The Theory of everything

The Theory of everything

by : Aria Ratmandanu 

               The universe is comprehensible because it is governed by scientific laws; that is to say, its behavior can be modeled. But what are these laws or models ?, The known forces of nature can be divided into four classes :

1. Gravity. This is the weakest of the four, but it is a long-range force and acts on everything in the universe as an attraction. This means that for large bodies the gravitational forces all add up and can dominate over all other forces.

2. Electromagnetism. This is also long-range and is much stronger than gravity, but it acts only on particles with an electric charge, being repulsive between charges of the same sign and attractive “between charges of the opposite sign. This means the electric forces between large bodies cancel each other out, but on the scales of atoms and molecules they dominate. Electromagnetic forces are responsible for all of chemistry and biology.

3. Weak nuclear force. This causes radioactivity and plays a vital role in the formation of the elements in stars and the early universe. We don’t, however, come into contact with this force in our everyday lives.

4. Strong nuclear force. This force holds together the protons and neutrons inside the nucleus of an atom. It also holds together the protons and neutrons themselves, which is necessary because they are made of still tinier particles, the quarks. The strong force is the energy source for the sun and nuclear power, but, as with the weak force, we don’t have direct contact with it.

               The first force for which a quantum version was created was electromagnetism. The quantum theory of the electromagnetic field, called quantum electrodynamics, or QED for short, was developed in the 1940s by Richard Feynman and others, and has become a model for all quantum field theories. As we’ve said, according to classical theories, forces are transmitted by fields. But in quantum field theories the force fields are pictured as being made of various elementary particles called bosons, which are force-carrying particles that fly back and forth between matter particles, transmitting the forces. The matter particles are called fermions. Electrons and quarks are examples of fermions. The photon, or particle of light, is an example of a boson. It is the boson that transmits the electromagnetic force. What happens is that a matter particle, such as an electron, emits a boson, or force particle, and recoils from it, much as a cannon recoils after firing a cannonball. The force particle then collides with another matter particle and is absorbed, changing the motion of that particle. According to QED, all the interactions between charged particles—particles that feel the electromagnetic force—are described in terms of the exchange of photons.

             One indication that unification is the right approach came from the theory of the weak force. The quantum field theory describing the weak force on its own cannot be renormalized; that is, it has infinities that cannot be canceled by subtracting a finite number of quantities such as mass and charge. However, in 1967 Abdus Salam and Steven Weinberg each independently proposed a theory in which electromagnetism was unified with the weak force, and found that the unification cured the plague of infinities. The unified force is called the electroweak force. Its theory could be renormalized, and it predicted three new particles called W+, W–, and Z0. Evidence for the Z0 was discovered at CERN in Geneva in 1973. Salam and Weinberg were awarded the Nobel Prize in 1979, although the W and Z particles were not observed directly until 1983.

                 The strong force can be renormalized on its own in a theory called QCD, or quantum chromodynamics “According to QCD, the proton, the neutron, and many other elementary particles of matter are made of quarks, which have a remarkable property that physicists have come to call color (hence the term “chromodynamics,” although quark colors are just helpful labels—there is no connection with visible color). Quarks come in three so-called colors, red, green, and blue. In addition, each quark has an anti-particle partner, and the colors of those particles are called anti-red, anti-green, and anti-blue. The idea is that only combinations with no net color can exist as free particles. There are two ways to achieve such neutral quark combinations. A color and its anti-color cancel, so a quark and an anti-quark form a colorless pair, an unstable particle called a meson. Also, when all the three colors (or anti-colors) are mixed, the result has no net color. Three quarks, one of each color, form stable particles called baryons, of which protons and neutrons are examples (and three anti-quarks form the anti-particles of the baryons). Protons and neutrons are the baryons that make up the nucleus of atoms and are the basis for all normal matter in the universe. 

