Einstein's box of phonons and energy-mass equivalence

In summary: So if Einstein's box 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.
  • #1
sunroof
20
0
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?
 
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  • #2
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.
 
  • #3
bcrowell said:
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?
 
  • #4
sunroof said:
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.
 
  • #5
bcrowell said:
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.
 

Related to Einstein's box of phonons and energy-mass equivalence

1. What is Einstein's box of phonons?

Einstein's box of phonons is a thought experiment proposed by Albert Einstein to illustrate the concept of quantized energy in a system. The box contains a fixed number of phonons, which are quantized units of vibrational energy, and the walls of the box are perfectly reflective so that the phonons cannot escape.

2. How does Einstein's box of phonons relate to energy-mass equivalence?

In this thought experiment, Einstein showed that the total energy of the phonons in the box is directly proportional to the mass of the box. This is similar to his famous equation, E=mc^2, which demonstrates the equivalence of mass and energy. Therefore, the concept of energy-mass equivalence can be understood through the behavior of phonons in the box.

3. What is the significance of Einstein's box of phonons in physics?

Einstein's box of phonons is significant because it demonstrates the fundamental relationship between energy and mass. It also serves as a key example of the quantization of energy, which is a fundamental concept in quantum mechanics. This thought experiment has been used to explain various phenomena in physics, such as the photoelectric effect and the behavior of particles in accelerators.

4. How does Einstein's box of phonons relate to the concept of blackbody radiation?

Einstein's box of phonons is closely related to the concept of blackbody radiation, which describes the thermal radiation emitted by a perfect blackbody. In this thought experiment, the walls of the box act as a perfect blackbody, absorbing and emitting radiation at a certain rate depending on the temperature of the box. This allows for the calculation of the energy and mass of the phonons in the box.

5. Can Einstein's box of phonons be applied to real-world systems?

While Einstein's box of phonons is a thought experiment, it can be applied to real-world systems in certain situations. For example, it has been used to explain the behavior of particles in a Bose-Einstein condensate, a state of matter where particles lose their individual identities and behave as a single entity. However, it should be noted that this thought experiment is a simplified model and does not account for all the complexities of real-world systems.

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