More than 2,000 years ago, the ancient Greeks asked a simple question: What is the world made of? In setting out to provide an answer using only the tools of logic and reason—and guided by careful observation—the Greeks set humanity on an epic journey spanning thousands of years to uncover the secrets and fundamental composition of the universe.
The Greeks suspected that—behind all the complexity and apparent diversity of nature—the universe is composed of a smaller set of simpler elements that obey natural, rather than supernatural, laws. Since then, philosophers and scientists throughout the ages have sought the holy grail of all science—the long-coveted theory of everything that can explain the universe in its entirety, from the smallest subatomic particles to the largest galaxies and beyond.
This incredible story of scientific discovery and human ingenuity is the topic of physicist Michio Kaku’s latest book, The God Equation: The Quest for a Theory of Everything.
While not the first book to recount the history of physics, The God Equation does uniquely capture the central role of unification in physics. Kaku demonstrates how the major advances in physics have always followed the unification of forces and concepts, captured in beautiful, symmetrical equations.
The story of unification—like so many others—begins in ancient Greece, where philosophers made the attempt to unify nature’s diversity into a single, fundamental substance. Thales of Miletus, often described as the first philosopher, proposed that all matter was made of water, while his student Anaximander thought the substance was an indefinite material called Apeiron. Anaximenes, Anaximander’s student, identified the fundamental substance as air, while Heraclitus thought it was fire.
While ultimately off-the-mark, these philosophers introduced a critical idea: that hidden beneath the apparent diversity of nature is a single substance, and, further, that all physical phenomena operate according to natural, rather than supernatural, laws. This eventually led to ancient Greece’s crowning scientific hypothesis: the atomic theory of matter. The ancient Greek conception of an atom was, of course, very different from the modern view, but the idea that there is an invisible, indestructible substrate to reality that operates according to rational mathematical laws is the foundation for all future advances in physics.
As kaku wrote:
“So at least two great theories of our world emerged from ancient Greece: the idea that everything consists of invisible, indestructible atoms and that the diversity of nature can be described by the mathematics of vibrations [as established by Pythagoras when he discovered the relationship between musical notes and scales and the physical vibrations of strings].”
Unfortunately, the rise of Christianity put a stranglehold on the rational and mathematical investigation of the world for about 1,000 years. In fact, it was not until the 15th century Renaissance—or the rediscovery of classical learning and culture—that humanity would once again break free of the shackles of superstition to pursue the project of unification.
The reintroduction of classical learning—and the idea that humans could transcend the teachings of the past and make progress in knowledge—led straight to Isaac Newton, who took the principle of unification to the next level. Building on the work of his predecessors, Newton demonstrated, through his universal laws of motion and gravity, that nature operates according to precise mathematical laws and that these laws hold anywhere in the universe. In other words—contrary to the religious teachings at the time—there were not separate laws for the earthly and heavenly realms, but rather one set of laws applicable across all of space and time. It’s hard to imagine how revolutionary this idea must have been to those living in the 17th century.
Newtonian physics—the driving force behind the industrial revolution and the operation of all mechanical devices—unified all natural phenomena anywhere in the universe as conforming to the same mathematical laws and principles. At the time, it may have seemed that Newton had, in fact, discovered the final theory of everything. But as scientific knowledge progressed, problems with Newton’s theory would emerge, as Albert Einstein would later demonstrate.
The next major milestone in unification came with James Clerk Maxwell’s unification of electricity and magnetism. In formulating the classic theory of electromagnetic radiation, Maxwell was able to show that electricity, magnetism, and light are all manifestations of the same phenomenon. Once again, apparently disparate elements of nature turned out to be, in reality, unified under a single mathematical framework.
There was a problem, however. The twin pillars of physics at the time—Newton’s laws and electromagnetism—turned out to be fundamentally incompatible, as Albert Einstein was to discover. In brief, since the speed of light must remain constant (according to Maxwell’s equations), space and time cannot be absolute (as described by Newton’s laws). And so Newton—long considered the greatest scientist of all time—turned out to be wrong, or at least his laws were incomplete.
In resolving the paradox, Einstein introduced yet another process of unification: this time, the unification of space and time and matter and energy, as captured in the theories of special and general relativity.
It turns out that space and time, contrary to what Newton believed, are not absolute; rather, spacetime is a single four-dimensional property of the universe that bends and curves and expands and contracts, and it is this curvature that creates the illusion of gravitational force. The sun, for example, does not “pull” the earth towards it with the force of gravity; instead, the mass of the sun warps spacetime—like a bowling ball set in the middle of a trampoline—and the planets, including earth, orbit this curved path.
