The God Equation

by Michio Kaku

  This is done by approximating space-time as a series of lattice points. Normally, we think of space-time being a smooth surface, with an infinite number of points. When objects move, they pass through this infinite sequence. But we can approximate this smooth surface with a grid or lattice, like a mesh. As we let the spacing between lattice points get smaller and smaller, it becomes ordinary space-time, and the final theory begins to emerge. Similarly, once we have the final equation for M-theory, we can put it on a lattice and do the computation on a computer.

  In this scenario, our universe emerges from the output of a supercomputer.

  (However, I am reminded of the Hitchhiker’s Guide to the Galaxy, when a gigantic supercomputer is built to find the meaning of life. After eons doing the calculation, the computer finally concluded that the meaning of the universe was “forty-two.”)

  So it is conceivable that the next generation of particle accelerators, or a particle detector deep inside a mine shaft, or a gravity wave detector in deep space, will find experimental proof of string theory. But if not, then perhaps some enterprising physicist will have the stamina and vision to find the final mathematical formulation of the theory of everything. Only then can we compare it with experiment.

  There are probably more twists and turns facing physicists before the journey is finished. But I am sure that we will eventually find the theory of everything.

  But the next question is: Where did string theory come from? If the theory of everything has a grand design, then did it have a designer? If so, then does the universe have a purpose and meaning?

  7

  FINDING MEANING IN THE UNIVERSE

  We have seen how the mastery of the four fundamental forces has not only revealed many of the secrets of nature but has also unleashed the great scientific revolutions that have altered the destiny of civilization itself. When Newton wrote down the laws of motion and gravity, he laid the groundwork for the Industrial Revolution. When Faraday and Maxwell revealed the unity of the electric and magnetic force, this set into motion the electric revolution. When Einstein and the quantum physicists revealed the probabilistic and relativistic nature of reality, this set into motion the high-tech revolution of today.

  But now we might be converging on a theory of everything that unifies all four fundamental forces. So assume for the moment that we have finally achieved this theory. Assume that it has been rigorously tested and universally accepted by the scientists of the world. What impact will this have on our lives, our thinking, and our conception of the universe?

  As far as a direct impact on our immediate lives, it probably will be minimal. Each solution of the theory of everything is an entire universe. Therefore, the energy at which the theory becomes relevant is the Planck energy, which is a quadrillion times greater than the energy produced by the Large Hadron Collider. The energy scale of the theory of everything concerns the creation of the universe and the mysteries of black holes, not the affairs of you and me.

  The real impact of the theory on our lives may be philosophical, because the theory may finally answer deep philosophical questions that have haunted great thinkers for generations, such as is time travel possible, what happened before creation, and where did the universe come from?

  As the great biologist Thomas H. Huxley said in 1863, “The question of all questions for humanity, the problem which lies behind all others and is more interesting than any of them, is that of the determination of man’s place in Nature and his relation to the Cosmos.”

  But this still leaves open a question: What does the theory of everything have to say about meaning in the universe?

  Einstein’s secretary, Helen Dukas, once mentioned that Einstein was overwhelmed with the mail he received pleading with him to explain the meaning of life, and asking whether he believed in God. He said he was helpless to answer all these questions about the purpose of the universe.

  Today, questions about meaning in the universe and the existence of a creator still fascinate the general public. In 2018, a private letter that Einstein wrote just before he died went up for auction. Surprisingly, the winning bid for the God letter was $2.9 million, even beyond the expectation of the auction house.

  In this and other letters, Einstein despaired of answering questions concerning the meaning of life, but he was clear about his thinking concerning God. One problem, he wrote, is that there are really two kinds of Gods, and we often confuse the two. First, there is the personal God, the God that you pray to, the God of the Bible who smites the Philistines and rewards the believers. He did not believe in that God. He did not believe that the God who created the universe interfered in the affairs of mere mortals.

  However, he believed in the God of Spinoza—that is, the God of order in a universe that is beautiful, simple, and elegant. The universe could have been ugly, random, chaotic, but instead it has a hidden order that is mysterious yet profound.

  As an analogy, Einstein once said he felt like he was a child entering a vast library. All around him, there were stacks of books that contained answers to the mysteries of the universe. His goal in life, in fact, was to be able to read a few chapters of these books.

  However, he left open this question: If the universe is like a vast library, is there a librarian? Or is there someone who authored these books? In other words, if all physical laws can be explained by the theory of everything, then where did that equation come from?

  And Einstein was driven by another question: Did God have a choice in creating the universe?

