String Theory Explained
In this post, I seek to explain the following:
A) What string theory is
B) Why is it necessary
C) How it has influenced other classes of physics or domains of science
The Summary
“What if the basic constituents of nature and matter were not little points, as had been presumed since the time of the Greeks? What if the seeds of reality were rather teeny tiny wiggly little bits of string? And what appear to be different particles like electrons and quarks merely correspond to different ways for the strings to vibrate, different notes on God’s guitar?” — Dennis Overbye in String Theory, at 20, Explains It All (or Not)
What is String Theory?
String Theory unifies all of our fundamental forces; it is a leading contender for the Theory of Everything. But above all, it is a unity of progress of the scientific method and decades of innovation.
String Theory underwent several periods of development; understanding the main developments of each section brings about a larger understanding of the scientific method and the sheer amount of work that is required to bring about scientific thinking. Here are the 6 time periods we will examine to answer what string theory is:
1. 1940s S matrix theory
2. 1949–1974, Dual Resonance Model
3. 1974–1984, Bosonic String Theory & Superstring Theory
4. 1984–1994, First Superstring Revolution
5. 1994–2003, Second Superstring Revolution
6. 2003 — present, leading thoughts…
Period One: S Matrix Theory
S Matrix Theory, which stands for Scattering Matrix Theory, developed the early roots of String Theory. Physicist and legend, Werner Heisenberg, in 1943, substantiated this theory — largely as a principal of particle interactions. It proposed that how particles interacted with each other is a result of their ability to scatter.
At this point, quantum mechanics has already been established and has been put in the forefront of physics. Experimental physics demonstrated that electrons behaved like both particles and waves; however, experiments showed that other sub-atomic elements like protons and electrons did not behave like point like particles. Compared to other similar point like particles with the same spin characteristics, they had different magnetic properties. These sub atomic particles had a strong nuclear interaction (one of the major forces) such that they scattered as if a sphere, and not a point.
Heisenberg attributed this to the unreliable nature of space and time at the quantum scale. S Matrix Theory was born. S-matrix theory proposed that because of this unreliability, one cannot calculate and understand how things happen at these smaller scales as it is much easier to calculate the probabilities of it occurring.
Eventually Quantum Field theory came in and overshadowed the practicality of the S Matrix Theory. Quantum Field Theory shows how particles move in the electromagnetic field among other fields. S Matrix Theory was shown the door because its calculations couldn’t compete with that of Quantum Field Theory. Quantum Field Theory is an important section in physics that we will discuss at another point.
However S Matrix Theory remained in the psyche of physicists and the ghosts of journals. Using methods from S Matrix Theory, we’ll see next that Gabriele Veneziano established the modern roots of what we know as String Theory.
Period Two: dual resonance model
Throughout this time period (late 1960's), there were two major threads in particle physics, which is the domain of particle interactions. There is a certain particle called a hadron particle within the nucleus that acts by the strong nuclear interaction to hold the nucleus together. Hadron particles were found to have hadron resonances (resonance occurs when a hadron particle decays rapidly giving, in the process, briefly, an excited state of the hadron particle), elucidating that hadrons are not elementary particles.
The second major thread was in the area of physicist Richard Feynman’s “parton” model. Richard Feynman suggested that the parton model could explain what happens when hadrons collide with each other. Since the growing research suggested that hadrons consisted of smaller particles, Feynman proposed that its point-like constituents were “partons”. This parton model was applied to the Stanford Linear Accelerator Center (SLAC) experiments, which probed the insides of hadrons.
In 1968, Gabriele Veneziano, a young physicist at CERN (which is a laboratory that accelerates particles in Geneva, Switzerland), found that one formula (concocted by the 18th century mathematician Leonhard Euler) could adequately describe numerous properties of the hadron particle. Hadrons are particles that interact by the Strong Force. Why could an old formula describe something so novel?
Veneziano, in specific, kickstarted modern string theory by proposing that the strong interactions followed these dual resonance models of hadrons being able to be excited in higher energy states.
