Is there a theory of everything? How close are we to finding it?
For centuries, scientists have sought a single theory that would provide one equation from which we can derive a complete understanding of the universe. In The God Equation: The Quest for a Theory of Everything, Michio Kaku suggests an approach that might be the path to uniting all the laws of nature.
Continue reading for an overview of this mind-bending book.
Overview of The God Equation: The Quest for a Theory of Everything
The science of physics is a fractured field. It studies the universe on the largest and smallest scales imaginable, from the beginning of time to the far distant future. Physics explores the underlying forces of nature, from the gravity that holds stars and planets together, to the electromagnetic attraction that drives chemistry and powers civilization, down to the microscopic forces that hold atoms together and break them apart.
Each of these aspects of nature functions by its own mathematical rules, some of which contradict each other, suggesting that our theories are incomplete and maybe flat-out wrong. For centuries, scientists have sought a resolution, which some call “the God equation”—a single theory that would unify physics, cancel out its contradictions, and provide one simple, underlying equation from which we can derive a complete understanding of the universe.
In The God Equation: The Quest for a Theory of Everything, published in 2021, theoretical physicist Michio Kaku suggests that an approach called “string theory,” which he’s researched since the early 1970s, might be the path to at last deducing the unifying principle behind every aspect of matter, energy, space, and time. Kaku is a professor at the City College of New York and is the author of many books on science and humanity’s future, such as Physics of the Impossible and The Future of the Mind. In addition to his published works, Kaku is a frequent contributor to TV science programs such as PBS’s Nova and BBC’s Horizon.
We’ll trace the history of scientific progress in terms of discoveries that unify areas of knowledge and reveal the underlying symmetries of nature, from the early days of physics to Einstein’s theory of relativity, from the initial discoveries of quantum mechanics to our present model of matter and energy. Finally, we’ll delve into string theory, the cutting edge of theoretical physics that might unify all our ideas of the cosmos into a single, overarching concept.
We’ll also define terms and concepts to give readers a better understanding of the topic. Finally, we’ll look at the philosophical implications that a search for a theory of the universe entails.
First Steps Toward Unification
Since the birth of classical physics, the greatest advancements in knowledge have come from bringing together different fields of study. In short, a theory is considered more powerful if it explains multiple phenomena at once. Kaku shows how even the early steps in physics united what were thought at the time to be wildly different areas of study, such as the motion of objects on the Earth and in the sky, as well as an unexpected unity between electricity, magnetism, and light. These examples show that a persuasive theory doesn’t just explain the subject being studied, but also reveals insights seemingly unrelated to the topic at hand. One such insight we’ll cover in this section is that the laws of nature are symmetrical, a concept that Kaku repeatedly invokes.
It all goes back to Isaac Newton, who from 1666-1687 worked out the first mathematical theory to explain the laws governing the motion of objects, as well as the “law of universal gravitation” that explained both how objects fall to Earth and how the planets orbit around the sun. Kaku says this was a breakthrough moment in science because Newton had shown through hard, solid math that celestial objects followed the same laws of motion as everyday objects in the world of human experience. Prior to Newton, religious leaders and philosophers had always considered the skies above to be separate from the Earth, but Newton’s mathematics, once confirmed by observation, proved that the two were the same.
Electromagnetism
The next major breakthrough that Kaku discusses came from studies of electricity and magnetism. We’ve been aware of both for thousands of years, but it wasn’t until 1831 that scientific experimentalist Michael Faraday discovered that electricity can be used to create magnets and vice versa. In other words, Faraday showed that electricity and magnetism are two sides of the same coin. Kaku writes that in describing his experiments, Faraday originated the concept of “fields”—in his case, electromagnetic fields—as a region of space in which forces and objects interact. The concept of fields would become a great unifier of disparate ideas within the realm of physics.
Since Faraday wasn’t a mathematician, the most powerful revelation from his studies didn’t come until 1861, when James Clerk Maxwell expressed the relationship between electricity and magnetism in mathematical form. When he did, Maxwell’s equations revealed that the back-and-forth between electrical and magnetic fields, in which one creates the other and vice versa, propagates at a constant speed—the speed of light! Out of the blue, Maxwell had discovered that light is a wave in the electromagnetic field. Not only that, but his equations predicted frequencies of light beyond what we can see—the entire invisible electromagnetic spectrum that astronomers now use to explore the depths of space.
