God's Equation: Einstein, Relativity, and the Expanding Universe by Amir D. Aczel

by Amir D. Aczel

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 honored role in God's Equation. --Rob Lightner

Genres: Science, Nonfiction, Physics, History, Mathematics, Biography, Astronomy

Hardcover

First published January 1, 1999

About the author

Amir Aczel was an Israeli-born American author of popular science and mathematics books. He was a lecturer in mathematics and history of mathematics.

He studied at the University of California, Berkeley. Getting graduating with a BA in mathematics in 1975, received a Master of Science in 1976 and several years later accomplished his Ph.D. in Statistics from the University of Oregon. He died in Nîmes, France in 2015.

Reviews

[Thomas Ray · Rating 2 out of 5]

God's equation : Einstein, relativity, and the expanding universe
Amir D. Aczel, 1999
236 pp.
ISBN 1568581378
Library-of-Congress QB981 A35 1999
worldcat: https://www.worldcat.org/title/gods-e...
https://search.library.wisc.edu/catal...

If the universe was much smaller 10 billion years ago, why didn't photons emitted then from quasars reach the edge of the then-much-smaller universe long ago? How did they keep coming all this time, and reach us only now? This book has a partial answer:

We observe light that left its galaxy seven billion years ago. When the light left its source, the galaxy that emitted it was actually about five billion light years from us. When its light arrives here, that same galaxy is at a distance of about twelve billion light years from us. [The distance increased about 7 billion light years in 7 billion years: the distance has been increasing at about the speed of light. How, then, did the light arrive at all? The book doesn't say.] The redshift we see is due to the stretching of space during the 7 billion years the photons were in flight. p. 8.

The most distant object yet seen is a galaxy 13 billion light years away, receding at .956 the speed of light. p. xiii.

Galaxies whose light has travelled 7 billion years to reach us are receding at about .5c (c = speed of light) pp. 5-6. Closer galaxies are receding /faster/. This means the rate of expansion is accelerating. p. 7. But wait. p. xiii says a 13-billion-light-year-distant galaxy recedes at .956c . Moreover, this is the opposite of the Hubble observation that recession speed is proportional to distance: the evidence of an expanding universe. The book doesn't address the disconnect.

The universe has perhaps 20% of the mass density it would need to stop universal expansion. pp. xiii, 11.

The brightest type of supernova brightens for about 18 days, then fades over the following month. p. 6.

Einstein looked for a way to describe gravitation that would:
Make Newton's laws the same under acceleration as in a gravitational field. p. 32.
Redshift light in a gravitational field. p. 32.
Deflect light in a gravitational field. p. 34.

A circle spinning in its plane about its center experiences length-foreshortening of its circumference, by special relativity; its diameter is unchanged. Circumference < pi*diameter. Space is non-Euclidean. p. 59.

Einstein's equation describing gravitational curvature of spacetime: where:
g_mu,nu is Riemann metric tensor: distance in curved space
T is energy-momentum tensor
R is Ricci curved-spacetime tensor
G is Newton's gravitational constant:
R_mu,nu - 1/2 g_mu,nu*R = - 8 pi G T_mu,nu p. 117.

The book is mostly nontechnical biography of Einstein and some of his colleagues. The equations are inadequately explained.

The author had a Ph.D. in statistics. He wasn't a physicist. He claims to understand general relativity, but this book isn't really an attempt to explain it.

Author's wikipedia page: https://en.m.wikipedia.org/wiki/Amir_...

Proof that sqrt(2) is irrational:
If rational, then there are integers a, b, with no common factor, where a^2 = 2*b^2.
If a is odd, a^2 is odd: but 2*b^2 is even. So a can't be odd.
If a is even, then for some c, a = 2*c; 4*c^2 = 2*b^2; b^2 = 2*c^2. So b is even: a and b have the common factor 2. So there are /no/ a, b with no common factor whose ratio is sqrt(2).
Quod erat demonstrandum. p. 49.

Also answers trivial questions like this:
https://www.goodreads.com/trivia/work...

ERRATA
P. 144 gives (Newtonian) element of distance as
ds^2 = dr^2 - r^2 dTheta^2
Surely he means /plus/.

"On a sphere, there are no nonintersecting lines." p. 51. Sure there are: parallels of latitude, for example. Or small circles generally. There are no nonintersecting pairs of great circles.

Hermann Minkowski lived 1864-1909, not 1909-1964 as on p. 18.

[Steven Percifield · Rating 4 out of 5]

This book was totally humbling and at the same time inspiring. As neither a mathemetician nor a physicist, it was humbling insomuch as it opened a door (just a small crack) into s discipline in which I have only a glimmer of a background.

It was inspirational insomuch as it showed how infinite the concept of the universe is and what an infinitesimaly small part of it each of us is.

