A Theory of Everything
In his introduction to The Feynman Lectures on Physics, physicist Richard Feynman wrote “I think I can safely say that nobody understands quantum mechanics. So do not take the lecture too seriously, feeling that you really have to understand in terms of some model what I am going to describe, but just relax and enjoy it. I am going to tell you what nature behaves like. If you will simply admit that maybe she does behave like this, you will find her a delightful, entrancing thing. Do not keep saying to yourself, if you can possible avoid it, But how can it be like that? because you will get down the drain, into a blind alley from which nobody has escaped. Nobody knows how it can be like that.”
Feynman did not receive the 1965 Nobel prize for being the great educator and popularizer of physics that he was, but his introductory passage is quite telling: physics is a description of nature, don’t worry about the complexity, enjoy its fascinating beauty.
Difficult or not, we will strive to achieve a basic conceptual understanding of the new science, while avoiding as much of the mathematical formalism as possible. Sometimes we may have to use uncommon sense to understand strange phenomena at the atomic level. Atoms are not like planets orbiting around the sun and do not obey Newton’s or Kepler’s laws. Their positions, velocities and motion are different. We have already seen that the theories of Planck, de Broglie and Einstein opened multiple paths of new research, which hit the scientific world like an avalanche. The interaction of light and mass became the new focus and an entire new area of physics developed, called quantum electrodynamics (QED). It is the quantum equivalent of classical electromagnetism. QED is the first theory that combined successfully the principles of quantum physics with special relativity, while quantum theory and general relativity are still incompatible and we will see further down what efforts are made to achieve agreement between the two theories.
English physicist Paul Dirac is one of the founders of QED. Born in 1902 in Bristol, Dirac studied electrical engineering and mathematics at the University of Bristol. Unable to find work as engineer, Dirac decided to do graduate work in physics at Cambridge, focusing on quantum theory and relativity. These fields of study were so new in the 1920s that there was only one professor at Cambridge who could supervise Dirac’s graduate work in quantum physics. In 1926 Dirac developed the first complete mathematical formulation of quantum mechanics and then focused his energy on a relativistic formulation of quantum theory.
The rest of Dirac’s story is just amazing! In 1927 he developed a quantum theory of radiation, where he came up with a brand new property called the electron spin, a measure of the electron’s angular momentum, that eventually became one of the fundamental concepts in particle physics. This was a spectacular achievement but Dirac knew from the very beginning that his theory had some serious problems. The mathematical equations yielded solutions that generally made sense. But there were certain credible conditions where the solutions did not make sense, as they required the electrons to have negative energy. Nobody knew what negative energy might be. You either have energy or you do not, you cannot have negative energy. Dirac was aware that a couple of years earlier a Swiss physicist named Wolfgang Pauli had proposed the exclusion principle that said that it is impossible for two electrons of the same atom to have the same values of the four quantum numbers.
The four quantum numbers are (1) the principal quantum number, which is the energy shell of the electron, that is the electron’s orbital level, (2) the azimuthal quantum number, which is the magnitude of the electron’s orbital angular momentum, (3) the magnetic quantum number, which is the projection of the orbital angular momentum along a specified axis, (4) the spin projection quantum number, which gives the projection of the spin angular momentum along a specified axis. These four numbers are the set of acceptable solutions to the Schroedinger wave equation for the hydrogen atom.
Pauli’s principle was an unexpected stroke of luck for Dirac, who could now consider that the unoccupied quantum states were holes with a positive charge. He thought of these as antielectrons. In other words, the forbidden positions were actually occupied by particles of the same mass as the electron but of the opposite electrical charge, a positive electrical charge. This is how the idea of antimatter was born. Now, if you think that this is too much speculative theory proposed for the sole purpose of making mathematical equations work, you will not be too far off the mark! But in another stroke of luck for Dirac, American physicist Carl Anderson accidentally discovered the antielectron in cosmic rays. A particle with the same tiny amount of mass as the electron but with a positive charge. This particle was named positron. The scientific community was astonished and Dirac’s theory was the talk of the day. Dirac was awarded the Nobel prize in 1933.
