Does the New Quantization Method Redefine Time Symmetry in Quantum Mechanics?

[naturale]

A new quantization method for relativistic fields has been recently proposed. Compact time naturally reproduces canonical quantum mechanics as well as the path integral formulation, and in a deterministic way (no hidden-variables)! It seems to be a new way of thinking to the concept of time flow with interesting consequences for the problem of time symmetry.

I recommend to read (and to try to figure out) about this nice idea. it represents a serious pice of work I believe! The paper has been regularly published in a conventional journal (http://www.springerlink.com/content/g324131430841515/").

Compact Time and Determinism for Bosons: foundations
Donatello Dolce​

"Free bosonic fields are investigated at a classical level by imposing their characteristic de Broglie periodicities as constraints. In analogy with finite temperature field theory and with extra-dimensional field theories, this compactification naturally leads to a quantized energy spectrum. As a consequence of the relation between periodicity and energy arising from the de Broglie relation, the compactification must be regarded as dynamical and local. The theory, whose fundamental set-up is presented in this paper, turns out to be consistent with special relativity and in particular respects causality. The non trivial classical dynamics of these periodic fields show remarkable overlaps with ordinary quantum field theory. This can be interpreted as a generalization of the AdS/CFT correspondence."

http://arxiv.org/pdf/0903.3680"

 

[zonde]

It is possible to formulate a consistent relativistic field theory of quantum mechanics without assuming any hidden-variable in the theory and using essentially deterministic mechanics (Compact time and determinism: foundation; Found. Phys, arXiv:0903.3680). The quantization is obtained by imposing a periodic boundary conditions to solve the relativistic wave equation. It is similar to the quantization of a particle in a box where the quantized energies are obtained by imposing boundary conditions to the matter waves. In this way there are not local hidden variable at all. The EPR problem and Bell theorem are bypassed.

You made this post in another thread. I hope it's ok to ask questions here.
You say that with your interpretation (I guess it can be called interpretation as there is "exact correspondence with ordinary quantum field theory") bypass Bell theorem as there are no hidden variables. But still it's deterministic.
So the question is what in this case determines probabilities of detection coincidences? Or what determines particular outcome of photon polarization measurement at one of the sites?

 

[naturale]

You made this post in another thread. I hope it's ok to ask questions here.
You say that with your interpretation (I guess it can be called interpretation as there is "exact correspondence with ordinary quantum field theory") bypass Bell theorem as there are no hidden variables. But still it's deterministic.
So the question is what in this case determines probabilities of detection coincidences? Or what determines particular outcome of photon polarization measurement at one of the sites?

This thread is to discuss about that intriguing idea.

From that paper:

"It turns out that if the time accuracy is ∆t ≫ T_t , at every observation the field Φ(x, t) [a quantum system] appears in an arbitrary phase |n⟩ [Hilbert eigenstate] of its cyclic evolution, so that the evolution has an apparent aleatoric behavior; as if observing a clock under a stroboscopic light [27], or a dice rolling to fast to predict the result. In fact, as already discussed in sec.(1.2), if the underlying periodic dynamics are too fast to be observe (~ 10^20s ), the time evolution between two column states |n⟩ [two Hilbert eigenstates] can only be described statistically".

T_t is the "de broglie internal clock" of the system: T_t = h / E. E is the energy of the quanta. A vibrating string with period T_t gives a harmonic quantized spectrum w_n = n w that is a quantized energy spectrum E_n = n h w. This is the quantized energy of a field (neglecting the vacuum energy).

Now you must consider that :

1) the quantum limit of electromagnetism arises at high frequencies.
2) "an electron at rest has an internal de Broglie clock of about T_t = 10^−20s [ T_t=L_c/c= h / m_e c^2, m_e= electron mass, L_c= 2.4263102175±33×10−12 meters meters = Compton wavelength ].
Consider that the period of the cesium atom is "by definition" ~ 10^10 s (nearly the same difference between a solar year and the age of the universe).

As far as I can understand from that paper (this is my interpretation), it is not possible to determine the exact outcome of a photon whenever:
1) the thermal noise is too big
2) the time resolution is poor w.r.t. the de Broglie internal clock. Since in the emission of polarized photon necessarily involves electrons, the time resolution must be better that 10^-20s. This is impossible to achieve at the present, "so that the evolution has an apparent aleatoric behavior".
But the underlying dynamics are deterministic like in a "dice rolling to fast to predict the result".

Thank you for your question (I hope I get it correctly).

 

[zonde]

This is impossible to achieve at the present, "so that the evolution has an apparent aleatoric behavior".

Or in short you have no idea, right?

I don't think that there is anything wrong with idea of "de Broglie internal clock" but it doesn't seems that the idea goes anywhere beyond that.
So to me it seems like rediscovery of some well known things. Or am I missing something?

 

[naturale]

What I wanted to say is that, in that theory, the outcomes of the measurements are determined by the intrinsic too fast periodic dynamics of the elementary systems (and interactions). We are not able to predict the outcome because of our poor resolution in time and we only see aleatoric results. But the aleatoric behavior is not fundamental. It is due to the fact that we can't measure with infinite precision the boundary conditions of a system, just like in Newtonian physics. The mathematics behind that is deterministic but this doesn't mean that we can predict everything.

That theory would represent a big conceptual difference with ordinary quantum mechanics and could bring to a enormous improvement in quantum computation techniques (the mathematics that reproduces quantum mechanics is extremely simplified).

So to speak, even if "God" seems to play Dice with us, He knows the outcomes as long as he has infinite time resolution or He knows exactly the boundary conditions (He doesn't cheat by using hidden variables or similar tricks).

 

[zonde]

What I wanted to say is that, in that theory, the outcomes of the measurements are determined by the intrinsic too fast periodic dynamics of the elementary systems (and interactions). We are not able to predict the outcome because of our poor resolution in time and we only see aleatoric results. But the aleatoric behavior is not fundamental. It is due to the fact that we can't measure with infinite precision the boundary conditions of a system, just like in Newtonian physics. The mathematics behind that is deterministic but this doesn't mean that we can predict everything.

Fine it's deterministic but we can't predict everything. Nothing wrong with that as I see.
But the question is what we can predict?

That theory would represent a big conceptual difference with ordinary quantum mechanics and could bring to a enormous improvement in quantum computation techniques (the mathematics that reproduces quantum mechanics is extremely simplified).

Give some simple example.

 

[naturale]

QUOTE=zonde;2864642]Fine it's deterministic but we can't predict everything. Nothing wrong with that as I see.
But the question is what we can predict?
[/QUOTE]

I think the most appropriate thread to discuss the philosophical implications of determinism could be for instance https://www.physicsforums.com/showthread.php?p=2864506#post2864506".
With determinism I mean mathematical determinism. In principle you can simulate a quantum system (such as an radioactive atom) and predict the outcomes exactly. In that simulation you can predict when the Schrödinger's cat is dead or alive. If this is nothing important for you, just take look to the history of physics of the last century.

Give some simple example.

For instance read the paper. Your question is not sufficiently specific. With that quantization prescription you can easily solve Schrödinger problems, superconductivity and it seems to give an intuitive interpretation of the AdS/CFT.

 

[DevilsAvocado]

So to speak, even if "God" seems to play Dice with us, He knows the outcomes as long as he has infinite time resolution or He knows exactly the boundary conditions (He doesn't cheat by using hidden variables or similar tricks).

This looks very interesting. As far as I understand both Bohr & Einstein believed in an "deeper" reality, that Bohr thought humans could never reach, and Einstein thought was possible to reach thru logic and mathematics.

