Customer Reviews

God's Equation: Einstein,Relativity,and the Expanding Universe

5 star:		(23)
4 star:		(12)
3 star:		(3)
2 star:		(2)
1 star:		(2)

 

 

I had expected this book (foolishly judging it by the cover) to present a new theological interpretation of cosmology, or perhaps a theory based on new astronomical observations. In fact it seems as if Aczel had the title "God's Equation" thrust on him by a publisher eager for more sales.

The book is actually a pretty enjoyable and readable introduction to special and general relativity, interwoven with some more modern physics and plenty of anecdotes about Einstein's life.

The author has conducted unique research of his own, commissioning his father to translate some of Einstein's previously unpublished letters. And so an intriguing character sketch emerges, blended seamlessly with the science. It dwells at length on the "greatest blunder", the cosmological constant, which is still debated by cosmologists today.

The explanations of the physics are really rather good. I would highly recommend this book to someone who's after an easier read than Hawking's Brief History of Time, and not yet ready for the Elegant Universe.

A very personal, thoughtful, and welcome book.

Aczel, whose book about Fermat's last theorem was an enjoyable romp through the history of mathematics, now turns his attention to Einstein's theory of general relativity and its implications for cosmology. Based on his work with some historians who are taking a fresh look at Einstein's life and work through recently discovered notebooks and correspondence (Renn, Stachel, et.al), Aczel is able to reveal some previously unknown factoids about the 20th century's greatest scientist. For example, a previously unknown notebook from about 1912 reveals that Einstein had produced his field equation for gravitation nearly 3 years earlier than its final publication in 1915. Apparently Einstein was not convinced of the accuracy of this equation, for he abandoned it, only to rederive it 3 years later with apparently no recollection that he'd been there before. Aczel also spends some effort refuting the popular myth that Einstein was no good at mathematics. He was a superb mathematician, says Aczel, and largely self-taught, which speaks to his agile intellect and intuitive sense for fruitful areas of research.

Unlike any other biographies of Einstein or expositions of relativity that I've read, Aczel takes a "mathematician's eye view" of general relativity, and spends considerable time tracing the development of the geometry of curved space through Gauss, Reimann, and several other lessor known contributors. He also reveals, which I had not known previously, that Einstein kept up an ongoing correspondence with the legendary British mathematician David Hilbert, and that Hilbert published some work of his own based on early copies of Einstein's field equations. This incident has apparently been fodder for considerable historiagraphical debate, and was only recently settled that there was no plagarism or other funny business occurring on the part of either man.

God's Equation is not all Einstein, however. Aczel also introduces us to many of the nagging questions in modern cosmology, and astronomers' attempts to reconcile the recently discovered accelerating expansion of the universe with current theories. Astronomer Saul Perlmutter is central to the story's recent developments, whose supernova observing program lent considerable weight to the accelerating expansion scenario. Taking center stage for this discussion is the resurrection of the cosmological constant, Einstein's famous "blunder," which Aczel argues, has never really left cosmology. As modern astronomers have looked further and further into the universe and back in time, the cosmological constant seems more and more necessary to some theorists, as a repulsive force to counteract the attractive force of gravity (which is itself a brute simplification, since anybody familiar with general relativity knows that gravity is not a force at all, but rather a result of curved spacetime).

Overall, I do recommend this book, though I'm frustrated that Aczel didn't do much more with this opportunity. This book could have easily been twice as long. I get the sense that he was hurried to get it to print for some reason, passing over stories that begged for further clarification (more, for instance, on the eclipse expeditions so central to providing proof for general relativity, and less on the roots of World War I, which delayed the expeditions). All in all, it's an excellent addition to the existing material on Einstein's life and work, and a teaser for more detail on what's really going on in modern cosmology (in the last two or three years, particularly). It makes me hunger for some publications based on Renn and Stachel's work on Einstein. I found a few typographical errors (in a discussion about the effect of Minkowski's lectures on Einstein while at the ETH, he gives a date for Minkowski's birth four years after Einstein published his paper on special relativity).

It's not Aczel who first brings up God, it's Einstein. One of the most thought-provoking things about this book is that for all our research and increasingly detailed knowledge of the way things work, most physicists are convinced that some sort of Creative Power underlies the workings of the universe. As a physicist and professor myself, I am impressed at the way Aczel clearly -- poetically, even -- lays out some of the more complicated cutting-edge concepts of contemporary science. He's extensively interviewed some of the most prominent figures in the field, and his good research (except for a couple of what I presume are typos regarding historical dates) shows. The previous reviewer must have some personal bone to pick with the author, because he/she and I didn't read the same book. Do read it; it will give you a glimpse -- however fleeting -- into the mind of one of humanity's greatest (Einstein): and therefore, perhaps, a glimpse at the awe-inspiring workings of the cosmos.