  Proving God’s Existence

  These questions, however, are not so clear when trying to use logic to prove or disprove the existence of God. Hawking, for example, did not believe in God. He wrote that the Big Bang took place in a brief instant of time, so there was simply not enough time for God to create the universe as we see it.

  In Einstein’s original theory, the universe expanded almost instantly. But in the multiverse theory, our universe is nothing but a bubble coexisting with other bubble universes, which are being created all the time.

  If so, then perhaps time did not simply spring into existence with the Big Bang, but instead there was a time before the beginning of our universe. Each universe was born in a brief instant of time, but the totality of universes in the multiverse could be eternal. So the theory of everything leaves open the question of the existence of God.

  Over the centuries, however, theologians have tried the opposite point of view, to use logic to prove the existence of God. Saint Thomas Aquinas, the great Catholic theologian of the thirteenth century, postulated five famous proofs of the existence of God. They are interesting because even today, they still raise deep questions about the theory of everything.

  Three are redundant, so there are actually three independent proofs (if we also include the ontological proof of Saint Anselm):

  Cosmological proof. Things move because they are pushed—that is, something sets 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 that does not exist. But if God did not exist, he would not be perfect. Therefore he must exist.

  These proofs of the existence of God lasted for many centuries. It wasn’t until the nineteenth century that Immanuel Kant found a flaw in the ontological proof, because perfection and existence are two separate categories. To be perfect does not necessarily imply that something must exist.

  However, the other two proofs have to be reexamined in light of modern science and the theory of everything. The analysis of the teleological proof is straightforward. Everywh
ere we look around us, we see objects of great complexity. But the sophistication of life-forms surrounding us can be explained by evolution. With enough time, pure chance can drive evolution via the survival of the fittest, so more sophisticated designs arise randomly from less sophisticated designs. A first designer for life is not necessary.

  By contrast, the analysis of the cosmological proof is not so clear. Physicists today can run the videotape backward and show that the universe started with a Big Bang that set the universe into motion. However, to go back even before the Big Bang, we have to use the multiverse theory. But even if we assume that the multiverse theory explains where the Big Bang came from, then one has to ask, Where did the multiverse come from? Finally, if one states that the multiverse is a logical consequence of the theory of everything, then we have to ask, Where did the theory of everything come from?

  At this point, physics stops, and metaphysics begins. Physics says nothing about where the laws of physics themselves come from. So the cosmological proof of Saint Thomas Aquinas concerning the First Mover or First Cause is left relevant even today.

  The key feature of any theory of everything is likely to be its symmetry. But where does this symmetry come from? This symmetry would be a by-product of deep mathematical truths. But where does mathematics come from? On this question, the theory of everything is again silent.

  Questions raised by a Catholic theologian eight hundred years ago are still relevant today, despite our enormous progress in understanding the origin of life and the universe.

  My Own Point of View

  The universe is a remarkably beautiful, ordered, and simple place. I find it utterly staggering that all the known laws of the physical universe can be summarized on a single sheet of paper.

  Contained on the paper is Einstein’s theory of relativity. The Standard Model is more complicated, taking up most of the page with its zoo of subatomic particles. They can describe everything in the known universe, from deep inside the proton to the very boundary of the visible universe.

  Given the utter brevity of this sheet of paper, it is hard to avoid the conclusion that this was all planned in advance, that its elegant design shows the hand of a cosmic designer. To me, this is the strongest argument for the existence of God.

  But the bedrock of our understanding of the world is science, which is ultimately based on things that are testable, reproducible, falsifiable. That is the bottom line. In disciplines like literary criticism, things get more complicated with time. Analysts forever wonder what James Joyce really meant by this or that passage. But physics moves in the opposite direction, becoming simpler and more powerful with time, until everything is a consequence of a handful of equations. I find this remarkable. But scientists are often reluctant to admit that there are some things beyond the realm of science.

  For example, it is impossible to prove a negative.

  Let’s say we want to prove that unicorns don’t exist. Although we have scoured most of the Earth’s surface and have never seen a unicorn, there is always the possibility that unicorns exist in some undiscovered island or cave. Thus, it is impossible to prove that unicorns don’t exist. This means that a hundred years from now, people will still be debating the existence of God and the meaning of the universe. This is because these concepts are not testable, and hence not decidable. They are outside the province of ordinary science.

  Similarly, even if we have never encountered God in all our travels in outer space, there is always the chance that God exists in regions we have never explored.

  Hence, I am an agnostic. We have just scratched the surface of the universe, and it is presumptuous to make declarations of the nature of the entire universe far beyond our instruments.

  But one still has to confront Saint Thomas Aquinas’s proof, that there must be a First Mover. In other words, where did everything come from? Even if the universe started according to the theory of everything, then where did the theory of everything come from?

