• Arpan Dey

The Theory Of Everything

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There has been no significant breakthrough in physics since the discovery and verification of the Standard Model. This is due to the five great problems with theoretical physics. Yes, there are, as Lee Smolin writes in his book The Trouble With Physics, five major problems in theoretical physics. First, the unification of the four forces and second, the reconciliation of general relativity and quantum mechanics. These two problems are perhaps interdependent: to solve one we need to solve the other. Next, the third problem is about the Standard Model. Although most of us believe it to be the most successful theory there is, it has a lot of constants with values we don't know the origin of. We can experimentally find the values, but we don't know why these constants have to take on those particular values. Plus we need to explain the mass of neutrinos and a lot of other things. The fourth problem is about dark matter and dark energy. We know very little about them, and they were postulated simply to explain away some crazy cosmological observations which couldn't be explained by our current theories. The last problem is, according to me, the most important problem in all of science. Making sense of quantum mechanics. The quantum measurement problem. The problem of consciousness. I have indirectly reflected on this problem in a previous blog. Did we just accidentally come to this world, which would exist even if we didn't? Or is consciousness something fundamental, and the very existence of reality depends on consciousness? You must keep in mind that a theory of everything, to be really a theory of everything, must solve each of these problems.

A theory of everything. Or in other words, a theory that would explain all possible interactions in Nature. Our universe is dynamic, and everything in it is changing. As you may know, force causes this change. Force can change the state of motion, direction and configuration of an object. There are many different forces, but often many forces are just different forms of the same fundamental force. Over the years, physicists have come to the conclusion that there are four fundamental forces. One, the gravitational force. Second, the electromagnetic force. Third, the weak nuclear force and finally, the strong nuclear force. These forces can pretty much explain every interaction that can possibly take place in our universe. Just think about it. All the possible interactions. Physicists today are trying to unify these four forces into a single theoretical framework. Then, in a single theoretical framework, we could explain all the interactions that can take place in this universe. Such a theory deserves to be called a theory of everything.

Perhaps the best example of unification in physics is the unification of electricity and magnetism by James Maxwell. Electricity and magnetism were understood to be different phenomena, initially. But then it was discovered that they can be unified into a single force called electromagnetism. There are electric fields and magnetic fields. A charge in rest produces an electric field, and a charge in motion produces a magnetic field. Electric field lines point away from positive charges and toward negative charges. A positive or a negative charge can exist independently, and so electric field lines can emerge out of a positive charge and spread till infinity. But in magnetism, we see that magnetic monopoles can't exist. If there is a north pole, there must be a south pole. Or in other words, a north pole can't exist independently from a south pole. Magnetic lines of force travel from the north to the south pole outside the magnet. Since monopoles can't exist, we see that the number of magnetic field lines entering a region must be equal to the number of field lines leaving that region. As there are no magnetic charges from which magnetic field lines emanate or at which magnetic field lines terminate, any magnetic field line entering must exit through the surface. Next, Michael Faraday discovered the phenomenon of electromagnetic induction. Just like a moving charge can produce a magnetic field, changing magnetic flux can produce electric current. This principle is used in generators, for instance. What Maxwell did was describe all of electromagnetism in four equations. These were not his own equations, but he did modify Ampere's law. Maxwell also found that electric fields and magnetic fields can 'reinforce' each other and propagate as an electromagnetic wave even in vacuum. He also found that the speed of the electromagnetic wave is equal to the speed of light, and from this he concluded that light is an electromagnetic wave. (Then it was well established that light has a wave nature. In Newton's day, light was thought to be made of a stream of 'corpuscles.' But to explain phenomena like interference, diffraction etc., it was proposed that light has a wave nature.)

Now, let us discuss gravity. Gravity here is the odd one out, because all the other forces can be explained in terms of exchange of certain fundamental particles. But we haven’t yet discovered such a particle for gravity. Today, most physicists see gravity as a force arising out of the curvature of spacetime. Albert Einstein, in his theory of relativity, proposed that matter and energy are basically the same thing, and so are space and time. The presence of matter/energy can curve the spacetime around it. And this curvature of spacetime affects the movement of the bodies present around. So in this view, two bodies are not exactly pulling each other. They are moving toward each other due to the curvature of spacetime. There is no particle exchange involved. However, recent discoveries, like gravitational waves from two colliding black holes, hint at the existence of gravitons. There are some problems with gravitons, like the fact that they are not renormalizable. Also, it is possible that the graviton may exist in a higher dimension.