The fact that it addressed the subject in terms simple enough that I can claim a glimmer of understanding is a testament not only to the genius of Einstein and his colleagues but that of the author as well.

A very interesting and challenging read.

[dejah_thoris · Rating 3 out of 5]

Can't help but love reading about Einstein and Aczel's lucid explanations of the seriously complex world of non-Euclidean geometry and advanced physics really helped clarify some theories I've read about previously.

[Beauregard Bottomley · Rating 5 out of 5]

The book was originally published in 2000. The only flaw with the book is that I listened to it in 2012. He explains the general theory of relativity so well that you will be able to explain it to others. He explains its relevance to the than recent discovery of the expansion of the universe and dark energy.

This book is well worth your time. Isaacson's Einstein biography better covers the general theory but is 21 hours long, and the "4 Percent Universe" covers the expanding universe and dark energy better, but this short book can be a good review or primer for those two books depending on which order you choose to read them.

[Ron · Rating 3 out of 5]

My head hasn't hurt this much since I read Hawking's Short History of Time.

More like a text than a story. Too much biography and extraneous details. If he wants to tell the history of the Cosmological constant, do so. Don't confuse matters with unrelated stuff.

I don't see that an open, expanding universe is such a problem.

(See my comment for a discussion of Missing matter.)

[Edward Amato · Rating 3 out of 5]

Interesting but makes the reader feeling small because: 1) the subject matter is about the formation and make up of our universe and Man's tiny part of it, and 2) my physics, astronomy, algebra and geometry education is fatally oxidized. I preferred the author's other book on the compass.

[Arden]

can't wait to revisit this with a better understanding of relativity :)

[Jake Wasdin · Rating 4 out of 5]

Great read. Aczel told how Einstein developed the theories of relativity with a special emphasis on the mathematics behind it and then told of later developments with the equation. However, the biographical information and story-telling attributes kept me engaged and there was a lot of look at the physics, cosmology, and astrology going on even though mathematics was obviously the focus.

[Max Ostrovsky · Rating 3 out of 5]

I've always been interested in the intersection of science and religion, thus an amateur lifelong fascination with physics (my math skills have long since left me). The technical writing of the book was easy to follow, yet I found the equations littered throughout a waste of space and eye-strain.
While I am sure our knowledge of physics must have changed in the 20+ years since this book was published, I was still intrigued with some of the information in it.
I knew that the universe is expanding. However, the book adds that the expansion isn't slowing down, as it had at first been assumed, but speeding up. That confounded me, especially since the book says that the universe is cooling. How can it be accelerating and cooling at the same time? I couldn't figure that out. Maybe there's new info out to explain or refute that.
Also, that many billions of years ago, the expansion slowed down drastically, slow enough for quasars to be formed, and then sped up again. Huh? What? I need more of an explanation for that.
It also showed three competing theories of the shape of the universe and praised Einstein's Universal Constant, which I've always had issue with.

[Z · Rating 4 out of 5]

As a lay person casually interested in science, I enjoyed the book a lot. Everyone knows Einstein, but it also introduced several other scientists and mathematicians a non-scientist may not have known about before. I was glad to learn about these other thinkers.

The history in the book was very interesting (for example, I enjoyed learning about the construction of neutrino detecting vats in mines around the world), and I was dog-earing and underlining on almost every page to remind myself to look more things up!

The closer to the end of the book I got, the more complicated it got, so a casual reader may have a hard time keeping up (I know I did). Mercifully, it is not a thick book. :) It did pose questions I never thought much about before (i.e, the shape of the universe -- flat, spherical, hyperbolic?) which I found to be a fun exercise.

After a mind-bending read, now I have lot of answers I need to find to more questions I have!

[Ella Catherall · Rating 2 out of 5]

I found this book to be really confusing. I'm a biologist by training, but I've had some teaching in physics and have read other Pop Sci about general relativity, but I still found this to be overly complicated. I have read and listened to other people explain the same ideas in ways that were far simpler than those used in this book. What would often happen would be that I'd read the start of a section and understand roughly what was going on, be absolutely flummoxed by the equations etc., and then understand the conclusion based on other things I'd read.

It was also written in a weird order that made it difficult to keep up with what was going on when.

[Clay Olmstead · Rating 3 out of 5]

This book takes on a monumental task: to document the history and implications of Einstein's General Theory of Relativity, and explain it at a layman's level, with almost no equations and in less than 300 pages. In doing so, however, much is left out, glossed over or given contradictory explanations. Ultimately, it was unsatisfying to me. The history of cosmology is still an interesting story, if you're willing to follow the author in skipping over the details. (But wait; is God in the details - or is that the Devil? I'm still confused.)

[Derek Dotson · Rating 5 out of 5]

Beautiful! The information is presented with depth, impact, and importance.