The Power of Symmetry
When discussing these early scientific breakthroughs, Kaku calls attention to the fact that all of the equations describing motion and electromagnetism are symmetrical. What does this mean? An image of a face is symmetrical if you can flip it from left to right and the image remains the same. A cube is symmetrical in three dimensions because you can rotate it in any direction and the overall shape is unchanged. In mathematics, an equation is symmetrical if you can rearrange its expressions without altering its results.
Symmetry is a powerful mathematical tool. If you assume that symmetry is a property of a phenomenon you’re trying to explain, then symmetry can show where there are gaps in your knowledge and suggest what the “missing pieces” of a puzzle might look like. For example, the quest for symmetry led scientists to deduce the existence of antimatter—the inverse and opposite of regular matter—decades before it was proven to be real. Scientists find symmetry to be aesthetically pleasing, even elegant, but Kaku warns that just because a theory is pretty doesn’t necessarily mean it’s true.
Nevertheless, Kaku illustrates that, the more we learn about the laws of nature, the more it seems that symmetry is built into the universe’s basic set of rules. Newton’s laws of gravity and motion are symmetrical because they don’t depend on your frame of reference. If you look at an object’s motion upside down or sideways, the equations that govern it produce the same result. Maxwell’s equations are likewise symmetrical because you can freely swap their electrical and magnetic components. The property of symmetry repeatedly appears to be a defining characteristic of the universe.
Einstein’s Relativity
Thanks to Newton’s and Maxwell’s equations, physicists at the start of the 20th century believed there wasn’t much left to explore. But, Kaku points out that there was a problem—under certain conditions, Newton’s and Maxwell’s theories were incompatible with each other. After explaining the nature of the problem, we’ll discuss how Albert Einstein solved it by reimagining Newton’s laws of motion and then rewriting Newton’s law of gravitation.
The contradictions between Newton’s and Maxwell’s laws appear when you consider objects moving near the speed of light. Suppose a cat is chasing a laser pointer at 600 million miles per hour. The beam of light from the laser pointer passes the cat at 671 million miles per hour. How fast would the beam of light appear from the cat’s point of view? Newton says that speeds add and subtract—the cat would see the laser beam moving at only 71 million miles per hour. However, Maxwell’s equations suggest that the speed of light never changes. No matter how fast the cat is chasing the pointer, it will always perceive the ray of light to be moving at 671 million miles per hour. Both answers can’t be true, so either Newton or Maxwell was wrong.
Special Relativity
Kaku writes that Einstein proposed a radical solution to the problem. For the speed of light to remain a fixed constant no matter how fast an observer is moving, space and time have to distort so the speed of light remains the same. This is the basis of Einstein’s theory of special relativity. In Einstein’s new equations governing objects in motion, Newton’s laws still apply if your speed is relatively slow, but as you accelerate, time slows down, space contracts, and the speed of light that you observe remains unchanged.
Einstein’s equations also add additional layers of symmetry to Newton’s. The first is that in relativity, you can substitute time for any direction in space. In other words, relativity is symmetrical in four dimensions, not just three. The second symmetry is similar to when Faraday showed that electricity and magnetism are interchangeable. In this case, Einstein revealed that energy and matter are equivalent to each other via his famous equation E=mc2 (energy equals mass times the speed of light squared). Therefore, says Kaku, special relativity unites energy and matter, as well as time and space.
General Relativity
Nevertheless, Einstein knew his theory was incomplete. It corrected Newton’s laws of motion but said nothing about the law of gravitation. According to Newton, the effects of gravity are instantaneous—if a source of gravity suddenly moves, the change in its force is immediately felt—but that contradicts the rule that nothing can travel faster than light, as established by Maxwell and Einstein. Kaku states that this was the next vital step in unifying physics—to combine Einstein’s theory of special relativity with Newton’s theory of universal gravitation.
Einstein’s solution was to propose that the force of gravity is actually an illusion caused by the deformation of space. Consider a marble rolling across a trampoline. If the trampoline is flat, the marble rolls straight across, but if there’s a bowling ball sitting in the middle, pulling the fabric of the trampoline down, the marble will appear to be “attracted” to the ball, no matter which way it was originally rolling. This is the essence of Einstein’s theory of general relativity, which shows that matter warps space around it—the greater the mass, the greater the “dent” it makes. Kaku lists ways that Einstein’s equations reveal things that Newton’s can’t—such as predicting how gravity causes light to bend or explaining the planet Mercury’s erratic orbit.