No one knew precisely why. Until, that is, Leonard Susskind, Yoichiro Nambu, and Holger Nielsen demystified the physics behind the Euler Beta Function and precisely why one particle’s characteristics could be explained by a formula written 200 years in the past.
The trio showed that if an elementary particle was modeled as if a tiny, vibrating, and one-dimensional, string then that elementary particle’s most fundamental nucleus interactions could be explained by Euler’s formula. To be specific, they showed that Veneziano’s dual resonance model is based on the quantum mechanics of these vibrating strings. The string was the structure of the particle, and the formula foreshadowed it.
When looking at these particles however, they would appear point-like at a distance, but string like at a closer proximity, so it fit experimental results as the data could only show it’s point-like behavior.
The train to the land of the string theory began, and it doesn’t appear to stop.
Period Three: Superstring and bosonic string theory
After the dual resonance model was cast aside because of how quantum chromodynamics was shown to be the correct quantum field theory to describe the strong force, there was a scientific thaw on string theory.
Quantum field theory is an exciting and accurate representation of our world. And again I’ll leave that for another day to explain properly.
In 1974, physicists John Schwarz and Joel Scherk developed a string theory where the strings correspond only to a certain particle called bosons; bosons are sometimes called force particles because they control the interaction of physical forces like electromagnetism.
In this theory, which was consistent with special relativity and quantum mechanics, our universe consisted of only bosons but also required 26 dimensions! This theory proposed the presence of tachyons, which had negative mass, and could move faster than light speed.
< side note on symmetry >
Symmetry is all around us. It is this idea that “physical laws do not depend on when or where you use them”, as Dr. Brian Greene explains. We expect the properties of particles to follow suit — in that they remain constant.
In particle physics, the theory that arranges everything into organization much like a periodic table does to elements, is the standard model. In the standard model, particles are in two classes: fermions and bosons. Fermions include electrons and quarks to form anything matter related. Bosons include photons and gravitons as anything that carries a force as photons due to electromagnetic force and gravitons to gravity. The standard model seeks to explain all the fundamental particles present and, as a result, merits its own blog post.
Supersymmetry proposes that bosons and fermions share similar properties, such that each particle has a partner with a certain spin. Supersymmetry states that each particle in the standard model has a corresponding antiparticle; and broader, each particle has a spin that differs by a half when compared to its antiparticle.
Anyhoot: adding supersymmetry to the bosonic string theory allowed for a new theory.
< side note on symmetry over >
In this new idea, termed bosonic string theory, these two researchers found that strings must have a vibrational pattern which has no mass and has a spin 2. This perfectly describes the hypothetical graviton.
< side note on graviton >
Each of the four fundamental forces in our world (gravity, the electromagnetic force, the strong nuclear interaction and the weak nuclear interaction) has an underlying particle that gives rise to its existence. Particles called photons give rise to electromagnetism. Gluons to the strong nuclear force. The W and Z bosons to the weak nuclear force. But gravity? Gravity has gravitons that mediate it. In superstring theory, they found that these gravitons are massless particles with spin two.
< < side note on gravitons whether or not gravitons exist > >
Detecting gravitons experimentally is challenging because gravity is an incredibly weak force. Because gravitons are so much more individually weak and so tiny, sensing just one small one would be an incredibly tall order. So they remain a hypothetical solution to a complicated problem — I wonder if quantum sensors could detect them *but most likely not, because gravitons are tiny*!
Some scientists have suggested that gravity accesses more than three dimensions; this might explain why gravity appears so weak because it is effectively diluted over several dimensions.
< side note on gravitons over >
In 1974, thus, Scherk and Schwarz proposed that string theory is a quantum theory incorporating the gravitational force, and this gravitational force is due to strings accounting for the graviton.
In the 1970s, this bosonic theory was revamped to form the superstring theory, with the super prefix coming from supersymmetry. Superstring theory reduced the number of dimensions required from 26 to 10. Superstring theory argues that there are 4 dimensions that we interact with (1 left/right, 1 up/down, 1 and 1 time) and there are 6 remaining dimensions.
On the topic of dimensions, where do these 6 dimensions that we do not actively perceive reside? In the smallest of scales, and in a curled up six-dimensional Calabi-Yau space. These spaces are depicted below.
