# Speed of Probability Waves?

1. May 21, 2008

### Usaf Moji

According to author John Gribbin, the state vector, or $$\Psi$$, or "probability waves" (whatever you want to call it) travels at the speed of light:

But all of this still applied only to electromagnetic radiation. The gian leap taken bhy John Cramer was to extend these ideas to the wave equations of quantum mechanics - the Schrodinger equation itself, and the equations describing the probability waves, which travel, like photons, at the speed of light. [p. 235, Schrodinger's Kittens and the Search for Reality - a very good book, btw]

My question is, how do we know $$\Psi$$ travels at the speed of light?

I had a look at John Cramer's article (see http://www.npl.washington.edu/npl/int_rep/tiqm/TI_toc.html) but couldn't find any clues there.

2. May 21, 2008

### clem

Have you considered the possibility that JG is wrong?

3. May 21, 2008

### peter0302

Cramer's model only gets the probability waves to travel at c by allowing them to travel backwards in time. It's just a mathematical model for what's going on, similar to the backwards-in-time interpretation of antimatter. No one knows if there's literally a boson or wave or what-have-you that travels at the speed of light that "enforces" the Schrodinger equation.

4. May 21, 2008

### rbj

i thought that the phase velocity of deBroglie waves were faster than c. at something like c2/v, where v < c and is the velocity of the particle with the wave expression of $\Psi$.

isn't that the case?

5. May 21, 2008

### peter0302

c^2/v isn't fast enough for photons - that would only be 'c'.

6. May 21, 2008

### rbj

photons don't move at a velocity v=c? and the corresponding wave speed for light is not c?

that c2/v expression for phase velocity actually came out of a ca. 1975 introduction to modern physics text. the group velocity was the same as the particle speed, v.

7. May 21, 2008

### DavidWhitbeck

Why are we even discussing photons in the context of non-relativistic qm?

Since the Schrodinger Eqn. is not Lorentz invariant, it's difficult for me to care about superluminal speeds from it.

That being said, wave propagation can be superluminal as long as causality isn't violated. It's what we measure that's important, and as rbj pointed out it ain't phase velocity.

8. May 21, 2008

### peter0302

Sure, the corresponding wave speed for light would be 'c', but unless you're going at 'c' _backwards in time_, you can't use a v=c wave to explain quantum phenomina. Experiments have shown that if a signal were transmitted between quantum particles, it would have to travel _faster_ than c between the two particles.