I will read the paper (slowly and repeatedly) in the weekend, but until then some questions:

When talking about "time resolutions", how is that related to relativity? Is there an "exact time"?

Is it possible to explain what happens in EPR-Bell?

If this bypasses Bell's Theorem with no hidden variables, what is gone – Locality or Realism (we can’t have both)?

I’ll get back later...

 

[naturale]

This looks very interesting. As far as I understand both Bohr & Einstein believed in an "deeper" reality, that Bohr thought humans could never reach, and Einstein thought was possible to reach thru logic and mathematics.

Logic is the wonderful weapon that we have to understand nature.

I will read the paper (slowly and repeatedly) in the weekend, but until then some questions:

Have fun, and if you have problems, just ask me.

When talking about "time resolutions", how is that related to relativity? Is there an "exact time"?

I am not sure I understand your question. The time periodicity (de Broglie internal clock) of a massive particle in its reference system define the mass of the particle and is proportional to the Compton wavelength T_\tau = \lambda_s/c = h / \bar M c^2. When you observe that particle with a time resolution \Delta t < T_\tau is like observing a field with a spatial resolution greater that the Compton lenght: you observe quantum effects because you excite many "harmonics modes" of the particle, or in ordinary field theory language you create pair of particles... In a different reference system the "de Broglie internal clock" of that massive particle transforms according to Lorentz.

Is it possible to explain what happens in EPR-Bell?

Bell is mentioned in this way: "Therefore model proposed in this paper is deterministic since it represents a possible way out of the Bell’s inequality or similar non-local-hidden-variable theorems [31]." Since there are no hidden-varialbes and an there is exact matching with ordinary QM (as Feynman said "same equation, same physics") the EPR experiment based on this deterministic theory should reproduce the same predictions of QM.

If this bypasses Bell's Theorem with no hidden variables, what is gone – Locality or Realism (we can’t have both)?

I’ll get back later...

As far as I can see there is local realism (but I am not sure if this is the correct interpretation of the theory).

 

[zonde]

I think the most appropriate thread to discuss the philosophical implications of determinism could be for instance https://www.physicsforums.com/showthread.php?p=2864506#post2864506".
With determinism I mean mathematical determinism. In principle you can simulate a quantum system (such as an radioactive atom) and predict the outcomes exactly. In that simulation you can predict when the Schrödinger's cat is dead or alive. If this is nothing important for you, just take look to the history of physics of the last century.

Probably you misunderstood my question.
I am not asking about philosophical implications of determinism. I am asking what can be predicted given all the technical limitations we have today.

For example, we have unpolarized beam of light and we pass it trough two polarizers. What determines intensity of light after second polarizer (given some relative angle between their polarization axes)?
You said there are no hidden variables. Does it mean that in my example two polarizers are somehow phase locked?

For instance read the paper. Your question is not sufficiently specific. With that quantization prescription you can easily solve Schrödinger problems, superconductivity and it seems to give an intuitive interpretation of the AdS/CFT.

I read the paper (at least partially). I did not see the simplification you claim. Therefore I asked you to demonstrate it with some example.

 

[naturale]

Probably you misunderstood my question.
I am not asking about philosophical implications of determinism. I am asking what can be predicted given all the technical limitations we have today.

For example, we have unpolarized beam of light and we pass it trough two polarizers. What determines intensity of light after second polarizer (given some relative angle between their polarization axes)?
You said there are no hidden variables. Does it mean that in my example two polarizers are somehow phase locked?

Sorry but I still don't understand your question. Polarization is an effect of transverse classical waves (fields) and the theory is based on fields (there are not \hbar involved). I don't see why you need "hidden variables" for that and what you mean with "phase locked".

I read the paper (at least partially). I did not see the simplification you claim. Therefore I asked you to demonstrate it with some example.

Quantization of relativistic fields without using ladder operators or the derivation of path integral as interference or classical paths ("without relaxing the classical variational principle") are simplifications in your opinion?

 

[zonde]

Sorry but I still don't understand your question. Polarization is an effect of transverse classical waves (fields) and the theory is based on fields (there are not \hbar involved). I don't see why you need "hidden variables" for that and what you mean with "phase locked".

Polarization is this "hidden variable" as it concerns Bell tests using photon polarization.
If you say that "polarization is an effect of transverse classical waves" then it contradicts your statement that there are no hidden variables (as it concerns Bell inequalities).
That's the reason why I asked if polarizers are "phase locked" because I got impression that you are saying that there are no such thing as classical polarization of photons.

Quantization of relativistic fields without using ladder operators or the derivation of path integral as interference or classical paths ("without relaxing the classical variational principle") are simplifications in your opinion?

Can't say anything about quantization of relativistic fields.

About the derivation of path integral - isn't it always derived as interference?
Only in this case it works at the scale of single period of de Broglie internal clock if I understand it correctly.
Classical paths are great. They appear at the scale bigger then de Broglie internal clock, right?

Only there are effects similar to those from small scale at larger scales. Is there anything about that? I believe that they necessarily involve interaction between individual particles and larger systems that we treat as measurement equipment.

 

[naturale]

Polarization is this "hidden variable" as it concerns Bell tests using photon polarization.
If you say that "polarization is an effect of transverse classical waves" then it contradicts your statement that there are no hidden variables (as it concerns Bell inequalities).
That's the reason why I asked if polarizers are "phase locked" because I got impression that you are saying that there are no such thing as classical polarization of photons.

Classical electromagnetic field has polarization without involving hidden-variables, no contradictions here. In that case it could be quantized by imposing periodic boundary conditions but the phase of the polarization depends on the the fast dynamics of the de Broglie internal clocks (of the sources for instance).

[/QUOTE]
Can't say anything about quantization of relativistic fields.

Knowledge of quantum field theory is necessary to understand that theory. However you can try to read it even if you do know quantum field theory. The formalism, as I was saying, is very simplified with respect the usual quantum field theory. Essentially it is used Fourier transform on a compact interval and relativistic wave equation.

About the derivation of path integral - isn't it always derived as interference?

Classically there is only a single path between an initial and final point. To have interference in the Feynman formulation you have to assume "off-shell" paths, "relaxing" the classical variational principle. The interference in the Feynman formulation can't be justified classically. But if you assume intrinsic periodicities you have many possible paths with different winding numbers (in a cylinder you can link to point with infinite paths). They are all classical paths and, as shown in that paper, they reproduce the Feynman path integral. That's the fundamental different between the two approaches.

Only in this case it works at the scale of single period of de Broglie internal clock if I understand it correctly.
Classical paths are great. They appear at the scale bigger then de Broglie internal clock, right?

Only there are effects similar to those from small scale at larger scales. Is there anything about that? I believe that they necessarily involve interaction between individual particles and larger systems that we treat as measurement equipment.

Probably you have to read completely the paper to have a complete idea of the theory. You will see that investigating a "de broglie internal clock" at time scales smaller than its periodicity you have a wave description. In this case the periodic boundary condition can be neglected. In the opposite limit you have a particle description since the effect of the periodic constraint is important. This description is totally consistent with ordinary quantum field theory. Think to the fact that the classical description of electromagnetism is in terms of waves and the classical description of massive fields is in terms of particles.

 

[DevilsAvocado]

(Forgive me for "bumping" in again... it’s late, we won the football match, and I had a beer [or two?], and if I’m mumbling you know why...)

Just some minor comments:

In a different reference system the "de Broglie internal clock" of that massive particle transforms according to Lorentz.

Okay, that explains it, "dynamics are too fast to be observe (~ 10^20s )" means relativistic seconds, right?