This is all quite amazing but the question arises: are we forcing nature to conform to a preconceived mathematical formalism? Are we forming perceptions of microcosmic reality that confirm predetermined and arbitrary notions? Is this a type of circular reasoning, where we discover what we want to discover? Is physics on a course of becoming a self-fulfilling prophesy? Does nature have to conform to mathematical symmetry? Is mathematical beauty a necessary and sufficient condition for physical truth?
The next events in Dirac’s life point to a negative response to these questions but that does not mean that the questions must be discarded. They are legitimate questions and we must be aware of them at all times. In a 1931 paper titled Quantised Singularities in the Electromagnetic Field, Dirac predicted the existence of another particle, the magnetic monopole but no such particle has been found. More than eighty years have passed and magnetic monopoles have not been found in nature, neither has it been possible to create them artificially.
Dirac’s greatest contribution is that his QED equations describe for the first time the motion and spin of the electron in complete consistency with both quantum theory and special relativity. QED rests on the idea that charged particles, such as electrons and positrons, interact by absorbing and emitting photons, the particles of light that carry electromagnetic radiation. These are virtual photons that do not exist outside of the interaction and only serve as carriers of momentum. These interactions are described intuitively by Feynman diagrams.
Everything that we have discussed in modern physics seems to point to a discrete rather than a continuous reality. Energy comes in tiny discrete packets called quanta. Electrons jump from one orbit to another and they simply do not exist in the space between orbits. Their path from one orbit to another is undefined. It is almost as if they are destroyed on one orbit and instantly created on another. They have discrete energy levels, discrete spin and angular momentum. There is no continuity and values between these quantized levels are forbidden, as if they do not exist. Pauli’s exclusion principle is all about quantized states. Maybe some theory will emerge that shows spacetime itself to be quantized. No wonder it is called quantum physics!
The quantum vision is not just a reality of discrete quantities, it is also a stochastic reality, a reality of probabilities and randomness. This randomness is actually what kept Einstein at a distance from quantum theory and made him declare that God doesn’t play dice! Einstein was the supreme determinist. He said that everything is determined by forces over which we have no control. It is determined for the insect as well as for the star. Human beings, vegetables, or cosmic dust, we all dance to a mysterious tune, intoned in the distance by an invisible piper.
In our discussion of Einstein we saw that he spent the last twenty years of his life trying to develop a unified field theory, a general theory that would unify the forces of the universe and the laws of physics into one framework. He was not successful and his lack of success may be partly due to his skepticism toward uncertainty and quantum mechanics. However, Einstein’s commitment to the unified theory motivated other physicists and opened up a worldwide multi-level effort of new research.
The quest for a general theory has engaged thousands of scientists around the world on multiple and wide ranging paths of new scientific inquiry. There is an important outcome that has filled many physicists with a renewed enthusiasm for the final solution, and others with intense skepticism. It is called the Standard Model. Like the Schroedinger equation and many other good things in modern physics, the Standard Model has been formalized in different versions. They all have the same variables and the same relations between variables and they all have the same underlying principle. Now, this is some serious physics. The Standard Model rules in physics today and we must know at least what it is. There is a side benefit in this discussion, as we will get acquainted with some interesting little particles that we have not talked about.
There are two types of particles in the Standard Model. Particles that make up matter, called fermions, and particles that transmit forces, called bosons. In the class of fermions we have the leptons and the quarks. There are six leptons: electron, muon, tau, and their three counterparts electron neutrino, muon neutrino and tau neutrino. In the class of quarks we have six types: up, down, charm, strange, top, bottom. The bottom quark is also known as the beauty quark, for reasons unknown. Remember, physicists are the type of folks who can find poetic beauty in the photoelectric effect.
