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

Amir D. Aczel
4.5 out of 5 stars  See all reviews (4 customer reviews)

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Book Description

Dec 2000
Are we on the verge of solving the riddle of creation using Einstein's "greatest blunder"?

In a work that is at once lucid, exhilarating and profound, renowned mathematician Dr. Amir Aczel, critically acclaimed author of Fermat's Last Theorem, takes us into the heart of science's greatest mystery.

In January 1998, astronomers found evidence that the cosmos is expanding at an ever-increasing rate. The way we perceive the universe was changed forever. The most compelling theory cosmologists could find to explain this phenomenon was Einstein's cosmological constant, a theory he conceived--and rejected---over eighty years ago.

Drawing on newly discovered letters of Einstein--many translated here for the first time--years of research, and interviews with prominent mathematicians, cosmologists, physicists, and astronomers, Aczel takes us on a fascinating journey into "the strange geometry of space-time," and into the mind of a genius. Here the unthinkable becomes real: an infinite, ever-expanding, ever-accelerating universe whose only absolute is the speed of light.

Awesome in scope, thrilling in detail, God's Equation is storytelling at its finest.

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Product details

  • Paperback: 236 pages
  • Publisher: Delta (Dec 2000)
  • Language: English
  • ISBN-10: 0385334850
  • ISBN-13: 978-0385334853
  • Product Dimensions: 20.8 x 13.7 x 1.8 cm
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (4 customer reviews)
  • Amazon Bestsellers Rank: 3,244,061 in Books (See Top 100 in Books)

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Amazon Review

Who would have thought a mathematical constant would make such an engaging character? God's Equation: Einstein, Relativity and the Expanding Universe, mathematician Amir Aczel's tale of the search for a scientific explanation of the universe, features the cosmological constant in a role as complex as Einstein's. The great genius referred to it as his "greatest blunder" but recent events in the world of astrophysics have brought the prodigal term back into the fold as an important part of his field equation. Aczel is a powerful storyteller and makes no secret of his admiration for Einstein; much of the book revolves around his conquest of general relativity. Integrating relativity with gravitation was no easy task (even for Einstein) but the author deftly steers the reader away from the sticky stuff and focuses attention on concepts of importance.

Aczel shows Einstein's aesthetic troubles with the cosmological constant, which preceded theoretical and experimental problems leading to its abandonment. The universe was caught in the act of expansion by Edwin Hubble and the constant, originally invoked to maintain a steady-state universe, was unnecessary. Fortunately, though, the mathematics underlying the constant had become important tools for physicists; observations in 1997 and 1998 by Saul Perlmutter, Neta Bahcall and others showed that the universe will continue expanding indefinitely and sent theorists back to the drawing board to revise their equations. The cosmological constant returned triumphant and, while its inventor might never have approved of it, today's scientific community gives it an honoured role in God's Equation. --Rob Lightner, Amazon.com --This text refers to the Hardcover edition.