Since there are no hidden-varialbes and an there is exact matching with ordinary QM (as Feynman said "same equation, same physics") the EPR experiment based on this deterministic theory should reproduce the same predictions of QM.
...
As far as I can see there is local realism (but I am not sure if this is the correct interpretation of the theory).

Okay, if the "new quantization method" predicts the same results as QM and local realism still hold, that must mean standard QM is somewhat 'wrong'... which is very interesting. (I’ll read the paper tomorrow and see if I make the same conclusion.)

...

I stumble over this article which is very exciting:

"[URL catch sight of trembling particle – physicsworld.com

[/URL]

And a sign that is strongly "correlated" is that it’s commented by "dolce". Can it be anybody else than Donatello Dolce??

As far I know evidences of this "periodic phenomenon" was first conjectured by de Broglie in 1924 and strictly related to the rest mass of any generic particle (not only fermions). It is called de Broglie internal clock and has been indirectly observed in a recent experiment. The reference is:

P. Catillon, N. Cue, M. J. Gaillard, R. Genre, M. Gouan`ere, R. G. Kirsch, J.-C. Poizat,
J. Remillieux, L. Roussel, and M. Spighel, “A Search for the de Broglie Particle Internal Clock by Means of Electron Channeling,” Foundations of Physics 38 (July, 2008) 659–664.

De Broglie associated a frequency to the energy of the quanta through the Planck constant: E = h v. Since the energy at rest is the mass of the particle E = m c^2, there is an intrinsic frequency associated to the mass of every elementary massive field M c^2 = h v. Actually, for the electron this frequency is 10^21 Hz.

Moreover, according to this paper the Zitterbewegung was originally discussed by Schrodinger in 1930. The de Broglie internal clock has recently inspired a novel and deterministic field quantization method.
Edited by dolce on Feb 3, 2010 11:23 PM.

Just a late-night-thought:

This (internal) trembling motion of an elementary particle is new to me (extern = not new = heat). I always thought that an elementary particle should be regarded as a "point". Isn’t this vibration a strong indication (proof?) that elementary particles are vibrating strings...?

This is also very interesting in the physicsworld.com article:

The researchers found that changes to the particle's effective mass while its momentum was kept constant led to the disappearance of zitterbewegung in the non-relativistic and highly relativistic limits (large and small effective masses, respectively). However, the quivering motion was clearly present in the regime between these limits.

Does this mean the quivering vibrating "string behavior" is related to mass?? Is mass the key to the transition between QM and classical behavior??

Maybe silly...

 

[naturale]

(Forgive me for "bumping" in again... it’s late, we won the football match, and I had a beer [or two?], and if I’m mumbling you know why...)

Just some minor comments:



Okay, that explains it, "dynamics are too fast to be observe (~ 10^20s )" means relativistic seconds, right?

Right! Thread https://www.physicsforums.com/showthread.php?t=425312"". The time periodicity in the rest frame for an electron is h/M c^2 = 10^-20 s (10^20 Hz). But if you give energy to the particle, the periodicity is even faster h/E < h / M c^2 since E > M c^2 , where M is the rest mass. For heavier masses the periodicity is faster.

Okay, if the "new quantization method" predicts the same results as QM and local realism still hold, that must mean standard QM is somewhat 'wrong'... which is very interesting. (I’ll read the paper tomorrow and see if I make the same conclusion.)

This means that quantum mechanics is an emerging phenomenon. It is the statistical description of too fast periodic dynamics.

I stumble over this article which is very exciting:

Physicists catch sight of trembling particle – physicsworld.com

And a sign that is strongly "correlated" is that it’s commented by "dolce". Can it be anybody else than Donatello Dolce??



Just a late-night-thought:

This (internal) trembling motion of an elementary particle is new to me (extern = not new = heat). I always thought that an elementary particle should be regarded as a "point". Isn’t this vibration a strong indication (proof?) that elementary particles are vibrating strings...?

This is also very interesting in the physicsworld.com article:


Does this mean the quivering vibrating "string behavior" is related to mass?? Is mass the key to the transition between QM and classical behavior??

Maybe silly...

Actually there is a deep analogy with string theory. The assumption of compact time (time periodicity) implies compact proper time or vice vera, according to Lorentz. Compact proper time means that the worldline parameter of the field is compact and it plays the role of the compact worldline parameter of strings.

 

[DevilsAvocado]

(Still reading...)

But I think I’ve found one important answer.

Okay, if the "new quantization method" predicts the same results as QM and local realism still hold, that must mean standard QM is somewhat 'wrong'... which is very interesting. (I’ll read the paper tomorrow and see if I make the same conclusion.)

This means that quantum mechanics is an emerging phenomenon. It is the statistical description of too fast periodic dynamics.

Compact Time and Determinism for Bosons: foundations (page 5)

It is important to note that, in our theory, by supposing that the quantum behavior arises from periodicity boundary conditions, we are avoiding the introduction of hidden variables and at the same time we are implicitly introducing a non-locality, so that our model is not constrained by Bell’s theorem [31].

Aha! Non-locality is the answer!

Why do I like this thing, more and more...

 

[naturale]

Compact Time and Determinism for Bosons: foundations (page 5)

It is important to note that, in our theory, by supposing that the quantum behavior arises from periodicity boundary conditions, we are avoiding the introduction of hidden variables and at the same time we are implicitly introducing a non-locality, so that our model is not constrained by Bell’s theorem [31].

Aha! Non-locality is the answer!

Why do I like this thing, more and more...

Yes, you are right. But this kind of non-locality is in agreement with relativistic causality.
Pag 20 "On the other hand the periodic conditions in eq.(3) can be regarded as an element of non locality (which is consistent with relativistic causality) in the theory." The reason is that the propagation of the energy is interpreted as a propagation of variation of periodicity (T=h/E) which is the "element of non locality in the theory".

Have a nice reading!

 

[zonde]

Classical electromagnetic field has polarization without involving hidden-variables, no contradictions here. In that case it could be quantized by imposing periodic boundary conditions but the phase of the polarization depends on the the fast dynamics of the de Broglie internal clocks (of the sources for instance).

I do not understand what you are saying here.
So classical electromagnetic field has polarization. Fine.
Now what is "phase of polarization"?

 

[naturale]

I do not understand what you are saying here.
So classical electromagnetic field has polarization. Fine.
Now what is "phase of polarization"?

I think your problem is not polarization, but the entanglement of polarized photons, isn't it?
In this case you must think to the EPR experiment by replacing the hidden-variable with some sort of deterministic dynamics that doesn't involve hidden variable. Shortly, imagine that the polarization of the two photons can be for instance determined (at the moment of the emission) by deterministic dynamics intrinsically too fast to be resolved experimentally (of the source)...

 

[zonde]

I think your problem is not polarization, but the entanglement of polarized photons, isn't it?

No.

In this case you must think to the EPR experiment by replacing the hidden-variable with some sort of deterministic dynamics that doesn't involve hidden variable. Shortly, imagine that the polarization of the two photons can be for instance determined (at the moment of the emission) by deterministic dynamics intrinsically too fast to be resolved experimentally (of the source)...

I have imagined that before and it didn't make sense then and there is nothing different now.
The problem is that polarizer apparently can resolve those hypothetical dynamics and give quite certain outcome.

 

[granpa]

http://physicsworld.com/cws/article/news/41352

The researchers found that changes to the particle's effective mass while its momentum was kept constant led to the disappearance of zitterbewegung in the non-relativistic and highly relativistic limits (large and small effective masses, respectively). However, the quivering motion was clearly present in the regime between these limits.

so zitterbewegung is somehow related to effective mass.