It should be noted that although general relativity has survived many stringent experimental tests, it breaks down inside a black hole or at the Big Bang. This only shows that general relativity is not a complete theory, and there is a deeper, all-encompassing theory which would account for dark matter, dark energy (etc.) naturally, unlike general relativity. Quoting Celia Escamilla-Rivera from this Quanta Magazine article, "The problem is that general relativity is not general enough. If you want to explain dark energy, this invisible energy that seems to be accelerating the universe’s expansion, you need an extra component in the equation, called the cosmological constant. This extra component doesn’t exist naturally in general relativity; you need to add it by hand." Please keep in mind that dark matter and dark energy are simply terms we have coined to phenomena which can't be explained at present. It is surely possible that we will discover some deeper theory in the future which would explain these phenomena, or shed light on what problems with our current theories have given rise to the misconception of the existence of these phenomena.

When Einstein was busy fighting his battle in the thickets of spacetime, other physicists were developing a new and revolutionary theory: quantum mechanics. (It should be noted that Einstein himself also played an important role in the development of quantum mechanics, although he later refused to accept quantum mechanics as a complete theory.) Quantum theory was born when Max Planck showed that energy can't be radiated constantly, but in discrete packets called quanta. This was an essential step in resolving the ultraviolet catastrophe. Planck showed that the energy is directly proportional to the frequency, and thus is equal to a constant multiplied with the frequency. This constant is what we call Planck's constant. It was Einstein's insight that to explain the photoelectric effect, we must think of light as a stream of discrete quanta, called photons. Einstein reintroduced the particle nature of light, and it was necessary. Today, we say that light has dual nature: the wave theory explains some phenomena while you need the particle theory for some other phenomena. Then we had Louis de Broglie's great idea that just like light (supposed to be a wave) has dual nature (particle nature in addition to wave nature), matter (supposed to be of particle nature) has a wave nature too. This has been verified by studying the diffraction of electron, and has wide ranging applications, like the electron microscope. The electron was thought of as a point-like particle. Then quantum theory proved that electron, and in fact everything else, has a wave nature too. Werner Heisenberg showed that it was impossible to determine both the position and momentum of a particle simultaneously. There is a certain amount of uncertainty in Nature deep down. Then came Schrödinger's equation. There was the interpretation of the wave function as a function the square of which gives the probability of finding the particle in the given region. Only on observing the particle (don't get me started on consciousness here), does the wave function 'collapse' to a distinct 'value,' and we observe the particle in a distinct location. Before observation, the particle has a non-zero probability of existing everywhere, even in distant galaxies. (Here I'm referring to the quantum measurement problem, and there are a lot of philosophical difficulties here. According to quantum mechanics, before a measurement or observation is made, an object exists in a superposition of all possible states, and in multiple places at the same time. Only on observation does it collapse to a distinct state. While it is not clear whether this observation requires consciousness, it is known for sure that measurement must be made for things to exist in a distinct state. There are some other interpretations like the many-worlds interpretation which says that the wave function never collapses. All the possibilities take place in different parallel worlds that are branching off from the original world every moment.) And, roughly speaking, Nature tries out all possibilities, so if we wait long enough, we can observe the effect of quantum tunneling: the particle can instantaneously disappear from here and appear in a distant location. Tunneling has been observed already. But don't expect we will be walking through walls any time soon! Anyway, quantum mechanics disproved all common sense notions about reality. In this new world, a particle can simultaneously pass through two slits, you have a certain probability of tunneling to a distant galaxy (although not in your lifetime, such extremely rare events will occur after a long, really long time) and you get the idea. There is a certain amount of randomness in Nature. We can't know everything precisely. Everything is reduced to probability. Some physicists accepted this revolution, while others were not so happy about this. But quantum mechanics has been repeatedly verified experimentally.

