# Einsteins though experiment and e=mc^2

I came across a book a few weeks ago that tried to explain how einstein "derived" the formula and wasn't sure how accurate the description was. I'll write it out as best I can so you can either pick faults with it or tell me it's correct:

In Einsteins thought experiment there is an isolated box in free space of length L and mass M. Photons are emitted from one with energy E and velocity c ( and so the photons have momentum E/c) causing the box to recoil with velocity v = -E/Mc.

After time dt, the photons hit the wall bringing the box to rest so the box has moved a distance of dx wher dx = v dt = -EL/Mc^2.

Since the box is an isolated system the centre of mass and its contents haven't moved and so the radiation has carried the equivalent of a mass m s.t,

mL + M dx = 0

so mL - EL/c^2 = 0

by factoring out L we get we get m - E/c^2 = 0

so E = mc^2

Was this thought experiment just a way for Einstein to deduce what the relationship between relativistic mass and enegy might be so he could work on a more rigorous proof or was the book making things up .

Also, could someone explain what the paragraph highlighted in red means Thanks

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uraknai said:
I came across a book a few weeks ago that tried to explain how einstein "derived" the formula and wasn't sure how accurate the description was. I'll write it out as best I can so you can either pick faults with it or tell me it's correct:

In Einsteins thought experiment there is an isolated box in free space of length L and mass M. Photons are emitted from one with energy E and velocity c ( and so the photons have momentum E/c) causing the box to recoil with velocity v = -E/Mc.

After time dt, the photons hit the wall bringing the box to rest so the box has moved a distance of dx wher dx = v dt = -EL/Mc^2.

Since the box is an isolated system the centre of mass and its contents haven't moved and so the radiation has carried the equivalent of a mass m s.t,

mL + M dx = 0

so mL - EL/c^2 = 0

by factoring out L we get we get m - E/c^2 = 0

so E = mc^2

Was this thought experiment just a way for Einstein to deduce what the relationship between relativistic mass and enegy might be so he could work on a more rigorous proof or was the book making things up .

Also, could someone explain what the paragraph highlighted in red means Thanks
That is not exactly Einstein's thought experiment. I posted the correct one in its entirety here

http://www.geocities.com/physics_world/sr/einsteins_box.htm

The part in red only means that since the center of mass must remain constant and radiation left one side and the box moved then the light must carry mass with it. Einstein then concluded that light has mass. He didn't state that explicitly in that part of the paper. He did state it in the second part of the paper though.

Pete

The experiment is discussed by Max Born, "Einstein's Theory of Relativity." Yes, the box, or railway car, is displaced by the transmission of radiation. On Page 284, it says "Then A experiences a recoil E/c... The displacement of the tube is X=EL/Mc^2.

Then Born goes on to say,"Now the bodies A and B may be interchanged (this may be done without using exterior forces). ....According to ordinary mechanics the tube as a whole must suffer no displacement..." Yes, but Born postulates that two men are situated in the tube, who exchange similar equipment from one side to the other in order to restore things as they originally were.

Wow...I never know it was THAT complex.

Gamecubesupreme: Wow...I never know it was THAT complex.

Well, another matter that Born gets into is that the "kick" from the radiation travels through the metal of the "railway car" at less than the speed of light.