 

[naturale]

The problem is that polarizer apparently can resolve those hypothetical dynamics and give quite certain outcome.

http://physicsworld.com/cws/article/news/41352
so zitterbewegung is somehow related to effective mass.

Yes. A de Broglie clock at rest has period T=h/M c^2. It can be used to define mass. For the electron it is 10^-20 s. The zitterbewegung model is based on the same idea.

The problem is that polarizer apparently can resolve those hypothetical dynamics and give quite certain outcome.

I have no idea if technically a polarizer can resolve dynamics faster than 10^-20 s.
From the physicsworld's article it seems hard to have such a resolution in time.

 

[zonde]

I have no idea if technically a polarizer can resolve dynamics faster than 10^-20 s.
From the physicsworld's article it seems hard to have such a resolution in time.

And ... how do you describe measurements involving pure states? Like those described by http://en.wikipedia.org/wiki/Malus_law#Malus.27_law_and_other_properties"?

 

[naturale]

And ... how do you describe measurements involving pure states? Like those described by http://en.wikipedia.org/wiki/Malus_law#Malus.27_law_and_other_properties"?

I think so. The important thing is that the effective description that you obtain for that theory is in terms of the usual Hilbert eigenstates and Hamiltonian time evolution, see pag.15 of the paper.

 

[zonde]

I think so. The important thing is that the effective description that you obtain for that theory is in terms of the usual Hilbert eigenstates and Hamiltonian time evolution, see pag.15 of the paper.

Malus law utilizes classical variables to describe polarization.
Polarization axis of first polarizer is described in real space, polarization axis of second polarizer is described in real space, polarization axis of light is described in real space.
So polarization is classical variable. In EPR case you have mixed state instead of pure state and therefore polarization is hidden.

 

[naturale]

But also the periodic fields is a superposition of pure states, it can written in terms of Hilbert eigenstates! See eq.(31) for the definition of a generic Hilbert state and eq.(41) for the definition of the expectation value of an observable. Why don't you read the paper instead of guessing what is wrong or doing riddles. There you can find all the answers you need.

 

[zonde]

Your logic is unbeatable:
1) You are right.
2) If I think that you are wrong I should reread the paper and proceed back to point 1.

 

[naturale]

If you want to criticize something, you need knowledge of it. Otherwise I should post the whole paper in this forum to replay to your question.
My logic is that:
1) you read the paper considering that it has passed a serious peer reviewed process.
2) if you see that there is something wrong (on the base of what you read and not on the base of what you imagine there is written) you can do all the criticisms that you what. Serious criticisms are welcome!
Since, as you said, you can't say anything about quantization of relativistic fields, I really doubt that you are able to do serious criticisms to that theory. So I add a zero point:
0) you should study quantum field theory.

 

[zonde]

If you want to criticize something, you need knowledge of it.

Agreed.
So what knowledge you have about EPR paradox, Bell inequalities, CHSH inequalities, actual Bell tests using polarization entangled photons?

Otherwise I should post the whole paper in this forum to replay to your question.
My logic is that:
1) you read the paper considering that it has passed a serious peer reviewed process.
2) if you see that there is something wrong (on the base of what you read and not on the base of what you imagine there is written) you can do all the criticisms that you what. Serious criticisms are welcome!
Since, as you said, you can't say anything about quantization of relativistic fields, I really doubt that you are able to do serious criticisms to that theory. So I add a zero point:
0) you should study quantum field theory.

Please understand that I do not intend to criticize idea that quantization results from "de broglie internal clock". I think that this idea is very sound.
I however say that discarding hidden variables does not make Quantum mechanics consistent. That concerns mainly correspondence between QM and physical reality. And for that deeper knowledge of relativistic quantum field theory is not required. It is enough to know some predictions of QM and how correspondence with physical reality is established in case of those predictions.

 

[naturale]

Agreed.
So what knowledge you have about EPR paradox, Bell inequalities, CHSH inequalities, actual Bell tests using polarization entangled photons?

Enough to say that the assumption of de Broglie clocks allows an EPR gedanken experiment without involving hidden variables in order to fulfill Bell or CHSH inequalities which can be tested by using polarized photons. From a mathematical point of view, the quantum states, superposition of pure states, are perfectly reproduced by quantizing a field by periodic boundary conditions. But don't ask me how this can be interpret in words. I have to think about that.

Please understand that I do not intend to criticize idea that quantization results from "de broglie internal clock". I think that this idea is very sound.
I however say that discarding hidden variables does not make Quantum mechanics consistent.

Well, about this point I go back to the Bell theorem and I remember you that theories with local hidden variable doesn't make quantum mechanics. More. from, http://arxiv.org/abs/0904.1655, State-independent experimental test of quantum contextuality
G. Kirchmair, F. Zähringer, R. Gerritsma, M. Kleinmann, O. Gühne, A. Cabello, R. Blatt, C. F. Roos
(Submitted on 10 Apr 2009 (v1), last revised 5 May 2009 (this version, v2))
Journal reference: Nature 460, 494 (2009)
DOI: 10.1038/nature08172 ,
it seems that generic (local or not) hidden variables have problems.

That concerns mainly correspondence between QM and physical reality. And for that deeper knowledge of relativistic quantum field theory is not required. It is enough to know some predictions of QM and how correspondence with physical reality is established in case of those predictions.

I do not agree completely with this. In fact the most peculiar quantum behaviors arise in the relativistic limit. Electromagnetic field is always relativistic and it is quantized at high frequencies. The quantum limit of massive particle is the relativistic limit. This is clear from the Feynman path integral. To understand the deepest nature of quantum physics one should investigate the relativistic limit, and more generically, the relativistic meaning of time. If you are interested on the non relativistic quantum mechanics you may read par.2.4 of 0903.3680v5 and the appendixes of 0903.3680v4. There are showed simple applications to Schrödinger problems.

 

[Dickfore]

From what I was able to understand by skimming through the text, the author is led by the discreteness of the Matsubara frequencies for the Fourier transform of the fermionic and bosonic Green's functions in the imaginary time formalism. It is true that this is a consequence of the periodicity in imaginary time, however, this periodicity is purely formal due to the similar form of the time evolution operator and the canonical statistical operator.

Eq.(2) seems to impose the periodic boundary conditions with respect to time in this way. However, I suspect that this actually ruins the Lorentz invariance. Namely, there is only one inertial frame where this condition can be stated in the given manner. In all other frames, these space-time points are not synchronous.

 

[naturale]

From what I was able to understand by skimming through the text, the author is led by the discreteness of the Matsubara frequencies for the Fourier transform of the fermionic and bosonic Green's functions in the imaginary time formalism. It is true that this is a consequence of the periodicity in imaginary time, however, this periodicity is purely formal due to the similar form of the time evolution operator and the canonical statistical operator.

In physics the boundary between mathematical tricks and physical reality is very tiny. But, w.r.t Matsubara, in that theory it is the real (minkowskian) time to be periodic and not the imaginary (euclidean) one. If you want you can think to the assumption of intrinsic periodic fields as a mathematical trick.

Eq.(2) seems to impose the periodic boundary conditions with respect to time in this way. However, I suspect that this actually ruins the Lorentz invariance. Namely, there is only one inertial frame where this condition can be stated in the given manner. In all other frames, these space-time points are not synchronous.

This is for sure the first thing that comes to mind. The author takes particular care to show that the consistence with Lorentz invariance and respect relativistic causality, see par.2.4 and fig.3.
It is important to note that together with time periodicity T_t, induced spatial periodicities \vec\lambda_x must be considered. The space-time periodicities are T^\mu = \{ c T_t , \vec\lambda_x \} . They are space-time intervals and therefore they transform according to Lorentz.

