A serious but not ponderous book about Relativity

by Walter Scheider

Using an informal style, introduces the special theory of relativity and includes extensive discussion of misconceptions about relativity.

Genres: Physics

246 pages, Hardcover

First published December 1, 2000

Reviews

[WarpDrive · Rating 4 out of 5]

This is an excellent treatment of special relativity. Precision, thoroughness and conceptual rigour are combined with a rich array of useful and pedagogically effective examples and exercises, without impairing the overall readability and accessibility of this book.

The derivation of Lorentz transformation equations is done brilliantly, using the familiar device of the light pulse clock: yes, it is not as general as the original, more abstract derivation by Albert Einstein in his 1916 book "Relativity", as it makes the assumption that the events are time-like. But it is much easier to follow and more grounded in tangibles.
The treatment of Minkowski diagrams is also done brilliantly, with several enlightening examples.

Special relativity is not about complex mathematics (the underlying mathematical underpinnings are trivial, at high school level), but it is first and foremost about conceptual clarity - and this is where many popular science books fail, and where this book succeeds brilliantly.

The only issue is that there are a couple of examples where the language is un-necessarily convoluted and probably misleading, and there are a few typos (one of them being quite funny, stating that the orbit radius of Mars around the Sun is around 3000 km - apart from the very dubious physical possibility of such orbit, it would make for a very balmy climate on its surface).

Apart from these minor issues, it is a very good book, a brilliant treatment of special relativity. 4 stars.

[Blair · Rating 3 out of 5]

When your understanding of the world leads to contradictory answers, it is time to think again. In the nineteenth century, Maxwell’s equations provided a complete description of the nature of electricity and magnetism. It predicted that these two forces combine to form an electromagnetic wave, and even calculated the speed of that wave, which was the same as the speed of light. But this triumph exposed a problem: the speed of light was a fixed value without any reference of what it was relative to. That made no sense according to the basic assumptions of Newton’s laws of motion.

This book does a wonderful job exploring how the search for a solution to this conundrum led to Einstein’s special theory of relativity. We are gently led to the consequences of this theory on our notions of space and time. A conundrum facing an author of a popular science book is that the audience has different levels of knowledge. His solution is to start with basic concepts and slowly increase the level of mathematical difficulty as the book goes on. Most chapters have practical problems that are solved mathematically.

Unfortunately, this leads to finding numerical solutions to problems before we properly understand the nature of space-time that relativity theory describes. Even worse, we never really get there. At one point he tells us, “It should be mentioned at the outset that not all physicists agree that the concept of relativistic mass is necessary.” Indeed, those physicists argue that it teaches misleading concepts that need to be unlearned later in exchange for computational convenience now. I think they are right.

The tool that has enabled me to grasp the nature of space-time is the Minkowski space-time diagram. Unfortunately, here it is treated as an afterthought, appearing near the end of the book, used mainly as a means to calculate Lorentz transformations. Space-time diagrams can explain why two events can occur in a different order in different reference frames, but this opportunity was lost. It did not help that, contrary to everyone else, his diagrams were drawn with a horizontal time axis.

“Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.”

It seems that every treatment of relativity (except this one) uses this quote from Hermann Minkowski. I wonder if it is a misleading translation. In English, shadows imply something spooky, unpredictable and best avoided. Mathematically, a shadow is a projection. The separate space and time that we experience is really a projection of unified space-time. We should embrace this concept, not avoid it.

I am going to spend the rest of this review talking about the example problem on page 118. Like everyone else, I suspect, at first I read through the solution and thought, OK, fine. But later I went back to it to see if I could rework it using time dilation rather than length contraction. This led me to realize that his solution is wrong. I don’t mean that he simply made an arithmetic mistake. I mean conceptually wrong. He appears to take literally the idea that moving objects shrink when observed from a different frame of reference. Instead, if you think of our experience of space-time as a projection, you realize that the entire space contracts, not simply the objects within it.

Here is the question: A boat travels at half the speed of light toward a dock. Does a light beam shone from the back of the boat reach the front before the boat reaches the dock?

The problem is examined in two frames of reference – the dock and the boat. In the dock reference frame he applies to Lorentz transformation only to the boat, but not the space it is in. But in the boat reference frame, the boat stays the same length (I suppose because we are on it) but the space it is in shrinks. He correctly says that the outcome should be the same in both reference frames, yet his own results say the boat takes twice as long to reach the dock in one frame than the other. These times are in different frames of reference, but the time dilation factor at half the speed of light is only 1.15, not nearly enough to account for the difference.

Using his logic, if the boat was going faster than 80% of the speed of light, its front would already be past the dock, and it would take negative time to get there.

When your understanding of the world leads to contradictory answers, it is time to think again. I think a teaching method is clearly flawed when it confuses not only the student but the teacher as well. Understanding space-time using the Minkowski diagram could have avoided these problems. So despite the fact that this book contains a lot of valuable material, I am afraid that my understanding of relativity benefited the most from the work I did uncovering and understanding the flaw in his example. That makes it hard for me to give a fully enthusiastic recommendation.