past exists.
"(Nothing prevents us from making axioms about ghosts, say, that they can appear only during a ghost hour, and the application of logic to these axioms will lead to a similar agreement between humans and aliens about some theorems about ghosts.)"

Not really. The existence of pi is testable by verifiable predictions such as the value of the nth digit. The existence of ghosts isn't. Of course, you cannot consider predictions that turn out to be true whether ghosts exist or not as tests of their existence.
"But about what type of existence Occam's razor is about? It is about the existence which is relevant in physical theories."

Occam's razor is not about reality. It is about how to compare theories. So it is not about physical existence. It gives you a condition on when you should assume an entity to be acceptable in a theory and when you should not.

"A realistic theory has to describe what really exists, in the sense of the cup of tea before me."

No, we are well beyond that stage. Kinetic energy certainly does not exist in the sense of the cup of tea before you. It is absent for some observers and present for others, even in Newtonian mechanics. Nevertheless it is real. So physics is not as narrow-minded in its conception of reality.

"That means, it has to define its ontology. "

Definitely not. Ontology is a concept invented before quantum mechanics. By people who believed in a deterministic and objective world. The concept may simply not be applicable to the real world. Note that objective and real are not the same thing. A length is real in special relativity but not objective because it is different for different observers.

"(There are also physical theories which don't give such a definition - like Bohr's version of quantum theory. For such theories, Occam's razor does not make sense, once we cannot even say how many entities exist in this theory. "

Occam's razor makes perfectly sense for theories without an ontology. An entity need not be defined by an ontology. The vector potential in electrodynamics is an entity but it is not ontological.

"The ontology of the spacetime interpretation is the 4D block world."

Well, I would not say it like that but if we accept that statement then we must say that the ontology of any *deterministic *theory is the 4D world. Because in any deterministic theory, past, future and present coexist in the same way as in relativity. Once you specify the "state of the world" at one time, it is fixed, inevitably, at all times. The only difference in comparison with relativity is that you have substructures of the world -- given by slices of constant time -- that are also absolute, i.e. the same for everyone. So you can define something that looks like a whole world at one time as if it were independent of the rest. But it is not, due to determinism, so the 4D block world is there as a necessary ontological concept as well. In special relativity, the slices are not absolute but conventional. You can also produce substructures such as past, present and future, but they are not absolute. Not that enormous as a difference. General relativity has solutions that do not allow a foliation, so things are a little different there.

"With me somewhere inside moving along a predefined trajectory, (seeing it like a film, which also exists completely now)."

No. It does not exist completely "now". That is the misunderstanding. There is no time in which the existence is simultaneous. It is not even an existence within time. That is just your film picture, but that picture is an analogy and not a perfect one.

"The ontology of the Lorentz ether contains only a 3D world, which changes."

No. As soon as you add determinism, all of the past and the future can be claimed to exist in precisely the same sense in which the spacetime continuum of special relativity exists. Not "now" of course, they do not exist "now" in spacetime. But inevitably.

"The fatalistic 4D world certainly contains much more than necessary. "

Fatalism is present in determinism, too.

"The entity "myself" is multiplied there an infinity of times, including my whole worldline, without necessity. "

I would dispute both the "without necessity" and the multiplicity.
"For you, a little bit Popper would do good, to prevent you from using the word "provable" in connection with theories of physics, SCNR."

I guess for you a little more careful reading of Popper would be good, too. Popper's statement about non-verifiability refers to theories, not to predictions of theories. Theories are only falsifiable. Their predictions are verifiable or falsifiable in each single instance. And even erroneously verifiable.

"So, no, Occam's razor does not tell us we should not use things in our theories if their existence is not provable, simply because nothing about the physical world is provable."

That is nonsense. If I do an experiment and the result is a pointer pointing on "4" (which may or may not be what the theory predicted), then I have proven that the pointer in that particular experiment may point on "4". I have disproved an impossibility. I have proved a possibility.

"BTW, this interpretation of Occam's razor would be deadly for relativists, because the existence of the 4D spacetime is obviously not provable. "

You are severely confusing things. I was talking of provable consequences, and maybe I should have said verifiable consequences. But otherwise, Occam's razor is about concepts that are not necessary (if a concept is necessary to explain an observation then it clearly cannot be eliminated by Occam's razor) and all concepts that strictly have no verifiable consequences do not seem absolutely necessary.

Now, I am not a purist in that regard. I do not want to throw out pure gauge quantities from physics just because they have no observable consequences. I would justify their "necessity" by their utility in simplifying the mathematics. On the other hand, Bohmian trajectories or the Lorentzian ether do not really simplify anything.

Even Hiley changed his mind about the true Bohmian trajectories in the ESSW experiment -- and he took decades for it. Now he thinks they agree with the path suggested by the which-way detectors; before, he thought the detectors were triggered by the wave function. If it is so difficult to figure out the true Bohmian trajectories in such a simple experiment and took more than 20 years to find agreement with the ESSW prediction from standard quantum mechanics, then these trajectories do not render quantum mechanics simpler.

Certain statements are alike in both macro and micro

Macro

50% probability alive and 50% probability dead

Micro

1/ sqrt(2) alive) + 1/sqrt(2) dead)

dont see much difference.

You superimpose any way you like.

"Occam's razor is not about reality."

Occam wrote "don't multiply entities without necessity". I would interpret this as being about the real entities in your theories.

"Fatalism is present in determinism, too."

