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New quantization method 
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#37
Sep810, 04:21 AM

PF Gold
P: 1,376

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 nogo 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 nonconclusive experiments but they can not be considered as a proof of violation of local realism. 


#38
Sep810, 04:26 AM

P: 6,863




#39
Sep810, 04:36 AM

P: 6,863

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. 


#40
Sep810, 06:05 AM

PF Gold
P: 1,376

[tex]\Phi(xx_0,t)\equiv\Phi(x_0x+\lambda ,t+2\pi R_t)\equiv\Phi(xx_0,t+4\pi R_t)[/tex] So you have particle at rest with "trembling" along x direction. 


#41
Sep810, 06:57 AM

P: 104

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. 


#42
Sep810, 07:06 AM

P: 104

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 spacetime point the string interact the periodicities change). 


#43
Sep810, 07:40 AM

PF Gold
P: 1,376

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. 


#44
Sep810, 08:07 AM

P: 104




#45
Sep810, 08:24 AM

P: 3,014




#46
Sep810, 10:32 AM

P: 104

It is very interesting because it shows a deep dualism of that theory with the KaluzaKlein 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 KleinGordon 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 KaluzaKlein theory. This is the main difference between the two. ( 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.) 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 propertime 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". 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 spacetime 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. I can try to provide further explanations if necessary. 


#47
Sep910, 12:58 AM

P: 6,863

Also, doesn't this require simultaneity? 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. 


#48
Sep910, 01:08 AM

P: 6,863

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. 


#49
Sep910, 01:13 AM

P: 6,863

One reason that I like the paper is that I have a soft spot in my heart for KaluzaKlein 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. 


#50
Sep910, 06:58 AM

P: 104

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: "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 quantumclassical 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), .... . 


#51
Sep910, 07:26 AM

P: 104

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 nogo theorems. 


#52
Sep910, 08:52 AM

PF Gold
P: 1,376

From your description it follows that Alice sees (after period T_1  T_0) classical variable that is produced at source  the face with an up arrow (down arrow) and the same for Bob (after period T_2  T_0). Please consider looking into this simple explanation of Bell's inequalities  http://www.physicsforums.com/showthr...38#post2817138 ignoring of course the final conclusion as it is not conclusively proved by experiments. This shows the problem with Bell's inequalities in very simple form. From this example it is clear that measurement of photon plays central role in this paradox and not exactly their production at source (this is just condition that we are free to adjust to our liking). 


#53
Sep910, 09:01 AM

PF Gold
P: 1,376

Maybe I have poor imagination but it seems to me that this doesn't quite work. Well maybe if you introduce speed of some interaction as mathematical extra dimension. 


#54
Sep910, 10:20 AM

P: 104




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