Schrödinger's Cormorant

3.6 Totally

Thinking about the physical meaning of the relativistic kinetic energy expression leads to Einstein's mass-energy relationship.

We have discovered that in the relativistic universe, the kinetic energy is expressed as a difference between two terms, both with units of energy, one of which depends on velocity while the other is constant, even when the particle is stationary. Let’s look at this result a bit more, to make sure we really get to grips with what it means. A tiny rearrangement of equation III-6 gives us:

The form of this equation is provocatively suggestive. The term on the left is a total amount of energy, which is the sum of kinetic energy and something else (mc2), which is independent of velocity. Your first thought might be potential energy but there was no potential in the derivation, so this won’t do. Instead, Uncle Albert reasoned, mc2 represents an energy that a particle has just by virtue of its mass, independent of whether it is moving or not. Therefore, we can rewrite equation III-7 as:

Where E is now identified as the total energy of the particle. So if a particle is at rest .....

Question 3-14

So you finally got there: E = mc2, Uncle Albert’s iconic mass-energy relationship. Congratulations.

If you look back at how we reached this conclusion, you’ll realise that though we have derived it, we can hardly be said to have proved it: it just seemed the most sensible interpretation of the form of the kinetic energy definition we arrived at. And that’s not because of any failings on our part; Uncle Albert did the same thing. And this is – by and large – how physics works. It’s what Newton did in his day too: you make a sensible suggestion that seems to fit with the evidence. But in the end it’s only through experiment that you can validate your suggestion and dignify your suggestion with the name theory. So let’s look at an example of some experimental evidence.

Question 3-15

As usual, Cormorant is eager to put all this in a context that he can relate to: a cormorant.

Question 3-16

Getting here is a huge achievement. Really well done, if you made it. There's a long way to go, though. If you want to use this as a step on the road to getting a grip on quantum theory, we need to push the relativity just a bit further.

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