On dimensions: now zooming in to these three dimensions of above, look closely at your finger. At lengths so very small, there will be these Calabi-Yau spaces which hold the other 6 dimensions.
But why are there 6 additional dimensions?
The 6 extra dimensions, as Dr. Greene notes, “determines fundamental physical attributes like particle masses and charges that we observe in the [3 dimensional world]”.
Superstring theory also slashes the existence of tachyons. And in addition, it includes fermions (which are the key building block for matter, as opposed to bosons which are for forces) to its calculations, which bosonic string theory didn’t include.
Superstring theory states that fundamental structures to our universe are, indeed, strings of the Planck length, which vibrate at certain frequencies. Each string out there has specific ways of vibrating. And the way they vibrate corresponds to which type of particle they become when many strings come together.
At this point, there are five types of Superstring Theory — each one proposes whether or not the string forms a closed or open rubber band like loop, if it is oriented in such a way that you can tell which direction you’re traveling along the string, and how readily a string’s boson can be transformed, or changed (“supercharged”), into a fermion and vice versa. Each type of superstring theory differs, thus, only in the fine points.
So superstring theory cuts at the heart of string theory and it appears all is well. Gravity has been included in it. At this point, string theory became a fringe subject as bosonic string theory couldn’t explain the strong nuclear force and superstring theory didn’t truly unify quantum theory with gravity.
That is, until the First Superstring Revolution.
Period Four: The First Superstring Revolution
In 1984, nearly a decade after previous breakthroughs in string theory came about, Michael Green and John Schwarz reignited curiosity in the subject. Scientists saw that string theory could describe all elementary particles and the interactions between them. What made their work so groundbreaking is the solution they provided; up until 1984, in both string theory and quantum mechanics, quantum anomalies occurred making both theories inconsistent with the breakthroughs of previous work. Everything seemed lost. Green and Schwarz, however, rescued string theory by showing that these quantum anomalies could be resolved; and in addition, the resulting string theory could incorporate all four forces and all of matter.
It is these moments of the scientific method which reinvigorate curiosity into a subject.
Period Five: The Second Superstring Revolution
The second superstring revolution brought together the five versions of string theory together. It proposed that M-theory could adequately unify all five into an encompassing framework. This occurred in 1995 with Edward Witten envisioning the unification of string theory.
M-theory proposes that there are 11 dimensions instead of 10. In M-theory, the additional dimension stems from the need to synthesize all 5 versions of string theory. Furthermore, the original calculations for the 10 dimensions were approximate and the new calculations were exact. The 11 dimensions, instead of 10, was also the result of including supergravity into string theory. Supergravity is the result of combining supersymmetry with the gravitational force.
M-theory also brought about that not only did vibrating strings exist as earlier conceived, but also vibrating three dimensional membranes, as if blobs, existed.
This brings up some questions: we leaped from fundamental particles being zero dimensional point particles, then one dimensional strings, to two dimensional and up membranes. Are there more higher dimensional ingredients in M-theory?
And throughout String Theory research, D-branes (dynamical membranes that allow for the attachment of strings) have been ever so important to its developments. As these represent membranes with a certain size to them, the researcher who uncovered D-branes, Juan Maldecena, in a 1997 paper opened a golden treasure chest of information. He found new symmetries in M-theory as a result researching the dimensions of these membranes; in specific, he related one quantum field theory (so quantum mechanics) with a region of a space and time that is different from our universe (called an anti-de Sitter space) that corresponds to the theory of gravity. This is called the Ads/CFT Duality. What is this?
Imagine a dog. It’s 3D right? You can pet it and it will run around.
Now if you have a photo of it, the dog is now 2D right?
Simply put, we can express higher dimensions using a holograph of them in lower dimensions.
Or in other complicated words: everything one needs to know about this anti-de Sitter space (Ads) is encoded in quantum interactions into a holographic representation of the particles of the quantum field theory. Maldecena showed how one fundamentally different universe still has a visual and spacial relationship to quantum mechanics using the principles of string theory; this is called the holographic principle.