So what, I'm not a fan of determinism. dBB is deterministic, but most other realistic interpretations are not. Nonethless, they also use continuous configuration space trajectories.

"As soon as you add determinism, all of the past and the future can be claimed to exist in precisely the same sense in which the spacetime continuum of special relativity exists."

This is mathematical existence only, and therefore as irrelevant as the existence of pi. Moreover, if I assume that a deterministic theory is only an approximation of a more fundamental random one, that predefined future disappears immediately into thin air.

"I have disproved an impossibility." Sorry for sloppy formulation, Poppers fallibilism is of course about general theories.

"Even Hiley changed his mind"

Please references to paper before and after, I would like to look at that. Whatever, it would be irrelevant if Hiley has made some error some time, this happens. The equations are simple enough.

"On the other hand, Bohmian trajectories or the Lorentzian ether do not really simplify anything."

They add a lot conceptual simplity. The measurement problem disappears, problems with realism and causality because of Bell's theorem disappear, we have a simple ontology, continuous trajectories, the quantum gravity problems disappear (we know how to quantize condensed matter theories, no topological foam or problem of time), we have no confusion with twin paradoxes and so on.

"Kinetic energy certainly does not exist in the sense of the cup of tea before you. It is absent for some observers and present for others"

Nice try, but in Newtonian mechanics we have absolute space, and in absolute space it is well-defined. It has already the same problems with observability because of Galilean relativity as absolute time in the Lorentz ether, that's all.

"It does not exist completely "now". That is the misunderstanding. There is no time in which the existence is simultaneous. "

That means, there is no difference in the status of existence between the the cup of tea before me now and the cup of tea before me tomorrow. Some guy which exists around now on Andromeda cannot tell which of the two is his "now", so either both exist in the same sense or none.

"The vector potential in electrodynamics is an entity but it is not ontological."

I disagree. You can, of course, use some mystic interpretation without ontology, but nothing prevents you from using the potential as the ontology. It makes sense, given that it is a much simpler ontology than the EM fields. In a theory with such an ontology it makes, of course, sense to have definite physical equations, so that the gauge condition gains the status of a physical equation. But so what? Similar to the Lorentz ether, where there is no candidate beyond harmonic coordinates for the preferred coordinates, there is only one plausible candidate equation for this, the Lorenz gauge.

The ontology should contain everything you need to make all physical predictions, via the equations of the theory. And for this purpose, it should be minimal. Thus, the "now" is sufficient, no need for the whole 4D.

Hi, @Klaus, how are you?

"*its no use getting incoherent...* "

"I don't know anything about how to construct a *beam splitter for a cat*. But that is not necessary.**" "**

YOU are incoherent. **You have no right to change what I said.** I say clearly that |S_{1}> and |S_{2}> are states of the microscopic system. You even quote me! What happens with you?

Can't be these states a photon beam travelling in the direction **x**, respectively an identical beam traveling in the direction -**x**?

"Quantum mechanics simply predicts the state of the cat in Schrödinger's example to be a superposition."

My dear friend, let the cat be a doll not a living cat, and let's change |living cat> into |doll O.K.> and dead cat into |doll damaged> (I don't have the heart to kill the cat). Then, let's be practical. **Please invite me to an experiment and show me a superposition of |doll O.K.> and |damaged doll>.** When the experiment is ready I'll give you my Skype address.

"*After the measurement, the object will be either dead or alive with certainty, even if it was in a superposition before. So there is no way to observe the superposition. But we know from theory that it is there, if the conditions of the experiment are met.*"

From which **theory** we know that it is there? Would you refresh your memory about Feynman's path integral **theory**? He proved that for an object for which the action function takes values by far greater than *ħ*, the object follows a well-defined trajectory, since the treatment is reduced to the principle of minimal action. A complex object, as a cat, or a human heart, (I prefer the doll) satisfies in full the condition that the action is much greater than *ħ. *On the other hand, the electron from your example with the spin, has the action function smaller of the order of *ħ *or less (essentially because of its very small mass).

sofia

Just look at my post before the last one.

What is wrong with alive with 50% probability and dead 50% probability?

This is not inconsistent.(before you lift the lid) That is the state of knowledge then.

Best wishes and maybe happy holidays

juan

Juan,

Yes, from the point of view of what we know, it's true. But phenomenologically it's incorrect - the nature does not allow.

Best wishes to you too

(Our holidays have past. When are they in your country?)

Sofia

Bohr said something like that the quantum is not about what things are really like, only about the information we have about them. So its the information, or non information which is counted.

January is typically when most have holidays, for some Feb. For me no difference. Sorry you missed holidays.

best regards, juan

q---

Could it be that it is impossible to prove that there is no such weird particle? Could it be that it though exists?

my ans----

it is possible to proove there is particle, but not that which u thinks, there is a particle which name is"Aryan particle" ultimately it will solve the problem of space as well as ether medium..

i am working on it, still its incomplete, but now i have decided to publish that incomplete theory because it is seems like it is complete and i dont have any other option to complete first then publish... it needs your point of views also... within 3 days i will publish it, and definitely u will get the answers which u really dont know.. please try it to read completely...

definitely if u understand it, u will be able to find many answers from that paper...

RAM NARESH YADAV,

The proof that such a particle exists, has to be EXPERIMENTAL. On the paper we can write whatever we want. To your attention, a particle as I described defies the relativity. But the relativity was NEVER contradicted.

