5th Jun, 2022

Discussion

Started 23rd Apr, 2022

# Quantum mechanics and the eternal background of TIME.

It is like Puzzle to all my physics family. If any body gives valid discussion or answer it would be helpful.

let me ask a question:

**if time is one dimensional background, what is the position of a particle on this one dimensional background of time?****How do you calculate position of a particle without the violation of law of conservation of energy on this one dimensional background of TIME?**

## Most recent answer

2nd derivative IS nonuniform motion. 3rd variation has no real/ physical meaning. I thought You know that.

## All replies (50)

24th Apr, 2022

Dear Hussainsha Syed

Time is the awareness of mutual changes. That means that the “subject” that is aware of change will be confronted with limitations. For example humans.

Every quantum of energy – energy is a quantity of change within/by the electric field – has the speed of light. Thus in every point within the volume of the universe there is a continuous change of the local amount of quanta and all these quanta have the speed of light. But we are not aware of this “quantum chaos”.

The nature of quanta – fixed amounts of energy – shows that we cannot observe a smaller change in time and position than provided by the structure of our universe at the smallest scale size. Werner Heisenberg (and others) did research on the topic because he supposed that the smallest scale size of the universe – termed “the minimal length scale” – was about 1 x 10

^{-15}m. In other words, if a quantum of energy passes on over a distance of 1 x 10^{-15}m with the speed of light the duration is 12 x 10^{-23}second. A constant of time that we can term “quantum time” if the proposed size of the minimal length scale is correct. Probably about 0,5 x 10^{-15}m is more accurate so the constant of quantum time will be 6 x 10^{-23}second. In between the minimal length scale and the constant of quantum time there is no observable/detectable change possible with the help of experiments (the core of Heisenberg’s uncertainty principle).But the fixed amount of energy is not the only quantity that changes in the universe. Because the electric field and the magnetic field are corresponding fields. That means that the pass on of 1 quantum over a distance of 1 minimal length (0,5 x 10

^{-15}m) generates a corresponding vector within the magnetic field. But vectors are not restricted by the speed of light like quanta.Thus if we have an instrument that can measure the change of the amount of quanta in 1 point of vacuum space (if all the changes are in the same direction) we will detect the increase/decrease of energy by one quantum at the time. But during the transfer of the quantum over a distance of 0,5 x 10

^{-15}m there is a fluent transfer of “infinite” small amounts of energy (because the electric field is a topological field) and all these “infinite” small amounts of energy together are exactly 1 quantum of energy (Planck’s constant) at the end of the duration of 6 x 10^{-23}second. However, the “velocity” of the change of a vector is instantaneous. Thus at the moment of the start of the pass on of 1 quantum the corresponding vector of the magnetic field starts to change its magnitude.The consequence is that “quantum time” (the fixed change by the electric field) isn’t identical to “vector time” (fluent mutual changes between the vectors of the magnetic field). The magnitude of a vectors originates from the corresponding amount of energy in 1 point in space (the local amplitude of the electric field). But because the magnitude of a vector is influenced by the existence of the other vectors around the “real” magnitude of the local vector is the result of summing up all the vectors in the same direction and by subtracting all the vectors from the opposite direction (all in that distinct point in space).

Vectors cannot exist on their own because vectors need a mediating rigid field. Simply because vectors are 1 dimensional. Only a quantum of the electric field represents 2 and 3 dimensional mathematical properties (the deformation of the volume and surface area in between the minimal length scale because the electric field is a topological field). The only rigid field in vacuum space is the Higgs field because every scalar of the Higgs field in vacuum space has exactly the same magnitude (the scalar lattice). The consequence is that local vectors of the magnetic field are interrupted by decreased scalars (rest mass and black holes). That is why the magnetic field only exists in vacuum space.

The origin of the change of a local vector is the corresponding local change of the electric field. Thus if we can create 1 vector with an enormous magnitude that can overrule all the other vectors in its direction within a distance of a number of light years the influence is only detectable by our measurement instrument after 6 x 10

^{-23}second (Heisenberg’s uncertainty principle). Fortunately we can detect the precise instantaneous influence over a long distance with the help of entangled photons.With kind regards, Sydney

P.S. The "tangible" existence of the minimal length scale is a bit more complicated.