                    After uniting the weak and electromagnetic forces, physicists in the 1970s looked for a way to bring the strong force into that theory. There are a number of so-called grand unified theories or GUTs that unify the strong forces with the weak force and electromagnetism, but they mostly predict that protons, the stuff that we are made of, should decay, on average, after about 1032 years. That is a very long lifetime, given that the universe is only about 1010 years old. But in quantum physics, when we say the average lifetime of a particle is 1032 years, we don’t mean that most particles live approximately 1032 years, some a bit more and some a bit less. Instead, what we mean is that, each year, the particle has a 1 in 1032 chance of decaying. As a result, if you watch a tank containing 1032 protons for just a few years, you ought to see some of the protons decay. It is not too hard to build such a tank, since 1032 protons are contained in just a thousand tons of water.

         Scientists have performed such experiments. It turns out that detecting the decays and differentiating them from other events caused by the cosmic rays that continually shower us from space is no easy matter. To minimize the noise, the experiments are carried out deep inside places such as the Kamioka Mining and Smelting Company’s mine 3,281 feet under a mountain in Japan, which is somewhat shielded from cosmic rays. As a result of observations in 2009, researchers have concluded that if protons decay at all, the proton lifetime is greater than about 1034 years, which is bad news for grand unified theories.

             Since earlier observational evidence had also failed to support GUTs, most physicists adopted an ad hoc theory called the standard model, which comprises the unified theory of the electroweak “forces and QCD as a theory of the strong forces. But in the standard model, the electroweak and strong forces act separately and are not truly unified. The standard model is very successful and agrees with all current observational evidence, but it is ultimately unsatisfactory because, apart from not unifying the electroweak and strong forces, it does not include gravity.

                                                Figure 1. Standard Model Lagrangian

              It may have proved difficult to meld the strong force with the electromagnetic and weak forces, but those problems are nothing compared with the problem of merging gravity with the other three, or even of creating a stand-alone quantum theory of gravity. The reason a quantum theory of gravity has proven so hard to create has to do with the Heisenberg uncertainty principle. It is not obvious, but it turns out that with regard to that principle, the value of a field and its rate of change play the same role as the position and velocity of a particle. That is, the more accurately one is determined, the less accurately the other can be. An important consequence of that is that there is no such thing as empty space. That is because empty space means that both the value of a field and its rate of change are exactly zero. (If the field’s rate of change were not zero, the space would not remain empty.) Since the uncertainty principle does not allow the values of both the field and the rate of change to be exact, space is never empty. It can have a state of minimum energy, called the vacuum, but that state is subject to what are called quantum jitters, or vacuum fluctuations—particles and fields quivering in and out of existence.

           One can think of the vacuum fluctuations as pairs of particles that appear together at some time, move apart, then come together and annihilate each other. In terms of Feynman diagrams, they correspond to closed loops. These particles are called virtual particles. Unlike real particles, virtual particles cannot be observed directly with a particle detector. However, their indirect effects, such as small changes in the energy of electron orbits, can be measured, and agree with theoretical predictions to a remarkable degree of accuracy. The problem is that the virtual particles have energy, and because there are an infinite number of virtual pairs, they would have an infinite amount of energy. According to general relativity, this means that they would curve the universe to an infinitely small size, which obviously does not happen!

           In 1976 a possible solution to that problem was found. It is called supergravity. The prefix “super” was not appended because physicists thought it was “super” that this theory of quantum gravity might actually work. Instead, “super” refers to a kind of symmetry the theory possesses, called supersymmetry.”

           In physics a system is said to have a symmetry if its properties are unaffected by a certain transformation such as rotating it in space or taking its mirror image. For example, if you flip a donut over, it looks exactly the same (unless it has a chocolate topping, in which case it is better just to eat it). Supersymmetry is a more subtle kind of symmetry that cannot be associated with a transformation of ordinary space. One of the important implications of supersymmetry is that force particles and matter particles, and hence force and matter, are really just two facets of the same thing. Practically speaking, that means that each matter particle, such as a quark, ought to have a partner particle that is a force particle, and each force particle, such as the photon, ought to have a partner particle that is a matter particle. This has the potential to solve the problem of infinities because it turns out that the infinities from closed loops of force particles are positive while the infinities from closed loops of matter particles are negative, so the infinities in the theory arising from the force particles and their partner matter particles “tend to cancel out. Unfortunately, the calculations required to find out whether there would be any infinities left uncanceled in supergravity were so long and difficult and had such potential for error that no one was prepared to undertake them. Most physicists believed, nonetheless, that supergravity was probably the right answer to the problem of unifying gravity with the other forces.