There is no contradiction between a sequence of actual observations (clicks in a detector), and talking in terms of probability, because in the quantum there is irreducible indeterminism. (although there are still unbelievers)

There is a priori probability and objective probability and we want the two to coincide.

Therefore the particle is real AND we have a mental representation.

My Juan,

THERE IS NO PARTICLE. Your arguments are not sufficient, rigorous proofs are needed.

A particle has to have at a given time, a definite position. But, assume that a particle A is entangled with another particle, B, for instance

(1) |**R**_{1}> |**Q**_{1}> + |**R**_{2}> |**Q**_{2}>.

Consider a a frame of coordinates F. If at a time t according to F, the position of A is **R**_{1}, the position of B should be Q_{1}. Then, if at a time t' > t the position of A changes to **R**_{2 }the position of B should change to Q_{2}.

But, let be a frame G, by which B reaches the position **Q**_{2} after A reaches **R**_{2}. According to the frame G, the entanglement (1) is violated. This is forbidden.

Sofia

A particle would not exist in the Classical sense, is that what you mean? Of course not.

If you mean it does not exist at all, then I do not know what to say, I will just let this matter pass.

You have to have some kind of language in order to describe things.

Your arguments seem to shift around a bit. I do the best I can to describe things.

If at each time you have a position, it has to jitter around. But that is still pretty much a clasical conception.

Do not totally follow your no entanglement argument, I think you mean it is relativistically untenable.

But of course, relativity is always classical and this conception will always clash with the quantum.

You do not have a true Quantum conception, it is tainted with Classical ideas.

I would say at each time a probability density.

best regards, juan

Juan, what I mean by the word "particle" is something floating inside the wave-packet and having at each time a well-defined position.

"*Do not totally follow your no entanglement argument, I think you mean it is relativistically untenable*."

"Place the finger" on the point where you lost me. If my example is not clear, I will explain. Anyway, an entanglement cannot hold only in one frame of reference. It cannot happen that the wave-function (in particular the wave-function of an entanglement) is true according to one frame of reference, and false according to another frame. Of course, positions, linear momenta, etc. change covariantly from frame to frame, but the entanglement has to be preserved.

Eq. (1) in my example says that the wave-packet |R_{1}> of particle A is entangled with the wave-packet |Q_{1}> of particle B. Also, the wave-packet |R_{2}> of A is entangled with the wave-packet |Q_{2}> of B. So, if we test A and find it in the wave-packet |R_{1}>, in a test of B the wave-packet |Q_{1}> has to give response, no matter at which time you do the measurement of B, and by which frame you judge.

Tell me if up to this point the things are clear to you.

Your formula (1) seems to say to me that either R1 is entangled with Q1 or that R2 is entangled with Q2, apparently with equal

amplitude for either happening. R1 and R2 are of particle A and Q1 and Q2 are of particle B

The only combinations are then between different particles.

Then upon measurement one of the two is true, and sais nothing about the other happening. Either way there will be entanglement between a state of A and a state of B

So, as you say, if A is in state R1, B is in a state Q1.

Fine. Then what? What is the problem? I cannot see that the frame has to do with entanglement. You can have a covalent bond between two atoms, and it will remain so in any frame. Because then A and B act as a single entity together.

My Juan,

"*Tomorrow is another day*!" Iam going now to take a sleep and with God's help I'll continue my explanation tomorrow.

Dear Sofia D. Wechsler

you write "Anyway, an entanglement cannot hold only in one frame of reference. It cannot happen that the wave-function (in particular the wave-function of an entanglement) is true according to one frame of reference, and false according to another frame."

But there is the counterexample of dBB theory - which has all the explicit formulas you need - together with the Lorentz ether (extended to relativistic gravity, see https://ilja-schmelzer.de/ether ) as a background, which shows that a theory where quantum theory holds in one frame is viable.

To clarify the logic behind this: The theory has one preferred frame, essentially the CMBR frame. It has continuous trajectories of the configurations q(t) (which may be particle positions in a particle ontology, may be not in other ontologies) and gives **in this frame** all the empirical predictions of quantum theory. This is a theorem.

To apply it to other frames is, according to the theory, erroneous, nonsensical, and does not describe reality. Nonetheless, this error does not lead to erroneous empirical predictions, That it does not have such consequences is also a theorem - else, those empirical predictions could be used to identify the preferred frame.

So, we have a theory where entanglement holds only in one frame of reference, it is explicitly constructed, and proven to be viable. So, your claim is wrong, and proven to be wrong.

It is, essentially, the dogma of a fundamentalist interpretation of relativity, which simply ignores or rejects theories with a preferred frame as anathema, even if they are as viable (making the same empirical predictions) as fundamentalist relativity.

You have, of course, any right to prefer, for whatever reasons, the fundamentalist interpretation of relativity. But you cannot claim that the Lorentzian alternative does not exist once it exists.

You can claim that it has some internal contradictions, ok, but this is a hard job, and essentially hopeless. And if you do it, you have to show internal contradictions of the Lorentzian alternative, but not that it is in contradiction with some ideas of the fundamentalist interpretation. Your theorem shows such a contradiction with fundamentalist relativity - the Bohmian trajectories would be different, for "the same" experiment described in different frames. So, if these trajectories would be real trajectories, there would have to be a preferred frame. But this is certainly not an internal contradiction of the Lorentzian approach.

Juan, good evening!

I want to continuw my explanation. O.K.?

As we agreed, if A is in the state R_{1}, B is in the state Q_{1}. Alternatively, if A is in the state R_{2}, B is in the state Q_{2}.