From the abstract: "The theory, whose fundamental set-up is presented in this paper, turns out to be consistent with special relativity and in particular respects causality." This can be seen in various ways.
1) Basically, periodic boundary conditions minimize the relativistic action at the boundaries. In this way the relativistic symmetries of the action are preserved.
2) The space-time periodicities are not static, of course! They are the usual de Broglie periodicities, T^\mu = h / p_\mu. They are dynamical by construction. This is similar to the fact that the euclidean periodicity of in field theory at finite temperature is "thermodynamical": when temperature changes, euclidean periodicity changes. In that theory when energy-momentum p_\mu changes through interaction or Lorentz transformations, the space-time periodicities T^\mu change as well. Since that field theory is based upon relativistic waves propagating with usual green function, the four-momentum changes according to the retarded potentials. Therefore the periodicities changes in agreement with relativistic causality.
3) The space-time periodicities T^\mu = h / p_\mu form a controvariant four vector in order to leave the phase of the field invariant under periodic translations. By definition space-time periodicity T^\mu means: exp[- i x_\mu p^\mu] =exp[-i (x_\mu + T_\mu) p^\mu].
4) At a more fundamental and conceptual level you have an highlighting justification. From par.3.2: "Paraphrasing the Newton’s law of inertia [p_\mu = const] and the de Broglie hypothesis of periodicity [T^\mu = h / p_\mu], we assume that every isolated elementary system (every free elementary field) has persistent and constant [space-]time periodicity (as long as it doesn’t interact)" . "But, as much as the Newton’s law of inertia doesn’t imply that every point particle goes in a straight line, our assumption of periodicity does not mean that the physical world should appear to be periodic. In fact there is not a single static periodicity which would serve as privileged reference. On the contrary elementary systems (that we represent as fields) at different energies have different periodicities.21" "Furthermore, through interactions the elementary systems pass from a periodic regime to another periodic regime, forming in general ergodic and even more chaotic evolutions."

Nice and easy!

The amazing point is that the assumption of periodicity provides a quantization condition for relativistic fields and the resulting theory matches ordinary quantum field theory!

P.S: There are problems with the mathematical environment of the Forum when you "go advanced" and see "preview".

 

[Dickfore]

This is for sure the first thing that comes to mind. The author takes particular care to show that the consistence with Lorentz invariance and respect relativistic causality, see par.2.4 and fig.3.

It is interesting you say that the author pays particular attention to this issue (in paragraph 1.3, not 2.4), but he only devotes barely a page of a 30 page booklet. In comparison, the Introduction is four pages long.

I stand on my assertion that eqn. (3) is not Lorentz invariant.

Also, what does "massive field rest frame" actually mean?

 

[zonde]

I stand on my assertion that eqn. (3) is not Lorentz invariant.

This assertion seems valid.
Under Lorentz transformation spacetime interval is invariant when it has the same "slope" as speed of light.
So if we rewrite eqn.(3) like that:
\Phi(x,t)\equiv\Phi(x+\lambda ,t+2\pi R_t)
or like that:
\Phi(x-x_0,t)\equiv\Phi(x_0-x+\lambda ,t+2\pi R_t)
we would have Lorentz invariance.
At least so it seems to me.

 

[naturale]

It is interesting you say that the author pays particular attention to this issue (in paragraph 1.3, not 2.4), but he only devotes barely a page of a 30 page booklet. In comparison, the Introduction is four pages long.

No. The issue is discussed throughout the whole paper. Par.1.3 (Lorentz transformations and covariance) and par.1.4 (Retarded potential and causality) are focalized essentially on that. But also par.1.1 and par.1.2 are devoted to build a relativistic field theory. Par.3.2 shows the conceptual meaning of the assumption of intrinsic periodicities.

I stand on my assertion that eqn. (3) is not Lorentz invariant.

Eqn.3 or eqn.2 are not covariant, right! but read few line above eqn.2: "For simplicity in this preliminary discussion we will concern only with time dimension boundaries." and few lines above par.1.1 : "Provided analogous periodic conditions along the spatial and, for massive fields along the proper time dimensions, such as to guarantee covariance, we shall see that this theory of periodic fields is consistent with special relativity." After that the author shows that time periodicity induces spatial periodicity "such as to guarantee covariance", see eqn.10, and for massive fields, proper time periodicity eqn.20 or eqn.16. "Induced" means that if you assume a relativistic wave with a give time period, of curse you automatically have a spatial periodicity.

Also, what does "massive field rest frame" actually mean?

[/QUOTE]

I can't find this expression in the arXiv version. Probably it means "the rest frame of the massive field". Intrinsic time periodicity for a massive field implies intrinsic periodicity of the proper time, see fig.(2). For massless fields the proper time periodicity is infinite, see.fig.1 (the photon can't be observed in its rest frame). The relation is
T_\tau^{-2} = T_t^{-2} - c^2 \lambda_x^{-2}, where T_\tau = proper time periodicity, T_t time periodicity, \lambda_x spatial periodicity. If you multiply this for "h" you obtain M^2 c^4 = E^2 - p^2 c^2, In fact h/T^2_\tau = M^2 c^4 eqn.16, h/T^2_t = E^2 eq.(8), h^2 c^2 / \lambda_x^2 = p^2 c^2 eqn.10 (T= 2 \pi R).

 

[naturale]

Right Zonde! That is the periodicity that you must consider (if you meant x -x_0 in both sides of the second equation)! The author says "there is a single periodicity which is induced to the other dimensions". If you start from time periodicity and you impose relativistic kinematics you necessarily obtain spatial periodicity, and proper time periodicity for massive objects. Defining T^\mu = \{c T_t, \vec \lambda_x \} you can write it in covariant way
\Phi(x^\mu_0)\equiv\Phi(x^\mu_0+T^\mu).

 

[zonde]

Enough to say that the assumption of de Broglie clocks allows an EPR gedanken experiment without involving hidden variables in order to fulfill Bell or CHSH inequalities which can be tested by using polarized photons. From a mathematical point of view, the quantum states, superposition of pure states, are perfectly reproduced by quantizing a field by periodic boundary conditions. But don't ask me how this can be interpret in words. I have to think about that.

If you want to defend your statement you have to provide some arguments and should be ready to argue against counter arguments.

Well, about this point I go back to the Bell theorem and I remember you that theories with local hidden variable doesn't make quantum mechanics. More. from, http://arxiv.org/abs/0904.1655, State-independent experimental test of quantum contextuality
G. Kirchmair, F. Zähringer, R. Gerritsma, M. Kleinmann, O. Gühne, A. Cabello, R. Blatt, C. F. Roos
(Submitted on 10 Apr 2009 (v1), last revised 5 May 2009 (this version, v2))
Journal reference: Nature 460, 494 (2009)
DOI: 10.1038/nature08172 ,
it seems that generic (local or not) hidden variables have problems.

Well you have to take in account something about no-go theorems and in particular their experimental verification.
Traditional theorems make positive statements and we know very well how to verify them experimentally. The question is can we do it the same way with no-go theorems.

Now imagine that we have space where we encircle some subspace and make a statement that some X is withing that enclosed area (A). To test this statement we have additional restriction that we can't use exactly the same subspace for testing purposes. We can only use bigger subspace (B) that encloses A or smaller subspace (C) that is enclosed within A.
Obviously for testing purposes we should use subspace C because if we would find out that X is within C it will be within A as well.

But now consider statement where we say that X is outside A.
Just as obvious that in this case for testing purposes we should use subspace B as in this case if we would find out that X is not within B it will not be within A as well.