Einstein also set out the equivalence of matter and energy in the famous equation E=MC2 that demonstrates that matter and energy are two sides of the same coin. This explains, among other things, why the sun shines (some of the mass of the hydrogen gets converted to energy at very high temperatures), and how atomic bombs work.
But this isn’t the end of the story. Einstein would spend the rest of his life trying (and failing) to pursue the final project of unification: the unification of general relativity (gravity) with the most mysterious scientific branch of all—quantum mechanics.
This is where we stand today. General relativity accurately describes large-scale phenomena, such as orbiting planets and the expansion of the universe, and is responsible for technologies such as GPS navigation, while quantum mechanics is equally successful at predicting small-scale phenomena such as atomic motion and decay and is responsible for various electronic technologies including the transistor, the laser, the electron microscope, and magnetic resonance imaging (MRI).
The problem is, while these two theories have been experimentally verified and are practically useful, they are also fundamentally incompatible, and present competing views of nature. Relativity, representing the force of gravity, presents a smooth, deterministic universe, while quantum mechanics, representing the three other physical forces (electromagnetism and the nuclear forces), presents a non-deterministic universe guided by the laws of probability and other counterintuitive laws that do not hold when scaled up.
We therefore find ourselves, as Kaku points out, in an analogous situation as the one faced by Einstein. As Kaku wrote:
“We saw earlier that around 1900, there were two great pillars of physics: Newton’s law of gravity and Maxwell’s equations for light. Einstein realized that these two great pillars were in conflict with each other. One of them would have to collapse. The fall of Newtonian mechanics set into motion the great scientific revolutions of the twentieth century.”
It seems as if history may be repeating itself. We currently have two great pillars of physics (relativity and quantum mechanics), and, since they are incompatible, it seems that one must fall if we are to ever achieve the next and final step in the unification project: the unification of all known forces into one mathematical equation—the God equation.
Kaku believes that we will eventually achieve this final grand unification and that it will be represented by some form of string theory, which replaces the point-like particles of particle physics with one-dimensional objects called strings. The vibrations of these strings are thought to account for all other emergent properties, including particle mass and charge and even gravity, thus providing a unified framework for all four physical forces. The problem is, string theory introduces an additional ten dimensions and, most critically, is impossible to directly test at the scales in which it deals. String theory therefore suffers from the following paradox: if it’s true, it’s too inaccessible to verify.
As Kaku admits, a particle accelerator the size of our galaxy would have to be built to directly test the theory. Still, he is confident that the theory can eventually be tested and confirmed via more indirect methods, or perhaps even mathematically.
The other possibility is that we’ve simply reached the limits of our understanding. Just as you can’t teach a dog calculus, perhaps we don’t have the cognitive or perceptual capacity to achieve a God-like perspective on the complete workings of the universe. After all, physicists know that dark energy—the mysterious force that drives the expansion of the universe but that we know very little about—makes up 68 percent of the universe. Additionally, dark matter, which is equally mysterious, makes up another 27 percent. So that means, everything on earth plus everything else we’ve ever observed with all our instruments adds up to less than 5 percent of the universe. It’s little surprise, then, that the theory of everything eludes us.
Kaku would point out, however, that decades and centuries can pass before the next great scientific revolution or between the proposal and confirmation of theories. Black holes, for example, were first predicted in 1783 by John Michell, but the first conclusive pictures of their event horizons were not produced until 2019, 236 years later.
String theory was first proposed only 60 years ago, in the 1960s. Perhaps we are still waiting for its confirmation. Some believe that, given the difficulty of directly testing string theory, we will be waiting indefinitely, but we should keep in mind that major scientific revolutions are rarely predictable.
We must also consider the following question: If we can’t test string theory directly, can we prove it mathematically, and, if so, does a mathematically consistent view of the universe necessarily correlate with its actual workings?
Alternatively, will some as of yet undeveloped theory unite the physical forces, or even demonstrate that either relativity or quantum mechanics is, in fact, wrong or incomplete, just as Newtonian physics was proven incomplete by Einstein in the early twentieth century? These are fascinating, open questions that are a long way from being resolved.
And so the quest for the theory of everything continues.
In addition to The God Equation: The Quest for a Theory of Everything, check out these books covering physics, quantum mechanics, string theory, and the many-worlds interpretation of quantum mechanics.
- The World According to Physics
- Einstein’s Unfinished Revolution: The Search for What Lies Beyond the Quantum
- The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory
- Something Deeply Hidden: Quantum Worlds and the Emergence of Spacetime
- Helgoland: Making Sense of the Quantum Revolution