Now, imagine yourself that at a time *t* according to a frame of coordinates F, the particle A makes a JUMP from the wave-packet R_{1} to R_{2}. Why such a jump is necessary I will explain you separately. IT IS NECESSARY - for the moment just believe me.

What is B supposed to do? It has to jump, on the spot, to Q_{2}, otherwise we can catch the two particles as disobeying the wave-function. No experiment, ever, showed that the wave-function is disobeyed.

Are you with me so far?

Kind regards!

Well, my view is that you are mixing clasical relativity with the quantum, an awful incompatible mixture

which will force you to either choose one theory or the other. That and only that is what you seem to have proved.

In the micro world I will stick with the quantum, the jumps you propose sound a bit fishy, but I will let that pass.

I dont think this is the first time you heard about such incompatibility, it is mentioned quite often as serious problem;

maybe not as bad as reconciling GR to the quantum, but joining just SR to the Quantum has its issues also.

Even in quantum field theory you have the problem of different time operators.

The best, juan

Ilja, good evening!

"*But there is the counterexample of dBB theory - which has all the explicit formulas you need - together with the Lorentz ether (extended to relativistic gravity, see **https://ilja-schmelzer.de/ether** ) as a background, which shows that a theory where quantum theory holds in one frame is viable*."

Ilja, an acquaintence of mine said that "*for Bohmians, the Bohmian mechanics is a religion*". There is NO THEORY that is SAINT. Any theory has to be checked. Bohm's mechanics introduces assumptions alien to QM, for which reason it was always suspect. It was shown to be incompetent with the relativity by HONEST BOHMIANS, Berndl and Goldstein, in 1992 in base of Hardy's paradox. In 2018 Wechsler D. Sofia showed in

Deleted research item The research item mentioned here has been deleted

that the Bohmian particle cannot exist, and the proof does not use relativity. It is valid even in the frame of the aether. See the section 5, named

I repeat, **the proof is in one single frame of reference. That frame may be the aether frame you speak of**.

One more thing: **for proving that a theory is correct, IT IS NECESSARY to show that it explains some experiments. But that IS NOT SUFFICIENT. One has to check, in addition, if there aren't experiments that the theory is unable to explain.**

Bottom line, read my section 5.** **

Dear Sofia D. Wechsler

we have discussed this, and I'm surprised about this new line of argument. There was agreement about the fact that the Bohmian trajectories would be different in different frames, which is a conflict with fundamental relativity. But there is no problem if only a single frame is used.

To quote myself: "The answer to your question "Where goes the initial electron, PLEASE TELL ME!" is, therefore, quite simple: If the experiment 1 is done first, and F1=F2=1, then there was a particle and it was in BS2. If the experiment 2 is done first, and F1=F2=1, then there was a particle and it was in BS1."

There are no contradictions if there is only one frame used, because in one frame the trajectories are defined in a well-defined, unique way. The proof constructs a contradiction by implicitly using different frames (or alternatively by ignoring the influence of the first experiment on the other side on the second experiment).

Last but not least, there is no way to prove a theory is correct. But what can be proven is the equivalence of the empirical predictions of two different theories. So, one can prove that an experiment can falsify the first theory (here dBB/Lorentz ether) only if it also falsifies the other theory (here QT, SR).

So, you have no proof that dBB trajectories fail, and I have a proof that they don't fail. And let's note that I'm not a Bohmian, I propose an own interpretation, see https://ilja-schmelzer.de/quantum/ so that even if that rant against Bohmians would be correct (it is bad style anyway even if attributed to "an asquaintance") it would be irrelevant.

Ilja,

I don't use the terminology "experiment 1" and "experiment 2." So, I don't know what you talk about. Also, in my proof no experiment is done first, all the detectors are at the same distance from the central beam-splitter that produces the wave-packets |u_{1}> and |u_{2}>.

I believe that you speak of another experiment than mine, and of another mathematical treatment than mine. If you want to criticize my conclusions you have to refer to my experiment, and my treatment. Your https://ilja-schmelzer.de/quantum/ does not refer to my experiment. You can't accuse John of a fraud by judging Tom, you have to judge John.

Juan,

you say: "*you are mixing clasical relativity with the quantum, an awful ncompatible mixture which will force you to either choose one theory or the other. That and only that is what you seem to have proved*."

What is "*classical* relativity"? Is there a *quantum* relativity? I don't do here with quantum gravity or other dinosaurs. It's our full right to write the wave-function according to whichever frame of coordinates we wish. Passing from the frame F to the frame G, whatever changes in the wave-function (1) is that we pass from the coordinates *t*, **r**, of F to the coordinates *t*', **r**' of G, by the Lorentz transformations. If one wishes to write explicitly the wave-function

(1) |**R**_{1}> |**Q**_{1}> + |**R**_{2}> |**Q**_{2}>,

in the frame G, one has to pass to the new coordinates.

Juan: "*which will force you to either choose one theory or the other. That and only that is what you seem to have proved*."

Ohoho! You touched the truth but not completely. I don't have to abandon eith QM or the relativity. What I have to abandon is the idea of a particle, jumping from one wave-packet to another. Our wave-packets are waves, not particles which jump from one region to another.

Now it's time to tell you why do I say that if we believe in particles, they have to jump from one wave-packet to another. Because both wave-packets of a particle have to be populated. How do we populate both |R_{1}> and |R_{2}> of A, when A is one single particle? By putting A to jump.