I thoroughly enjoyed Fermat's Last Theorem, also by Aczel, so perhaps I came to this book with unfairly high expectations, but I was a little disappointed. Make no mistake, it's a good read and the author's account of Einstein's struggle to get experimental verification of relativity (including showing his tendency to be unduly harsh in dealing with others) humanizes the great physicist in a way few volumes have. But there are some flaws, some minor, others more serious.

One minor gripe is that the pacing of the book is uneven; it drags in places and picks up in others. Interestingly but perhaps not surprisingly considering the author, the pace seems to pick up just at those times when Aczel is discussing the mathematics involved. I could almost feel his enthusiasm for his subject rising. (Those discussions are excellent, by the way.)

I also confess to being annoyed at how, if you follow Aczel, no one measures up to Einstein, everyone falls short, everyone is in his shadow and if only somehow he had lived longer he would have solved - as only he could - all these questions which now plague astrophysics. Admiration is one thing, hero-worship is another.

A more serious flaw is that Aczel, while a master of the mathematics involved, seems to be not well-versed in the state of observational knowledge of cosmology. He says, for example, that just a few years ago, most scientists maintained that the expansion of the universe would slow, stop, and reverse into a "Big Crunch." Some, he says, held it would slow to a stop and then maintain a steady state, neither expanding nor contracting - and "only a few" believed the expansion would continue forever. Actually, the most common belief among astronomers and astrophysicists was none of these but closest to the last: The expansion would gradually slow down but never actually stop. That is, the expansion would continue forever but at an ever-slower rate.

Later on, he says that "everyone" - including scientists - had hoped for either a static or an oscillating universe (with a Big Bang eventually collapsing into a Big Crunch which produces a new Big Bang), ideas that astronomers had dumped long ago.

It's that misunderstanding, I expect, that leads him to more than once refer to the "surprising" announcement in 1998 that the universe is expanding. But the surprise in that announcement was not that the universe is expanding - that was old stuff - but that the expansion is accelerating! It's expanding faster now than in the past! An amazing discovery which calls for a re-think of our understanding of the nature of existence.

Which brings me to the final flaw: In the time since its creation as the (in)famous fudge factor Einstein stuck in his equations to make general relativity describe a static universe (in line with the belief of the time), the notion of a "cosmological constant" has gone through so many incarnations that it's simply not proper to equate what cosmologists are talking about today with Einstein's self-proclaimed "blunder."

Overall final judgment: Could have been better, but worth the read for the story of Einstein's struggles and the clear descriptions of the basics of non-Euclidean geometry central to relativity and cosmology.

Amir Aczel describes Einstein's equation of general relativity that governs the behavior of the universe from its birth to a possible role in the near future. The story is beautifully woven together with the latest finding in cosmology and the riddle of creation. While a few lines of equations are shown, their meaning is explained by simple terms that can be understood by lay readers.

On the basis of Einstein's letters that became accessible recently, Aczel tells for the first time the great physicist's efforts to get a prediction of his theory experimentally proved. Thus the author well succeeds in revealing a human side of the person who discovered God's Equation. This is quite a readable and absorbing book.

In the Preface, Aczel observes: "I was determined to explain to myself [italics] the exact relationship between an ever-expanding universe, Einstein's ingenious field equation of general relativity, and the enigmatically curved universe in which we live." After extensive and intensive research, "I was able to tie together the cosmological theories, the astronomical discoveries, the physics of gravity and spacetime, and Einstein's personal odyssey of discovery." The reader accompanies Aczel every step of the way to reaching this synthesis.

Along the way, he discusses the contributions of Saul Perlmutter, Albert Einstein's early years, his solution of the "Euclid Riddle", his relationship with Marcel Grossman, his years in Berlin, Arthur Eddington's verification of several of Einstein's theories, explications of Einstein's equations of general relativity by Steven Weinberg, Alexander Friedman, and Alan Guth, the quantum theory's relationship to the discovery of previously-unknown particles of matter, the "geometry of the universe", Neta Bahcall's research on the density of mass, and the incorporation of quantum considerations into the theory of relativity.

