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Is quantum field theory really lorentz invariant? 
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#19
Sep2210, 03:53 AM

P: 1,411

That is a good subject for a private email but not for a paper in a peerreviewed journal with a high impact status. Nicolic did not do his homework and reports his failure. The referees did not do their job.



#20
Sep2210, 04:40 AM

P: 46

Hi Demystifier,
I read your suggested article on Bohmian relativistic QM and I'm still not convinced. Nicolic defines a parameter s for the world lines of all the particles in the system, but the question of how to make the parametrization seems ambiguous. It is clear that different parametrizations produce different results. Even if we say ds = d(proper time) for each particle, it is still unclear at which point in a given particle's world line we say s = 0. And which point we select matters. Next, for everybody, I have a question on the Copenhagen interpretation's dealing of the EPR experiment. I would like to recall Einstein's actual quote: "If, without in any way disturbing the system, we can predict with certainty (i.e. with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity." If I understand this, it would mean that when we make a measurement and go from a superposition of spincorrelated states u,D> + d,U> to a single one, that is, either u,D> or d,U>, then even though our measuring device is near the lowercase particle, since we know the value of the upercase particle's spin with certainty, it's a variable with physical reality. But this would mean that the physically real quantities are not lorentz invariant! One could refute this argument by saying that we did not directly measure the uppercase particle's spin and that therefore it never gained any physical reality. This would be saying that Einstein's criterion of reality is wrong. Then the physically real quantities are lorentz invariant. So the lesson is that only what we directly measure gains physical reality, and further, that the physically real quantities must be covariant. I feel, however, that there is a problem with the idea that only what we "directly" measure gains physical reality. In the Copenhagen interpretation, we make a cut between our quantum system and our classical measuring apparatus, and where we place the cut is, according to Bohr, arbitrary. Let's say we are measuring the position of an electron. If we say that only the electron is part of the quantum system, then after the measurement, the electron position is a physical reality, since we directly measured it. However, let's say we include a pointer (that correlates with the electron position) in the quantum system as well. Then in the new systemapparatus framework, the electron and the pointer are entangled, and we "directly" measure not the electron, but the pointer. It is clear that the pointer gains a position, and this is a physical quantity. However, this situation is very similar to EPR, and with similar reasoning, one would have to say that the electron did not gain a position. One would have to say that only when we "directly" measure the electron it gains an element of physical reality. So this is really problematic. If we assume that the particle we don't directly measure gains an element of physical reality (as Einstein says), then we must say that physical quantities are not lorentz invariant. But if we assume that the particle we don't directly measure does not gain an element of physical reality, then we have the problem mentioned in the previous paragraph: by placing the cut between system and apparatus differently, our electrons will never gain definite positions, spins, etc. 


#21
Sep2210, 05:22 AM

Sci Advisor
P: 4,591

http://xxx.lanl.gov/abs/quantph/0512065 http://xxx.lanl.gov/abs/1006.1986 


#22
Sep2210, 08:16 AM

Sci Advisor
P: 4,591

And this principle is not invented by those who obey it. 


#23
Sep2210, 08:46 AM

P: 1,411

I know the principle. I used to be guilty of this myself. It is partly because of this principle that we are really reading less and less papers. Comparing the quality of so called scientific publications 100 years ago and now  the emerging picture is not very encouraging. But that's another subject. Good thing is that now I have Nicolic's "Superluminal velocities" paper on my desk and it looks like it's gonna be an interesting read.



#25
Sep2210, 06:59 PM

P: 46

Furthermore, if the probability of a given spacetime point at s=0 is psi^2, then what is the probability of a given spacetime point at s=1 or s=2? I seriously doubt that it is also given by psi^2. But then we have a problem, since the time evolution of psi is given by the KleinGordon or Dirac equation, which don't have s anywhere. Then, wouldn't the probability for every value of s be psi^2? 


#26
Sep2310, 02:52 AM

Sci Advisor
P: 4,591




#27
Sep2310, 02:53 AM

P: 196

That the collapse is instaneously if you mak one measurement (which is the case in both QM and QFT!), is not relevant for the theory to be relativistic or not. But is faster than light communication between two events/ measurement possible or not, that matters! 


#28
Sep2310, 03:41 AM

P: 1,411




#29
Sep2310, 11:46 PM

P: 46

Professor Nikolic, I have just one more question. In your papers you emphasize that the relativistic wavefunction is a function on the 4n dimensional configuration space. However, in nonrelativistic mechanics, it appears as if the wavefunction lives in 3n dimensional configuration space and evolves in time according to the Schrodinger equation. Specifically, at low energies it appears as if the wavefunction on 4n dimensional configuration space has a nonzero value only when the time coordinates for all the particles are equal, and I'm still not clear how that mathematically arises. I still don't have a clear picture how the relativistic case reduces at low energies to nonrelativistic Bohmian mechanics.
Thanks for helping me out. 


#30
Sep2410, 03:16 AM

Sci Advisor
P: 4,591

S. Tomonaga, Prog. Theor. Phys. 1, 27 (1946). The usual singletime nonrelativistic QM is just a special (coincident) case of the more general manytime nonrelativistic QM. For example, if you want to calculate the expectation values of products of observables measured at DIFFERENT times, the manytime formulation of nonrelativistic QM is a very convenient way to do this. By the way, thanks for not writing my name as "Nicolic", which for some reason many people do. :) 


#31
Sep2410, 03:45 AM

P: 1,411




#32
Sep2410, 07:18 AM

Sci Advisor
P: 4,591

By the way, if you write "Nicolic" in the google, the first thing it writes is:
"Did you mean: Nikolic" 


#33
Sep2510, 11:36 AM

P: 582

[tex]\frac{\partial}{\partial t}\int{\psi(x,t)^2 d^3x}\rightarrow 0[/tex] so that we can normalize the integral over space and use the wavefunctionsquared as a probability density at each time t, so that time reduces to a parameter. For multiple particles, you would have to express the wavefunction in a manytime formulation, as Demystifier says, so that the wavefunction would represent the probability amplitude of observing the first particle at x1,t1, the second particle at x2,t2, etc. The nonrelativistic limit would be letting c go to infinity and setting t1 = t2 = ... = tn = t. But the wavefunction is not necessarily zero if the times are unequal. It's just that you can only restore the usual timeparametrized Schrodinger picture by setting them equal. I'm glossing over some fine points, but that is essence of it . 


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