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First Sentence
Saul Perlmutter sat in his office high in the Berkeley hills overlooking the San Francisco Bay and watched the sun set below the Golden Gate Bridge. Read the first page
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Most Helpful Customer Reviews
4 of 4 people found the following review helpful
5.0 out of 5 stars Einsteins struggle for the final equation 29 Mar 2003
Format:Paperback
Inspired by the fact that the universe is ever expanding,
Aczel wrote the history from Einstein to the present
of the thoughts around Einsteins cosmic constant. The main
part deals with Einsteins struggles with his main equation
and the discovery of the first proof for general relativity,
the bending of star light around the sun. This history part
is presented in kind of zooming in at those times and people,
so that one temporarely becomes part of the times of the
process of verificaton and recognition of general relativity.
From the statements about the cosmic constant the author
then leads the reader into modern times, but this time rather
zoomed out, mentioning many people an theories.
It's all gripping to read, but one does not get answers about
the phenomena which introduced the book, namely, how the
universe could possibly accelerate it's expansion.
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2 of 2 people found the following review helpful
4.0 out of 5 stars einstein: not quite for beginners 7 Dec 2003
By gwi
Format:Paperback
Aczel's first book, Fermat's Last Theorem, received deservedly high praise although it deals with an historical curiosum. God's Equations is an account of Einstein achievements, a far more difficult subject on which the popular literature is considerable. Aczel's gift is to tell a good story simply without losing substance, and although this book is less easily accessible than his first, it is arguably better.
Einsten's first contribution in 1905---the special theory of relativity which says is essence that the speed of light is constant regardless of how fast the source of light moves towards or away from the observer---is set out simply and clearly as are its scientific antecedents; ie, the advances in physics (Michelson-Morley), non-Euclidian geometry (Riemann, Grossman), and mathematics (Gauss, Minkowski) which underlay the Special theory and, crucially, the later General Theory. The latter was published in the late 1920s and in effect links the Special Theory to Gravity, producing what is referred to today as the first unified field equation.
Two further points are worthy of mention. One is Aczel's extraordinary grasp of the history of science; to take but one example, Aczel traces the progress of Euclidian geometry from ancient Greece via Ptolemy of Alexandria and the Persian mathematician, Nasiraddin, its smuggling Cordoba by Adelhart of Bath in the 12th Century, from whence it was published in Latin in Venice in 1482. The second is Aczel's account of the relevance of Einstein achievements to the breathtaking world of modern physics and cosmology. All this is accomplished with the greatest simplicity in the space of just over 200 pages.
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1 of 1 people found the following review helpful
5.0 out of 5 stars Difficult but rewarding read 31 May 2003
By Pieter Uys HALL OF FAME TOP 500 REVIEWER
Format:Paperback
In this book, Aczel proposes that Einstein's Cosmological Constant, discarded and by the genius himself considered his greatest blunder, is in fact an integral part of the equation that defines the nature of the universe, its past and its future. Some mysterious force is accelerating the expansion of the universe, pushing out on space, countering gravity and making the universe accelerate towards infinity. Aczel argues that in addition to the four known forces: gravity, electromagnetism, the weak and the strong nuclear forces, there is a fifth: the cosmological constant which is the quintessence of the universe. He spoke to many experts in the fields of mathematics, physics, astronomy and cosmology and integrated the ideas of prominent scientists like Eddington, Penrose and Grossman. The chapters deal with stuff like Euclid's Riddle, Riemann's Metric, the expansion of space, the nature of matter and the geometry of the universe but it also serves as a type of biography of Einstein and a history of the development of his theories. There are quotes from Einstein' work and the text is enlivened by portraits, photographs and illustrations. Although an engaging and thought provoking text, it is sometimes difficult to grasp all of the intricacies as there are many formulas that a non-mathematician would not understand. Nevertheless a uniquely stimulating work that concludes with a helpful bibliography and thorough index. I also recommend Marcus Chown's The Universe Next Door, Mark Ward's Universality: Beyond Chaos and Martin J. Rees' Before The Beginning: Our Universe And Others.
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4.0 out of 5 stars Relativley Easy Reading 4 Sep 2000
By A Customer
Format:Hardcover
I was surprised to find that this book was not as technical as I expected. Much of it is biographical but gradually blends into the more complicated and perplexing findings of Einstein and others. For this reason I found the book enjoyable and interesting as well as stimulating. Those looking for glimpse into the life and insights of Einstein or for those with an interest in physics and cosmology, I would suggest this book .
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Most Helpful Customer Reviews on Amazon.com (beta)
Amazon.com: 4.2 out of 5 stars  45 reviews
33 of 34 people found the following review helpful
4.0 out of 5 stars A pleasant surprise - short and light 13 Jun 2000
By Vincent Toolan - Published on Amazon.com
Format:Hardcover
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.
33 of 35 people found the following review helpful
5.0 out of 5 stars A stunning read 19 Nov 1999
By A Customer - Published on Amazon.com
Format:Hardcover
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.
28 of 30 people found the following review helpful
5.0 out of 5 stars A good read... 27 July 2000
By John Rummel - Published on Amazon.com
Format:Hardcover
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).
14 of 14 people found the following review helpful
3.0 out of 5 stars A good read - flawed, but not fatally so 18 Oct 2002
By LarryE - Published on Amazon.com
Format:Paperback
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.
9 of 9 people found the following review helpful
5.0 out of 5 stars Aczel's Odyssey 17 May 2000
By Robert Morris - Published on Amazon.com
Format:Hardcover
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."
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