On the Reality of the Psi-Function

[Anamitra]

It is often argued that the psi-function exists only in the context of calculations.But is this concept true if we take into consideration the celebrated Aharonov-Bohm Effect where interference is produced by differences in the phase factors of the psi-function? It seems that there is a certain amount of reality in the psi-function!
If the above idea is accepted then there is a great problem.We have several instances where the psi function travels faster than light. I have tried to discuss these issues in my article "Superluminal Speeds in Quantum Mechanics" which has appeared in the European Journal of Scientific Research,Euro Journals. [Vol 37,No 3].The file has been attached for the convenience of perusal.
The whole situation needs to be re-investigated in the light of the above stated facts.

Anamitra Palit

 

[xepma]

Let me quote the following:

"Such waves [solutions to Dirac equation] travel with a speed of $$\frac{E}{|p|} = \frac{mc^2}{mv} = \frac{c^2}{v}$$"

This is simply wrong. You actually have a "v" in this equation, which stands for the velocity of the particle. Solve for this v and you get: $$v= |P|c^2/E$$ which is always smaller or equal to c.

What you're calculating is the phase velocity, which is E/|p| or w/k (angular frequency/wavenumber). Phase velocities are known to exceed the speed of light; even in the classical case.

What you want to determine is the velocity at which the "information" (energy) is carried by the wave. But this is simply given through the relation $$E = \gamma m c^2$$ (solve for the v in the Lorentz factor gamma).

As for the "reality" of the wavefunction: we can extract amplitudes from the wavefunction and these amplitudes provide us with predictions on experiments through some probabilistic manner (e.g. interference patterns). The fact that phase factors influence these amplitudes shouldn't come as a surprise anymore.

 

[Anamitra]

The problem in this case is that the phase part here seems to have a "physical reality" if we keep in our mind the Aharonov Bohm Effect----- that the differences in phase produce interference effects. If the phase part is physically meaningful then its propagation should be given a serious consideration from the physical point of view.How do we get the interference pattern if the the phase part is not physically meaningful?

 

[TMM]

What's the difference between being part of physical reality and being part of a calculation that describes physical reality?

Seems like a silly discussion to me.

 

[alxm]

Who said that phase is not physically meaningful? If it wasn't, then we'd just throw it out and only deal with real-valued wave functions and real-valued coefficients.

Changing the overall phase, will not change any observable $$\psi e^{i\theta})^*\hat{O}(\psi e^{i\theta}) = \psi^*\hat{O}\psi$$. But you do not get the same end result for changing the phase of a single eigenstate.

 

[Anamitra]

If the phase of the psi-function plays a role central of the effect of the interference being produced[in the Arranov-Bohm effect] is it not important to give due consideration to the phase speed? Would it be right to dismiss it as something irrelevant from the physical point of view?

 

[Anamitra]

The basic point is "What is it that really interferes in the Aharonov -Bohm Experiment?" If it is wave represented by the psi-function ------"What is the speed of such a wave?"