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The position, as a function of time, in classical mechanics, is calculated using the equations of motion, deduced from, either Newtonks laws, or the least action principle. In both cases, the equatiins are the same and conservation of energy isn’t a problem.

This is material that’s, usually, covered in all introductory physics courses that are supposed to be passed by all science and engineering students.

In quantum mechanics the corresponding quantity is the probability distribution of the position, deduced from the Schrödinger equation, that’s discussed in all courses on quantum mechanics. In this case conservation of energy isn’t an issue, either.

In both cases conservation of energy expresses invariance of the equations under time translations.

My dear Preston forget about eternal, just consider only our observation 13 billion years or 14 billion years and also consider Time is relative.

Now assume in front of you 14 billions years are there, now tell me the position of a particle on this 14 billion years without violating the law of conservation of energy?

25th Apr, 2022

Dear Hussainsha Syed

Sorry, I am afraid there is some misunderstanding of concepts. Einstein's theory of Special relativity is about the rate of change of observable/detectable

**compositions**of energy (like a particle or a macroscopic object). But time is a more foundational concept and not only restricted to matter.The origin of Einstein's relative time is quantum time and quantum time is a constant (if we are talking about energy, actually the electric field). The existence of the constant speed of light (the velocity of the free quantum of energy) and Planck's constant (the fixed amount of energy) determines the duration of all the changes by the electric field in our universe. And the smallest duration that we can detect is the constant of time, quantum time.

The consequence is that your assumption that energy conservation and relative time result in the violation of the law of conservation of energy is not correct.

Try to imagine a particle that moves with a moderate velocity. The particle is a composition of energy (actually a local concentration of energy) and every quantum of the particle that change position has the speed of light. Because the speed of light is a property of space itself. The particle has a spin so most of the energy of the particle is involved in a loop. Only a small part of the energy of the particle is involved in linear motion.

If we accelerate the particle to nearly the speed of light nearly every quantum of the particle has a linear motion. Thus the spin (loop of energy) of the particle has nearly stopped. The spin of a particle represents its internal changes. Actually the particle is comparable with a clock. If we accelerate a clock till it nears the speed of light the clock hands nearly stop.

In other words, the observation that the "internal" rate of change of objects slows down if its velocity is increasing shows that the energy of the object is conserved.

With kind regards, Sydney

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Dear Sydney thank you so much for valuable writing.

let us leave everything, now let us have layman picture:

imagine in front of you there is a time line of 1AM to 7AM, where do you place a particle on this time line?

you can tell any placement in between 1AM to 7AM. Based on your answer we can proceed further.

Thank you.

25th Apr, 2022

Dear Hussainsha Syed

A time line is part of a diagram. Mostly a 2D drawing with a metric to express the changes of the subject (e.g. time) with the help of a (curved) line.

But if we want to describe time as an independent physical quantity we encounter conceptional problems. Because what is our daily time? It is a composition of the rotation of the earth and the trajectory of the earth around the sun. That is why philosophers concluded that time is (observable) change between observable/detectable phenomena. In physics we use the term “energy” for every change (actually it is a general term for the unknown underlying mechanism that creates the change). Einstein used objects (matter) as point of reference and in this way he created a new description of mutual relations without a clear metric: relative time.

In the microcosm we can determine that the change of position of 1 quantum over a fixed distance – the metric of space itself – has a fixed duration because the linear velocity of every quantum is a constant velocity, the speed of light. If you think about it you will notice the similarity between daily time and quantum time because without a constant (or a reference object like the sun) there is no possibility to determine a metrical relation between the observable changes.

Our universe is an enormous volume and the volume has a structure (that is what we see if we look around). We can detect the mutual relations between the properties of the units of this structure because that is what we have termed “fields”. Thus in QFT the distinct universal quantum fields represent the mutual (local) differences between the basic properties of the structure of the universe.

That is why we can conclude that there are 2 types of differences at the smallest scale size:

- differences between the local “magnitudes” of one universal field (e.g. the electric field);
- differences between the local “magnitudes” of 2 or more universal fields (e.g. between the electric field, the magnetic field and the Higggs field).

Everything that I describe above is about change. Thus it is about time… Moreover, every object moves in relation of the structure of the universe. The structure is in rest and the object is a local concentration of energy that passes on within the structure and the pass on itself is caused by the properties of the structure too.

