Relativity and FTL

The good news is, I was featured in an article about faster-than-light travel in the August 1998 issue of Discover magazine.

For the most part, it's a pretty interesting article. I would, however, like to correct some of the exaggerated credit that was given to me. From the article, the reader would think that I am one of the world's top researchers in the field of general relativity... in real life, I have a lot of fun studying general relativity, but I am hardly the world's expert. The first time I saw the actual text of the article was when it hit the newsstands, and I was slightly amazed to find I was prominently featured. Understanding general relativity is rather a hobby with me (I'm an experimental solid state physicist, not a theoretical physicist). The fact that I'm interested in the far-out stuff like wormholes, black holes, and warp drives is more driven by my science fiction background than by my background as a physicist.

Some background references on wormholes include Robert Forward's review article "Space Warps: A Form of Propulsionless Transport" in Journal of the British Interplanetary Society Vol. 42, pp. 533-542, 1989; and the 1977 book by Kaufmann, The Cosmic Frontiers of General Relativity.

OK. Once you keep firmly in mind that I am not claiming to personally be the world's expert on the subject, general relativity is an extremely interesting study, and I suggest that anybody interested should dive in! Here are some entry points.

Some books about black holes and general relativity

For people who want to know more about General Relativity and Black Holes, there seem to be literally tons of books about black holes, and I can't claim to be an expert on all of them. Here is a review of a few that are on my desk.

For a readable overview, I recommend:
Kip Thorne, Black Holes and Time Warps: Einstein's Outrageous Legacy. Norton 1994, $30 hardcover. Probably the best overall non-technical book on the subject, highly readable and very informative, and written by one of the scientists responsible for our understanding of black holes. The history section shows us Einstein at work, and gives us a feeling of just how incredibly hard it was for Einstein to come up with the theory of general relativity. [The usual books just pass this off with, "ten years later, Einstein unveiled a general theory which incorporated gravity into relativity."] The book is also unusual for an American book in that it discusses Russian contributions in just as detail as American contributions to the study of black holes. Highly recommended.

A nice book about black holes in astrophysics (not a whole lot of explanation about general relativity, but superb pictures) is:
Gravity's Fatal Attraction: Black Holes in the Universe by Mitchell Begelman and Martin Rees, Scientific American Library, 1996, ISBN 0-7167-5074-0

If you want to learn some of the mathematical background about general relativity, but without hitting the heavy parts of the math, you might try Robert Geroch's book General Relativity from A to B, University of Chicago Press 1978. He shows how relativity is a theory of four-dimensional geometry, and in doing so gives a mostly readable introduction that does exactly what the title says: it gets you to the starting point of understanding the background concepts of relativity.

If you are actually serious about learning the subject, let me urge you to learn physics from textbooks, rather than from popularizations: the popularizations of physics are often good entertainment, but in trying to make physics accessible to a general audience, popular physics books often treat the subject at a level of superficiality that ends up being misleading (or even downright incorrect). There is no substitute for an actual physics textbook, both reading through a textbook and doing the problems.

Before you start to learn general relativity, you ought to have a working knowledge of special relativity. E.F. Taylor and J.A. Wheeler's Spacetime Physics (W H Freeman & Co.; ISBN: 0716723271) is one classic textbook on the subject. The follow-on book Exploring Black Holes will give you everything you need to know about black hole physics, without extensive math (that it, it doesn't require theory of differential manifolds to understand!). There are also many other texts on special relativity.. Again, let me urge you to learn from a textbook, not from a popular science article.

For technical reference, if you want the real physics of general relativity, undiluted by popularization and with the equations intact, I recommend several text books:

I.R. Kenyon, General Relativity, Oxford Science Publications, Oxford 1990, hardcover/trade paper. This would be my recommendation for a textbook to learn GR. A thin book that is quite readable, focusing on the physics and leaving out the heavy details of the derivation of the mathematics. It also has the great advantage that Kenyon leaves the factors of G and c in, instead of dropping them in the assumption that the physicist can put them in later. The section on black holes is much briefer than that in Wald, and for this reason I don't find it as good a reference.

Robert Wald, General Relativity, University of Chicago Press, Chicago 1984. This is a commonly-used textbook about general relativity. It takes a mathematics approach, rather than a physics approach, and is going to be mighty tough sledding for anybody without a physics or math background. Chapter 6, "The Schwarzschild Solution," is a good reference about black holes.

W. Pauli, General Relativity, Dover books, paperback. A very old book still in print, quite concise. Good as a reference book on general relativity, not very useful as a reference book about black holes.

C. Misner, K. Thorne and J.A. Wheeler, Gravitation, Freeman, San Francisco, 1973. This is the classic textbook about general relativity, a textbook thicker than most dictionaries that covers everything. As an undergraduate, I found MTW written in an attempt at a breezy style that was hard to follow. As a physicist, I find their notation idiosyncratic. As a reference book, this is the book that all the other textbooks refer to with words such as "for a more complete discussion, see Misner, Thorne and Wheeler."

If you actually want to learn general relativity, I suggest trying John Baez's General Relativity Tutorial on the internet. This won't tell you anything about black holes or wormholes, but general relativity is worth learning just as a chance to stretch your mind, and this tutorial is the most readable introduction to the subject I've ever come across.

Another page that takes the reader from special relativity through General Relativity is the internet textbook Modern Relativity by David Waite. This book does go on to derive some of the interesting metrics of faster than light travel, including wormhole metrics and warp drives.

Some other non-technical books include:

John Gribbin, Unveiling the Edge of Time. Harmony Books, NY, 1992, $20 hardcover. One of the better popular books; covers much of the territory of Thorne, with a long historical discussion of the development of the ideas behind black holes (starting with Newton) and ending with wormholes, but from a different view.

Stephen Hawking, A Brief History of Time. One of the most celebrated books of the last decade. It is not per se about black holes, but is a historical overview of the development of modern cosmology with Hawking's commentary and doses of philosophy interspersed. I found it a little irritating: in working to make the book accessible to a non-technical audience, Hawking simplified some parts so much that what he says borders on being incorrect. This is an good book to read for pleasure, but not a good one from which to learn about black holes from, it is written at a rather low level for non-specialist audience.

Stephen Hawking, Black Holes and Baby Universes, trade paper. This one is a series of essays, loosely connected. I hoped from the title that it might tell me a lot about wormholes, but I found it very superficial.

Clifford Pickover, Black Holes: A Traveler's Guide. Wiley, New York, 1996, $24.95 hardcover. The smarmy "sci-fi" sections that punctuate the chapters are absolutely horrible, much of the book consists of pretty but irrelevant color computer graphics, and about half of the book has nothing to do with the subject. But, despite these flaws, the book has one overwhelming feature that endears it to me: it actually includes equations. It doesn't just tell you about black holes, it gives you the equations and encourages you to work things out yourself.

John F. Gott III, Time Travel in Einstein's Universe. This is a new one; it got a good review in Physics Today, so I just ordered a copy.

Some other technical books include:

S. Hawking and G. Ellis, The Large-Scale Structure of Space Time, Cambridge University Press, 1973. If you want to see Hawking when he is not being superficial, this is the book for you, dense with math. Too dense for me, alas.

Matt Visser Lorentzian Wormholes, AIP Press 1995. This one is the premier textbook on the subject of wormholes. It is extremely mathematics heavy, but in between the mathematics he makes it a specific point to make clear exactly what we know and what we do not know.

Some web references

Page by Geoffrey A. Landis, copyright 1998