As a child, I was deeply curious about the universe and the world we live in. As I grew older, this curiosity grew considerably which led me to appreciate and enjoy studying physics during my time in school. Physics and especially theoretical physics is a topic I enjoy reading about and exploring to this very day. Although, I’m not a physicist, I’ve always dabbled in and enjoyed reading the works of our generation’s great physicists.
If you follow my blog, you’d know that I like to explain these concepts & theories I come across in the simplest fashion, much like what theoretical physics essentially does i.e. breaking down our universe and its phenomenons into simpler parts – theoretical and mathematical.
You can check out my earlier posts in this ‘Exploring Reality’ series of posts: Part I : How We Perceive And Know The World Around Us and Part II : Evolution’s Argument Against Our Perceived Reality. Another one of my posts, if you’re curious about Dark Matter is this one The Hunt For Dark Matter: The Mysterious Element Which Makes Up The Universe.
Two books I bought some years ago, Brain Greene’s ‘The Hidden Reality‘ and Michio Kaku’s ‘Parallel Worlds‘ are books I’ve been reading slowly and gradually in parts to understand and fully grasp the concepts and theories mentioned in them. Both Greene and Kaku, are pioneers of ‘String Theory’ and use it to explain our universe and the infinite possibilities the theory implies.
This post is based on Kaku’s Parallel Worlds
What Is String Theory In A Nutshell?
In the simplest form, string theory suggests that the fundamental indivisible particles of the universe, the most familiar being — electrons, quarks and neutrinos — are made up of smaller particles i.e. vibrating strings.
These strings are small vibrating filaments of energy that give the particles their unique characteristics.
The theory further suggests that these small filament-like vibrating strings are the reasons why subatomic particles exhibit their unusual behaviour like the Heisenberg Uncertainty Principle and Wave-Particle Duality.
The vibration of these strings inside subatomic particles explains a number theories about our universe and the mathematics behind them.
To further understand string theory, we’ll explore its unusual history, but all you need to remember for now is that, in essence, every particle is made up of small vibrating strings.
The History Of String Theory: Beginnings
String theory has the most bizarre history in the annals of physics. It was discovered by accident, applied to the wrong problem, relegated to obscurity, and then suddenly resurrected as a theory of everything.
The reason why its history is strange is because it evolved backward. Usually, in a theory like for example Einstein’s relativity, you start with fundamental principles. Later, these principles are honed down to a set of basic classical equations. Lastly, you calculate quantum fluctuations and match the equations to quantum principles.
String theory, on the other hand, evolved in the complete opposite way.
The origin of string theory dates back to 1968 when two young physicists Gabriele Veneziano and Mahiko Suzuki at the nuclear laboratory at CERN, Geneva, were flipping through a math book and stumbled upon the Euler Beta function, an obscure 18th century mathematical expression discovered by Leonard Euler, which unbelievably, seemed to describe the subatomic world.
They were surprised to find that this abstract mathematical formula seemed to describe the collision of two π meson particles at enormous energies.
This caused a huge stir in physics at the time, with hundreds of papers published attempting to generalise it to describe nuclear forces.
Physicists and scientists use billions of dollars to create particle accelerators or “atom smashers” to analyse subatomic particles because they can’t be seen with the naked eye. These particle accelerators are used to determine a series of numbers, called the scattering matrix, or S-matrix.
The S-matrix is crucial because it encodes within it all the information of subatomic particles i.e. if you know the S-matrix, you can deduce all the properties of elementary particles.
One of the goals of elementary particle physics is to predict the mathematical structure of the S-matrix. Determining the values of the S-matrix seemed so difficult that some physicists believed that it was beyond the boundaries of known physics at that time.
That’s why Veneziano and Suzuki’s theory caused a huge sensation because they simply guessed the S-matrix by flipping through a math book!
However, there were still some deficiencies in Veneziano and Suzuki model but physicists soon discovered that their model was just the first and most important term in calculating the S-matrix and not the whole picture. In other words, it was just the first term in the series that had possibly infinite terms.