Also, it is such a wonderful read decades after its publication. The book is an interesting amalgamation of the cutting edge research, people, and speculation of physics at the time. It is very interesting to be able to see this information with the benefit of hindsight.

[Gary · Rating 4 out of 5]

Really good book, but definitely a hard read. The history of how Einstein’s General Theory developed, and the depth and meaning behind it all is absolutely mind bending! What a GENIUS!!! I’d highly recommend this book to anyone interested in the development of our Universe.

[Larry · Rating 3 out of 5]

Liked the book but mathematical details lost me big time. Interesting to see the progresion of Einsteins work. Too much biographic detail of some of the sub characters. Would hae loved more about his later life. Gave me some new insights into Generla Relativity and non Euclidian space.

[Paul Spiegel · Rating 5 out of 5]

Loved this book which is part biography of Einstein, part history of Physics. The book was trucking along dealing with relativity and then came to a bit of an abrupt end (unlike the expanding universe).

[James McDonald · Rating 4 out of 5]

Excellent book on astronomy, space-time and Einstein's cosmological constant.

[Max Skidmore · Rating 4 out of 5]

Doubt I will live long enough to fully understand this.
Best statement from book about Albert Einstein, “Even when he thought he was wrong, he was right!”

[Kyle · Rating 5 out of 5]

Absolutely amazing

[Kailee Harris · Rating 4 out of 5]

This was an excellent read if you are looking for an informative timeline on the development of "God's Equation" also known as Albert Einstein's General Relativity Theory equation.

[Imzen · Rating 4 out of 5]

This book was an interesting read. This shows how far we have come and the quest for a theory of everything.

[Robert Maier · Rating 3 out of 5]

You want to read this book because you think it will reveal the deepest secrets of the universe and answer, why? It offers much to think about, and pretty clearly shows the progression of the Big Bang origin of the universe which began with astronomers like Galileo and advanced maths of the 1700s. Einstein built his theories of relativity on many shoulders.

At the end of the day (spoiler)there are still several competing theories leading to a universal theory of how the universe sprang from nothing, and will it ever end. No one seems near a conclusion or real proof that explains matter and space-- God's Equation.

Aczel's inclusion of personal material about Einstein, his muses and colleagues, provides a good break from the science. The mathematics was way over my head. I still don't understand how time can be a fourth dimension, how gravity works, or how matter can travel near the speed of light for billions of years and not slow down, or how an arrow shot into the air would eventually return to its starting point.

For the non-mathematical person, the key point is that the universe is such a complex system with many different rules governing operations that are inconceivable for anyone living now. If the human race survives a few thousand more years, we may understand more, but much of what we know already has been used and studied for more than 2,000 years, when Euclid "founded" geometry. Considering the universe, with it's unfathomable distances and unimaginable speeds, geometry is woefully inadequate, and even much of Einstein's work only scratches the surface for why the universe appears to be expanding or where did all the matter come from, or why is there life on earth.

This book is a good mental exercise, but you could ponder the birds at your bird feeder and come up with just as few answers. On the one hand the universe came from nothing, but as atoms and sub-atomic particles formed and became molecules, they must have followed some rules, but where did the rules come from? Many people are happy with the answer "God," was always here, created the rules, and guides and adjusts them to his whims. Problem is, where did God come from.

Good question. It's fun to see people asking, and though we certainly know much more about the world than we did 5,000 years ago, it's like scooping up a handful of sand on the beach and saying you know everything about the world.

[Darren · Rating 4 out of 5]

Thankfully, for a book with God in it's title, there is zero religious connotation in it's content; it is pure science. However, there are more than a few equations cited in this book, but the reader need not fret as the equations do not hinder nor strengthen the books overall effect; they do give the story validity - there is no stronger proof than a mathematical one.

Soon after publishing the special theory of relativity in 1905, Einstein started thinking about how to incorporate gravity into his new relativistic framework. In 1907, beginning with a simple thought experiment involving an observer in free fall, he embarked on what would be an eight-year search for a relativistic theory of gravity. After numerous detours and false starts, his work culminated in the presentation to the Prussian Academy of Science in November 1915 of what are now known as the Einstein field equations. These equations specify how the geometry of space and time is influenced by whatever matter and radiation are present, and form the core of Einstein's general theory of relativity.

Aczel effectively chronicles the history of Einstein's rise to fame due to the fateful 1919 observation of the bending of light by the sun during a solar eclipse. This eclipse was photographed from the expedition of Sir Arthur Eddington to the island of Principe (off the west coast of Africa). Positions of star images within the field near the Sun were used to test Albert Einstein's prediction of the bending of light around the Sun from his general theory of relativity. These observations vindicated Einstein's General Relativity over Newton's light-particle theory, and catapulted him into unparalleled world fame for a physicist.

Despite knowing the story from several other books and courses, I was pleased to learn some new tidbits from this book, like the fact that Einstein was not INFORMED of the vindication of GR for many months after it was experimentally observed! That could not happen in today's socially networked world.