Bottom line: there is **no incompatibility** between quantum theory and relativity. The idea that there is a particle floating inside a wave-packet and triggering a detector, is incompatible with relativity. As I showed you, when thinking of entanglements, we get contradictions.

Wow, the night is almost gone. I need a few hours of sleep.

I speak about the two measurements on the two sides. So, "experiment 1" means the measurement done to measure C1 and D1 and "experiment 2" is the measurement of C2 and D2.

Ok, this was sloppy language on my side, these are measurements and only the combination of both are a the experiment.

You wrote "Also, in my proof no experiment is done first, all the detectors are at the same distance from the central beam-splitter that produces the wave-packets |u1> and |u2>."

No. The two measurements are done at very different places, and there will always be also some, however minor, difference in absolute time between them. In the relativistic context, both measurements are space-like separated, and it depends on what is the ether frame which one happens first.

The page https://ilja-schmelzer.de/quantum/ refers to my interpretation of quantum theory, just to explain you that I'm not even a Bohmian (even if my interpretation shares a lot of formulas with Bohmian mechanics, it differs in many parts, and, in particular, I propose a field ontology instead of a particle ontology. So, nothing of which you attack here is even part of what I believe, so that an accusation that I defend here some own religious dogma is off.

This is a very simple problem (PR-2.pdf), but interpreting the result seems to be quiet difficult. Please, leave a comment with your opinion.

Discussion

8 replies

- Asked 6th Feb, 2022

- José Luis Junquera

Why quantum mechanic exist?

Discussion

113 replies

- Asked 23rd Sep, 2019

- Mazen Khoder

Why quantum mechanic exist?

Why the elementary particle doesn't follow newton law?

Why we need a quantum mechanic for the tiny object?

Bohr said that quantum mechanics does not produce classical mechanics in a similar way as classical mechanics arises as an approximation of special relativity at velocities very slow than light speed.

He argued that classical mechanics exists independently of quantum mechanics and cannot be derived from it.

Max Jammer has said: quantum mechanics and classical dynamics are built on fundamentally different foundations!

No one can derive the newton law from the Schrodinger equation.

only the behavior of systems described by quantum mechanics reproduces in a statistical way the classical mechanics in the limit of large quantum numbers.

I don't understand why scientists don't give this point a big attention.

The real interpretation of quantum mechanics need to give an answer to this question:

why quantum mechanic exist?

I start from the concept of the motion itself and assume that the motion (in the quantum world and classical world) is a sequence of appearances and disappearances events in space and time:

The idea that affirms that the motion happened by disappearing and appearing actions give us God willing a beautiful answer about this question.

The Newton law said:

"In an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force".

But this law is not compatible with the disappearance and appearance idea!

this law is not always acceptable since the particle might easily appear (if the quantum jump is enough) in a forbidden (have a variation to a very large potential field like for example the particle in an infinite potential well) place after some quantum jumps in the direction of the movement of the particle!

so for a huge number of particles that jump in the subatomic level, the newton law may put our universe in an unstable situation!, and this might happen specifically when the length of the jump is close (or greater) to the length of the field's fluctuations (that frequently happens in subatomic level).

But in the case where the length of the quantum jump is very small (for example for large quantum numbers or in classical case) compared to the length of the field's fluctuations then the first law of Newton will be applicable because in this case, we can be sure that the particle will feel the force before that the force gets altered.

We usually deal with the motion like it was related only with the particle itself, but in my opinion, this is not true, I think we have two players in the motion:

1- The particle itself.

2- The space-time itself.

At each time, space itself allows the particle to appear in some multiple positions with certain preferences based on a new quantum action principle named "alike action principle" (that can lead us to Schrodinger equation) that ensures the existence of physical harmony within our universe, and the particle chooses randomly between these preferences.

So this is the role of space-time in the motion process, like for example preventing the particle from easily reaching to forbidden locations (guarded by fields of great forces). Therefore, in general, this new constraint in movement could be valid at multiple positions at the same time, so in general, we have multiple acceptable positions to appear at it. Thus the probability of existence came up in our descriptions of the movement in the quantum world.

With kindest regards.

On topics in special and general relativity, supporting 4D spacetime

Discussion

10 replies

- Asked 5th Dec, 2018

- Ed Gerck

The title is expanded below, for discussion, results are valid for both SR and GR.

Opinions on if spacetime is real, as a "physical thing", are not metaphysics-- and this is evidenced just by asking the very question and even doubting it. For example, asking about virtual particles or hidden states is not metaphysics, as most physicists would agree (as seen in citation references).

Some may think it is not real, but evidence points -- for more than 100 years -- that it is as real as movement. We do not wage to think we are immobile, and that movement is a mathematical concept. The consequences of spacetime, and further dimensions yet unexplored in physics, are part of a 4D+ reality where they show new aspects. One of these aspects is a fusion of space and time that we cannot uniquely separate.

Of course, by asking for opinions, we are positively using RG, far away from a supposed confidence on any person, no matter how famous or capable.

Rather, we are not positioned as ad hominem targets, but as partners in a dialogue. Opinions are fallible, including mine. My opinion is in this discussion head, and below. The theme is gathering importance, the decision time is closer, and there are optons. We want to hear.

PROLOGUE -- Welcome to the party!

The discussion is not about contesting SR. We just do not believe in it, it has been observed too many times to not be real, and calculated, coherently.