Finally, two physicists named Yoichiro Nambu and Tetsuo Goto from the University of Chicago and of Nihon University respectively, identified the key feature that made this model work – a vibrating string.
They postulated that the subatomic particles were made up of strings with different vibrations. In other words, each particle is nothing but a vibration or note on the string.
They found that when a string collides with another string, it created the S-matrix described by the Veneziano model. And so, string theory began its tryst with modern physics.
The History Of String Theory: Schwarz & Kaku’s Contribution To ‘The Field Theory Of Strings’, Flaws & The Dimension Debate
In 1971, three physicists John Schwarz, Andre Neveu and Rierre Ramond generalised the string model so that it included a new quantity called spin (All subatomic particles, as physicists observed, spin almost like a miniature top which produce quantum units, as integers like 0,1,2 of half integers like 1/2, 3/2). This made string theory a realistic candidate for particle interactions.
However, all of physics for the past 150 years up to that point had been based on “fields”( Think electric, magnetic, or nuclear fields or gravity). So the question was “why should strings be any different?”. What was needed was a “field theory of strings” that would allow one to summarise the entirety of the theory into a simple equation.
In 1974, Michio Kaku decided to tackle this problem head-on. Kaku successfully extracted the field theory of strings into an equation barely an inch and a half long. His equation, summarised – all the properties of the Veneziano model, all the terms of infinite perturbation approximation, and all the properties of spinning strings of the Schwarz-Neveu-Ramond model – into one grand equation.
After Kaku revealed the equation and theory to the world in a conference at Aspen Centre, Colarado, Nobel Prize winning physicist Richard Feynman told the Japanese physicist, “I may not agree totally with string theory, but the talk you gave is one of the most beautiful I have ever heard.“
However, string theory would hit a major stumbling block in the years following Kaku’s hypothesis.
Claude Lovelace of Rutgers University discovered that the original Veneziano model had a minor mathematical flaw that could only be eliminated if space-time had twenty-six dimensions. Similarly the Schwarz-Neveu-Ramond model could only exist in ten dimensions. This stunned physicists. Nowhere in the history of physics could a theory select its own dimensionality.
For example, Newton and Einstein’s theories can be formulated in any dimension. Newton’s inverse square law of gravity could be generalised to an inverse cube law in four dimensions.
String theory, on the other hand, could only exist in specific dimensions. This was a gaping flaw.
Our world, it was universally believed throughout the physics community, exists in three dimensions of space(length, width & breadth) and one dimension of time. To postulate that our universe was ten-dimensional bordered on science-fiction.
So string theory and string theorists became the butt of many jokes amongst sceptics of the theory.
Richard Feynman joked to John Schwarz while riding in an elevator one day saying, “Well, John, and how many dimensions do you live in today?”
No matter how many physicists tried to salvage the model, it quickly died.
The History Of String Theory: The Mystery Particle & Resurrection
What followed were some bleak years for string theory. It seemed to be relegated to obscurity. However, Schwarz of Cal Tech and Joel Scherk of Ecole Normale Superieure, Paris continued to explore it further.
There was a problem: the model predicted a particle with zero mass that possessed 2 quantum units of spin. All attempts to get rid of this pesky particle failed. Every time they tried to eliminate this spin-2 particle, the entire string model collapsed. But somehow, as Kaku writes, “this unwanted spin-2 particle seemed to hold the secret of the entire model”
Then came a huge breakthrough. Schwarz and Scherk theorised that if they reinterpreted this worrisome spin-2 particle as a graviton(a particle from Einstein’s theory), then string theory actually incorporated Einstein’s theory of gravity! (In other words, Einstein’s theory of general relativity simply emerges as the lowest vibration or note of the string)
In the history of quantum field theories until then, the standard field theories failed for decades to incorporate gravity. However, in the case of string theory, it amalgamated gravity seamlessly. In fact, string theory actually demanded the inclusion of gravity to stay consistent.
