The opportunity and challenge of Superstring Theory (v1.0)

 

Much of the material is from the book by Lee Smolin called the trouble with Physics.

Since the mid-eighties, very few fundamental foundational advancements have been made in physics. The key ones of lower significance are finding that neutrinos have mass, verifying the fundamental particle Higgs Boson exists, sustained fusion for 5 seconds achieved in a lab, and that there is something unknown called dark energy accelerating the universe expansion. Historically speaking that is unusual. In physics, for a theory to be believed it must make at-least one new prediction that no other theory makes that is later verified. This has not happened with theories towards unification like superstring theory. This is a crisis for theories that have gone beyond the standard model of particle physics.

Superstring theory arising in the 70’s and 80’s came with great promise and excitement. It posits that the world contains yet unseen dimensions and many more particles than currently known. At the same time, all the particles and forces arise from the vibrations of a single entity – a string – that obeys simple and beautiful laws. It claims to be the one theory that unifies all the particles and all the forces in nature and both quantum mechanics and general relativity. The problem is that string theory comes in a vast number of variations – 10 ** 500!! There is little hope we can come up with an outcome of an experiment that is not encompassed by one of them. It therefore can never be disproved or proved. In-fact there is no common definition of it, or any common formulation written down and agreed. It is based on hunches, with scant experimental evidence. So far it has made no predictions. Is string theory a bottomless pit sucking up all talent and funds? Is fixation on it the cause for the drought in widely accepted breakthroughs since mid-eighties? Who knows? But the equations are beautiful, and the concept is elegant!! But we are at a point where the whole foundation of physics must be rethought to some extent and that is never easy. For example, Einstein took 10 years for special relativity, then 10 more years for general relativity, then many decades on a unified theory which ultimately failed. A unified theory is hard and must be done in steps!! But superstring theory is the whole thing and is a package deal. Either everything is solved, or nothing is. Superstring theory will either be the biggest failure in history or the biggest success. Having said this caveat, I will now describe it. But first, need to touch on the standard model of particle physics.

In the 70’s, it was discovered that all three forces (strong, weak, electromagnetism) were based on a gauge principle and spontaneous symmetry breaking. This laid down the idea that they can be unified. The weak and electromagnetic forces were unified based on the gauge principle and spontaneous symmetry breaking with the electroweak theory. Symmetry breaking also required a Higgs boson particle that was eventually discovered which mediated the Higgs field. Also, the gauge principle resulted in the forces being described by particles. Quantum electrodynamics had already unified quantum mechanics, special relativity and electromagnetism and quantum chromodynamics had already unified quantum mechanics, special relativity, and the strong nuclear force. Also, matter was made up of 6 quarks and 6 leptons. That is substantial progress and some degree of unification. But why are there so many particles and why do they have the properties they have? Why is there a distinction between force particles and matter/antimatter particles? Why is there a distinction between quarks and leptons? And why are there 19 parameters that must be plugged into the standard model without deriving them from first principles? Why wasn't the standard model unified with general relativity? Is general Relativity wrong at the plank scale since it predicts absurdities like infinities which never occur in practice? Although General relativity and the standard model together explained all known experiments to date, these questions implied the theory was not complete or has an underlying unknown foundation and the search for unifying must continue. But progress has been frustratingly slow.

