Is there a theory of everything? How close are we to finding it?<\/p>\n\n\n\n
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<\/em>, Michio Kaku suggests an approach that might be the path to uniting all the laws of nature.<\/p>\n\n\n\n Continue reading for an overview of this mind-bending book.<\/p>\n\n\n\n\n\n\n\n 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.<\/p>\n\n\n\n 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 \u201cthe God equation\u201d\u2014a 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.<\/p>\n\n\n\n In The God Equation: The Quest for a Theory of Everything<\/em><\/em><\/a>, published in 2021, theoretical physicist Michio Kaku suggests that an approach called \u201cstring theory,\u201d which he\u2019s 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<\/a> and is the author of many books on science and humanity\u2019s future<\/a>, such as Physics of the Impossible<\/em><\/a> and The Future of the Mind<\/em><\/a>. In addition to his published works, Kaku is a frequent contributor to TV science programs such as PBS\u2019s Nova<\/em><\/a> and BBC\u2019s Horizon<\/em><\/a>.<\/p>\n\n\n\n In our guide to The God Equation<\/a><\/em>, we trace the history of scientific progress<\/a> in terms of discoveries that unify areas of knowledge and reveal the underlying symmetries of nature, from the early days of physics to Einstein\u2019s theory of relativity<\/a>, from the initial discoveries of quantum mechanics to our present model of matter and energy. We also discuss string theory<\/a><\/em>, the cutting edge of theoretical physics that might unify all our ideas of the cosmos into a single, overarching concept.<\/p>\n\n\n\n We also define terms and concepts to give readers a better understanding of the topic. Finally, we look at the philosophical implications that a search for a theory of the universe entails.<\/p>\n\n\n\n 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.<\/strong> 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\u2019t just explain the subject being studied, but also reveals insights seemingly unrelated to the topic at hand. One such insight we\u2019ll cover in this section is that the laws of nature are symmetrical<\/em>, a concept that Kaku repeatedly invokes.<\/p>\n\n\n\n It all goes back to Isaac Newton<\/a>, who, from 1666 to 1687, worked out the first mathematical theory to explain the laws governing the motion of objects, as well as the \u201claw of universal gravitation\u201d 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<\/strong> 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\u2019s mathematics, once confirmed by observation, proved that the two were the same.<\/p>\n\n\n\n The next major breakthrough that Kaku discusses came from studies of electricity and magnetism. We\u2019ve been aware of both for thousands of years, but it wasn\u2019t until 1831 that scientific experimentalist Michael Faraday<\/a> 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.<\/strong> Kaku writes that in describing his experiments, Faraday originated the concept of \u201cfields\u201d\u2014in his case, electromagnetic <\/em>fields\u2014as 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.<\/p>\n\n\n\n Since Faraday wasn\u2019t a mathematician, the most powerful revelation from his studies didn\u2019t come until 1861, when James Clerk Maxwell<\/a> expressed the relationship between electricity and magnetism in mathematical form. When he did, Maxwell\u2019s 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\u2014the speed of light! Out of the blue, Maxwell had discovered that light is a wave in the electromagnetic field.<\/strong> Not only that, but his equations predicted frequencies of light beyond what we can see\u2014the entire invisible electromagnetic spectrum that astronomers now use to explore the depths of space.<\/p>\n\n\n\n When discussing these early scientific breakthroughs, Kaku calls attention to the fact that all of the equations describing motion and electromagnetism are symmetrical<\/em>. 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.<\/strong><\/p>\n\n\n\n Symmetry is a powerful mathematical tool. If you assume that symmetry is a property of a phenomenon you\u2019re trying to explain, then symmetry can show where there are gaps in your knowledge <\/strong>and suggest what the \u201cmissing pieces\u201d of a puzzle might look like. For example, the quest for symmetry led scientists to deduce the existence of antimatter<\/em>\u2014the inverse and opposite of regular matter\u2014decades before it was proven to be real. Scientists find symmetry to be aesthetically pleasing, even elegant<\/em>, but Kaku warns that just because a theory is pretty doesn\u2019t necessarily mean it\u2019s true.