In the final chapter, Aczel suggests that "Mathematicians will develop the tools, physicists will apply them, astronomers will verify the theories and provide data, and cosmologists will generate the big picture of the universe." Although "Euclid's Riddle" may have been solved, the formulation of "God's Equation" continues. Aczel then goes on to say:

"Once each discipline is supported by developments in the others, we may begin to understand the ultimate laws of nature and to formulate our human estimate of God's Equation. When the final equation is constructed, we should be able to use it to solve the wonderful riddle of creation. And perhaps that's why God sent us here in the first place."

God's Equation offers intellectual stimulation and nutrition of the very highest quality. It is a pleasure as well as a privilege to accompany Aczel on his own "personal odyssey of discovery."

"God's Equation" has great value as an engrossing and fairly lucid account of the complex and relatively inaccessible issues that make up current cosmology; Mr Aczel should be congratulated.

On the other hand ... halfway along Aczel claims Euclid didn't use the Fifth Postulate in the first book of "The Elements". Euclid proved the Pythagorean Theorem and many other, simpler concepts in Book One, which simply don't hold in non-Euclidean geometry: five minutes of research on Aczel's part would have set him straight. Aczel even claims in the same paragraph that Euclid described the properties of triangles and parallelograms (!) in the first book. Five seconds of thought would have set him straight. He claims the Fifth Postulate isn't really necessary for these things (in Euclidean geometry); if he can show that it isn't, he should publish his thoughts on the subject: authors 200 years from now would be writing about *him*.

It is silly to be offended by an author's factual or logical errors, especially if they don't directly impact his main argument, but I was a little hurt. And if the author can make such basic mistakes in geometry, how can I trust what he says in wider areas like cosmology? This book is clearly geared for neophytes; how can they trust anything at all?

Overall, I still enjoyed "God's Equation" and learned a lot (I think). I do wish I felt Aczel had researched it or thought it through better. Perhaps there will be improved editions in the future.

The book is very well written, however the author's main intent aside from examining einstein's search for relativity, seems to be to show that scientists are 'realizing' that Einstein's "mistaken" addition of the 'cosmological constant' into the theory of relativity wasn't a mistake at all. That is fine, however the author gives a lop sided view - basically giving all the reasons and theories as to why the cosmological constant is valid - you are lead to believe that it has been 'proven' correct - while virtually ignoring the numerous other valid theories. One notable example of this is the author's dismisal of the 'string' theory in less than a paragraph somewhere near the end of the book with no good argument or explanation as to WHY he feels the string theory is bogus. considering the physicist brian green was able to write an entire book about why he feels the string theory is not only valid but very likely correct (the elegant universe), I would have hoped that the author of 'god's equation' would have come up with some sort of 'proof' as to why the 'cosmological constant is any more valid. Otherwise, this is a very interesting book, with interesting insights on Einstein himself, and even a good primer for Einstein's own book, "Relativity".

This is a review of the AUDIBLE.COM version of this book.

Although I enjoy books on science, I was hesitant to purchase this one. I am not very interested in mathematics and was unsure how interesting the book would be. I was surprised to discover that this is a thoroughly enjoyable book. Aczel is able to take topics that many people would consider to be dry and uninteresting (unless you're a mathematician) and weave them in a captivating tale. Through Einstein's writings and those of others, we follow Einstein along his life's journey as he developed his theory general relatively and ultimately to his search for the structure of the universe. Along the way we meet many interesting physicists, mathematicians, and astronomers - each of which adds another piece to the puzzle or provides real-world proof of Einstein's theories.

Even if you have a mild interest in Einstein and theoretical physics I think that you will enjoy this book.

In "God's Equation", Amir Aczel explores the recent history of cosmology and physics, interwoven with a biography of Albert Einstein. Despite the fact that he is discussing complex ideas and topics, Aczel manages to explain concepts in an easy-to-understand fashion.

Perhaps the most enjoyable part of the book was the biography of Einstein infused in the chapters. Einstein was an amazing scientist and a fascinating person, and Aczel reveals his life in an interesting way. The reader also learns of the great work of a number of scientific/mathematical genuises of the past- such as Euclid, Planck, and Reimann. Their discoveries, like Einstein's are explained to the reader in a surprisingly accessible way.

The most interesting conclusion of this book is that the universe is expanding, and will expand forever. This seems counterintuitive, for it implies a universe that began a finite time ago and will never re-contract. This is perhaps one of the most important discoveries of all time.

Overall, "God's Equation" is a highly accessible and highly recommended book. It is a fast read, and one that won't be regretted.