Michio Kaku: THE GOD EQUATION (Doubleday, 2021)

Here’s a book I thought suspect on two or three counts, but which turned out to be quite worthwhile. It’s a succinct, crisp history of physics, from the Greeks to the present, and ending with, though not dwelling too much on, string theory. Along the way we meet all the famous physicists we’ve heard about, matched up to their key discoveries, and in turned matched up to how those discoveries changed human history and have played out in the modern world.

Why suspect?

  • First, because Kaku, perhaps unfairly, has a reputation as a popularizer of science whose books seem to slide over a bit too far into speculative fiction, in titles like The Future of Humanity and The Physics of the Future. An article I saw a few months ago that critiqued popular science books used him as an example of a writer overly given to hyperbole.
  • Second, the book’s title is designed to appeal to laymen (as did books about “the God particle”) who presumably hope that science is somehow validating their God. These titles are disingenuous, and their publishers surely know that, but hey they’re out to sell books. And scientists do use such terms, albeit very loosely. Einstein talked about the “God of Spinoza” and Hawking “the mind of God,” but in neither case did they mean an invisible man in the sky who answers prayers.
  • Third, the physical book is a smallish hardcover like others that have become popular in recent years, slightly smaller than the standard hardcover, as if to suggest a relatively lightweight or non-technical book. Not that there’s anything wrong with that; several of E.O. Wilson’s last books were in this format, and I can spot similarly-sized titles on my shelves by Carl Rovelli, Henry Gee, and Alan Lightman.

Still, Kaku *is* a professor of theoretical physics who has been working in the field of string theory since 1968, and even though we realize he’s reviewing the history of physics as the background for his claims for string theory, it’s a fascinating background, the content of any number of other books (by Brian Greene, Lawrence M. Krauss, Stephen Hawking, and others), trimmed down to a neat 200 pages. A refresher course.


Ch1, Unification—the Ancient Dream

  • The Greeks toyed with ideas of atoms and mathematical rules.
  • The western world fell dark for 1000 years; the church.
  • Renaissance, 17th century: Kepler, Bruno, Galileo made progress, despite the church.
  • Then Newton, perhaps the greatest scientist who ever lived. His laws of mechanics predicted the return of Halley’s comet, the discovery of Neptune, the nature of heat; thus the steam engine and railroads and increases in the standard of living.
  • 200 years later, Faraday and Maxwell understood electricity and magnetism. Light was an electromagnetic wave. Hertz thereby discovered radio. Then came the whole spectrum of EM waves, connecting visible light to radio waves, then infrared light, and ways to send power over electrical wires (DC and AC, Edison and Tesla; the latter won).
  • By 1900 some scientists thought everything about physics was known. They didn’t realize Newton’s and Maxwell’s equations contradicted each other. One would have to fall.

Ch2, Einstein’s Quest for Unification

  • Einstein realized that Maxwell’s equations said velocities don’t add; all light beams speed away at the same velocity. Contradicting Newton, and common sense. Einstein’s insight was that space and time must be distorted to keep the speed of light constant. Time slows down the faster you move. This was “special relativity.” The faster you move, the heavier you become; the mass comes from the energy of motion; energy is turned into mass, via e=mc2.
  • To a physicist, beauty is symmetry. Einstein’s equations can be rotated space to time and vice versa. They are symmetric in four dimensions, including time. And gravity is curved space. At age 36 it occurred to Einstein that acceleration and gravity are the same… That space curves. Gravity doesn’t pull; space pushes. This was “general relativity,” verified through observations of Mercury, and the bending of light from stars passing near the sun.
  • Our GPS technology depends on both special and general relativity to work, confirming E’s theories.
  • Einstein tried for a greater theory but never found it. As quantum theory emerged, he didn’t like it.