<\/p>\n\n\n\n Nevertheless, Kaku illustrates that, the more we learn about the laws of nature, the more it seems that symmetry is built into the universe\u2019s basic set of rules. Newton\u2019s laws of gravity and motion are symmetrical because they don\u2019t depend on your frame of reference. If you look at an object\u2019s motion upside down or sideways, the equations that govern it produce the same result. Maxwell\u2019s 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.<\/strong><\/p>\n\n\n\n Thanks to Newton\u2019s and Maxwell\u2019s equations, physicists at the start of the 20th century believed there wasn\u2019t much left to explore. But, Kaku points out that there was a problem\u2014under certain conditions, Newton\u2019s and Maxwell\u2019s theories were incompatible with each other. After explaining the nature of the problem, we\u2019ll discuss how Albert Einstein<\/a> solved it by reimagining Newton\u2019s laws of motion and then rewriting Newton\u2019s law of gravitation.<\/p>\n\n\n\n The contradictions between Newton\u2019s and Maxwell\u2019s 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\u2019s point of view? Newton says that speeds add and subtract\u2014the cat would see the laser beam moving at only 71 million miles per hour. However, Maxwell\u2019s equations suggest that the speed of light never <\/em>changes.<\/strong> 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\u2019t be true, so either Newton or Maxwell was wrong.<\/p>\n\n\n\n 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. <\/strong>This is the basis of Einstein\u2019s theory of special relativity<\/em>. In Einstein\u2019s new equations governing objects in motion, Newton\u2019s 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.<\/p>\n\n\n\n Einstein\u2019s equations also add additional layers of symmetry to Newton\u2019s. 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<\/sup> (energy equals mass times the speed of light squared). Therefore, says Kaku, special relativity unites energy and matter, as well as time and space.<\/strong><\/p>\n\n\n\n Nevertheless, Einstein knew his theory was incomplete. It corrected Newton\u2019s laws of motion but said nothing about the law of gravitation. According to Newton, the effects of gravity are instantaneous\u2014if a source of gravity suddenly moves, the change in its force is immediately felt\u2014but 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\u2014to combine Einstein\u2019s theory of special relativity<\/a> with Newton\u2019s theory of universal gravitation.<\/p>\n\n\n\n Einstein\u2019s solution was to propose that the force of gravity is actually an illusion caused by the deformation of space.<\/strong> Consider a marble rolling across a trampoline. If the trampoline is flat, the marble rolls straight across, but if there\u2019s a bowling ball sitting in the middle, pulling the fabric of the trampoline down, the marble will appear to be \u201cattracted\u201d to the ball, no matter which way it was originally rolling. This is the essence of Einstein\u2019s theory of general relativity<\/em>, which shows that matter warps space around it\u2014the greater the mass, the greater the \u201cdent\u201d it makes. Kaku lists ways that Einstein\u2019s equations reveal things that Newton\u2019s can\u2019t\u2014such as predicting how gravity causes light to bend or explaining the planet Mercury\u2019s erratic orbit.<\/p>\n\n\n\n While Einstein was solving the riddles of gravity and motion, another field of exploration\u2014quantum mechanics\u2014was 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.<\/strong> In this section, we\u2019ll 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<\/a> and Maxwell\u2019s light equations.<\/p>\n\n\n\n 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<\/a> noticed something strange about atomic behavior when he investigated the light given off by hot materials. According to equations based on Newton\u2019s 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\u2019t add up\u2014the wavelengths of light emitted by hot, glowing matter didn\u2019t match the predictions of Newtonian thermodynamics.<\/p>\n\n\n\n Kaku writes that Planck found a solution that was just as shocking to the norms of science as Einstein\u2019s theory of relativity. In essence, Planck determined that the energy released by matter as it cools doesn\u2019t diminish on a linear scale but as tiny bundles called \u201cquanta.\u201d<\/strong> It\u2019s as if when an atom cools, its energy level doesn\u2019t 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\u2014photons<\/em>\u2014that exactly match the energy of light given off by heated objects.