Thus if we want to understand the consequences of a time line in relation to the motion of an object we are simplifying physical reality. And that is what physics is: a method to create some “structure” in the never ending changes/mutual relations in the universe with the help of measurements and conceptual simplifications.

Back to the start. A time line is thus a simplification of reality and if you want to use a time line you are simplifying the properties you want to relate to this time line (that is the consequence because time is change). But in practice physics is more or less a number of tricks to calculate relations between the phenomena. However your discussion is about understanding the underlying “mechanism”. Thus the question is if you are satisfied with a simplification or do you want to understand “everything”? And if you prefer the latter we have to think about the right “gedanken experiment” to avoid too much simplifications. Do you have a useful “gedanken experiment”?

With kind regards, Sydney

Dear Preston,

let us leave everything, now let us have layman picture:

imagine in front of you there is a time line of 1AM to 7AM, where do you place a particle on this time line?

you can tell any placement in between 1AM to 7AM. Based on your answer we can proceed further.

Sydney Ernest Grimm

let us leave everything, now let us have layman picture:

imagine in front of you there is a time line of 1AM to 7AM, where do you place a particle on this time line?

you can tell any placement in between 1AM to 7AM. Based on your answer we can proceed further.

Thank you.

26th Apr, 2022

To answer your question by selecting a time between 1AM and 7AM would be a fault because energy does not arise within the confinement of 'moments'.

The view of time in moments, which comes from holding energy at some subtle level as static, leads to many incoherences which can only be resolved through a momentless arising.

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“…

*let me ask a question: if time is one dimensional background, what is the position of a particle on this one dimensional background of time?**How do you calculate position of a particle without the violation of law of conservation of energy on this one dimensional background of TIME*?…..”

- to answer to this question it is necessary before to understand – what is “Time” - and so what is “time” – and what are “Space” and “space”, though. That is possible, and is explained, only in framework of the Shevchenko-Tokarevsky’s “The Information as Absolute” conception https://www.researchgate.net/publication/260930711_the_Information_as_Absolute DOI 10.5281/zenodo.268904, though brief, but clear enough, definitions of Time/time and “Space”/“space” are given on first few pages in

Quite briefly: Time is “space for changing states of changing informational patterns/systems”, and that, with “Space” actualization, is actualized absolutely necessarily and objectively in/for any/every concrete changing patterns/systems as concrete spacetimes,

- where the time coordinate/dimension differs from any space coordinate/dimension practically only in that whilst there can be any number of different space dimensions for different patterns/systems, all patterns/systems change their states only in the unique, common ad universal for all/every patterns/systems, time dimension.

More see the link above; it is useful to read comments to some typical mainstream philosophical paper “Time Might Not Actually Exist, Researchers Say” in https://www.researchgate.net/project/Creative-Particles-of-Higgs-or-CPH-Theory/update/6264c902aaa86b722b946609

Cheers

Dear Gemma, let us think for a moment out of box to have some discussion.

In between 1AM to 7AM, where do you place a particle on this time line?

Dear Gemma Thank you...

now let us move further. If you choose 6AM, what about 1, 2, 3, or at any instant in between the time line of 1AM to 7AM?

energy neither be created nor be destroyed, then you must place a particle at every instant in between the time line of 1AM to 7AM, not just at 6 AM.

how do you place a particle such that it must exist at any instant of time (energy neither be created nor be destroyed concept must be preserved)?

26th Apr, 2022

A particle at 6AM can only look at 1AM in a theoretical manner because we cannot say that what is past exists now or what is to come (future) has already happened.

It, therefore, seems to me that your question is only valid in the context of all times (1AM...7AM) existing simultaneously where energy is a type of entity existing solidly at every moment, negating the possibilities of transformation.

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Dear Gemma, yes question is only valid in the context of all times and transformation is secondary, only primary thing is neither be created nor be destroyed...hence the discussion on the background of one dimensional background of time.

I am requesting you

how do you place a particle such that it must exist at any instant of time (so that energy neither be created nor be destroyed concept must be preserved)?

Dear Hussainsha Syed ,

Whenever the Hamiltonian of a physical system is invariant under the time-translation, then the total energy of that physical system is conserved according to the celebrated Noether's theorem.

With best regards,

N. Gurappa.

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Einstein said something like:

time is that which is given to you by the pointers of your clock.

I think he was right. If you use a different clock, your time may be a different one.

There is nothing ``eternal'' to time.