Quantum Mechanics
While Einstein was solving the riddles of gravity and motion, another field of exploration—quantum mechanics—was opening up. Scientists studying the building blocks of matter discovered that on the level of the atom, the laws of nature follow a strange set of rules known as quantum mechanics. In this section, we’ll trace the road to quantum mechanics from attempts to explain how objects radiate heat, to the discovery that some subatomic particles also behave like waves instead of matter, and finally to a unification between the new quantum theory and Maxwell’s light equations.
In the early 1900s, our model of the atom was like a miniature solar system with a tiny, dense nucleus of protons and neutrons surrounded by orbiting electrons. However, theoretical physicist Max Planck noticed something strange about atomic behavior when he investigated the light given off by hot materials. According to equations based on Newton’s laws of motion, the atoms in hot materials vibrate faster than those at cooler temperatures, and they release their excess energy in the form of light. However, the math didn’t add up—the wavelengths of light emitted by hot, glowing matter didn’t match the predictions of Newtonian thermodynamics.
Kaku writes that Planck found a solution that was just as shocking to the norms of science as Einstein’s theory of relativity. In essence, Planck determined that the energy released by matter as it cools doesn’t diminish on a linear scale but as tiny bundles called “quanta.” It’s as if when an atom cools, its energy level doesn’t slide down a ramp but instead walks down a flight of stairs where each step is a specific amount of energy. This energy emerges as packets of light—photons—that exactly match the energy of light given off by heated objects.
Particles and Waves
The problem with photons being particles of light is that Maxwell’s equations show that light is an electromagnetic wave. It turns out that light has properties of both waves and particles, depending on how it interacts with matter. But, Kaku writes that the mystery grew deeper because researchers found that the same was true of electrons. Instead of being envisioned as a particle in orbit around the nucleus, an electron is better described as a wave that wraps the nucleus in a shell. That wave can only exist at specific energy levels that match the quantum orbits in which electrons are found.
So, when we say that electrons are waves, it simply means that you can’t pin one down—you can only determine the probability of its location at any given point, and that probability flows like a wave. This goes against all our prior conceptions of motion. Imagine if you can’t tell where the moon is in the sky—you can only compute where it’s likely to be. This makes no sense in our macroscopic world governed by laws of relativity, but it’s exactly how electrons and photons, as well as other particles, behave. Clearly, says Kaku, if we’re to uncover one universal theory, it will have to reconcile quantum mechanics with Einstein’s special relativity.
The Heart of the Atom
The quest to unify relativity and quantum theory is ongoing. In the meantime, scientists pushed quantum mechanics further so they could unravel the secrets of the atom. To enter the subatomic realm, we’ll explain researchers’ methods to pry open the atom’s nucleus, the discovery of even smaller subatomic particles, and how combining the mathematical models of the forces which interact inside the atom leads to a theory of how all matter functions.
The only way to look inside atoms is to break them apart. Using accelerators, researchers smash atomic nuclei together and study the pieces found in the wreckage. When this was first done, physicists were surprised to find that protons and neutrons are composed of even smaller particles known as quarks. Studies revealed different types of quarks, and that protons, neutrons, and even stranger particles are made from arrangements of groups of three quarks each. Kaku says the equations governing quarks are symmetrical because you can move around any of the three quark components and the particle they create stays the same.
What holds quarks together into protons and neutrons, and holds neutrons and protons together in the atom, is the most powerful force known in nature—the strong nuclear force. This force is an extremely short-range field of attraction generated by a particle called a gluon (because it glues subatomic particles together). This field can be described mathematically using a modified version of Maxwell’s equations that covers fields of attraction and repulsion beyond that of electromagnetism. Kaku writes that equations such as these that explain different forces are key steps along the path to a unified theory of physics.
The Weak Interaction
In addition to electromagnetism, which keeps electrons in orbit around the nucleus, and the strong nuclear force, which holds the nucleus together, there is also the “weak interaction,” also known as the weak nuclear force. Whereas the strong force holds atoms together, the weak nuclear force breaks particles apart and can even change them from one form to another.
In beta decay, the weak force breaks a neutron apart into a proton, an electron, and the electron’s phantom partner, the neutrino. Neutrinos have no electric charge and virtually no mass. As such, a neutrino can pass through stars and planets without stopping. Nevertheless, Kaku says the neutrino fills a key gap in the atomic model that was predicted by symmetry—if the proton has an electrically neutral counterpart (the neutron) shouldn’t the electron have one too? Their existence was purely theoretical until they were observed in 1956.