<\/p>\n\n\n\n The problem with photons being particles of light is that Maxwell\u2019s equations show that light is an electromagnetic wave. It turns out that light has properties of both waves and particles,<\/strong> 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.<\/p>\n\n\n\n So, when we say that electrons are waves, it simply means that you can\u2019t pin one down\u2014you can only determine the probability <\/em>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\u2019t tell where the moon is in the sky\u2014you can only compute where it\u2019s likely <\/em>to be. This makes no sense in our macroscopic world governed by laws of relativity, but it\u2019s exactly how electrons and photons, as well as other particles, behave. Clearly, says Kaku, if we\u2019re to uncover one universal theory, it will have to reconcile quantum mechanics with Einstein\u2019s special relativity.<\/strong><\/p>\n\n\n\n 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\u2019ll explain researchers\u2019 methods to pry open the atom\u2019s 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.<\/p>\n\n\n\n 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.<\/strong> 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<\/a> components and the particle they create stays the same.<\/p>\n\n\n\n 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\u2014the strong nuclear force.<\/strong> This force is an extremely short-range field of attraction generated by a particle called a gluon <\/em>(because it glues subatomic particles together). This field can be described mathematically using a modified version of Maxwell\u2019s 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<\/a> of physics.<\/p>\n\n\n\n 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 \u201cweak interaction,\u201d also known as the weak nuclear force<\/em>. Whereas the strong force holds atoms together, the weak nuclear force breaks particles apart<\/strong> and can even change them from one form to another.<\/p>\n\n\n\n In beta decay<\/em>, the weak force breaks a neutron apart into a proton, an electron, and the electron\u2019s phantom partner, the neutrino<\/em>. 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\u2014if the proton has an electrically neutral counterpart (the neutron) shouldn\u2019t the electron have one too? Their existence was purely theoretical until they were observed in 1956.<\/p>\n\n\n\n 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\u2019s understood that electromagnetism and the weak nuclear force are one and the same,<\/strong> now referred to as the electroweak <\/em>force. Kaku affirms that this is the path that the search for a unifying theory<\/a> has taken\u2014merging separate theories about phenomena until there\u2019s only one left.<\/p>\n\n\n\n Though scientists have yet to figure out the unifying theory\u2014Kaku\u2019s \u201cGod Equation\u201d\u2014physicists have made a great deal of progress using an intermediate step toward that theory referred to as the Standard Model. In this section, we\u2019ll 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.<\/p>\n\n\n\n Beginning in the 1970s, physicists stitched together the equations for the strong nuclear force, the weak nuclear force, and electromagnetism to produce what\u2019s 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.<\/strong><\/p>\n\n\n\n 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\u2014a chimeric creation of theories stitched together in a way that isn\u2019t completely plausible and contains mathematical terms that aren\u2019t greatly understood. On the plus side, the equations for the Standard Model are symmetrical<\/strong>, but Kaku says that in this case, that\u2019s a problem. The universe around us isn\u2019t <\/em>symmetrical\u2014matter 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.<\/p>\n\n\n\n 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 \u201cHiggs boson\u201d consistent with the Standard Model that unbalanced the cooling universe\u2019s symmetry and led to the variety of particles known today. Sometimes called the \u201cGod particle,\u201d the Higgs boson created regions of space within which other particles began to have mass.<\/strong> 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.<\/p>\n\n\n\n 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\u2019ll explain the struggles involved with incorporating gravity into the Standard Model and several discoveries that have been made along the way.