Einstein's box of phonons and energy-mass equivalence

[sunroof]

If Einstein's box (http://galileo.phys.virginia.edu/classes/252/mass_and_energy.html ) is full of phonons instead of photons, the momentum is Mv=E/c' and time is t=L/c' where c' is the velocity of a phonon. The result should now be E=mc'^2 rather than E=mc^2.

E=mc^2 is tenable to photons in vacuum but invalid to phonons?

 

[bcrowell]

You seem to be assuming p=E/c' for phonons, but that relationship isn't valid for phonons.

Given that E=mc2 is valid for one form of energy, it has to be valid for all other forms of energy. Otherwise a sealed box could change its own inertia by transforming energy from one form into another.

Again, the c in relativity has nothing to do with light. It's a property of spacetime, the maximum speed of cause and effect. Light just happens to travel at c.

You might want to make some efforts to show that you're absorbing people's replies and thinking about them before starting new threads.

 

[sunroof]

You seem to be assuming p=E/c' for phonons, but that relationship isn't valid for phonons.

Given that E=mc2 is valid for one form of energy, it has to be valid for all other forms of energy. Otherwise a sealed box could change its own inertia by transforming energy from one form into another.

Again, the c in relativity has nothing to do with light. It's a property of spacetime, the maximum speed of cause and effect. Light just happens to travel at c.

You might want to make some efforts to show that you're absorbing people's replies and thinking about them before starting new threads.

Thanks for your review. But how to interpret Debye's theory to specific heat where p=E/c' to a phonon?

 

[bcrowell]

Thanks for your review. But how to interpret Debye's theory to specific heat where p=E/c' to a phonon?

Here is some information about the momentum of phonons: http://en.wikipedia.org/wiki/Crystal_momentum The interpretation is fairly complicated.

The real question is what you think you're gaining by taking a simple thought experiment and making it more complex. If you take a complex physical situation, form an argument based on it, and end up with a result that violates the basic principles of relativity, then the conclusion is that you over-simplified your argument. The cure for that problem is to go back and spell out your argument in more detail, rather than just sketching it out in a couple of sentences. You can't expect other people to fill in all the details of your argument for you, and then detect all the mistakes in the details.

 

[sunroof]

Here is some information about the momentum of phonons: http://en.wikipedia.org/wiki/Crystal_momentum The interpretation is fairly complicated.

The real question is what you think you're gaining by taking a simple thought experiment and making it more complex. If you take a complex physical situation, form an argument based on it, and end up with a result that violates the basic principles of relativity, then the conclusion is that you over-simplified your argument. The cure for that problem is to go back and spell out your argument in more detail, rather than just sketching it out in a couple of sentences. You can't expect other people to fill in all the details of your argument for you, and then detect all the mistakes in the details.

In the theory of specific heat capacity, the energy is E=hf and the momentum of a phonon is p=hk (k=1/wavelength). E/p=f/k=c'(velocity of a phonon) and c' is much less than the light speed c in vacuum.