Once neutrinos were confirmed to exist, they gave insights into the weak nuclear force that let physicists unite it with the electromagnetic force. Today it’s understood that electromagnetism and the weak nuclear force are one and the same, now referred to as the electroweak force. Kaku affirms that this is the path that the search for a unifying theory has taken—merging separate theories about phenomena until there’s only one left.
The Standard Model
Though scientists have yet to figure out the unifying theory—Kaku’s “God Equation”—physicists have made a great deal of progress using an intermediate step toward that theory referred to as the Standard Model. In this section, we’ll go over the basis of the Standard Model as well as its theoretical problems, including cumbersome mathematics, a mismatch between the theory and the observable universe, and its current inability to account for the force of gravity.
Beginning in the 1970s, physicists stitched together the equations for the strong nuclear force, the weak nuclear force, and electromagnetism to produce what’s now called the Standard Model. This mathematical expression of those fundamental forces presumes that in the extreme conditions that existed moments after the Big Bang, all of the forces acted as one and only diverged as the universe cooled.
However, the Standard Model is woefully incomplete. One issue that Kaku is quick to point out is that the Standard Model is an unsightly mess—a chimeric creation of theories stitched together in a way that isn’t completely plausible and contains mathematical terms that aren’t greatly understood. On the plus side, the equations for the Standard Model are symmetrical, but Kaku says that in this case, that’s a problem. The universe around us isn’t symmetrical—matter is clumped into stars and galaxies with vast expanses of empty space between them. If the Standard Model were true, the universe would instead be a perfectly uniform sea of particles. Obviously, something is amiss.
For the Standard Model to produce the asymmetrical universe of today, something must have shattered the initial symmetry shortly after the Big Bang occurred. Researchers proposed an undiscovered “Higgs boson” consistent with the Standard Model that unbalanced the cooling universe’s symmetry and led to the variety of particles known today. Sometimes called the “God particle,” the Higgs boson created regions of space within which other particles began to have mass. Kaku writes that, because of this imbalance, the original ruling force split into the strong and weak forces, electromagnetism, and gravity. Confirming the existence of the Higgs boson was one of the missions of the Large Hadron Collider, which it accomplished in 2012.
The Gravity Problem
Despite the work done to confirm the Standard Model, it only applies in the realm of quantum mechanics. To achieve a theory unifying all of physics, gravity will have to be folded into the equations for all the other forces. Here, we’ll explain the struggles involved with incorporating gravity into the Standard Model and several discoveries that have been made along the way.
The trouble with gravity is that it’s by far the weakest of the universal forces, so it’s virtually impossible to observe on the quantum scale. While Einstein defines gravity as a curvature in space, there’s no way to express this in the mathematics of quantum mechanics. Instead, physicists have tried another tack—to model gravity as a force created by a particle. Just as gluons transmit the strong nuclear force, scientists have proposed the existence of gravitons that govern gravitational fields. While plausible, Kaku writes that so far no one’s been able to create a mathematical model of gravitons that produces meaningful results.
Despite the problems of incorporating gravity into quantum mechanics, that hasn’t stopped people from trying. Famed physicist Stephen Hawking has done so by considering what happens in the subatomic world in the one place where gravity can’t be escaped—the event horizon of a black hole, or the dividing line around a black hole’s zone of no return. Black holes are objects so massive and dense that their gravity stops even light from escaping. Kaku says that in this realm of gravitational extremes, Hawking discovered that quantum forces slowly drain energy and mass from a black hole’s gravitational field.
This takes place because, in the subatomic world, empty space isn’t really empty. Kaku points out that in quantum mechanics, empty space is actually a bubbling sea of symmetrical positive and negative particles that pop into being and cancel each other. Normally, these particles vanish before they affect their surroundings, but near a black hole, half of the pair may be sucked in while the other flies free. Since energy can’t be created or destroyed, the energy to create this particle must be subtracted from the black hole, reducing its gravitational pull. In other words, near a black hole, gravity and the quantum world intersect.
Back to the Beginning
Another point in space and time where quantum mechanics and gravity overlap is in the moment of the Big Bang itself. Kaku writes that because of this, physicists are determined to study and model the first fractions of a second of the universe’s existence. In the first instants of time, all the fundamental forces of nature interacted with each other before branching off into their own domains. We study the conditions in those first moments by recreating them in supercolliders and by looking into the farthest depths of space, which—because light takes time to travel—also entails looking backward in time.
