E=mc2 and all that jazz

Relativity

by Albert Einstein

Considering the number of books I’ve read about Einstein’s theories of Relativity, and about Einstein himself, it’s surprising I didn’t acquire this one until quite recently. As so often happens, I was probably browsing the shelves for something else.

In case anyone doubts, this is THE book about Relativity, the original, the authoritative, by the great physicist himself.

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Published originally in 1916 in German as Über die Spezielle und die Allgemeine Relativitätstheorie, this English edition from 1920 (updated 1954) is an authorised translation by Robert W Lawson.

Relativity presents an introduction to the Special and General Theories and discusses the connection between the two and their relationship with classical dynamics. It is not an easy book; some knowledge of both physics and mathematics is assumed, especially algebra and Cartesian geometry.  As the author himself admits in his preface, the ‘work presumes . . . a fair amount of patience and force of will on the part of the reader.’

The book is divided into three parts and appendices. Part 1 deals with the Special Theory, Part 2 with the General Theory and Part 3 cosmological considerations.

‘If a mass m is moving uniformly in a straight line with respect to a co-ordinate system K, then it will also be moving uniformly and in a straight line relative to a second co-ordinate system K’, provided the latter is executing a uniformly translatory motion with respect to K.’

Using simple analogies – a moving train, an observer on a railway embankment, and a man walking on the train, Einstein introduces us to the principle of relativity. Simple equations relate the co-ordinate systems, ie man/train – train/embankment. However, when one substitutes for the man a beam of light, things become more complicated. We find an apparent contradiction between the relativity principle and the laws governing the propagation of light – both already demonstrated by experiment. In order to retain both (and it seems we must) we are led to some very counter-intuitive concepts: identical clocks which tick at different rates; measuring rods that shorten when they move.

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‘The non-mathematician is seized by a mysterious shuddering when he hears of “four-dimensional” things, by a feeling not unlike that awakened by thoughts of the occult.’

The universe does not – of course – behave like a man in a train and a railway embankment. Time is not an absolute. My time is not the same as that of (let’s say) Supergirl speeding overhead faster than a bullet. And it is on the variability of time that the Special Theory hinges. If you are interested, read up on the Michelson/Morley experiments, or Google the names.

So far, Relativity has considered only uniform motion. Now, having established the idea that all motion is relative – for example, train to embankment, man to train, man to embankment – we are ready to move on to Part 2 and a discussion of the General Theory. Here, we are concerned with all motion, uniform, linear or otherwise. As most first year high school students know, according to Newton’s Second Law, the force acting on a body is equal to its inertial mass times its acceleration. [F=ma] They will also know most probably that, as Galileo demonstrated, bodies falling in a gravitational field accelerate at a rate independent of their nature or constitution.

‘In gravitational fields there are no such things as rigid bodies with Euclidean properties; thus the fictitious rigid body of reference is of no avail in the general theory of relativity.’

Here, the arguments become a bit more complex and some fundamental knowledge of calculus is assumed before delving into Minkovski’s space and the geometry of Gauss. The space-time continuum of the General Theory of Relativity is not the Euclidean space  with which we are most familiar – the one on which the theorems of school geometry depend. It is a living, dynamic structure permeated by an invisible force (gravity )that rules our every day lives every bit as much as it dictates the motions of the stars and planets.

In the short Part 3 of the book, Einstein considers the nature and structure of the universe from the standpoint of his theories. The appendices present extensions of some of the physical and mathematical ideas contained in the first three parts and are not essential reading for a general understanding of the principles behind those theories.

Relativity is a ‘popular science’ book from which one gets according to what one puts in. I have read it twice and still feel some of its ideas strange and the concepts difficult to grasp [and I thought I understood relativity, so a third reading is on the cards]. However, it is worth remembering that physics has moved on since 1916 and that our understanding of the physical universe has changed. Even Einstein himself lived to  develop his ideas and question some of his assumptions. Yet no one in the century since Relativity was written has managed to come up with a better theory about how the universe – and time and space – works.

I would add that for anyone interested in the physical theories without the mathematics, there are almost certainly other books on the market that explain them in more rudimentary terms. The attraction of this particular volume is that we learn from the master himself. The decades roll away and we can read in his own words how he wished his insights presented, how he developed his ideas and what they mean for science as a whole. For anyone interested in science, Relativity by Albert Einstein is an historical landmark.

*****

 

 

 

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2 thoughts on “E=mc2 and all that jazz

  1. Thank you! Sorry I didn’t reply sooner but I’ve been away with poor internet access. The edition I have was published in 1993 by Routledge Classics ISBN 0-415-25538-4 or 0-415-25384-5, respectively HB and PB. As far as I know it follows the Methuen Edition of 1954 but I haven’t checked.

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