Overall an enjoyable science-packed read.

[Brian · Rating 5 out of 5]

I solved the equation and my book burst into flames. That can't be a good sign. I loved that book too.

[Brent · Rating 3 out of 5]

Amir D. Aczel has an amazing penchant for taking highly technical and scientific concepts and communicating them in a very clear and, I suppose, dumbed down manner for those of us who haven't studied physics or mathematics. He does exactly that in this book as he covers Einstein's development of the general theory of relativity and it's implications on our understanding of the beginnings and future of our universe.

I was really fascinated by the concepts in general. As a humanities guy, I never spent time in the world of physics, yet have always wondered about so many of the concepts. And getting a cursory view into cosmology was really fun. The problem for me, though, was that I believe Aczel must have thought the only audience that would be interested in this subject would be those with a decent background in mathematics and/or physics. As a result, often he casually drops in discussions of equations and such that must be considered common knowledge for those with a minimal education in math or physics. Unfortunately, I'm not one of them. So I was often lost, particularly in the details. In the long run, I felt myself treating those sections much like I did many a math class long ago - the equations were Greek to me, so I tried my best to understand the surround materials and explanations. That worked for the most part, but it did make for very slow and concentrated reading.

All in all, though, it was a compelling look into the world of cosmology and getting a peak into the make up of the four dimensions of time and space and how our understanding of these dimensions may help us to finally understand our universe, and therefore, creation as a whole.

[Erin · Rating 5 out of 5]

Who can I persuade to read this book? Must you be a mathematician to get excited about it? Einstein said, "Math is Nature's language for describing herself" (or something very near that). This book, wonderfully written in very comfortable prose, made me see math as a language for the very first time, and to catch a fleeting glimpse of the joy of math. Can you believe I said that? I am NOT a mathematician and only a B student at it, but perhaps this book is what high school math teachers should offer, if only to respond to the question "when will I ever use this" complaint frequently offered up by bored or confused students. What this book is is a history of the evolution of the equation e=mc2. What shoulders Einstein stood on, how math described natural phenomena. What layman ever knew that it could? There is more to math than making change and balancing your checkbook, if only to connect with nature in a new way.

It probably didn't hurt that I read this book shortly after viewing The Learning Channel videos Universe 2001, Beyond the Millenium (4 parts). It gave me the visual I needed to organize the concepts from the book in my head.

[Tom Schulte · Rating 3 out of 5]

The Einstein field equations (EFE; also known as "Einstein's equations") are the set of 10 equations in Albert Einstein's general theory of relativity that describes the fundamental interaction of gravitation as a result of spacetime being curved by matter and energy. The Einstein field equations (EFE) may be written in the form:

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This is, basically, "God's Equation" here and the history of its development. As such, it is a biography of Einstein, including some very human revelation about Einstein's ability to use people and be self-promoting. The main scientific advancements in the prelude to the field equations are special and general relativity developed in fits and starts revealed in Einstein's notebooks against the backdrop of WW I emerging and challenges to using eclipses to get validation of gravitational theories.

[Ed Terrell · Rating 5 out of 5]

At a point, some 13.8 billion years ago, there was nothing. Then came the big bang. Time and space emerged from a white hole. January 1, on the cosmic calendar. It was "a day without a yesterday".

Aczel is a great writer and makes any subject that he tackles enjoyable and enduring. God's Equation, starts with Einstein and special relativity where the mathematical tools (Lorentz transformations and math of space-time worked out by Minkowski) required already existed. It took Einstein 10 more years to publish his theory on general relativity and to develop new tools involving non-Euclidean space and tensors.

The book touch on just enough mathematics to make it interesting without being over powering. But, its not just about theories, its about people, the times they lived, astronomy and the experimenters that helped to prove Einstein right and to launch him onto the world stage.

[Lim · Rating 5 out of 5]

I still remember vividly the day I picked it up in 10th grade. It was meant as a birthday gift for a friend who was into Physics yet I ended keeping it for myself. Although I couldn't understand half of what the author was saying, I could hardly put the book down. At times it felt like a gentle, captivating narrative into the formation of general relativity and theories about our expanding universe for the layman, while at others it left so much for later investigation when I become more informed on the subject. And the account of Arthur Eddington's expenditure to measure the deflection of light and confirm Einstein's relativity theory is just brilliant.

[Ema · Rating 4 out of 5]

I had no idea what to expect from this book, but I picked up this book wanting to understand better what Einstein's theories were. Even though there was very little math, the mathematics was over my head, but somehow the book kept me interested to the end. Having come no step closer to understanding Einstein's general theory of relativity I still enjoyed reading this book. It gave a very readable portrayal of how Einstein came to discover his theories as well as his quest for the unifying theory which eluded him all his life.