Every other unified theory could not successfully include gravity. Every time someone tried to artificially marry gravity with other quantum forces, it lead to mathematical inconsistencies that would end up as a stumbling block, effectively killing the theory.
In 1984, the tide against string theory suddenly shifted. John Schwarz of Cal Tech and Mike Green, then at Queen Mary’s College, London proved that string theory was free of mathematical divergences and also free of anomalies. As a result, string theory became the leading(and today, the only) candidate for a theory of everything.
Suddenly, string theory, which was considered dead, was resurrected. From a “theory of nothing” it became the new “theory of everything”.
Soon hundreds of papers were published and physicists started to toy with the idea of parallel universes and if they exist because string theory demanded these extra dimensions.
An old study and theory published in 1921 by Theodor Kaluza and Oskar Klein known as the Kaluza-Klein theory was also simultaneously resurrected from the ashes because it suggested the presence of more dimensions(In their case five). Although it was published during the time of Einstein and received severe backlash during those years, it also came to the fore after nearly 8 decades.(Which Brian Greene will explain later in this post)
So, in a complete u-turn coming back from the dead, string theory would dominate the world of physics for the coming decades.
How Strings Explain Sub-Atomic Particles
According to string theory, if you had a supermicroscope and could examine the heart of an electron, you would see not a point particle, but a vibrating string. The string is extremely tiny at the Plack length of 10-33 cm, a billion, billion times smaller than a proton, so all subatomic particles appear point like.
If you pluck the string, the vibration would change i.e. the electron might turn into a neutrino. If you pluck it again it might turn into a quark. In fact, if you plucked it hard enough, it could turn into any of the known sub-atomic particles. In this way, string theory can effortlessly explain why there are so many sub-atomic particles in the universe.
Music And String Theory: The Cosmic Music Of String Theory
In a brilliant analogy(and I really like this), string theory has often been compared to music. The beauty of string theory is that it can be explained through music in a simple way. And so, rather grandly, music provides the metaphor by which we can understand the nature of the universe.
Using the analogy, proponents of string theory suggest that different sub-atomic particles are nothing but different “notes” that one can play on a superstring.
If you compare string theory to a violin, it perhaps gives you the best idea (Fun fact: Einstein was an accomplished violinist).
While playing the violin, you can generate all the notes of the musical scale by simply plucking the string in different ways.
In the same way that you play different notes on the violin by changing the vibration of the string, so too can you create different sub-atomic particles if the string inside them is vibrated to the needed frequency. These vibrations are the “harmonies” of the universe.
In the quantum world, electrons and quarks are not fundamental but the string is.
Not only does string theory explain the particles of the quantum theory as the musical notes of the universe, it also explains Einstein’s relativity theory – the lowest vibration of the string, a spin-two particle with zero mass, can be interpreted as the graviton, a particle or quantum of gravity. If you calculate the interactions of these gravitons, you can find precisely Einstein’s old theory of gravity in quantum form.
As celebrated violinist Yehudi Menuhin once wrote, “Music, creates order out of chaos; for rhythm imposes the unanimity upon the divergent; melody imposes continuity upon the disjointed; and harmony imposes compatibility upon the incongrous“
Historically, the link between music and science was forged as early as the fifth century B.C in Greece when Greek Pythagoreans discovered the laws of harmony and reduced them to mathematics, or even before that in ancient India, if you read an old post of mine about the Natyashastra in “What is the point of music?”
This is why string theory is the cosmic music of the universe.
Higher Dimensions And The Fish Analogy
So, if higher dimensions actually exist in nature and not just in the mathematics of string theory, string theorists have faced the same problem that bothered Kaluza and Klein back in 1921 when they formulated the first higher-dimensional theory: where are these higher dimensions?
Kaluza was a previously obscure mathematician. After he postulated his theory, he wrote to Einstein proposing to formulate Einstein’s equations in five dimensions(one dimension of time and four dimensions of space). The letter, however, contained a startling observation: if you manually separate out the fourth-dimensional pieces contained within five-dimensional equations, you would automatically find Maxwell’s theory of light!