Bosons are hypothetical particles the Standard Model requires to explain the transmission of four types of forces: the strong nuclear force, the weak nuclear force, the electromagnetic force, and the gravitational force. Of these forces, gravity is the weakest but has an infinite range, albeit with a strength that declines as the square of the distance, as we know from school physics. The electromagnetic force also has an infinite range but is much stronger than gravity. We already know what the boson of this force is: our familiar photon! The wave-particle that light is made of, the energy quantum that carries electromagnetic energy. The weak and strong nuclear forces have a very small range and are required to keep the nucleus together as a compact unit. The weak force is carried by the W and Z bosons and the strong force is carried by the gluon. As its name suggests, it keeps protons and neutrons glued together in a compact nucleus.
So we have described the bosons that carry three of the four fundamental forces in the universe, but what about gravity? Standard Model physicists are assuming there is another particle, the graviton, that carries gravitational force. This particle has never been detected in any experiments and gravity is still not part of the Standard Model. Newtonian gravity is not included nor is Einstein’s distortion of spacetime around large masses. This is actually the model’s most serious deficiency right now.
It is quite amazing if you think about it. The one force that we are all familiar with and experience in our daily life cannot be explained by the new physics! But there is a good reason for this. The Standard Model is tuned to microscopic phenomena, where gravity is so weak as to be unimportant. Gravity dominates in the macrocosm but is a negligible force in the microcosm. Does this mean that the Standard Model cannot become a theory of everything?
You might guess that the Standard Model will prove much better at explaining microcosmic than macrocosmic phenomena. This is not so strange if we think that the model is deeply rooted in quantum mechanics. But what is so different between the macrocosm and the microcosm? Nothing really, except that humans stand between the two. Everything that is visible to us belongs in the macrocosm and everything else is in the microcosm. It is a difference of scale and a difference of human perspective. But the universe is a continuum of spacetime that does not care about human perspective. So the distinction between macrocosm and microcosm is not a fundamental distinction of the universe but a distinction of human perspective. It may well be that the two can be related with one another through a relativistic reference frame. An observer-dependent frame.
The Standard Model is an impressive piece of physics. But the cockpit of a Boeing 747 is also impressive if you know what every switch does and even more impressive if you do not know what anything does. While searching for a unified theory, a search that led to the Standard Model, physicists found a whole bunch of new particles. In other words, the search for simplicity led to more complexity. The diversity that we observe in nature when we watch those stunning National Geographic films seems to have an underlying diversity in the microcosm of elementary particles. Can all these new particles and their interactions be fit into the straightjacket of a single equation or a single law of physics?
We know today that stars can be created and destroyed. Elementary particles are also created and destroyed. Tiny mass particles are annihilated when converted into energy packets. In our ever changing dynamic universe, is it possible that new laws of physics are randomly created and destroyed?
The mathematical formalism of the Standard Model belongs in an advanced textbook of modern physics and we will resist the temptation to duplicate it here. The mathematics looks intimitading, mostly because of all the Greek letters and the multitude of terms. It is actually much simpler than it looks. It is basically a mathematical expression of linear and non-linear terms. The problem is not with the formalism but with the conceptualization. The great detail of interactions described in the model convey a sense of arbitrariness. We cannot explain something, so we invent a new term, a new particle, stick it somewhere in the equation and we are done! Well, that is an exaggeration, it is not exactly like that. Physicists may be inclined to speculate more than the rest of us but speculation is an important element in scientific discovery.
There are skeptics and there are physicists who are trying to shatter the Standard Model and build a brand new theory. As it stands now, the Standard Model is work in progress. Some of its terms, such as the terms relating to the Higgs boson, are yet to be verified. The Standard Model is not scientific fact, it is still a theory that needs to become verifiable and falsifiable. It has predicted the existence of unknown particles that have since been discovered but there are serious gaps that still need to be filled.
The Standard Model is unlikely to become a theory of everything and it may no longer be the holy grail of physics, but it has achieved rock star popularity nevertheless. There are T-shirts and coffee mugs with the equation printed on them. But even without the Standard Model, physics continues to produce new incredible discoveries that reveal unknown aspects of our world while making our lives much more interesting through exciting practical applications. Lasers, transistors, superconductivity, high definition TV, wireless communications and laptop computers have changed our lives for ever.