Review: The God Equation
December 2024
I enjoyed this book for two reasons. First, I love theoretical physics. I've read many books on the subject and in them we see a big picture perspective of how the world works. Physics describes this on both the large and small scale. Some of these descriptions are the stuff of legends. Proof of this is found in the endless number of recent Hollywood movies drawing on these ideas. Second, I enjoy trying to understand our place in the universe. I appreciate others who ponder these same questions. Theoretical physics is often the boundary line between science and philosophy.
In the first three-fourths of the book, Dr. Kaku offers a sweeping history of the theory of everything. While he touches on some ancient history, such as the Greeks, Galileo Galilei, and others, he primarily focuses on Albert Einstein and the last century. His commentary on physicists is informative, entertaining, and personal. He shares about Einstein's failures and successes, a famous argument with Niels Bohr, and lists which scientists agreed or disagreed with major shifts in theoretical physics. At each stage, Kaku shows how scientists sought to combine more and more of nature's forces together into one comprehensive understanding. This started with the electrical and magnetic forces under Michael Faraday and James C. Maxwell. Then the quark model combined the strong nuclear force with the work of Murray Gell-Mann. The weak nuclear force was explained by gluons, worked out by Gerad 't Hooft. These theories were all combined into what is called The Standard Model, which is the widely accepted model of our day.
Dr. Kaku's style reminds me of Neil deGrasse Tyson, but less caustic. This history is not all fluff. Dr. Kaku's mathematical understanding vastly exceeds mine and his plain language description of famous equations was helpful. Little tidbits such as if the Plank constant goes to zero, quantum mechanics reduces to Newtonian equations is new to me. Dr. Kaku has an eye for "beautiful" equations, and by this he means ones which are simple and symmetric. We see later this becomes a key philosophical point. He paints humanity's dream of a unified theory of everything as a grand quest... one sought for but out of reach.
It is not until chapter six, out of seven chapters, that the book arrives at String Theory. This is "The God Equation" referenced in the title. It is the leading contender for a theory of everything. The Standard Model has failed to combine gravity with quantum theory. String Theory seeks to combine these twin pillars. String Theory posits all subatomic particles are made of strings vibrating at different frequencies. Each is merely a musical note, so to speak, of the foundation of the universe. Dr. Kaku argues gravity is necessarily included by the formulas and so it successfully unites gravity with quantum theory. This, and other mathematical simplifications, make it superior to the Standard Model. He acknowledges String Theory offers surprises. It only works out if there are ten dimensions, even though we've only been able to observe four dimensions thus far. String Theory advances the idea of "supersymmetry". Just like symmetric equations allow physicists to eliminate extra terms in quantum theory, supersymmetry allows them to make sense of quantum gravity by canceling variables that would otherwise be infinite. Each particle of matter and each particle of energy are theorized to have symmetric counterparts which make the math work out. This allows physicists to combine different particles up into larger logical units, making them interchangeable with each other at high enough energy levels. The Big Bang would then no longer be a confusing mess of different systems mashed together, but rather one system that sequentially "broke symmetry" or differentiated itself to present the diversity of particles we see today. At the moment of the Big Bang, everything would be dictated by this super force. Then, as the universe cooled, gravity would break out, then the weak nuclear force, the strong nuclear force, the electrical force, and the magnetic, leaving us with the world of seemingly separate forces that we experience now.
In addition to the counter-intuitive ten dimensions, String Theory has another wrinkle. There are five different systems of equations which all work. M-Theory seeks to unite these five systems by suggesting the strings are actually collapsed membranes. Imagine you deflate a beach ball and twist it until it appears to act like a thread. The five systems then become five different ways membranes could collapse into strings. This unites the various versions of String Theory but at the price of postulating an eleventh dimension. Further simplifications by Juan Maldacena show the behavior of ten dimensional strings is mathematically equivalent to the behavior of subatomic particles in four dimensions. This may mean subatomic particles are how we see strings behave at four dimensions, indicating a substance to String Theory.
Dr. Kaku admits the biggest drawback of String Theory / M-Theory is the difficulty to test it. To achieve concrete examples of supersymmetry, we'd need colliders and instruments capable of levels of energy representative of conditions during the Big Bang. Nothing we have so far can achieve this. While mathematical beauty is a goal, this does not prove it is a correct representation of reality. Each solution of String Theory represents a separate universe, but how can we observe any besides our own? Dr. Kaku proposes testing for extra dimensions by seeing if gravity operates outside the inverse square law. This is how gravity works in four dimensions, if we can find quantum variations, perhaps this indicates additional dimensions at play. Thus far, no results have contradicted the inverse square law. Dr. Kaku is troubled by the so-called, "landscape problem" where String Theory does not necessarily define OUR universe but rather the rules of potentially many, many universes. Therefore, it does not explain how our particular universe came to be. He would prefer a precise mathematical description requiring our universe to exist the way it does. He is hopeful future String Theory will show other solutions to be unstable or decay down to our universe.
