# New quantization method

1. Aug 26, 2010

### 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 (Found. Phys.).

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."

arXiv:0903.3680v5 [hep-th]

Last edited: Aug 27, 2010
2. Sep 2, 2010

### zonde

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?

3. Sep 2, 2010

### naturale

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).

4. Sep 2, 2010

### zonde

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?

5. Sep 2, 2010

### 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).

Last edited: Sep 2, 2010
6. Sep 3, 2010

### zonde

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?

Give some simple example.

7. Sep 3, 2010

### 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 Susskind and Hawking on hard determinism.
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.

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.

Last edited: Sep 3, 2010
8. Sep 3, 2010

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...

9. Sep 3, 2010

### naturale

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

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

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.

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.

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

10. Sep 3, 2010

### zonde

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?

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.

11. Sep 3, 2010

### naturale

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".

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?

12. Sep 3, 2010

### zonde

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.

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.

13. Sep 3, 2010

### naturale

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.

14. Sep 3, 2010

(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...)

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

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.)

...

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...

15. Sep 4, 2010

### naturale

Right! Thread Deriving the De Broglie Wavelength". 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.

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

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.

Last edited: Sep 4, 2010
16. Sep 4, 2010

But I think I’ve found one important answer.

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

17. Sep 4, 2010

### naturale

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".

18. Sep 6, 2010

### zonde

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

19. Sep 6, 2010

### naturale

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)....

20. Sep 6, 2010

### zonde

No.
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.