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27th Apr, 2022

From your statement, I infer (might be wrong) that when you think of 'placing a particle' your mental visualization of that particle is an enclosed geometrical shape (let's say a sphere) depicted on top of a line's segment (an instance of time).

Quantum physics has experientially demonstrated that particles fundamentally do not exist as solid independent and static units in space, and therefore it is impossible to 'place particles' in the way you describe because it is not how energy truly exists.

There are different views/models on what fundaments make up energy.

One problem with imagining a particle as a sphere in a segment 'one' and then a sphere in a segment 'two' is that one is leaving aside the transition between 'one and 'two'.

Think for example of the moment a seed transforms into a sprout: in your view, there is a seed in moment 'one' and a sprout in moment 'two' -> In which way can the connection between these two moments explain the fact that energy is not created or destroyed but continuously transforming?

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ha ha from you it was really good way of interpreting transforming continuously and good analogy also. this was absolutely fine to me.

now coming to our actual discussion or puzzle, let us least bother about shape of a particle. let us imagine an electron as a particle and place this particle on the time line what we are discussing so far.

let us have a clue also : quantum mechanics

From the last series of rather strange posts it looks as worthwhile to point here that in the yesterday SS post above the problem what is “time”- and so the thread question - are quite clearly answered – “time” is absolutely obligatory dimension of every concrete spacetime, where space is a number of absolutely obligatory space dimension also, of every concrete changing informational pattern/system, again more see at least first few pages in

- and as the dimension the time dimension by no means differs in this case form any space dimension in spacetimes.

Including when a pattern/system change in a time interval “

*Δt*”, it moves in the time dimension on the interval “*Δt*”, just as, say, if a pattern/systems moves in any space dimension it moves on a step “*Δx*”.At that in the above the intervals “

*Δt*”, “*Δx*”, are in the quotes, because of both – space and time, composing every concrete spacetime of every concrete patter/system, really compose some logical “empty container”, where the pattern/ system exists and changes, and where the dimensions are fundamentally infinite;- whereas the emptiness fundamentally hasn’t some own “intrinsic” measure in both, space and time dimensions; and so the space and time intervals can be measured only relatively – comparing with some universal etalons. In physics that are “meter” for space and “second” for time, and the quotes above disappears if the etalons are applied.

Including in space/time dimensions there are no some special/preferred own “intrinsic” points, and so in every concrete case any observer at observing/describing what happens in the spacetime can – and does that – assign in his reference frame some arbitrary point in the space and time, where x/y/z=0, t=0.

That’s all, whereas, say, that

“…

*A particle at 6AM can only look at 1AM in a theoretical manner because we cannot say that what is past exists now or what is to come (future) has already happened.**It, therefore, seems to me that your question is only valid in the context of all times (1AM...7AM) existing simultaneously…”*

- is rather strange claim, nothing bad is in “all times (1AM...7AM) existing simultaneously”, that is by definition of the time dimension, where all infinite “number” of the dimension’s points continuum exist, of course, simultaneously, and absolutely independently on – somebody looks at a clock and see “1AM...7AM”, or not; and on exists somebody or not at all.

Cheers

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Dear Hussainsha Syed ,

I found this line, <...let us imagine an electron as a particle and place this particle on the time line...> in your latest response to Gemma F. Lopez.

I got a doubt! What do you mean by placing a particle on the timeline? Before placing, where was it?

With best regards,

Gurappa.

Dear Gurappa,

Placing on timeline is analogous to placing on space.

before placing it may be anywhere that is not our consideration.

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Dear Hussainsha Syed ,

HS: <Placing on timeline is analogous to placing on space.>

NG: How? It can’t be due to the arrow of time. For example, a pendulum can oscillate between two spatial locations, but can’t between two-time points.

Much more can be said about how it can’t be based on the signature of Minkowski’s metric, but before that, let me express another doubt:

You said, <before placing it may be anywhere that is not our consideration.>

In our physical Universe, placing an object somewhere happens only by displacement. Therefore, its location before placing is equally important to its location after placing.

With best regards,

Gurappa.

dear Gurappa,

we can represent position of particle spatially or on the background of space, this is very easy for us.

this discussion is like out of box where we need to represent position of a particle on the background of time.

so I am asking how do you represent position of a particle on the background of time?

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Dear Hussainsha Syed ,

Yes, your question seems to be out of box, but I am trying to get it. Many doubts are arising!

