I was walking on the street the other day and thought to myself, maybe E=mc2 can be derived from information theoretic principles.

I did not do too much work on this, just want to brainstorm a bit.

Something along these lines: entropy is the -log of accessible microstates.

So there are two ways of increasing the entropy:

  • adding energy
  • adding mass ( a particle ).

You can immediately have the gut feeling that perhaps this can lead to an alternative and interesting derivation of E=mc2 (assuming a closed system and equilibrium in both cases which are divided into two subsystem that can exchange particles and energy, the total energy is constant, the total entropy is constant, the total mass is constant, in principle E=mc2 should be able to be derived from this idea ... or am I wrong ?).

This idea is so trivial and obvious that I am sure somebody has done it already.

Any idea if this has been done before ? Goggle gave me nothing useful....


closed as off-topic by Aaron Stevens, Mozibur Ullah, John Rennie, user197851, Ben Crowell Dec 8 '18 at 17:47

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  • 1
    $\begingroup$ "In principle E=mc2 should be able to be derived from this idea". And in practice? Did you elaborate on that? Just a couple of things to add to the list of ways of increasing entropy: i) adding volume; ii) increasing the mass of all the particles (see the mass dependence in the Sakur-Tetrode formula. Last, but not least, all these properties hold independently if the hamiltonian is classical or relativistic. Do you think E=mc$^2$ is valid for classical mechanics too? $\endgroup$ – GiorgioP Dec 8 '18 at 15:14
  • $\begingroup$ Isn't it somehow obvious that this equation has to be true (up to a constant factor) ? Simply based on the fact that information is conserved ? Is that not "intuitive"? I mean, if this equation (with any choice of constant factor) is not true then information is not conserved. Is that not enough? Is my argument correct? Or am I making a logical mistake? If information is conserved and kinetic energy can be turned into particles then there has to be an equation like this (with some constant factor). Or not? $\endgroup$ – jhegedus May 5 at 20:50