new quantization method

naturale

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 spacial 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.


[/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
[tex]T_\tau^{-2} = T_t^{-2} - c^2 \lambda_x^{-2}[/tex], where [tex]T_\tau [/tex] = proper time periodicity, [tex]T_t[/tex] time periodicity, [tex]\lambda_x[/tex] spatial periodicity. If you multiply this for "h" you obtain [tex]M^2 c^4 = E^2 - p^2 c^2[/tex], In fact [tex]h/T^2_\tau = M^2 c^4[/tex] eqn.16, [tex]h/T^2_t = E^2[/tex] eq.(8), [tex]h^2 c^2 / \lambda_x^2 = p^2 c^2[/tex] eqn.10 [tex](T= 2 \pi R)[/tex].

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 [tex]T^\mu = \{c T_t, \vec \lambda_x \}[/tex] you can write it in covariant way
[tex]\Phi(x^\mu_0)\equiv\Phi(x^\mu_0+T^\mu)[/tex].

zonde

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

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 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

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.

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

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

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:
[tex]\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)[/tex]
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! 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
[tex]\Phi(x,t)\equiv\Phi(x+\lambda ,t+T_t)\equiv\Phi(x+n \lambda,t+n' T_t)[/tex] with n and n' integer numbers (if in a certain space-time point the string interact the periodicities change).

zonde

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

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

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:

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 [itex]dS^{2} = 0[/itex]. 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 meant specifically the continuation of the last paragraph from p.8 on p.9 and the footnote 3. A quote:

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

No. The parameter [tex] s [/tex] is the worldline parameter, proportional to the proper time [tex] s = c \tau [/tex]. 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 [tex] \lambda_s [/tex], by discrete Fourier transform and by using [tex] \hbar [/tex] you obtain a quantized mass spectrum [tex] M_n = \frac{n h}{\lambda_s c} [/tex]; exactly as a compact time dimension with length [tex] T_t(\mathbf p) [/tex] gives a quantized energy spectrum [tex] E_n(\mathbf p) = n h / T_t(\mathbf p) [/tex]. In fact, this relation evaluated in the rest frame ([tex] \mathbf p = 0 [/tex]) gives the Kaluza Klein tower: [tex] E_n(0)= M_n c^2 [/tex], see figure.2.b. The Kaluza Klein tower is the energy spectrum evaluated at [tex] \mathbf p = 0 [/tex]. 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 [tex]T_t(\mathbf p)[/tex] 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.



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 [tex] \Gamma^M[/tex] is [tex] \Gamma^5 = - i \gamma^5 [/tex] ( and [tex] \Gamma^\mu = \gamma^\mu [/tex] ). In that paper, however, only bosons are considered.)


A four dimensional massless field lives on the four dimensional light-cone [itex]ds^{2} = 0[/itex], which is a lower-dimensional surface. Similarly a massless five dimensional field eqn.15 lives on the five dimensional lightcone [itex]
dS^{2} = c^{2} dt^{2} - d\mathbf{x}^{2} - ds^{2} = 0
[/itex] 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 [itex] ds^{2} = c^{2} dt^{2} - d\mathbf{x}^{2}[/itex].
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".

(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.




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


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

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.

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?

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.

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.

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

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

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.


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 [tex] |\phi > = 1 / \sqrt{2} (|up>\otimes |down> - |down> \otimes |up>)[/tex], where [tex] \otimes[/tex] 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:

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), .... .

naturale

That's true. Extra dimensions are between the most appealing theories of new physics on the market.

However, in that paper the fields are four dimensional fields, there are not "real" extra dimensions. That fields with intrinsic periodicity, which can be matched with ordinary second quantized fields, are "dual" to extra dimensional fields. The author says in the last paragraph that this is a "close parallelism with the AdS/CFT correspondence".

The theory is four dimensional, and I appreciate it because is physics that de Broglie, Einstein, Planck, Bohr & C could use at that time.
It is not simple to do good physics without playing with additional variables.

If you add an extra time dimension to reproduce quantum mechanics you end up to a theory with hidden variables and related no-go theorems.