You wrote, < so I am asking how do you represent position of a particle on the background of time?>.

What do you mean by representing “position” of a particle, if the background is only “time”? Where does that particle exist then? In space also or only in the time background?

With best regards,

NG.

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Dear Hussainsha Syed ,

Does something exist only in time background? No space at all? Then, you may be having a zero-dimensional point-Universe at all times! Location of that point on time-axis can be arbitrary!!

With best regards,

NG.

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dear Gurappa,

Already you understood it is out of box, then no need to pull in box things.

please just let me know how do you represent position of a particle on the background of time?

Gemma already in sync with this discussion let us wait of Gemma next response and I already given clue as QM.

Dear Hussainsha Syed ,

If I didn't understand your question, I can only ask my doubts for clarification.

Since, you started a discussion rather than asking a question in RG, I took some liberty in asking my doubts.

That's why I gave my answer along with my doubts as questions, <Does something exist only in time background? No space at all? Then, you may be having a zero-dimensional point-Universe at all times! Location of that point on time-axis can be arbitrary!!>, in my latest response.

Thank you for your kind responses so far and carry on your discussion.

Good bye!

With best regards,

NG.

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let me add my view:

when a particle is a wave as we know already from quantum mechanics, we can place a particle on the background of time as a wave without violating energy neither be created nor be destroyed.

because a particle can exists at all possible positions on the background of time. If a particle does not exist at any possible position on the background of time, said to be energy is destroyed.

Therefore it is merely my assumption that quantum mechanics makes more sense when the background is time rather than the space.

It looks more acceptable that a particle can exists simultaneously at two places on the background time, rather than on the background of space.

moreover if quantum entanglement happening on the background of time, it looks much acceptable!

This is my new perspective and I welcome any suggestions with all your freedom please.

considering the experimental verifications of both sr and gr, could we say that processes take place differently in different referentials, whereas time and space are still absolute?@

15th May, 2022

Time is not 1-dimensional. My definition of time is: time is motion. Motion must be described by using variation of space and variation of variation of space, i.e.: time is (at least) 2-dimensional (curvature increases the number of dimensions).

in gr, we say time runs differently at different altitudes in a gravitational field; but when we measure time, we are dealing with processess; could we say they occur all differently in absolute time, due to the presence of gravity?; could we say that gravity interacts with everyting?@

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23rd May, 2022

Indeed, case time runs differently at different altitudes in gravitational fields, it has to be measured by using 2 variables (variation of space and variation of variation of space), i.e. time is 2-dimensional.

The thread question is rather clearly and concretely answered in the SS post April 27 above; whereas after the post some rather vague series of posts appeared. So repeat the main point – everything in Matter exists and changes everywhere – on the QM and “classical” scales – absolutely fundamentally on some “eternal background of TIME” , i.e. in the true ct-dimension of the Matter’s fundamentally absolute, fundamentally flat, and fundamentally “Cartesian”, [5]4D spacetime with metrics (

*cτ,X,Y,Z,ct*),- and time is in this case nothing else/more than usual dimension, completely similar to any space dimension,

- besides the fundamental difference, that there can be arbitrary number of space dimensions, when there exist the unique, and ultimately universal time dimension, where everything in Matter, and outside in the absolutely fundamental and absolutely infinite “Information” Set, moves on some step

*Δt*[for Matter it is well convenient to introduce steps*Δct*] at every change.More see at least first few pages in

Though in the thread new poster’s posts appeared, which are well rational and really relate to what really happens in Matter, so

“…

*considering the experimental verifications of both sr and gr, could we say that processes take place differently in different referentials, whereas time and space are still absolute*?…”- the answer to this question is: the same processes in the same all/every material object are different in relatively moving reference frames and in fields of fundamental Nature forces, really that is possible in the long range Forces, i.e. Gravity and Electric Forces,

- while Matter’s spacetime is fundamentally absolute [see above], and is by scientific definition fundamentally nothing else that some infinite “empty container”, where Matter – and everything in Matter – exist and change their states. Concretely, because of Matter on ultimately fundamental level is based on some binary reversible logics, Matter’s spacetime is as is pointed above, and

- which fundamentally cannot be “contracted”, “dilated” either moving reference frames in the SR or “spacetime curvature” in the GR, “curved”, etc., by anything in Matter; and, reversibly, fundamentally cannot to contract lengths of material bodies, slow clocks’ tick rates, force Earth rotate around Sun, etc. – all these “fundamental relativistic properties and effects” really fundamentally cannot, and so don’t, exist.