What I want to say with this example is that requirement to close detection and locality loopholes in the same experiment is not just folly of proponents of local realism but quite valid requirement.

Of course it is useful to analyze even non-conclusive experiments but they can not be considered as a proof of violation of local realism.

I do not agree completely with this. In fact the most peculiar quantum behaviors arise in the relativistic limit. Electromagnetic field is always relativistic and it is quantized at high frequencies. The quantum limit of massive particle is the relativistic limit. This is clear from the Feynman path integral. To understand the deepest nature of quantum physics one should investigate the relativistic limit, and more generically, the relativistic meaning of time. If you are interested on the non relativistic quantum mechanics you may read par.2.4 of 0903.3680v5 and the appendixes of 0903.3680v4. There are showed simple applications to Schrödinger problems.

I do not quite see your point. Entanglement is explored mainly within non relativistic setups i.e. there is laboratory frame and everything is analyzed within that frame. And your statement that I am questioning is about entanglement.

 

[twofish-quant]

But also the periodic fields is a superposition of pure states, it can written in terms of Hilbert eigenstates! See eq.(31) for the definition of a generic Hilbert state and eq.(41) for the definition of the expectation value of an observable.

eq.(31) and eq.(41) will work for a single particle, but the problem with Bell's inequality comes up when you have a field consisting of multiple particles where you have correlations between the that you can't get assuming that the particles are independent probabilistically.

There you can find all the answers you need.

I did. It's a *very* interesting paper, and it's *possible* that you can structure the fields in a way that you get back quantum mechanics, but that hasn't been done yet, and eq. (31) to eq.(41) is insufficient to convince me that they've resolved the Bell's theorem issues.

 

[twofish-quant]

Right Zonde! That is the periodicity that you must consider (if you meant x -x_0 in both sides of the second equation)! The author says "there is a single periodicity which is induced to the other dimensions". If you start from time periodicity and you impose relativistic kinematics you necessarily obtain spatial periodicity, and proper time periodicity for massive objects. Defining T^\mu = \{c T_t, \vec \lambda_x \} you can write it in covariant way
\Phi(x^\mu_0)\equiv\Phi(x^\mu_0+T^\mu).

I think there is a way of doing an experimental test of this. You use the "strobe light" effect. Suppose you have something that is periodic at period n where n is much smaller than what you can detect. If you perform an experiment that samples a particle at 100000.1 n, then you ought to see a systematic strobe light effect.

I'm still not sure how you get Bell's inequality to work. The problem is that the field that you are looking at may be periodic, but you can control the experiment so that time (and hence the state when the particle his the polarizer) is random.

 

[zonde]

if you meant x -x_0 in both sides of the second equation

No I meant what I wrote. Otherwise particle would move at speed of light but that's the first equation. You can apply second equation two times and you get:
\Phi(x-x_0,t)\equiv\Phi(x_0-x+\lambda ,t+2\pi R_t)\equiv\Phi(x-x_0,t+4\pi R_t)
So you have particle at rest with "trembling" along x direction.

 

[naturale]

I try to adapt the ERP experiment to our case.

Let's suppose a coin with arrow up and arrow down on the two sides respectivelly. This coin rolls with period 10^-21 s (~ ZHz). This rolling is not given by any hidden variable, but it is given by the intrinsic periodicity T associated to the mass of the electron at rest which is T~10^-21 s . We must suppose that the coin rolls in the dark and suddenly a stroboscopic light is turned on for an infinitesimal instant. This corresponds to the emission of the polarized photons from the electron. Then Alice and Bob see up and down or down and up, but if their resolution in time is poor they can predict the outcomes only statistically, and the probabilities are 50% and 50%. As Alice see the up arrow, she automatically knows that Bob will see the down arrow or vice versa. Since no hidden variables are involved, we are not in the hypothesis of the Bell theorem and the model can in principle satisfy the Bell inequality.

To resolve the deterministic mechanics of such a coin you need to measure time with a clock whose period is smaller than 10^-21 s (the emission of the polarized photon necessarily involved an electron). To have a precision of T*100000.1 you need a clock with periodicity faster than 10^-22 s in order to be sure to turn on the stroboscopic light at the right instant. The cesium atomic clock has a period of 10^-10 s. The difference between the cesium atomic clock and the de broglie clock of an electron is similar to the difference between a year and the age of the universe! I fear that it is impossible to achieve this time resolution. But if you are able to build such a clock you could in principle predict the outcomes.

 

[naturale]

No I meant what I wrote. Otherwise particle would move at speed of light but that's the first equation. You can apply second equation two times and you get:
\Phi(x-x_0,t)\equiv\Phi(x_0-x+\lambda ,t+2\pi R_t)\equiv\Phi(x-x_0,t+4\pi R_t)
So you have particle at rest with "trembling" along x direction.

No! You have not to considering a particle moving between 0 and T_t, but a string vibrating in space-time with intrinsic space-time periodicities or in compact space-time dimensions. Think to a guitar string, for instance or to the quantization of a "particle" in an infinite well.

The correct condition that you must impose (if you suppose no interactions) is
\Phi(x,t)\equiv\Phi(x+\lambda ,t+T_t)\equiv\Phi(x+n \lambda,t+n&#039; T_t) with n and n' integer numbers (if in a certain space-time point the string interact the periodicities change).

 

[zonde]

I try to adapt the ERP experiment to our case.

Let's suppose a coin with arrow up and arrow down on the two sides. This coin rolls with period 10^-21 s (~ ZHz). This rolling is not given by any hidden variable, but it is given by the intrinsic periodicity T associated to the mass of the electron at rest which is T~10^-21 s . We must suppose that the coin rolls in the dark and suddenly a stroboscopic light is turned on for an infinitesimal instant. This corresponds to the emission of the polarized photons from the electron. Then Alice and Bob see up and down or down and up, but if their resolution in time is poor they can predict the outcomes only statistically, and the probabilities are 50% and 50%. As Alice see the up arrow, she automatically knows that Bob will see the down arrow or vice versa. Since no hidden variables are involved, we are not in the hypothesis of the Bell theorem and the model can in principle satisfy the Bell inequality.

Photons are produced at place S and time T_0. They are measured at place A after time T_1 and at place B after time T_2. You measure photons after two different time periods.
If we take your dice rolling in the dark then we make observations at two different times. There is no reason so far why they should produce the same result.

 

[naturale]

Photons are produced at place S and time T_0. They are measured at place A after time T_1 and at place B after time T_2. You measure photons after two different time periods.
If we take your dice rolling in the dark then we make observations at two different times. There is no reason so far why they should produce the same result.

Use a little bit of imagination. I meant that the stroboscopic light is tuned on and shows the coin at place S and time T_0 for an infinitesimal instant. Alice looks at a face of the coin and B looks at other side. Alice in A and at time T_1 (that is after a time delay T_1 - T_0 depending on how far she is from the coin) sees the face (the photon emitted by the that face of the coin at T_0 and S) with an up arrow (down arrow) whereas Bob in B sees the other face (the photon emitted by the other face at T_0 and S) with the down arrow (up arrow) at time T_2. Alice knows at T_1 what Bob will see at time T_2. It is clear now?

 

[Dickfore]

No. The issue is discussed throughout the whole paper. Par.1.3 (Lorentz transformations and covariance) and par.1.4 (Retarded potential and causality) are focalized essentially on that. But also par.1.1 and par.1.2 are devoted to build a relativistic field theory. Par.3.2 shows the conceptual meaning of the assumption of intrinsic periodicities. Eqn.3 or eqn.2 are not covariant, right! but read few line above eqn.2: "For simplicity in this preliminary discussion we will concern only with time dimension boundaries." and few lines above par.1.1 : "Provided analogous periodic conditions along the spatial and, for massive fields along the proper time dimensions, such as to guarantee covariance, we shall see that this theory of periodic fields is consistent with special relativity." After that the author shows that time periodicity induces spatial periodicity "such as to guarantee covariance", see eqn.10, and for massive fields, proper time periodicity eqn.20 or eqn.16. "Induced" means that if you assume a relativistic wave with a give time period, of curse you automatically have a spatial periodicity.