Ch3, Rise of the Quantum

  • About the periodic table, radioactive elements, thus evidence the earth must be billions of years old.
  • Quantum mechanics tried to explain all this. Einstein deduced that light consisted of packets of energy, photons. Yet somehow light behaved as both a particle and a wave. The famous two-slit experiment.
  • The periodic table was explained. But a famous debate in 1930 pitted Einstein and Schrodinger on one side, Bohr and Heisenberg on the other. There’s never been a consensus on Schrodinger’s famous thought experiment about the whether the cat is dead or alive. Yet the older “Copenhagen” interpretation has given way to the “many worlds” interpretation.
  • Spectra of the sun and other stars explained why the sun shines.

Ch4, Theory of Almost Everything

  • After the war Einstein drifted, unable to find a unifying principle. Progress was made with QED, quantum electrodynamics; earlier problems with infinities were solved via “renormalization,” an arduous and ugly method.
  • From QM came the high-tech revolution, leading to transistors and lasers, then computers and the internet.
  • Could QM solve the issue of life, replace the old idea of a “life force”? The master molecule to pass along the genetic code was proposed in 1944, then found by Watson and Crick in the ’50s, who discovered the structure of DNA.
  • QED was applies to subatomic forces, studied in particle accelerators. Lots of new particles were found this way. Gell-Mann proposed that all of them were composed of even smaller particles called quarks. Further discoveries involved the weak force and neutrinos, and an “electroweak” force to unify the weak with EM.
  • In 1954 came the Yang-Mills theory, about the fields that hold quarks together; it became QCD, quantum chromodynamics, accounting for the strong nuclear force, and a field called a gluon.
  • All of this formed the Standard Model. But it wasn’t known how the four forces unite; perhaps they were united at the big bang, obeying some master symmetry that broke as the universe expanded. The Higgs Boson would explain how this happened; the relevant equation would be the God equation.
  • Higgs was found in 2012, at LHC outside Geneva. This was the theory of almost everything (diagram p100 with 36 quarks and 12 leptons). The big problem is none of this accounted for gravity. Attempts to accommodate a particle, the graviton, led to infinities in the equations.

Ch5, The Dark Universe

  • So physicists consider the quantization of ordinary matter. A 2019 photo of a black hole triggered renewed interest in Einstein’s theory of gravity.
  • In 1916 Schwarzschild had solved Einstein’s equations for a point, and conceived the idea of a black hole and its event horizon. Much later Hawking applied QM to black holes, deducing that quantum radiation would cause them to evaporate, in trillions of years.
  • Further speculation involved wormholes, the idea of white holes, and whether the arrow of time might be reverse. Would that enable time travel? Or would this all imply parallel universes?
  • Einstein realized the universe was either expanding or contracting; when Hubble discovered the universe was expanding, Einstein adjusted his equations; he had second-guessed himself. And the age of the universe was deduced. The big bang was verified by the existence of the residual afterglow, just a couple degrees above absolute zero, found in 1964 by Penzias and Wilson.
  • There was a problem with the ‘flatness,’ uniformity, of the resulting universe. Guth proposed a brief period of massive “inflation” early in the universe, perhaps stopped by some boson that broke an early symmetry. This implies new universes might be born out of our own all the time, a multiverse.
  • Would the universe keep expanding, or slow down and collapse? In 1998 it was discovered the rate of expansion was increasing! A runaway universe. Why? Perhaps these unknown things dubbed dark matter and dark energy. But there are large mismatches between theory and observation of such concepts.

