Schrödinger's Cormorant

3.7 Energy & Momentum

Derivation of the relativistic energy-momentum relation.

Remember that we set out on this exploration of special relativity because Uncle Albert advised us that this would allowed to investigate the strange phenomenon of photon momentum and this, in turn, might become our starting point for getting into quantum theory. It is time now, therefore, to play around a bit more with the slightly mysterious looking total energy term, defined by equation III-8, to see if we can find the connection to momentum.

Question 3-17

If you worked through this rather convoluted derivation, you should now have arrived at another iconic equation of physics. It is called the relativistic energy-momentum relation:

E = √(m2c4 + p2c2) III-9

This is a very useful relationship between the total energy, mass and momentum of any particle. You can see that for a particle that isn’t moving and therefore has zero momentum, it reduces to the familiar E = mc2.

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