God's Equation - Einstein, Relativity, and the Expanding Universe by Amir Aczel.
Review by John Loofbourow, MD
Though written in a clear, clean style, the book is peppered with mathematical jargon, sometimes explained using more of the same. Reading the explanation was like using soapy water to rinse dishes: the explanation was as slippery and opaque as the original. The scope of the book is remarkable, as the author takes us from Berkeley to Babylon and back again. From Euclidian to Non-Euclidian, to topologic mathematics; from Pythagoras to Newton, Plank, Einstein, and Hawking, with frequent stops in between. He does not neglect astronomy, cosmology, or quantum physics.
Finally the reader is deposited on some far shore, presumably in sight of "God's Equation," a unifying formula that unites the physics of the universe within the holy sphere of mathematics. The equation is not merely E = mc2. Though its terms are vaguely explained in the text, not until the very last chapter (p 219) is it brought together. Even then, I confess to being only vaguely aware of what the terms stand for, let alone their significance. I quote:
"This is Einstein's field equation with the cosmological constant, which is our best estimate of God's Equation:
R:< - ½ g:< - 8g:< =- 8 B G T:<. ,"
where R:< is the Ricci tensor, R is its trace, 8 is the cosmological constant, g:< is the measure of distance - the metric tensor of the geometry of space, G is Newton's gravitational constant, T:< is the tensor capturing the properties of energy, momentum and matter, and ½ and 8 are numbers. I understood the numbers ½ and 8.
I was sometimes seasick during the voyage, and would not recommend it as casual reading, unless one is mathematically sophisticated. Still there were two aspects of the book which I enjoyed thoroughly.
First, this odyssey of math contained interesting biographical details of Einstein's life and his interaction with his peers. These include the two ecliptic expeditions to confirm that light is curved around massive objects. Einstein’s effort to show this during an eclipse in the Crimea was ruined by the outbreak of WWI. (Does Sarajevo sound familiar?) Its failure led to estrangement between Einstein and his colleague Freundlich, who actually was arrested by the Russians as a spy suspect, along with all his telescopic and photographic gear. The other expeditions by the British astrophysicist, Arthur Eddington, was organized after Einstein managed to smuggle a copy of his work to England during the war. In Brazil and Africa both, Einstein's predictions were confirmed, though Einstein was never informed of the result by Eddington or his colleagues.
Also interesting for me were the findings that the universe is apparently expanding at an ever increasing rate, so that the farthest objects we can see are moving away from each other at 0.95 times the speed of light. The rubber band analogy (p178) implies that there is no center to our universe, or the center is everywhere, so that we too are nearing the speed of light. There is not enough mass in the universe to make it fall back in upon itself through the forces of gravity. This leads some to conclude that the universe will never be pulled back together, simply aging into a series of lost old black holes.
Yet, in my innocence, and ignorance, I wonder. If time moves more and more slowly as velocity approaches that of light, could it not be that our expanding universe, now exploding at nearly light speed, could reach and pass that limit, so that time would stop and then run backwards? If so, the universe would collapse into itself inevitably back to the Big Bang, if that is where it began. If infinity means what we suppose, this cycle has occurred an infinite number of times. Will I be, have I been, a better man in other universes, or do I make the same mistakes over and over? I'll call it Loofbourow's hypothesis, comforted by the thought that it won't soon be tested.