Now, we all know what a charge is. It is an intrinsic property of some particles, and the electron carries the smallest amount of charge that can exist independently. The electron carries a charge which is in nature very different from the charge carried by protons. There are two types of charges, positive and negative and unlike charges attract one another while like charges repel one another. This attraction and repulsion fall under the electromagnetic interaction. This attraction holds the nucleus and electrons in an atom together. The strong nuclear and weak nuclear forces operate on a much smaller scale and hold the nucleus of the atom together. These three forces are all caused by the exchange of fundamental particles called bosons. In fact, there are two types of fundamental particles. Bosons, which give rise to forces, and fermions, which make up the matter. At this point, it should be noted that the unification of even just these three forces was not easy. After Einstein published his geometrical theory of gravity, he, along with many other scientists, started looking for a geometric interpretation of electromagnetism. The weak nuclear and strong nuclear forces were not known at that point. It was soon discovered, by Theodor Kaluza, that the existence of an extra, hidden dimension can account for electromagnetism in a world which is consistent with Einstein's general relativity. In other words, Kaluza, as Lee Smolin writes in The Trouble With Physics, "applied Einstein's general theory of relativity to a five-dimensional world and found electromagnetism." Oskar Klein further developed the theory and, as Smolin writes, "gravity and electromagnetism [were] unified in one blow, and Maxwell's equations are explained as coming out of Einstein's equations, all by the simple act of adding a single dimension to space." The weak and strong nuclear force can also be, in some sense, unified with gravity and electromagnetism by adding even more dimensions. But why don't we see these dimensions? The initial response was that these dimensions were curled up to very small lengths and to make these theories work, you also have to 'freeze' the geometry of the extra dimensions. Plus, such solutions are unstable. Plus there were a lot of possible unified theories, and it was difficult to choose one out of them. As Smolin writes, "Over and over again in the early attempts at unifying physics through extra dimensions, we encounter the same story. There are a few solutions that lead to the world we observe, but these are unstable islands in a vast landscape of possible solutions, the rest of which are very unlike our world."

The best candidate we have for a theory of everything is, perhaps, string theory. If string theory turns out to be correct, then the correct question about the final theory should be asked not in terms of forces or fields or particles, but in terms of strings. String theory proposes that one dimensional ‘strings,’ the different modes of vibrations on which correspond to the different particles, are the most fundamental building blocks of the universe, and no particle is any more fundamental than any other particle. In string theory, forces arise from the joining and breaking of strings. All forces and particles can be explained by assuming strings propagate in a fixed background in such a way so as to minimize the area taken up. String theory basically replaces the idea of zero dimensional point particles with the idea of a one dimensional string of energy. Interestingly, string theory was initially developed as a theory of the strong nuclear interaction. But then it was discovered that string theory includes all the three forces plus gravity. The latter, as a requirement, must be included for the theory to work. Gravitons, according to string theory, arise from the vibrations of only closed strings. This suggested that instead of just describing the strong nuclear interaction, string theory is in fact the theory that unifies all the four forces of Nature. There were problems, however. Some string theories predicted the existence of faster-than-light particles called tachyons which rendered the theories unstable. Okay, tachyons can be eliminated by using supersymmetry. But string theory requires twenty-five spatial dimensions and one time dimension to work. (At this point, it would be interesting to consider the arrow of time, and ponder whether string theory allows for more than one time dimension, or whether time can after all be treated as just another spatial dimension.) After supersymmetry was incorporated into string theory, we could reduce the number of required dimensions to ten (nine spatial dimensions). The initial explanation was that these dimensions are curled up to such small lengths that they are not perceivable. But, as Smolin writes in The Trouble With Physics, "This gave rise to great opportunities, and great problems... earlier attempts to use higher dimensions to unify physics have failed, because there were too many solutions... It also led to problems of instabilities, because there are processes by which the geometry of the extra dimensions unravels and becomes large and other processes whereby it collapses to a singularity." More problems remained, and new problems came up as string theory developed. There was still excitement, for it was proved that string theory is finite and consistent. All the previous quantum gravity theories were not finite and consistent. String theory promised to be a ray of hope. String theory is beautiful and elegant. But we must also remember that beautiful theories have failed before. And then it was discovered that string theory is not a unique theory. Five different versions of superstring theory were discovered. The hope was that all these theories are different manifestations of some deeper, underlying theory. There is one more problem with string theory. String theory is background dependent. We describe strings moving in a fixed background, in fixed space and time. But general relativity is background independent. And as far as we know, a final theory must also be background independent. Background independence requires that, quoting from Wikipedia, "the defining equations of a theory to be independent of the actual shape of the spacetime and the value of various fields within the spacetime. In particular this means that it must be possible not to refer to a specific coordinate system - the theory must be coordinate free. In addition, the different spacetime configurations (or backgrounds) should be obtained as different solutions of the underlying equations." The background evolves, and is not fixed. And this should be the case with a fundamental theory. The background must be derivable from first principles, and not be fixed. As is explained in the Wikipedia article, we must not increase the number of inputs the theory needs to make its predictions. Well, string theorists assume the background to be almost fixed with small disturbances, and use perturbation techniques to account for these disturbances. And there is also some hope that the different background dependent versions of string theory are emergent from a deeper, background independent theory.