That may be so, but now I find an even deeper problem. From the first paragraph on p.9:

We approach the theory as a Kaluza-Klein theory for a massless five-dimensional Klein-
Gordon field with periodic extra-dimension s and periodic real time. In fact the resulting
five-dimensional metric is dS^{2} = c^{2} dt^{2} - d\mathbf{x}^{2} - ds^{2} = 0 , so that assuming s = c \tau we recover the usual four-dimensional Minkowskian metric eq.(1). For this reason we will say
that the proper time acts as a “virtual” extra-dimension4 whose length is therefore fixed
by the time periodicity in the rest frame.

Now, there are 3 IMPORTANT, but IMPLICIT assumptions made here:

1. That space time is actually five dimensional. This would mean that the general Lorentz transformations belong to the group SO(1, 3 + 1) and this one has different irreducible representations from the ordinary SO(1, 3) group. Since the spin of the particles is exactly dependent on the representations of this group, the author could have at least given an effort to clarify this issue a bit more, since the whole subsequent derivation hinges on this fact;
2. That they only consider null geodesics dS^{2} = 0. I don't see any a priori reason for this and it is a huge constraint by itself. Saying the field is massless 5d is not an answer. The existence of a space-time metric between any two points should have nothing to do with the matter fields;
3. That one of the dimensions is compactified. In doing this, you essentially break the Lorentz invariance of the theory.

I can't find this expression in the arXiv version. Probably it means "the rest frame of the massive field". Intrinsic time periodicity for a massive field implies intrinsic periodicity of the proper time, see fig.(2). For massless fields the proper time periodicity is infinite, see.fig.1 (the photon can't be observed in its rest frame). The relation is
T_\tau^{-2} = T_t^{-2} - c^2 \lambda_x^{-2}, where T_\tau = proper time periodicity, T_t time periodicity, \lambda_x spatial periodicity. If you multiply this for "h" you obtain M^2 c^4 = E^2 - p^2 c^2, In fact h/T^2_\tau = M^2 c^4 eqn.16, h/T^2_t = E^2 eq.(8), h^2 c^2 / \lambda_x^2 = p^2 c^2 eqn.10 (T= 2 \pi R).

I meant specifically the continuation of the last paragraph from p.8 on p.9 and the footnote 3. A quote:

The key assumption for a massive relativistic field is that it is possible to choose a reference
system (the rest frame) where the real time and the proper time can be identified.3
Therefore, for massive fields, we must consider that the compactification of the real time
induces a compactification of the proper time, as well.

The basic characteristic of fields is that they can support excitations that propagate and carry certain momentum and energy. However, the number of excitations is essentially unlimited (except by the Pauli Exclusion Principle for fermionic fields). In this way, we might as well have two particle excitations moving in opposite directions. What is the rest frame of the field in this case?

 

[naturale]

That may be so, but now I find an even deeper problem. From the first paragraph on p.9:
Now, there are 3 IMPORTANT, but IMPLICIT assumptions made here:
That space time is actually five dimensional.

No. The parameter s is the worldline parameter, proportional to the proper time s = c \tau. It is not a "real" extra dimension, in fact it is called "virtual" extra dimension. This is a mathematical trick.
It is very interesting because it shows a deep dualism of that theory with the Kaluza-Klein theory. If you suppose a compact worldline parameter with length \lambda_s, by discrete Fourier transform and by using \hbar you obtain a quantized mass spectrum M_n = \frac{n h}{\lambda_s c}; exactly as a compact time dimension with length T_t(\mathbf p) gives a quantized energy spectrum E_n(\mathbf p) = n h / T_t(\mathbf p). In fact, this relation evaluated in the rest frame (\mathbf p = 0) gives the Kaluza Klein tower: E_n(0)= M_n c^2, see figure.2.b. The Kaluza Klein tower is the energy spectrum evaluated at \mathbf p = 0. From this you can obtain the energy spectrum in a generic reference system by Lorentz transformation. Figure.2.a shows how the time periodicity transforms from the rest frame to a generic frame. This implies that every level of the energy spectrum follows the relativistic dispersion relation as shown in figure.2.b. That's why eqn.19 is the sum over a single index n (and not a sum over several n indexes, one for every compact dimension). Eqn.19 is also an infinite sum of Klein-Gordon lagrangians. All these energy eigenmodes are the harmonic modes of the same field with periodicity T_t(\mathbf p) in a generic frame and they can't be separated. They are part of the same fields and not different fields as in the Kaluza-Klein theory. This is the main difference between the two.

This would mean that the general Lorentz transformations belong to the group SO(1, 3 + 1) and this one has different irreducible representations from the ordinary SO(1, 3) group. Since the spin of the particles is exactly dependent on the representations of this group, the author could have at least given an effort to clarify this issue a bit more, since the whole subsequent derivation hinges on this fact;

The author has actually tried to clarify this point. Read the last paragraph of par.2.3.

( A five dimensional Dirac field is a sum of left handed and right handed four dimensional Dirac fields (with spin 1/2). This is because the fifth component of the five dimensional Clifford algebra \Gamma^M is \Gamma^5 = - i \gamma^5 ( and \Gamma^\mu = \gamma^\mu ). In that paper, however, only bosons are considered.)

That they only consider null geodesics dS^{2} = 0. I don't see any a priori reason for this and it is a huge constraint by itself. Saying the field is massless 5d is not an answer. The existence of a space-time metric between any two points should have nothing to do with the matter fields;

A four dimensional massless field lives on the four dimensional light-cone ds^{2} = 0, which is a lower-dimensional surface. Similarly a massless five dimensional field eqn.15 lives on the five dimensional lightcone <br /> dS^{2} = c^{2} dt^{2} - d\mathbf{x}^{2} - ds^{2} = 0<br /> which is a four dimensional surface. There, a virtual five dimensional massless fields is supposed, which is not really a five dimensional field. Since the compact extra dimension is the compact worldline parameter, you obtain the Minkowski metric ds^{2} = c^{2} dt^{2} - d\mathbf{x}^{2}.
Consider the first half page of par.1.2 a mathematical trick whose meaning will be clear later. The reason is to write an action that automatically take into account that the proper-time is compact for massive fields. This is the hardest part from a mathematical point of view, but it is definitively consistent even though it may seem artificial.

The term "compact dimension" could be somehow misleading. If so, just replace it with "periodic dimension".

That one of the dimensions is compactified. In doing this, you essentially break the Lorentz invariance of the theory.
I meant specifically the continuation of the last paragraph from p.8 on p.9 and the footnote 3. A quote:

(Are you reading the found. phys. version of the paper and do you mean footnote.4?)

It is well know in extra dimensional theories that compact dimensions don't necessarily mean that the Lorentz (or the gauge) invariance is broken. Consider eqn.4. This is a theory in compact space-time dimensions but it is Lorentz invariant as long as you consider that also the boundary must be transformed. Also Eqn.6 is four dimensional Lorentz invariant even if it is a sum over three dimensional actions. In fact, as long as all the modes n are considered eqn.6 is equivalent to eqn.4. The Lorentz invariance is broken only if you cut the tower, that is only if you consider a finite number of eigenmodes.

