Einstein's Box

energy

emit photons

This thought experiment proposed by Albert Einstein in 1906 considers a box of mass

M

and length

L

in which a quantity of radiant energy

E

is emitted from one end toward the other. The box moves a distance

Δx

(exaggerated in the picture) in a time

Δt

with a velocity

v

in the opposite direction to the photons, which carry the equivalent of a mass

m

. The momentum carried by the radiation is given by

p=E/c

. Assuming conservation of momentum and energy (for the case

v<<c

) leads to Einstein's celebrated equation

E=m

2

c

, applicable, at least, to photons.