In a small second hand store I was browsing books and there I saw this book for only €1.50! It’s a distillation from a few chapters from his famous The Feynman Lectures and concern special and general relativity. As a physicist both the author and the topics excite me, so I managed to read through it quite quickly. For non-physicists I wouldn’t recommend the book as it is quite technical (though everyone online contradict me), but for anyone either studying or have studied physics it’s a good read. It’s nice to reminisce some of the topics I studied at university, but at the same time I got a bit annoyed. Feynman explains the need for each theory and also which symmetries of nature we put into the theory. Everything is done with very little math with a focus on understanding everything intuitively. The reason why it’s a bit upsetting, is that I realize how bad some of the lectures at university were. Special relativity was taught to me as more or less: “Einstein says light speed is constant for all observers, let’s see what that means”. No discussion around the history, no discussion around Maxwell’s equations, no mention of the fact that length contraction and time dilation were already known (with an incorrect interpretation). Same for general relativity. It was taught by introducing tensors, some tensor algebra rules and we spent 3 months calculating Ricci tensors, Levi-Civita symbols, covariant derivatives. I managed to pass the exam without understanding anything, by just memorizing some math rules. It was so dramatic that after 3 months I still didn’t even know what a tensor was, apart from that if it transforms like a tensor, it is a tensor.

Of course later on you read some stuff online, watch some youtube videos and you slowly learn the history and intuition behind it. But why not teach it properly the first time?

In any case, the book can be summarized with the following ideas:

  1. All mechanics should not depend on which units you use, nor where you place the origin of the coordinate system you measure in. In a sense, this means that if I want to understand the game of billiards from a physics perspective it doesn’t matter if I use grams or ounces, nor does it matter if I stand on one side of the table, or the other. I can even walk around the room while taking measurements, and the laws of physics should remain the same. We call this Galilean invariance.
  2. Einstein (in part also Poincaré) comes along and says: not only mechanics, but all of physics should remain invariant. If I sit in a car, or in a spaceship I should not be able to create any experiment that can tell me how fast I’m moving (without looking outside). This is called the relativity principle. From here we can choose two philosophical paths:
    • The speed of light is constant. And from there we derive a new set of rules that are called Lorentzian invariance.
    • You can show that the relativity principle implies either Galilean invariance, or Lorentzian invariance. Then experimentally we see we need to choose Lorentzian invariance, and that the constant c that appears must be (up to experimental precision) identical to the speed of light.
  3. And finally, Einstein in another stroke of brilliance says: not only should all of physics be the same when moving with a constant velocity, it should also be the same both in a falling elevator, and in an accelerating spaceship. In a sense equating acceleration to gravity and claiming that they are one and the same. This is called the principle of equivalence.

So in short, most of modern physics was invented by a few philosophical leaps: starting from the fact that all of mechanics should be the same (at constant velocity), to all of physics should be the same (at constant velocity), and finally to the idea that all of physics should be the same in gravity and when accelerating.

Presenting it this way gives me a much better appreciation of physics, but it also shows how special and general relativity follows quite naturally from classical mechanics. Something quite fundamental, but still missing from my education unfortunately.

Besides these ideas Feynman also goes a bit more into detail of time and space dilation, why clocks move slower in stronger gravity (think of the movie interstellar) and what it means that space has a “geometry”.