There are alternatives to string theory. The best alternative being loop quantum gravity which attempts to apply the principles of quantum mechanics to gravity. General relativity, as we know, describes gravity as a consequence of the curved geometry of spacetime. Loop quantum gravity, however, suggests that space itself is discrete, quantized and granular (not continuous). Loop quantum gravity assumes that space is emergent from discrete building blocks. Loop quantum gravity makes some testable predictions, and may also be a successful, finite and consistent theory of quantum gravity. And loop quantum gravity is background independent as well.

Anyway, the problem with string theory is that there is no concrete experimental support for it. String theory has made no unique and viable prediction. The predictions of string theory, if proved to be true, will not conclusively prove that string theory is true. And even if these predictions are false, string theory might still be true. So far, there have been no exciting findings regarding cosmic strings or extra forces or if you believe in the supersymmetric string theory, superpartners. In conclusion, it can be said that physics may take an unexpected turn any moment now (for instance, the muon g-2 experiment points at the existence of new particles and makes us think twice about the Standard Model, which is supposed to be perhaps the most successful theory, and although the Standard Model can be modified to account for the mass of the neutrino, there are other problems with the Standard Model), and it is really difficult to predict whether we are actually close to finding a theory of everything, because future discoveries can make the task more complicated than it seems now. As of now, we have some really good insights like the AdS/CFT correspondence, which likely will take us a long way toward a theory of everything. The journey so far has been incredible, and is bound to be more so in the future. Coming to the Standard Model, it is mainly based on two principles: gauge principles (which has unified all the three forces except gravity) and spontaneous symmetry breaking (which explains the difference between these forces). It may be the case that initially there was a single force, which due to spontaneous symmetry breaking gave rise to three different forces. Breaking of symmetry (which introduces differences in the system) is essential for stability. Water is, by itself, symmetric (there is no particular asymmetry in it, it just assumes the shape of its container). Now cool it. You get ice, which is not perfectly symmetric. (Ice assumes the shape of its container as well, but in general, the formation of ice doesn't follow any symmetry.) We know that hotter things have more energy, and are less stable. Everything wants to lose energy and gain stability. For that, it needs to cool down, and break symmetry in the process. Symmetry only exists at high energies. And this is a very fundamental idea. But I am not going into this here. I have left out important bits of the story, like the Higgs field which is responsible for spontaneous symmetry breaking, SU(5) symmetry and proton decay. But let's keep it for another day.

In the end, I would like to say that some people believe that once we find a theory of everything, physics would come to an end. Of course not. We have just started unravelling the mysteries of the universe, and there are more surprises in store for us. If you would ask me whether I believe we are going to find the theory of everything, I would say maybe yes, in the course of time. String theory and loop quantum gravity are promising approaches, and eventually I believe we would either discover the final theory or discover the incompleteness of our current understanding of the world. We will definitely discover something. I have this gut feeling that near-future discoveries in physics will be changing the way we see the world. A final theory is definitely possible, but we don’t understand the problems well enough yet, so it is not possible to comment on how far away the solution is.

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