  I believe that the theory of everything exists because it is the only theory that is mathematically consistent. All other theories are inherently flawed and inconsistent. I believe that if you start with an alternate theory, then ultimately you can prove that 2 + 2 = 5—that is, these alternate theories contradict themselves.

  We recall that there is a blizzard of obstacles to a theory of everything. When we add quantum corrections to a theory, we find that the theory usually blows up, with infinite divergences, or the original symmetry is ruined by anomalies. I believe that there is perhaps just one solution to these constraints that fixes the theory, ruling out all other possibilities. The universe cannot exist in fifteen dimensions, since such a universe would suffer from these fatal flaws. (In ten-dimensional string theory, when we calculate quantum corrections, they often contain the term (D − 10), where D is the dimensionality of space-time. Obviously, if we set D = 10, then these worrisome anomalies disappear. But if we don’t set D = 10, then we find an alternate universe full of contradictions, where mathematical logic is violated. Likewise, when you add in membranes and calculating with M-theory, we find unwanted terms that contain the factor (D − 11). Hence, within string theory, there is only one self-consistent universe where 2 + 2 = 4, and that is in ten or eleven dimensions.)

  This then is a possible answer to the question raised by Einstein in his search for the theory of everything: Did God have a choice in making the universe? Is the universe unique, or are there many ways in which a universe might exist?

  If my thinking is correct, then there is no choice. There is only one equation that can describe the universe, because all others are mathematically inconsistent.

  So the final equation of the universe is unique. There might be an infinite number of solutions of this master equation, giving us a landscape of solutions, but the equation itself is unique.

  This sheds some light on another question: Why is there something rather than nothing?

  In the quantum theory, there is no such thing as absolute nothing. We have seen that absolute blackness does not exist, so black holes are really gray and must evaporate. Similarly, when solving the quantum theory, we find that the lowest energy is not zero. For example, you cannot reach absolute zero, because atoms, in their lowest quantum energy state, are still vibrating. (Similarly, according to quantum mechanics, you cannot reach zero energy quantum mechanically, because you still have zero point energy—that is, the lowest quantum vibrations. A state of zero vibration would violate the uncertainty principle, since zero energy is a state of zero uncertainty, which is not allowed.)

  So where did the Big Bang come from? Most likely, it was a quantum fluctuation in Nothing. Even Nothing, or a pure vacuum, is frothing with matter and antimatter particles continually jumping out of the vacuum and then collapsing back into the vacuum. This is how something came from nothing.

  Hawking, as we saw, called this the space-time foam—that is, a foam of tiny bubble universes continually popping up and disappearing back into the vacuum. We never see this space-time foam, because each bubble is much tinier than any atom. But once in a while, one of these bubbles does not disappear back into the vacuum but continues to expand, until it inflates and creates an entire universe.

  So why is there something rather than nothing? Because our universe originally came from quantum fluctuations in Nothing. Unlike countless other bubbles, our universe jumped out of the space-time foam and kept on expanding.

  Did the Universe Have a Beginning or Not?

  Will this theory of everything give us the meaning of life? Years ago, I saw a strange poster from a meditation society. I recognized that it faithfully published all the details of the supergravity equations, in their full mathematical glory. Attached to each term of the equation, however, there was an arrow that said “peace,” “tranquility,” “unity,” “love,” etc.

  In other words, th
e meaning of life was embedded in the equations of the theory of everything.

  Personally, I think it is unlikely that a purely mathematical term in an equation from physics can be equated to love or happiness.

  However, I do believe that the theory of everything might have something to say about meaning in the universe. As a child, I was raised as a Presbyterian, but my parents were Buddhists. These two great religions have, in turn, two diametrically opposed points of view concerning the Creator. In the Christian church, there was an instant of time when God created the world. The Catholic theologian and physicist Georges Lemaître, one of the architects of the Big Bang theory, believed that Einstein’s theory was compatible with Genesis.

  However, in Buddhism, there is no God. The universe had no beginning or end. There is only timeless Nirvana.

  So how can one resolve these two diametrically opposite points of view? The universe either had a beginning. Or it didn’t. There is no middle ground.

  But actually, the multiverse theory gives a radically new way of viewing this contradiction.

  Perhaps our universe did have a beginning, as mentioned in the Bible. But perhaps Big Bangs are happening all the time, according to the inflation theory, creating a bubble bath of universes. Perhaps these universes are expanding in a much larger arena, a Nirvana of hyperspace. So our universe had a beginning and is a three-dimensional bubble floating in a much larger space of eleven-dimensional Nirvana in which other universes continually arise.