Ch6, Rise of String Theory: Promise and Problems

  • By now we have two pillars in gravity and quantum theory. Can these be unified?
  • String theory emerged in 1968 when scientists noticed that an old formula by Euler in the 18th century described the scattering of subatomic particles – and that this formula represented the interaction of two strings. Many more formula like it were found, and mapping them to physics, they accounted for gravity as well!
  • Then it was found the theory can exist only in 10 dimensions. Did this mean it was obviously wrong? Certainly all rival theories were shown to be wrong. String theory avoids the flaws of earlier theories that attempted to marry gravity with quantum theory.
  • It did it with the concept of supersymmetry. Dirac discovered two types of particle spin: integral, and half-integral. Those with the former are bosons, the latter fermions, p148. Bosons are forces, fermions matter. Further, string theory has supersymmetry. Each particle has a super partner. When combined, the signs cancel, leaving a finite result. Thus gravity can be unified with quantum theory. Like turning marble into wood and back again.
  • But there were five versions of string theory. In 1995 another theory emerged, M-theory, superseding the five with a single theory based on membranes in 11 dimensions; there are five ways to reduce an 11-dimensional theory to 10 dimensions. (The Hawking book about this is reviewed here.)
  • But the theory is highly controversial. It has no predictions, no evidence. Criticisms include that beauty is an unreliable guide; that it predicts too many universes; that it is untestable. To test it, to detect the energy of gravitons, would require an accelerator the size of the galaxy. But perhaps we can look for indirect evidence. One possibility is dark matter.
  • We know something we call “dark matter” exists because without it the milky way wouldn’t hold together; it’s spinning too fast. Finding the relevant particles will involve even bigger colliders.
  • Then came gravity waves, detected in 2016, as Einstein had predicted. Could the inverse square law be true in all dimensions?
  • There is also the “landscape problem,” the issue of parallel universes. Wouldn’t a “theory of everything” predict just one universe? Or would it predict many, including our own, which, per the anthropic principle, we are aware of because in most other universes everything is dead and no one is there to observe them.
  • Author’s own view is that string theory is not finished. Its discoveries are like working down from the top of a pyramid showing just above the sand, deeper and deeper into further layers below. It may not need experimental evidence, if the theory explains first principles that determine the constants of nature.

Ch7, Finding Meaning in the Universe, p182

  • Finally the author addresses what impact this theory would have on our conception of the meaning of the universe. Did God have a choice in creating the universe? Author reviews the classic notions of proof of the existence of God.
  • Author’s own point of view is that, since the laws of the universe (even now) can be written down on a single sheet of paper, suggests advance planning, the hand of a cosmic designer.
  • Still, one cannot prove a negative, as with God. So the author is agnostic. But what about the classical argument about the first mover?
  • Author believes the theory of everything – i.e. something that string theory is working toward — is the only theory that is mathematically consistent. If so, there was no choice in making the universe.
  • Why is there something rather than nothing? Because there’s never such a thing as nothing. The Big Bang was likely a quantum fluctuation in Nothing.
  • Did the universe have a beginning or not? Perhaps our universe had a beginning, but within a multiverse that is eternal.
  • Then what is our meaning? We create our own meaning. If the universe is doomed to die, it’s hard to see how it has meaning. But that’s true only in a closed system. Perhaps wormholes could take us to another universe. Thus the theory of everything could be our salvation.
  • Conclusion: Perhaps we are like two-dimensional flatlanders recreating the 3-dimensional crystal they fell from. Two pieces of theory didn’t fit together until lifted into a third dimension.
  • And a final quote from Stephen Hawking, the final lines from A Brief History of Time, about “knowing the mind of God.”



  • String theory has been controversial because there seems to be no actual “evidence” for it. The theory, which Kaku says is incomplete, hasn’t “predicted” anything that can be verified. It’s a “pretty” theory, with all its symmetries and relationships in higher dimensions, but plenty of physicists, from Roger Penrose to Michael Strevens, have warned against the idea of mathematical “beauty” as being a guide toward truth.
  • Yet in Kaku’s telling the remarkable aspects of the theory emerge. In particular, how the concepts of gravity and quantum theory seem to make sense when both are twisted into higher dimensions… with his analogy, at the very end, of flatlanders fitting pieces together in a third dimension. Is this mere coincidence? Or is this evidence of a higher order that humans simply can’t, intuitively, perceive?
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