In other words, Maxwell’s theory of electromagnetic force tumbles out of Einstein’s equations for gravity if you add the fifth-dimension.
This is a hugely gratifying because physicists and engineers had to memorise Maxwell’s difficult equations for 150 years. Now, these complex equations emerge on their own as the simplest vibration in the fifth dimension.
Although we can’t see the fifth dimension, according to string theory, ripples form on the fifth dimension, which correspond to light waves.
An analogy to explain this can be to use the example of fish.
Imagine fish swimming in a shallow pond, thinking that their “universe” is only two dimensional. Our three-dimensional world is beyond their comprehension. But there is a way they could detect the presence of the third dimension i.e. if it rains they can see shadows of the ripples travelling on the surface of the pond. Similarly, we can’t see the fifth dimension, but ripples in the fifth dimension appear to us as light.
String Theory In The Words Of Brian Greene
Renowned physicist Brian Greene is someone I closely follow and as I’ve mentioned earlier, I’m also reading his book ‘The Hidden Reality‘. He is a huge proponent of string theory and has been working on developing it further for his entire career.
As he writes in Smithsonian Mag,
“The idea underlying string unification is as simple as it is seductive. Since the early 20th century, nature’s fundamental constituents have been modeled as indivisible particles—the most familiar being electrons, quarks and neutrinos—that can be pictured as infinitesimal dots devoid of internal machinery. String theory challenges this by proposing that at the heart of every particle is a tiny, vibrating string-like filament. And, according to the theory, the differences between one particle and another—their masses, electric charges and, more esoterically, their spin and nuclear properties—all arise from differences in how their internal strings vibrate.”
– Brian Greene for Smithsonian Mag
In his TED Talk, Brian Greene explains string theory in detail, simplifying it so that anyone can understand it. Along with visuals and the history of the theory, it’s a useful resource to check out which summarises this post of mine in a well-delivered, short twenty minute talk.
String Theory As A Unified Field Theory & The Implications Of Higher Dimensions
The term “unified field theory” was coined by Einstein and although previous attempts at a unified field theory have failed, string theory has survived all challenges. It has not immediate rival. It’s the closest thing we have to a “theory of everything”.
The reason string theory has succeeded is because it’s based on an extended object or, the string, and so it avoids the divergences associated with point particles.
String theory explains how the fundamental particles of the universe are created, the way they behave and interact and it also satisfies Newton, Einstein and Maxwell’s fundamental theories along with supporting the mathematics behind it.
String theory offers explanations of quantum theory and the nature of quantum particles which has always been a stumbling block for unified field theories in the past.
However, there are a number of questions that arise: is string theory true? Can we detect strings? Can we prove that there are other dimensions, as the math suggests?
The major problem is that if strings are at the heart of sub-atomic particles, it’s very difficult for us to detect them because they’re so small.
As Brian Greene writes in Smithsonian Mag,
The description I’ve given suggests an experimental strategy. Examine particles and if you see little vibrating strings, you’re done. It’s a fine idea in principle, but string theory’s pioneers realised it was useless in practice. The math set the size of strings to be about a million billion times smaller than even the minute realms probed by the world’s most powerful accelerators. Save for building a collider the size of the galaxy, strings, if they’re real, would elude brute force detection.
– Brian Greene for Smithsonian Mag
String theory suggests that there must be at least ten or eleven dimensions and in some cases even twenty-six dimensions.
Although we can’t see these dimensions, the implications of this suggests possibilities of a multiverse and parallel universes(which I will get to as this Exploring Reality series continues). Physicists are divided in opinion about them but that discussion is for another day.
However, string theory is the closest thing to a unified theory we have in the modern day.
Will we ever find a unified field theory? Is string theory the answer?
We don’t know. But the future is certainly exciting.
There’s hope that we might unravel this mystery further in the coming five or six decades.
Until then, string theory remains the most intriguing way in which we can describe our universe.
Words For Reveries 