<\/p>\n\n\n\n The trouble with gravity is that it\u2019s by far the weakest of the universal forces, so it\u2019s virtually impossible to observe on the quantum scale. While Einstein defines gravity as a curvature in space, there\u2019s no way to express this in the mathematics of quantum mechanics. Instead, physicists have tried another tack\u2014to model gravity as a force created by a particle. Just as gluons transmit the strong nuclear force, scientists have proposed the existence of gravitons <\/em>that govern gravitational fields.<\/strong> While plausible, Kaku writes that so far no one\u2019s been able to create a mathematical model of gravitons that produces meaningful results.<\/p>\n\n\n\n Despite the problems of incorporating gravity into quantum mechanics, that hasn\u2019t 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\u2019t be escaped\u2014the event horizon of a black hole, or the dividing line around a black hole\u2019s 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.<\/strong><\/p>\n\n\n\n This takes place because, in the subatomic world, empty space isn\u2019t 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\u2019t 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.<\/strong><\/p>\n\n\n\n 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\u2019s existence. In the first instants of time, all the fundamental forces of nature interacted with each other<\/strong> 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\u2014because light takes time to travel\u2014also entails looking backward in time.<\/p>\n\n\n\n Indeed, Kaku affirms that there are several observations about the Big Bang that can only be explained using quantum mechanics.<\/strong> By treating the Big Bang as a source of quantum radiation, researchers were able to compute the temperature of the Big Bang\u2019s leftover heat, which was confirmed when the Cosmic Microwave Background<\/a> (CMB) was discovered in 1964. Another issue is the universe\u2019s rate of expansion, as measured by the stretched-out light waves detected from distant galaxies, which is much faster than Einstein\u2019s 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.<\/p>\n\n\n\n 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\u2019ll 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.<\/p>\n\n\n\n The basic assertion of string theory is that all particles can be described as vibrations on subatomic strings<\/strong> that constitute the basis of energy and matter. Kaku writes that each different type <\/em>of particle is produced by a different vibration. One of string theory\u2019s strong appeals is that its equations produce gravitons as being the lowest string vibration, removing the conflict between Einstein and quantum mechanics<\/a>. String theory also supports physicists\u2019 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\u2019re all just different frequencies of the same foundational strings.<\/p>\n\n\n\n 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\u2014bosons<\/em> representing the fundamental forces, such as gluons, photons, and gravitons; and fermions <\/em>comprising the building blocks of matter, such as protons, neutrons, and electrons. In the math for string theory, bosons and fermions are interchangeable,<\/strong> just like time and space are in relativity, as well as electricity and magnetism in Maxwell\u2019s equations. This feature of string theory, called supersymmetry<\/em>, unites every observable property of space, time, energy, and matter into the interactions of vibrating strings.<\/p>\n\n\n\n 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<\/strong> instead of the four that we\u2019re 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\u2019t see are so small that they\u2019re 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.<\/p>\n\n\n\n The trouble with these other six dimensions is that we don\u2019t know what they represent, but their existence is required by string theory\u2019s equations. For this reason among others, many scientists reject string theory as a piece of mathematical sleight-of-hand.<\/p>\n\n\n\nOverview of The God Equation: The Quest for a Theory of Everything<\/em><\/h2>\n\n\n\n
First Steps Toward Unification<\/h3>\n\n\n\n
Electromagnetism<\/strong><\/h4>\n\n\n\n
The Power of Symmetry<\/strong><\/h4>\n\n\n\n
Einstein\u2019s Relativity<\/strong><\/h3>\n\n\n\n
Special Relativity<\/strong><\/h4>\n\n\n\n
General Relativity<\/strong><\/h4>\n\n\n\n
Quantum Mechanics<\/strong><\/h3>\n\n\n\n
Particles and Waves<\/strong><\/h4>\n\n\n\n
The Heart of the Atom<\/strong><\/h4>\n\n\n\n
The Weak Interaction<\/strong><\/h4>\n\n\n\n
The Standard Model<\/strong><\/h3>\n\n\n\n
The Gravity Problem<\/strong><\/h4>\n\n\n\n
Back to the Beginning<\/strong><\/h4>\n\n\n\n
The Promise of String Theory<\/strong><\/h3>\n\n\n\n
The String Theory Debate<\/strong><\/h4>\n\n\n\n