Energy-Mass Equivalence

By the beginning of the twentieth century it had been realized that electromagnetic radiation, such as light, carries momentum with it. For example, it is the momentum of solar radiation (along with the effect of interactions with charged particles in the solar whind) which causes comet tails to point away from the sun.

Image of Comet Hyakutake by R.L. Hawkes March, 1996.

It is observed that the momentum carried by the electromagnetic wave, and the energy carried by the wave, are related by the following equation:

In 1906 Einstein considered a "thought experiment" in which one had a closed box. Some photons of radiation depart from the left end of the box moving towards the right as shown below.

Since these photons carry some momentum, in order to conserve momentum it is necessary that the rest of the box move to the left as shown below.

But the box + photons constitute a closed system, and the centre of mass cannot move without external forces. This is only possible if the light energy of the photons is considered to have some mass. With relatively simple calculations one can derive the following relationship:

Now directly this relationship only applies to light. However, Einstein boldly proposed that this must be a general relationship. As such, it implied that objects with more energy would have more mass, and that mass and energy were convertible into each other (the latter is the foundation for all nuclear reactions, whereby one adds up the masses before the reaction, adds up the masses afterward, and if there is less afterward, the reaction will give off energy according to this relationship). At a more extreme scale, particle creation-annihilation depends on this relationship.

This material is part of an electronic text to support the Physics 4701 (Relativity) course at Mount Allison University. Site maintained by Bob Hawkes (send comments to rhawkes@mta.ca)
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