Dr. Kaku goes over several arguments for the necessity of the beginning of the universe. The first argument is from thermodynamics. If the energy in the universe is pushing outward faster than gravity pulls things inward, we'd experience the Big Freeze, where eventually all galaxies fly apart, stars burn out, and even black holes radiate away. Alternatively, if gravity is stronger throughout the universe pulling things inward, overpowering the energy pushing outward, we'd experience the Big Crunch. This is where all galaxies would eventually mash together into a supermassive black hole or potentially crunch into a new singularity. Since neither of these have happened, either the universe is completely stable, with the forces in equal balance, or the universe had a beginning. This infers that not enough time has passed for the Big Freeze or the Big Crunch. The author cites arguments for why the universe being stable is not likely. The traditional evidence of the cosmic microwave background radiation (CMB) shows the temperature cooling of the Big Bang is still happening, yet had it been infinitely in the past, it would have dissipated already. Second, the Doppler effect of the galaxies around us shows that almost all galaxies are moving away from each other. For a stable universe, galaxies would need to remain fixed distances from each other or oscillate between moving closer and farther. This means the universe is expanding rather than staying stable. As modern telescopes have improved, scientists have been able to measure the rate of expansion is actually speeding up. Galaxies are moving away from each other faster now than in the past. This means the universe had a beginning or galaxies would already be infinitely apart from each other. The universe being finite has important philosophical ramifications, as the author readily acknowledges.
A lot of philosophy is crammed into the final chapter, Finding Meaning in the Universe. This chapter briefly summarizes Thomas Aquinas's five arguments for God, though he reduces these down to three before listing them.
- Cosmological proof. Things move because they are pushed- that is, something set them into motion. But what is the First Mover or First Cause that set the universe into motion? This must be God.
- Teleological proof. Everywhere around us we see objects of great complexity and sophistication. But every design eventually requires a designer. The First Designer was God.
- Ontological proof. God, by definition, is the most perfect being imaginable. But one can imagine a God who does not exist. But if God did not exist, he would not be perfect. Therefore, he must exist.
The author argues Immanuel Kant has already answered the Ontological proof, since to be perfect, things need not necessarily exist. Evolution is invoked to explain away the need for a first designer. This leaves only one of the three areas left. Dr. Kaku claims the cosmological proof is unclear. This is the area of concern in the book, and the one he's the most interested in solving.
Dr. Kaku asserts the multiverse String Theory implies time may have existed elsewhere before it existed as spacetime in our universe. Multiverse theory suggests tiny bubbles of universes may getting created one after another. (This is confusing since it must mean prior in sequence than in time as we know it since spacetime exists inside the universes themselves.) He finds this multiverse theory somewhat unsatisfying. The author hopes we will eventually prove a single theory of everything, showing alternate universes or dimensions are either self-contradictory or reduce down to the universe we have. This would help assert why we find ourselves in THIS universe out of potentially infinite. A unique solution for a unique universe.
I appreciate Dr. Kaku's admission that in quantum theory there is not actually nothing. When discussing where the Big Bang came from, he acknowledges "empty space" is in fact teeming with quantum energy. So he infers, the multiverse "foam" of energy must also not be true nothing, but some sort of quantum energy. This energy is capable of generating universes. Unfortunately, he labels this as Nothing in the book. Others have failed to make this semantic distinction and I believe it leads to confusion. An extra dimensional, all encompassing super-universe foam which creates Big Bangs is not nothing. For me, this is where multiverse theory breaks down as a pure physical system, theorizing a spacetime foam outside of the spacetime of our universe. I am not suggesting it is impossible, but rather pointing out this medium has both sequence and dimension. The sequence or "time" comes from the fact bubble universes are described to not exist, then exist, then many of them cease to exist. There's some order or sequence here, which is not nothing. The dimensions come from the presumption the bubble universes do not overlap. Therefore, they are spread out, but spread out in what? This is some other dimension of being outside our universe but essentially with time and space. This is not really much different than proposing a spiritual dimension outside our own with the power of creation, except this theory has an impersonal force rather than a personal God.
Dr. Kaku admits things are bleak for us in a closed universe. Most likely the cold death of expansion will continue, until nothing meaningful exists. Planets, stars, and even black holes will dissipate until atoms are so far apart from each other, no complex life or structures exist. However, he rightly argues this is only our fate in a closed system. If energy can enter from the outside, we could potentially continue to organize life forever. Or if our far future descendants can flee this universe to another, they could be preserved, hopping from one universe to another. This dream makes me smile. This is a description of heaven, but of lower quality than the major religions offer. What we need is a benevolent outside force to help us. Or another realm to live in where we can be safe. Dr. Kaku has already theorized supraphysical dimensions beyond the ones of our perception. How different are these from a spiritual realm? These realms could contain beings of a different nature than our own. He postulates there is not really Nothing, but a greater universe beyond the part we see. Though Dr. Kaku calls himself an agnostic, his theories lead us down a familiar road. At the very end of the book, he describes humanity as a bunch of flatlanders, living in two dimensions, who fail to think about the third dimension. Perhaps the third dimension is considered a superstition. Dr. Kaku, and others, search the stars for the mind of God. But what if God has made the first move and contacted us already? The irony of the flatlander example is humanity has scientifically brilliant minds, some of whom consider the spiritual realm superstitious. Yet it is the very consideration of realms like these which ancient man's revelations and modern man's theories both exhort us to consider.