What String Theory Can Do For You/Science?
String Theory has had recent applications in the following places.
Quantum Information Mathematics
The math of string theory to describe black holes has been used to describe four entangled qubits in quantum computing. Pretty great application! For more info on quantum computing, read my posts on quantum mechanics, or read more about string theory & quantum mechanics here.
Black Holes and String Theory
Black holes are pretty cool.
What is the simple explanation of Black Holes?
Black holes are ruptures in space time. Einstein predicted them in his theory of General Relativity.
Black holes have an “event horizon” which describes a point of no return. Nothing can escape a horizon, including light. This is what makes a black hole per se black.
Inside a black hole is a singularity, where matter is so incredibly dense. You’d be crushed as if a hydraulic press if you were at this point. Spooky.
In the 1970's, Stephen Hawking showed that black holes emit radiation called Hawking Radiation. This is because of quantum mechanical fluctuations.
To be more specific, when one particle has an anti-particle and they annihilate each other on the event horizon, one particle will quantum tunnel, or escape past the event horizon barrier, beyond the black hole.
Not all particles can do this. From quantum mechanics, we understand that particles can also behave as waves. Only those particles with a very long wavelength can do this. A very long wavelength means that it has a very low energy.
Thus, black holes aren’t really per se black. They glow with the release of radiation, which comes in very trace amounts.
This has great consequences:
- Black holes thus have a temperature. We understand that temperature is the result of how fast the molecules within something are moving. In black holes, the only thing moving is gravity, which is the interactions of space and time. In addition, we understand that entropy is the number of microscopic disorder one thing has. Greater entropy means more disorder. Hawking’s formula for a black holes’ temperature explains to us that this is related to the entropy of a system.
- Black holes can evaporate. If radiation is being released, that means that energy is being released. Thus, mass is being released away. At some point, if a black hole is left alone, it should disappear and evaporate away.
- The information paradox. When a black hole evaporates, where would all the Planets, and the Asteroids, and the other stuff it sucked in go? The information of this stuff — its properties — would have all been erased. However, in quantum mechanics, the wave function of a particle includes all possible quantum states and thus information up until the wave function collapses. So: if something gets sucked into a black hole, what will happen to its properties, and information, if it gets destroyed for good, but also if according to quantum mechanics, the information will never get destroyed and contain information about its past?
The developments in String Theory catalyzed major developments in our understanding of black holes.
String Theory contains not just strings, but also other objects called D-branes. These have a great spacetime ripples and are particle-like objects. Simply put, a large number of D-branes is necessary to warp space time and to produce a black hole.
In addition, String Theory’s Holographic Principle (from M Theory) which showed that the volume of a space is encoded to a lower dimensional boundary of that space, allowed physicists to understand black holes better. We now know because of this holographic principle that the information lost in a black hole isn’t lost; it’s just on the edge of the higher dimension, fluctuating on the edge of the boundary of the black hole’s event horizon — and still accessible in our physical world. This fixes the paradox: information is conserved (in line with quantum mechanics), and, yet, information is still lost but only in the sense of where it is located.
To Recap and Conclude
Just as the wheels of justice turn slowly, scientific progress is a cumulative process full of adjustment and improvement.
Why String theory:
String Theory is the leading contender for a theory of everything. It combines quantum mechanics with gravity and explains all the four forces and matter. It explains what happens at the most smallest of levels, as does quantum mechanics, with the large scale effects of gravity.
Is it Right?
There is no empirical evidence to support most successful version of String Theory, M theory, as the Theory of Everything. There are other contenders: Loop Quantum Gravity; Asymptopically Safe Gravity; and Causal Dynamical Triangulations, among others.
But out of these, String Theory is the most mathematically consistent. And now, scientists are examining evidence to refute or support String Theory.
Sources Considered:
Note: I relied on the following sources for wonderful explanations and their fountain of knowledge. Please consider this blog post as a collection of sources and their viewpoints rather than my own take on String Theory. Although I am highly interested in physics and did every effort to check, I lack the authority to be an expert on this topic, and therefore, there may be error in my own communication.
The Elegant Universe by Dr. Brian Greene