“The idea of supersymmetry was the key to the creation of supergravity, but the concept had actually originated years earlier with theorists studying a fledgling theory called string theory. According to string theory, particles are not points, but patterns of vibration that have length but no height or width—like infinitely thin pieces of string. String theories also lead to infinities, but it is believed that in the right version they will all cancel out. They have another unusual feature: They are consistent only if space-time has ten dimensions, instead of the usual four. Ten dimensions might sound exciting, but they would cause real problems if you forgot where you parked your car. If they are present, why don’t we notice these extra dimensions? According to string theory, they are curved up into a space of very small size.

             In addition to the question of dimensions, string theory suffered from another awkward issue: There appeared to be at least five different theories and millions of ways the extra dimensions could be curled up, which was quite an embarrassment of possibilities for those advocating that string theory was the unique theory of everything. Then, around 1994, people started to discover dualities—that different string theories, and different ways of curling up the extra dimensions, are simply different ways of describing the same phenomena in four dimensions. Moreover, they found that supergravity is also related to the other theories in this way. String theorists are now convinced that the five different string theories and supergravity are just different approximations to a more fundamental theory, each valid in different situations.

              That more fundamental theory is called M-theory, as we mentioned earlier. No one seems to know what the “M” stands for, but it may be “master,”  or “mystery.” It seems to be all three. People are still trying to decipher the nature of M-theory, but that may not be possible. It could be that the physicist’s traditional expectation of a single theory of nature is untenable, and there exists no single formulation. It might be that to describe the universe, we have to employ different theories in different situations. Each theory may have its own version of reality, but according to model-dependent realism, that is acceptable so long as the theories agree in their predictions whenever they overlap, that is, whenever they can both be applied.

               Whether M-theory exists as a single formulation or only as a network, we do know some of its properties. First, M-theory has eleven space-time dimensions, not ten. String theorists had long suspected that the prediction of ten dimensions might have to be adjusted, and recent work showed that one dimension had indeed been overlooked. Also, M-theory can contain not just vibrating strings but also point particles, two-dimensional membranes, three-dimensional blobs, and other objects that are more difficult to picture and occupy even more dimensions of space, up to nine. These objects are called p-branes (where p runs from zero to nine).

               What about the enormous number of ways to curl up the tiny dimensions? In M-theory those extra space dimensions cannot be curled up in just any way. The mathematics of the theory restricts the manner in which the dimensions of the internal space can be curled. The exact shape of the internal space determines both the values of physical constants, such as the charge of the electron, and the nature of the interactions between elementary particles. In other words, it determines the apparent laws of nature. We say “apparent” because we mean the laws that we observe in our universe—the laws of the four forces, and the parameters such as mass and charge that characterize the elementary particles. But the more fundamental laws are those of M-theory.”

               The laws of M-theory therefore allow for different universes with different apparent laws, depending on how the internal space is curled. M-theory has solutions that allow for many different internal spaces, perhaps as many as 10⁵⁰⁰, which means it allows for 10⁵⁰⁰ different universes, each with its own laws. To get an idea how many that is, think about this: If some being could analyze the laws predicted for each of those universes in just one millisecond and had started working on it at the big bang, at present that being would have studied just 10²⁰ of them. And that’s without coffee breaks.

Figure 2. 11-Dimensional Supergravity equation

                Centuries ago Newton showed that mathematical “equations could provide a startlingly accurate description of the way objects interact, both on earth and in the heavens. Scientists were led to believe that the future of the entire universe could be laid out if only we knew the proper theory and had enough computing power. Then came quantum uncertainty, curved space, quarks, strings, and extra dimensions, and the net result of their labor is 10⁵⁰⁰ universes, each with different laws, only one of which corresponds to the universe as we know it. The original hope of physicists to produce a single theory explaining the apparent laws of our universe as the unique possible consequence of a few simple assumptions may have to be abandoned. Where does that leave us ? If M-theory allows for 10⁵⁰⁰ sets of apparent laws, how did we end up in this universe, with the laws that are apparent to us ? And what about those other possible worlds ?