We also see, everyday, relativistic accelerators of neutral particles -- a frequent philosophical objection to SR, that one would not see time dilation or length contraction with neutral particles, but here they are, provided by nature [1]. There is no ontological question anymore, as we shall see, no question about SR to accelerate neutral particles. We refer the reader to [1], to further explanations on why this point might be important. See also [2,3].

The current 4D spacetime formulations, in SR and GR, see [4,5], are confirmed, when space transforms into time, and vice-versa, plus the other arguments below. Rather than "fighting" the other formulations, such as the original formulation by Einstein, and others, they are included, also Clifford(3,1), where nature is 3D +1D, as right. Some even say 3D, such as Newton, which is also considered right.

How? Any of these 3D and 3D+1D theories are right, because 4D ⊃ 3D +1D ⊃ 3D, in set theory, a fundamental theory in maths. In other words, the other theories with less dimensions are grandfathered in 4D spacetime, with nothing left to discuss about this.

Their region of validity, though, is less. Someday, if the universe is revealed to be 5D, the same will happen with the current 4D theory -- it will continue to be right, in its region of validity. And the same is true even for the 3D Newtonian theory today, where time is absolute -- useful, as comoving observers feel no effect in SR, and no effect in GR if in free fall in a gravitational field.

The working assumption of this discussion is that at least 4D spacetime exists, while 3D +1D, 3D, and even 2D (as the rock example can show, in [1]) exist too. Welcome to the party!

IF SR EXISTS... THEN GR...

This discussion -- IF one will "believe" in SR -- is about how to measure time and space in SR and GR. Since both SR and GR depend on spacetime, as we are using the Minkowski formulation for SR, we can treat them together, even though the metric differs.

This a standard technique in the scientific method, to take the IF YES branch and investigate what would happen, used also in maths with the yet unproven Riemann Hypothesis, no one is blocking. Let us take the IF YES, as one may say, in spite of the facts already showing SR.

A rock thrown on Earth, with a clock attached to it, will follow an accelerated motion, then decelerate to a stop. After the apex, the rock is in free fall in the gravitational field, including the Earth, the Moon, the Sun and other influences, here assumed as all just gravitational.

The trajectory can be calculated using SR in the 4D spacetime formulation, which works with accelerated motion, but not using the original SR formulation by Einstein, that works only with inertial motion.

The original formulation, however, is still taught today in US colleges and Ivy League universities in undergraduate studies, for example using the physics textbook by Serway.

The clock, comoving with the rock, will measure what is called the proper time, an invariant in 4D spacetime, calculated by the inverse function of the arc-length function, and the space coordinates will be zero, it does not travel in space. To an observer at rest in the ground frame, the rock does travel in space coordinates, and the time coordinate measured is dilated.

Time and space do not exist without the other. We see in our measurements in nature, such as the rock above, that the existence of 4D spacetime, is not just mathematical but experiential (see below). Thus, the 4D spacetime SR is also the law in the universe, even far away from the Earth and the rock [1, 2].

There is no valid ontological question anymore, as we show below, space and time can transform into each other, in nature that we can experience. One can still, of course, discuss the acceptance of this fact, here on Earth, consciously, freely, openly, but without ontological questions left on the nature of the universe, as far as, literally, anyone can see, billions of years in the past.

ONTOLOGICAL QUESTION

Turning to the ontological question, what is place in the scheme of things in nature, of SR 4D spacetime: maths or physics?

Is 4D spacetime just a use of mathematics, or does it represent nature in ways that using lesser dimensions just can not do?

Is 4D spacetime like a spreadsheet of calculations, not really necessary, for a reality that is entirely experienced as 3D +1D, or even 3D with time as a parameter?

Names seem to not matter, as expected, in physics. it would seem that it does not matter, then, if someone, for example, chooses a geodesic to extend Newton's First Law, overcome beautifully our limitation then (to define "straight line"), and designates it as an extended "inertial motion" -- the geometric basis is the same, the physics did not change. Or, like Mashhon, describe an infinte family of comoving observers, 3D, each one as a flash in time. One would seem to need less mathematics, it can all be solved in 3D +1D, even 3D, not needing 4D. But the context is just more limited, the region of validity is less, as we show next.

It is physically limiting to use names that do not distinguish curvature as stretching (as done in 4D spacetime), only considering curvature as bending. The spacetime that was being considered is flat, it can be seen in 3D like a stretched, flat pizza dough. The spacetime is flat but if the world trajectory is curved, it still fits with curvature as intrinsic, as stretching, so not just world straight lines "fit" in flat spacetime!

The 4D spacetime, in SR or GR, therefore, works for world-curves, as they may curve, in the world we see as flat spacetime, locally, as SR, or curved spacetime, as we see in GR. Only the 4D spacetime formulation of SR and GR can do that, we cannot use lesser dimensions, may be more.

The visible world, however, as viewed, is NOT 4D spacetime, it seems at first sight. The world is apppearing to us as 3D +1D, or 3D plus time as parameter. But, the world is governed in 4D spacetime, which manifests itself through laws that 3D or 3D+1D cannot represent, but we can see in everyday experience -- just like we do not see the Earth going around the Sun, we see the Sun going around the Earth, apparently, but we do have seasons, and the ancient Greeks measured the circumference of the Earth, with no rockets, quite correctly, through mathematics.

Therefore, the relatity, the world we live in, the truth-conditions, is at least 4D. Some just experience life less, as 3D+1D, or 3D, or even 2D. But the mechanism works in at least 4D, and 3D cannot represent it, as shown in SR and GR experiments. For example, with length contraction or time dilation for non-comoving observers, only.