Indeed, Kaku affirms that there are several observations about the Big Bang that can only be explained using quantum mechanics. By treating the Big Bang as a source of quantum radiation, researchers were able to compute the temperature of the Big Bang’s leftover heat, which was confirmed when the Cosmic Microwave Background (CMB) was discovered in 1964. Another issue is the universe’s rate of expansion, as measured by the stretched-out light waves detected from distant galaxies, which is much faster than Einstein’s equations predict. Kaku argues that quantum theory accounts for this discrepancy by showing that the universe expanded more rapidly in its early stages than was previously thought.
The Promise of String Theory
Though physicists have yet to reconcile relativity, gravity, and quantum mechanics, Kaku argues we may already know what form the eventual solution will take. The answer comes from the field of string theory, which Kaku himself has been working to advance for all of his professional career. In this section, we’ll explain what string theory is, how it suggests higher orders of symmetry in the universe, and why it appears that the universe we see is merely a projection of something much greater.
The basic assertion of string theory is that all particles can be described as vibrations on subatomic strings that constitute the basis of energy and matter. Kaku writes that each different type of particle is produced by a different vibration. One of string theory’s strong appeals is that its equations produce gravitons as being the lowest string vibration, removing the conflict between Einstein and quantum mechanics. String theory also supports physicists’ long-held belief that in the beginning, there was one unifying force in the cosmos by showing that the particles transmitting those forces are symmetrically interchangeable since they’re all just different frequencies of the same foundational strings.
Another argument in favor of string theory is that it introduces a new symmetry not present in previous theories. Kaku says that in the Standard Model, there are two families of subatomic particles—bosons representing the fundamental forces, such as gluons, photons, and gravitons; and fermions comprising the building blocks of matter, such as protons, neutrons, and electrons. In the math for string theory, bosons and fermions are interchangeable, just like time and space are in relativity, as well as electricity and magnetism in Maxwell’s equations. This feature of string theory, called supersymmetry, unites every observable property of space, time, energy, and matter into the interactions of vibrating strings.
String theory equations have bizarre implications, the most fundamental of which, according to Kaku, is that string theory only works if the universe has ten dimensions instead of the four that we’re aware of (three dimensions of space and one dimension of time). One hypothesis scientists use to explain this is to suggest that the other six dimensions we can’t see are so small that they’re imperceptible even on a subatomic scale. Another idea that Kaku puts forward is that our four-dimensional universe is a holographic image of the actual 10-D universe around us, just as an optical hologram is a 3-D image imprinted on a 2-D surface.
The trouble with these other six dimensions is that we don’t know what they represent, but their existence is required by string theory’s equations. For this reason among others, many scientists reject string theory as a piece of mathematical sleight-of-hand.
The String Theory Debate
Despite the encouraging direction string theory provides to theoretical physics, it hasn’t met with universal acceptance within the scientific community. The objections to string theory revolve around the fact that a scientific hypothesis has to be tested for it to be considered a viable theory, and so far string theory has failed to suggest even a method to test it. We’ll conclude by addressing these concerns and offering several potential avenues by which experimental data might confirm string theory’s claims.
Kaku says the most direct test of string theory would be to produce and observe a graviton to see if it conforms to string theory’s predictions. However, to observe a graviton with our current methods would require a particle accelerator the size of our whole solar system. Another facet of string theory that gives physicists pause is that string theory’s equations don’t just allow for a single universe, but a potentially infinite multiverse. To this, Kaku replies that we don’t even have a final version of string theory’s equations as of yet. Perhaps there really is a multiverse out there, or maybe whatever the true God Equation is, there is only one viable solution, with the others being too unstable to exist.
To the charge that we can’t directly test string theory, Kaku points out that science often tests its theories indirectly. One avenue might be through astrophysicists’ search for the unseen dark matter that permeates the universe. String theory predicts several options for what dark matter might actually be, such as microscopic black holes or particles called photinos. If any of these are eventually found, it would strengthen string theory’s overall standing. Another option comes from the recent discovery of gravity waves, as predicted by Einstein. Kaku writes that if we can detect gravity waves generated by the Big Bang itself, they may confirm or deny string theory’s predictions about the nature of the universe’s origin.
If we do find that string theory is correct, will it make a difference in our everyday lives? Kaku admits that it probably won’t—the energies involved in making use of string theory are orders of magnitude beyond what we possess. Its biggest impact might be felt in the circles of religion and philosophy. If one equation explains the entirety of the cosmos, it may change how we conceive of God and our place in the universe. Though Kaku describes himself as agnostic, he finds it amazing that all the laws of physics can be summarized succinctly and display such symmetry. For him, the mathematical beauty of the laws of physics opens the door to the possibility that there might actually be a grand design.
