[saspinski (OP)]

I found an explanation for the e=mc2 equation at this address: http://www.adamauton.com/warp/emc2.html

Basicaly, it is a thought experiment where one photon is emmitted from one side to the other side of a box at rest. By moment conservation, the box is shifted to the other side and stops moving when the photon finishes its journey. As the final position is different from the initial position, but the center of mass should be invariant (no external forces), some "mass" was removed from one side and placed in to the other one. The equations gets E=mc2. It is assumed low speeds.

The equation uses only that light has momentum. So, even while it is explained there that the famous formula comes from special relativity, there is nothing of relativity in the deduction.

Question: Is relativity only necessary to extend the concept to high speeds? 

[jeffreyH]

Because special relativity operates in inertial frames of reference and the laws of physics are invariant in those frames then this result follows naturally. It is only when the velocity of a reference frame approaches the speed of light that things change. This has implications for simultaneity.

[PmbPhy]

I found an explanation for the e=mc2 equation at this address: http://www.adamauton.com/warp/emc2.html

A more detailed description/derivation is at: http://www.newenglandphysics.org/physics_world/sr/einsteins_box.htm

Basicaly, it is a thought experiment where one photon is emmitted from one side to the other side of a box at rest. By moment conservation, the box is shifted to the other side and stops moving when the photon finishes its journey. As the final position is different from the initial position, but the center of mass should be invariant (no external forces), some "mass" was removed from one side and placed in to the other one. The equations gets E=mc2. It is assumed low speeds.

The equation uses only that light has momentum. So, even while it is explained there that the famous formula comes from special relativity, there is nothing of relativity in the deduction.

Yes. That's true.  But one has to keep in mind that E = mc2 was derived even before Einstein invented relativity.

Question: Is relativity only necessary to extend the concept to high speeds? 

No. Relativity consists of two postulates. The first postulate is  that the all the laws of physics are the same in all frames of reference. That makes no reference to how fast a frame is moving. Also it can easily be shown that two events space far enough apart in space which are simultaneous in one frame can be quite apart in time in another frame from even a very slowly moving frame of reference.

Sorry Jeff but you need to study the Lorentz transformation for time more closely.

[jeffreyH]

Pete my head is full of linear algebra, vectors, tensors and the kitchen sink at the moment. I am in overload. I am currently looking at coordinate transformations. To little time, too much data!

[saspinski (OP)]

   So, E=mc2 doesn't come from relativity. It doen't need quantum mechanics also, because we can replace "photon" by "pulse of light" with momentum.

   It's relation to atomic bomb was also never clear to me.

On one hand all types of bomb release heat, part of it in the form of radiation, eletromagnetic waves or photons, that comes from its original mass according to the equation. Nothing specific to the A-bomb.

On the other hand, the researches leading to the A-bomb are related to radioactive decay. Among the key factors were nuclear chain reaction and critical mass. I don't see where the equation was necessary.

[evan_au]

So, E=mc² ...It's relation to atomic bomb was also never clear to me.

Take the components of a typical nuclear fission reaction, and look them up on a periodic table.

• Add up the atomic masses of the original U235 + neutron
• compare this with the atomic mass of the daughter nuclei and released neutrons
• you will find that there is some "missing mass"
• This "missing mass" is released as energy in the explosion

In the case of Uranium fission, this missing mass is slight, but readable from a periodic table.

• In the case of Hydrogen fusion, this missing mass is more dramatic, making up about 0.1% of the original mass, and is easily readable from a periodic table.
• In the case of burning coal to CO₂, the energy released is so small that you can't read the answer from a periodic table (the atomic masses aren't known to enough decimal places).

See: https://en.wikipedia.org/wiki/Nuclear_fission#Origin_of_the_active_energy_and_the_curve_of_binding_energy