The basic characteristic of fields is that they can support excitations that propagate and carry certain momentum and energy.

Do you mean the momentum and the energy of the quanta of the field?

However, the number of excitations is essentially unlimited (except by the Pauli Exclusion Principle for fermionic fields). In this way, we might as well have two particle excitations moving in opposite directions. What is the rest frame of the field in this case?

If those particles are the quanta of the field, they must be off-shell to have opposite directions. Otherwise they are described by different field with different frequencies and wave-vectors. In a periodic field the unlimited particles are its harmonic excitations, that is its energy eigenmodes. But this eigenmodes are all on-shell. There is no violations of the energy conservation and it is not necessary to relax the classical laws of physics (that's why it is a deterministic theory). The rest frame is where all them have zero momentum, that is when the field (which is the sum all the nergy eigenmodes) has infinite spatial periodicity (infinite spatial compactification length).


I can try to provide further explanations if necessary.

 

[twofish-quant]

We must suppose that the coin rolls in the dark and suddenly a stroboscopic light is turned on for an infinitesimal instant.

But there has to be one and only one strobe light in the universe right? If you have people doing measurements with independent strobe lights, then the difference in timings between the independent strobe lights will introduce dynamics.

Since no hidden variables are involved, we are not in the hypothesis of the Bell theorem and the model can in principle satisfy the Bell inequality.

Yes. If there is a single strobe light in the universe, then Bell's inequality works. However, I think I can be clever and come up with another experiment that causes issues.

Also, doesn't this require simultaneity?

To resolve the deterministic mechanics of such a coin you need to measure time with a clock whose period is smaller than 10^-21 s (the emission of the polarized photon necessarily involved an electron). To have a precision of T*100000.1 you need a clock with periodicity faster than 10^-22 s in order to be sure to turn on the stroboscopic light at the right instant.

You don't. The period between pulses can be much larger than 10^-21s. The important part is that the pulse itself be timed to within 10^22 s. You can do this with some sort of mirror. If I take a mirror and have a laser bounce back and forth, the difference in A->B and B->A can be tiny even through the time it takes for the laser to travel A->B is large.

The difference between the cesium atomic clock and the de broglie clock of an electron is similar to the difference between a year and the age of the universe!

So build a clock based on two electrons, or one based on one proton and one electron. If you can use a de broglie clock of an electron to time the observation of another electron, then you should be able to think of some sort of experimental difference with QM.

Also it doesn't matter that the cesium atomic clock has a huge number of cycles, as long as the time between cycles is less than one fraction of the de broglie clock.

I fear that it is impossible to achieve this time resolution.

To convince people that the theory is correct, then you have to make it possible, and I don't see any physical reason why it won't work.

 

[twofish-quant]

Alice knows at T_1 what Bob will see at time T_2. It is clear now?

No. The problem is that Alice and Bob aren't talking to each other so neither knows at what precise time the other is looking at the coin.

Let me ask this question. Suppose Alice and Bob both look at the coin a difference in interval that is several times smaller that the deBroglie clock period. i.e. we can create an experiment so that A looks at the coin, and then B looks at it 1s +/- 1.5x10^-26 second later.

If Alice sees something, then would it be possible to determine exactly what Bob sees?

Also what is the decoherence time? i.e. how long does it take for A or B to take a measurement.

 

[twofish-quant]

One reason that I like the paper is that I have a soft spot in my heart for Kaluza-Klein models and so when I read the paper, that was the first thing I thought of.

One thing that I find nice about the paper is that if the entire universe has another time dimension which extremely small then you can communicate quickly between two different parts of the universe that seems spatial separated.

One crazy idea is that it's believed that cosmic inflation was causes when something happened to cause 3 space dimensions to suddenly get big. So it would be interesting to think about what the universe would look like if there were a lot of time dimensions that are tightly wound out, and then something happened to cause the universe to massive expand in the time direction.

 

[naturale]

No. The problem is that Alice and Bob aren't talking to each other so neither knows at what precise time the other is looking at the coin.

With rolling coin I mean flipping coin. Probably the misunderstood is originated by this.

I am absolutely not says that A and B talk with each other. The only thing they know could be their position w.r.t. the coin, which is the source of entangled photons.

To define even better this gedanken experiment we must suppose that
0) when the stroboscopic light it turned on, the coin will be forced to be orientated in such a way that it shows a face to Alice and the other face to Bob.

In this way what Alice and Bob see is entangled, they see two different faces of the same coin in S and T_0. In this case Alice knows what Bob will see (or have seen) without speak each other.

Let me ask this question. Suppose Alice and Bob both look at the coin a difference in interval that is several times smaller that the deBroglie clock period. i.e. we can create an experiment so that A looks at the coin, and then B looks at it 1s +/- 1.5x10^-26 second later.

If Alice sees something, then would it be possible to determine exactly what Bob sees?Also what is the decoherence time? i.e. how long does it take for A or B to take a measurement.

Now I try to replay to you specific question. First let me point out that 1s is an "eternity" with respect to the De broglie clock of an electron. The mass of the electron 9.10938215(45)×10−31 kg is known with a precision of 8 digits. To know the number of periods of a electron de Broglie clock in 1s we should know the mass of the electron with a precision of 20 digits, and we are quit far from that!

So we must imagine that:
1) if we know the mass of the electron with precision > 20 digits
2) if we have a clock with precision > 26 digits [the precision of the cesium atomic clock is 10 digits]
3) if the stroboscopic light doesn't introduce an additional element of randomness
4) if the coin in the first half period shows up (down) and in the second half down (up) to Alice (Bob)
5) if in a 1s you suppose to know exactly that the coin flips an even (odd) of half periods.
6) if during that "eternity" of 1s the coin is completely isolated, i.e. its periodicity is not changed by interactions or thermal noise
7) if ...
8) if ...
9) if ...
...

In this case I would say that if Alice sees up and coin flips an even (odd) of half periods, then Bob will see down (up). So to speak, the can see the classical evolution of the coin.

If some of the above conditions are not fulfilled (decoherence), the outcomes can be only described statistically through the usual laws of quantum mechanics. The generic Hilbert state defined before eqn.(31) in this case is |\phi &gt; = 1 / \sqrt{2} (|up&gt;\otimes |down&gt; - |down&gt; \otimes |up&gt;), where \otimes is the tensor product of two pure states of the periodic fields described in the paper.

But this is only my guess, it is how I interpret that theory.

The author demonstrates that the Feynman path integral eq.(40) "has been obtained just assuming relativistic periodic waves without any further assumption". To me this is sufficient to say that the theory reproduces ordinary quantum mechanics. If this is true, I believe it is true also because the paper has been peer reviewed, there is nothing more to say.EDIT:

Also what is the decoherence time? i.e. how long does it take for A or B to take a measurement.

From wikipedia :

"Quantum decoherence:

In quantum mechanics, quantum decoherence (also known as dephasing) is the mechanism by which quantum systems interact with their environments to exhibit probabilistically additive behavior. Quantum decoherence gives the appearance of wave function collapse and justifies the framework and intuition of classical physics as an acceptable approximation: decoherence is the mechanism by which the classical limit emerges out of a quantum starting point and it determines the location of the quantum-classical boundary. Decoherence occurs when a system interacts with its environment in a thermodynamically irreversible way. This prevents different elements in the quantum superposition of the system+environment's wavefunction from interfering with each other."

I would say that in our case decoherence is a possible thermal noise such that one or more of the possible conditions above are not verified. Most likely condition 0) could be disturbed by the presence of thermal noise, other candidates are conditions 3), 4), 6), 7), 8), 9), ... .