Superstring theory has garnered a lot of attention. In string theory, particles are not treated as point particles, but as vibrating strings. These "strings" vibrate in multiple dimensions and, depending on how they vibrate, they might be seen in three-dimensional space as matter, light or gravity. It is the vibration of the string that determines whether it appears to be matter or energy, and every form of matter or energy is the result of the vibration of strings. On distance scales larger than the string scale, a string will look just like an ordinary particle, with its mass, charge, and other properties determined by the vibrational state of the string. In this way, all of the different elementary particles may be viewed as vibrating strings. The strings can be open or closed. An open string is a line. A closed string is a loop. Open strings can combine at their ends, or the same open string can combine at its ends to form a closed string. Closed string can combine to form a bigger closed string. A string can break into two strings. The joining or breaking of strings is force. The end of an open string can be seen as a charged particle. For example, one end can be seen as an electron and the other end a positron. The massless vibration of the string between them can be seen as the photon that carries the force between them. Nature produces collisions between particles and antiparticles. They annihilate each other creating a photon. This is described in string theory by the two ends coming together and joining to form a loop. Closed strings are essential for gravitational force. Thus, you get particles and forces alike from open string and the theory can produce all the forces and particles in the standard model as well as gravity. The difference between gravity and other forces is naturally explained as the difference between open and closed strings. In most theories, particle motion and the fundamental forces are two separate things. In String theory, the laws of motion dictate the laws of the forces. All forces in string theory come from the same breaking and joining of strings. Force and motion are unified. There are only two fundamental constants. The string tension describes how much energy is there per unit of length. The other is the string coupling constant which is the probability of a string breaking into two strings giving rise to force. All the other constants in physics are related to these. For example, Newtons Gravitational constant is related to the product of the two values. Actually, to be more accurate, the probability for a string to break or join is fixed not by the theory but the environment – the particular multidimensional world it lives in. As a one-dimensional string moves in time, it makes a two-dimensional surface in spacetime. This surface has an area. The string moves to minimize this area. This is the whole law!!

String theory achieves all the following.

1. Superstring theory is finite (will only give finite results as predictions as the result of any experiment) and consistent (including consistent with quantum mechanics).

2. Automatically gives unification of all the elementary particles. All come from vibrations of one fundamental kind of object. Automatically gives unification of all the forces including gravity.

3. Superstring theory automatically gives us gauge fields responsible for electromagnetic force and the two nuclear forces. This comes from vibrations of open strings.

4. Superstring theory automatically gives us gravitons (for gravity) which comes from vibrations of closed strings. Any quantum theory of strings must include closed strings. So, we got for free unification of gravity with the other forces.

5. Superstring theory achieves effortlessly a natural unification of the laws of motion and the laws of forces.

6. A super symmetric string theory unifies the forces (bosons) with the matter (fermions) unifying all the forces with all the particles. Supersymmetric string theory is deeply elegant.

7. There are only two fundamental constants.

Given superstring theory gives everything a physicist can dream of it is natural it generated so much excitement since the 80’s. No other theory offers so much with one simple idea. But does it work? What is the cost? What are the challenges? Does it make any new predictions that can be experimentally verified?

In the first phase of string theory, 4 problems surfaced.

The first problem cropping up was that supersymmetric string theory could be consistent only if the universe has nine dimensions of space. That forced physicists to curl up 6 of the space dimensions (example going around a thick wire as a dimension). It was also shown that there were 5 consistent string theories, but there are many ways to handle the extra dimensions, and this exploded the number of possibilities!! More dimensions also multiply the number of fundamental constants. Lots of complications!!

An advancement came when some theorists concluded that the 6 dimensions were Chalabi-Yau spaces (a 6-dimensional mathematical geometry) which reproduces a version of the supersymmetric standard model. Unfortunately, there turned out to be many Chalabi-Yau spaces (at-least a few 100 thousand). Each version gave rise to a different version of particle physics. So, nothing was explained!!

The second problem that cropped up was that the 20 constants in the standard model were not derivable from constants in any of the string theories.

The third problem was that the exact observed combination of particles did not come out of the equations.

String theorists were discouraged by early 90’s. String theory was revived again in 1995, when M-Theory arose to unify the candidate consistent string theories, to start a second phase. M-theory increased the total dimension to 11 and besides strings added another thing called branes (2 or 5 dimensional) in the background of strings. But the descriptions and space dimensions beyond 3 and the branes are way beyond me. But THE theory that applies to our universe remains elusive. Observations and predictions have played no role so far!! Different than any other theory of physics!! It is not clear it will ever be proven true.