This is, perhaps, new to philosophers only.

GAUSS AND DIFFERENTIAL GEOMETRY

In 4D spacetime, the worldline curvature is measurable without any external reference frame. Following Gauss, this does not imply that an absolute reference frame exists, nor that an extrinsic reference frame is even need.

This cannot be done with space as 3D and time separare as a passing parameter. This falsifies ANY SR and GR theories, such in SR the original Einstein formulation, Clifford(3,1), Lorentz ether, and by Mashoon, that do NOT consider a "fusion" of at least a 4D spacetime. In those theories, at least one external, inertial reference frame must also be used, which is limiting. Also, as shown elsewhere, they cannot fully represent non-eucliden geometry.

Higher dimensions than 4D are possible, not less. Also, 4D spacetime is not equal to geometric 4D, as the interval can be zero or negative, but a geometric metric has to be positive definite. Thus, 4D spacetime coordinates are not somehow geometric dimensions that we see, but that we experience through a particular 3D space plus a particular time. This difference, between seeing and experimenting, has been a stumbling block for many.

CURVATURE IN GR, MEASURING TIME

If there is no curvature of the worldline, or if there is cartesian translational symmetry, it is inertial motion. This is possible when sufficiently away from any mass.

On the other hand, worldline curvature <--> no cartesian translational symmetry <--> no inertial motion. Free fall is not inertial motion, and always follows a geodesic, a path defined by the external gravitational field. The center of mass (CM) of a body in free fall obeys SR.
For a man in a box, the box can be not locally relevant, insofar it does not shield, increase, or decrease, the external gravity.
The CM of the man is in free fall, obeys SR.

Any point non-comoving with the CM should be affected locally, including centripetal and coriolis forces, which are locally representable, therefore locally exist in the GR formalism.

The experimental difficulty to measure time at all, or to be be comoving, can be removed under the criteria that small defects are acceptable, vanishingly small to some, but still the main objection remains, as shown elsewhere.

The lack of cartesian translational symmetry (as Stefano Quattrini pointed out, when it crashes...) or when it curves, in both cases with a curvature of the worldline, shows that the motion is not inertial.

MINKOWSKI: FUSION IN SPACETIME

More than 100 years ago, Minkowski and Einstein, by way of Gauss, made new mathematics. They fit all the known experimental facts, uniquely, without exception, creating a "fusion" that we can distinguish only globally -- here one sees time, there one sees space -- but they must stay together locally, as one and single expression of spacetime -- there are no two spacetimes.

Opinions may seem to totally diverge from each other, in that for one, time is all that exists, for other only space exists, for another time is not even seen. But, actually, such divergent views are a proof of the "fusion" of space and time. How? This "fusion" happens so that there is no unique way to split spacetime into space and time, all observers explained by the same theory, of "fusion". One can separate differently than another, all thereby valid, intersubjectively.

This universe is, in all aspects we can see now, including Hubble flow and quantum mechanics, at least 4D. Note that comoving and non-comoving, as well as length contraction and time dilation, are not just words or optical illusions -- what they denote can cross a barrier, can produce thermodynamic work. They define different physics, different truth-conditions, not just different truth values.

Note also that length contraction and time dilation manifest, or not, always in the same conditions. They only exist for non-comoving observers, and do not exist for comoving observers. In cosmology, there is the non-conflicting addition of the Hubble Flow, which allows comoving observers to separate.

In all cases, there is only some sort of union we cannot separate -- or "fusion" -- between space and time. In other words, this "fusion" happens so that there is no unique way to split spacetime into space and time. But, we can have slices of 3D here and 2D there, or even 1D behavior. Likely we can have more, in dimensions to infinity, and even beyond.

The spacetime is exactly the same, 4D as it should be, in special relativity and general relativity, as (t,x,y,z). The metric is different, because the former is certainly flat and the later can be curved as well, with gravity modelled as curvature, but that "fusion" concept in 4D spacetime stays exactly the same, it just "fuses" differently (with a different metric). In cosmology, the metric also gets to be different, but spacetime remains as a kind of "fusion" in the same 4D.

NOTES:

A. In SR and GR spacetime, accelerated motion is defined absolutely, for example, with no absolute reference system or geodesics, of course, by extrinsic and intrisic geometric properties of the curvature.

Names seem to not matter, as expected, in physics. it would seem that it does not matter, then, if someone, for example, chooses a geodesic to extend Newton's First Law, overcome beautifully our limitation then (to define "straight line"), and designates it as an extended "inertial motion" -- the geometric basis is the same, the physics did not change. Or, like Mashhon, describe an infinte family of comoving observers, 3D, each one as a flash in time. One would seem to need less mathematics, it can all be solved in 3D +1D, even 3D, not needing 4D. But the context is just more limited, the region of validity is less, as we show next.

It is physically limiting to use names that do not distinguish curvature as stretching (as done in 4D spacetime), only considering curvature as bending. The spacetime that was being considered is flat, it can be seen in 3D like a stretched, flat pizza dough. The spacetime is flat but if the world trajectory is curved, it still fits with curvature as intrinsic, as stretching, so not just world straight lines "fit" in flat spacetime.

The 4D spacetime, in SR or GR, therefore, works for world-curves, as they may curve, in the world we see as flat spacetime, locally, as SR, or curved spacetime, as we see in GR. Only the 4D spacetime formulation of SR and GR can do that, we cannot use lesser dimensions, may be more.