Including in

“…

*in gr, we say time runs differently at different altitudes in a gravitational field; but when we measure time, we are dealing with processess; could we say they occur all differently in absolute time, due to the presence of gravity?; could we say that gravity interacts with everyting*?…..”- time and space are dimensions of the Matter’s spacetime above, and so fundamentally both, (3+1) space dimensions, and the real – “

*ct*” – time dimension, fundamentally cannot run to anywhere.However if some material objects compose by some Nature Force some stable system, say, being coupled by Gravity, a system “Earth+ a clock”, because of the Gravity impacts on intrinsic processes in both, Earth and a clock, are slowed down; and, since clocks are some specifically constructed material objects that show how their intrinsic processes run, that can be measured; at that the more Gravity potential, the more the ticks are slowed.

Nothing, of course, happens with time, and, though that is seems only one really fundamental finding in the GR that clocks ticks rate slow in Gravity fields - in 1916 such physical effect was completely unknown, and so despite the fundamentally wrong postulates, some rational points in the GR contains,

- however really this slowing practically for sure is two times lesser than that the GR predicts, what can be quite easy now tested if ~$200 000 would be spent, see https://www.researchgate.net/publication/277710038_The_informational_model_-_gravity_a_next_experiment

More about what is Gravity – and Electric – Forces see the initial 2007 SS&VT model in https://www.researchgate.net/publication/354418793_The_Informational_Conception_and_the_Base_of_Physics ; section 2.9 “Mediation of the forces in complex systems”.

Cheers

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as long as qm continue to use classical variables, instead of its proper ones(unknown yet), it cannot avoid the uncertainity principle@

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“…

*as long as qm continue to use classical variables, instead of its proper ones(unknown yet), it cannot avoid the uncertainity principle*…”- that isn’t correct, QM fundamentally correctly uses “classical variables”, transforming them into QM operators, and QM equations must reduce – and when QM is correct are reduced – to classical equations at

*ћ→*0. So, say, the quantum Gravity theory will be based practically for sure only after the really scientific classic Gravity theory will be developed.And the uncertainty principle fundamentally cannot be avoided from QM, since on QM scale the objects/events/ processes are fundamentally random. That is another thing, that that isn’t completely arbitrary randomness, as that now Heisenberg principle states, say,

*ΔPΔh≥ћ, ΔP*and*Δx*are random independently. Really, as that is well rationally suggested in the SS&VT physical model that isn’t so, and these components are random subject to*ΔPΔh=ћ*.More see the last link in the SS post above, whole paper.

Cheers

sergey, i meant that if qm would use its own(unknown yet) variables, it would have deterministic laws, avoiding, among others, the heisenberg's principle

3rd Jun, 2022

... but neither RT nor QT are deterministic; RT fails in its own singularities.

Mircea Ciobanu, time is not 2-dim because I'd measure it twice, but because I define it to be variation of space and variation of variation of space, ergo it is depending on 2 variables. Case space s(x,y,z) is 3-dim, and time t(v,a) is 2-dim, space-time is 5-dimensional. In other words, one needs (at least) 5 coordinates to locate some()thing in space-time. I said 'at least' because curving would imply at least 1 more dimension.

4th Jun, 2022

Mircea Ciobanu, I do define time: time is motion., so it IS 2-dimensional.

Case you are sure that time is not 2-dim, then how do you define time?

paul pistea, conformal to the dictionary, space and time are forms of the existence of matter; aristotle defined time as the number of motion; i'm sorry, but i don't see any link between time being motion and its 'two' dimensionality@

5th Jun, 2022

Mircea Ciobanu, one must use variation of space and variation of variation of space (ergo 2 variables) to describe time. That is what I am claiming. I know what current books say. Entire physics must be rewritten in the language of functionals- for instance m=m0/sqare-root(1-v^2/c^2) already IS a functional- to be handled by using distributions theory. I have built my own theory, which unifies RT and QT(!!!), so that I express my own thoughts/results.

and how do you treat nonuniform motions?(i.e. when the acceleration is not constant); you consider a supplementary dimension of time, so time is 3d?

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