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S4.7 Relativity: Mass, Momentum and Energy

This section is included for general interest. It is not part of the examinable programme of the course.

[A] Next steps

Working from just these two postulates:

  1. the laws of physics are the same in all inertial reference frames
  2. the speed of light in empty space always has the same value, c

Einstein was able to show that we have to radically revise our notions of space and time. In particular he discovered:

So what happens to our ‘commonsense’ (Newtonian) notions of mass, momentum and energy? Do these need revision too?

[B] The ‘ultimate speed’ experiment

[C] Energy and momentum of photons: an aside

[D] A gendanken experiment: Einstein’s box

[E] Energy, momentum and mass

Let’s try and synthesise all of these results

There are two ways of combining these results:

[F] A new type of energy

[G] Kinetic energy

[H] Inertial mass

[I] A summary

If we define a new quantity

\[ \gamma = \frac{1}{(1-v^2/c^2)^{1/2}} \]

we can define forms for mass, energy and momentum that are relativistically correct, and reduce to the correct Newtonian forms for small v

m=γm0

p=γm0v

E=γm0c2

[J] Is it correct?

In deriving the above, we

Are such conclusions justified on the basis of such flimsy evidence? The answer is a resounding yes. We have faith in these results because

Learning Resources

Textbook: The presentation here is taken mainly from ‘Special Relativity’ by A.P. French (Van Nostrand Reinhold (UK) Ltd: Wokingham)