The visible world, however, as viewed, is NOT 4D spacetime, it seems at first sight. The world is appearing to us as 3D +1D, or 3D plus time as parameter. But, the world is governed in 4D spacetime, which manifests itself through laws that 3D or 3D+1D cannot represent, but we can see in everyday experience -- just like we do not see the Earth going around the Sun, we see the Sun going around the Earth, apparently, but we do have seasons, and the ancient Greeks measured the circumference of the Earth, with no rockets, quite correctly, through physics and mathematics.

It all works for geodesics, world-curved as they may in the world we see as flat spacetime, locally, which is NOT spacetime but governed by a flat spacetime, there is no ontological status anymore, and this is beautiful, not just right. This is also, perhaps, new to philosophers.

B. In summary:

The usual 4D spacetime, such as in the Minkowskian signature, and similar in GR, are non-Euclidean.

We sit, at least, in a 4D spacetime reality. This can be locally Euclidean and globally non-Euclidean, and defines what and how we live, even though we daily experience 3D and passing time.

The acts that shape 4D spacetime, also shape existence in models below, in 3D+1D, 3D + time, 2D, and even in 1D plus time.

When something is correct, this is a sign that it can be be proved in more than one way. In support of this question, we found evidence of the same answers, in additional diverse ways. References are provided, see [1-11], and in self search.

There is no ontological question anymore, on the nature of 4D spacetime reality as we do see it. We just see through a "filter" that we do not identify commonly, reality looking to an observer at rest like if it exists (i.e., as a persistent illusion) in 3D and time is just passing.

Spacetime "fusion" of space and time, Euclidean and non-Euclidean, here discussed in depth, is critical to the effects we observe in 3D, not just to the understanding of the maths.

[2] Cosmology, SR, and GR, at http://www.astro.ucla.edu/~wright/cosmo_02.htm

[3] H. Minkowski. Space and Time: Minkowski's Papers on Relativity. 2012. Online at: http://rgs.vniims.ru/books/spacetime.pdf

[4] C. P. Burgess. General Relativity: the Notes. 2009. Online at: http://www.physics.mcmaster.ca/~cburgess/Notes/GRnotes.pdf

[5] While the original but limited formulation of special relativity is still taught at various college-level textbooks, such as
Article Physics: For Scientists and Engineers J. .W. Jewett and R.A. Serway. Physics for Scientists and Engineers with Modern Physics. Thomson Brooks/Cole. 2012

[6] In another version of the SR, by Mashhoon, an accelerated observer is in effect replaced — on the basis of the hypothesis of locality — by a continuous infinity of hypothetical momentarily comoving inertial observers. Here, the accelerated observer and the otherwise identical instantaneously comoving inertial observer have the same velocity and position. In SR, two observers comoving are defined as having the same velocity and position. Cited by 36 references, with 14 occurrences of "comoving", Mashhoon paper at arXIv may further his treatment of accelerated motion in SR, and illuminate the use of "comoving" in SR and Newtonian mechanics,, where it is described as a "material point":
at https://arxiv.org/pdf/0805.2926

[7] For the spacetime formulation, also this book:
Taylor and Wheeler. Spacetime Physics. . W. H. Freeman and Company. 1966.

[9] This question, and links as well as comments, even apparently dissonant comments, may help provide a solution to craft more free time in undergraduate courses, and today:
https://www.researchgate.net/post/Should_college_students_learn_about_electromagnetism_before_mechanics

Is dimensional analysis valid in the multidimensional space? What is natural system of units? Introduce your source.

Discussion

10 replies

- Asked 29th Jul, 2020

- Bahram Kalhor

Consistent with the experimental value, the theoretically calculated proton radius from the theory that mass is of EM origin, what do you think?

Question

14 answers

- Asked 16th Oct, 2019

- Krzysztof Brzozowski

Assuming that particle consists of a photon that moves circularly in the loop, creating standing wave obeying the rule that its closed path 2*Pi*R=n*Lambda (1) (resonator where resonator length 2*Pi*R is „n” times photon wavelength) and knowing particle's mass (experimental value), we can calculate its radius.

Lets put c/v (2) for Lambda in the above equation (1), where v is photon frequency. We get then 2*Pi*R=n*c/v (3). Now if we assume that particle's mass is of EM origin and m=E/c^2 (4) where E=hv (5) is the energy of circulating photon as described above we can rewrite (4) as m=hv/c^2 (6) or v=mc^2/h (7) (letter h stands for Planck constant of course). Now lets put (7) into (3) and we get 2*Pi*R=n*c/(mc^2/h) (8) or simplifying R=n* h/2*Pi*mc (9).

Now, let's take proton for our considerations. Assuming n=4 in eq. (9) and m=1,672621637(83)*10^(-27)kg (experimental value) we can calculate proton's radius to be R=**0.84124 fm** which stays in agreement with the experimental value of **0.84184 fm +/- 0,00067 fm** (the most accurate experimental value measured in a Hydrogen atom with a Muon in 2010).

You can read more about that theory and mechanism in my paper here:

https://www.researchgate.net/publication/333732258_GENERAL_not_grand_UNIFICATION_THEORY_Quantum_Gravity_and_Schwarzschild_Particles

What do You think?

Preprint

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- Jan 2006

In the last decade, El Naschie published a series of seminal papers where he introduced the idea of conjugate complex time and developed his famous fractal E(∞) space-time theory, which reconciles general relativity with quantum mechanics by formulating both theories in the context of a transfinite geometry. In this paper, we put together ingredien...

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