Relativity: The Special and the General Theory (original 1916; edição 2010)

“The universe of these beings is finite and yet has no limits.” – Albert Einstein, in chapter XXXI

So says one of the great thinkers – perhaps, the great thinker – of the twentieth century in explaining his general theory of relativity. While there was much mathematical in its derivation, Einstein explains it in common language to the educated reader in this short work. He also explains the special theory of relativity here. While such things are hard to digest (at least at first), they are certainly able to be digested in this format. That this presentation exists in such clarity at all bespeaks to Einstein’s genius.

I once took theology classes at a seminary on Mercer Street in Princeton, just down the street from where Einstein used to live. Stories about his commonness yet uncommonness still filled the town. He amazingly had the gall to claim that the universe was circular or elliptical – and then attempted to prove it. He did so by clear thought, not by experiment as he was a theoritician, and this book contains an accessible version of those thoughts. For that reason alone, the curious reader is encouraged to dwell deeply within this record of his understanding.

Like mathematics, physics is a field full of geniuses whose ingenuity is common with respect to each other. I am not a physicist, and I will not attempt to comment on the science presented. From what I understand, some of Einstein’s formulations have been questioned by contemporary experiments, and string theory (though still unproven) attempts to generalize even further. To me, neither of these discredits Einstein’s accomplishment with regards to relativity. Of course, his annus mirabilis (“miracle year” of 1905) included other important findings like Brownian motion, and for better or for worse, his legacy will forever be bound with the Manhattan project and its atomic bomb.

Thumbing through a work like this and dwelling on the beauty of its contents surely provide one of the greatest experiences humans can have. Only a handful of works, like those by Immanuel Kant or Isaac Newton or Augustine of Hippo, reach the heights like this. As such, anyone with any inkling of interest in physics should attempt to study these theories, and who better to read than the author of them himself? I enjoyed my time reading this work immensely. The translation is clear and scientific, but reading still is a little difficult due to the complex subject matter. Nonetheless, being a dog eating the crumbs from Einstein’s table still provides quite a treat! ( )

The aim of this book is to introduce people without a strong physics (or even scientific) background to the special and general theories of relativity - theories that Einstein was the primary developer of. Einstein assumes the reader has passes a "university matriculation exam." What that meant in the first half of the 20th Century, I don't know but in practice what's required is the level of algebra I had by age 16 plus a smattering of mentions of the square root of minus 1. I also found basic calculus useful for one section, though it is possible to do without it.

For the most part this book is excellent, introducing the minimal amount of mathematics and formal language necessary to understand the most important and fundamental concepts of Einstein's theories in a way that is accessible whilst concise. It might be possible to do it better with a bigger book, a less formal style and a lot more diagrams but it very interesting to get Einstein's unique perspective as originator of the theories and insight into his thought processes.

A few sections are remarkable in contrast with the rest, for being unclear. The section on addition of velocities in special relativity leaves rather more to the reader than anything else in the book, mathematically, and when I looked it up it turned out to be much easier to work out using basic calculus than algebraic division - and the bit that wasn't clear was that a division of two equations was what was required. This section could be skipped without losing much.

The remainder of the muddy sections come at the back end of the section on general relativity. The simplest precise mathematical formulation of this theory is expressed using tensors - and tensor algebra is way beyond what anybody encounters in standard school maths or physics curricula. Einstein makes no attempt to explain it and in fact never shows the fundamental equation of general relativity. This makes it very hard for him to explain how gravitational fields and space-time interact, which leads to the lack of clarity in the latter stages of this part of the book. Things get easier and clearer again when he moves on to relativity and cosmology.

The final part of the book is a collection of appendices expanding on things discussed earlier on. I required pen and paper to check the derivation of the Lorentz Transformations from first principles - but this section could just be skipped if the maths bothers you - it doesn't add a lot but it is interesting to see it, if your algebra is up to it.

The most rewarding thing for me, since nothing here is completely new to me, was listening to Einstein's voice. He seemed to come at things from a viewpoint much more generally philosophical than most present day physicists would, discussing Kant, Descartes and Hume, for instance. The section on the concept of "empty space" was fascinating - he concludes that general relativity precludes this notion - one cannot have space-time without it containing "fields." What he means is fields of force - the electromagnetic field, gravitational field etc. This implies the notion of a field being present even if its magnitude is zero - which is a bizarre concept. Modern quantum mechanics backs these ideas to the hilt and leads me to think that one of the most important areas of inquiry for fundamental physics as it stands is the connection between the classical idea of space-time and the quantum idea of the vacuum. The fundamental nature of both is obscure - and in some sense they should be the same thing.

Overall this is an excellent introduction to special relativity and at least the conceptual underpinnings of general relativity, if not of the full theory, which really just can't be explained properly without knowledge of tensors. ( )

This was one of the first opportunities for Americans to read about relativity. ( )

Well-written discussion of a complex subject. Unfortunately, Einstein's ideas on time and synchronicity do not comply with quantum mechanics. Given that quantum theory has an extensive set of experiments demonstrating these concepts it is a shame that Einstein was never able to bring his theory into alignment with reality. Still a great read though. ( )

In one of the magically aimless opportunities afforded by a liberal arts education, I took an honors sciences class sophomore year on the Theory of Relativity. Over the course of the semester, we studied the theory, its associated maths, and its implications. It was possibly my favorite class over the course of 19 years of formal education. We of course read and discussed this book, which is remarkably approachable. ( )