‘String Theory’ is defined as “a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings”, and string theory aims to describe how these postulated strings interact through space. It is currently proposed as a theory of quantum gravity (‘quantum’ and ‘gravity’ are two words which are somewhat of a physics oxymoron — since there is a huge problem when linking the two together)

The earliest form of string theory was ‘Bosonic’ string theory, which only incorporated bosons. In fact, string theory was originally proposed in the 1960s as a theory of the strong nuclear force, it was soon realised that it wasn’t suitable for nuclear physics – and was not long after abandoned for quantum chromodynamics (which involves ‘colours’ for quarks and gluons to better describe the strong interaction).

Bosonic string theory was later then developed into superstring theory. Superstring theory postulates a unique connection called ‘supersymmetry’ (hence the ‘super’ in superstring) between two classes of particles: bosons and fermions. Superstring theory then developed until into five versions of superstring theory: type I, type IIA, type IIB, heterotic SO(32) and heterotic E8×E8. Yet in the 1990s, a speculation was made that all of these were in fact 5 different cases of a single theory in eleven dimensions called ‘M-theory’.

How does it work?

Due to it being a proposed theory of quantum gravity, on a large scale, a string looks like an ordinary particle, with the properties of the string are determined by the vibrational state of the string (like mass and charge). This theory also incorporates the graviton – a theoretical quantum particle which mediates the force of gravity – which also has a vibrational state that corresponds to this specific particle.

So far string theory has been applied to:

Black hole physics – Cosmology

The Early universe – Nuclear physics

Condensed matter physics – As well as major developments in pure mathematics

String theory is also believed to potentially be able to be a unified description of gravity and particle physics, since it’s believed that all quarks and leptons and bosons are actually strings, just at different frequencies and different vibrational states. Of course, if this is true, then we could prove its purpose – to be able to link quantum mechanics and gravity – but with our current knowledge we can’t do that, and I’ll get on to that a bit later on.

Does the maths behind it make sense?

For us? No.

In our 3D world none of the mathematics behind it makes sense, it doesn’t even work.

It doesn’t even work if we add an extra dimension, or two extra dimensions, or three, or even four!

In fact, we need 11 dimensions to make the maths work (for M-theory).

One of the most amazing things about string theory is the number of dimensions:

Bosonic String Theory has 26 dimensions

Superstring Theory has 10 dimensions

M-theory has 11 dimensions

How can there be so many dimensions?

For Bosonic String Theory:

When finding the lowest energy level of a string:

each harmonic of the string can be viewed as: (the dimension of space-time) — 2 x (independent quantum harmonic oscillators)

The quantum harmonic oscillator is simply the quantum mechanical analog of the classical harmonic oscillator (since classical and quantum systems cannot be used interchangeably)

The classical harmonic oscillator is a system that when something is displaced from its equilibrium position, it experiences a restoring force: F = -kx, where x is the displacement and k is a positive constant (the displacement and the force are directly proportional)

The reason there are 2 independent quantum harmonic oscillators being subtracted from the dimension of space-time is so there is one being subtracted from each transverse direction

A transverse direction is simply the two different directions that a transverse wave oscillates in (both perpendicular to the direction of motion, of course)

It is known that if we call the fundamental oscillation frequency ‘?’, then the energy in an oscillator for the nth harmonic = n??/2

Fundamental frequency is just the lowest periodic point on a wave (on a standing wave this is an antinode)

And ? is the reduced plank constant (or the Dirac constant) = h/2?

So if one uses the divergent series, the sum of all the harmonics can be written as ???(D ? 2)/24

Because of this, as well as combined with the Goddard-Thorn theorem, it’s shown that bosonic string theory fails to be work or be consistent in dimensions other than 26

The Goddard-Thorn theorem is a theorem that describes the properties of a function that quantises (forms into quanta) bosonic strings

For M-Theory:

M-theory actually has the same number of dimensions as superstring theory, but an extra dimension of energy, as at high energies, the five postulated forms of superstring theory are actually all the same thing.

The ‘No-Go theorems’ (a set of theorems which are effectively quantum rules) state that only the 11th dimension can resemble our laws of physics, any higher or lower versions will give unphysical results

Physicists such as Brian Greene, believe that on a microscopic scale there are dimensions curled up, that we simply haven’t seen yet as they’re actually tucked into the fabric of space itself. This actually isn’t that hard to comprehend when one realises that at large distances, a two dimensional surface with one circular dimension looks one-dimensional, this would be exactly the same for higher dimensions, they’d appear to us as three-dimensional objects.

However the other dimensions are on such a small scale – they appear on the Planck scale (the scale at which the effects of quantum gravity are believed to become significant), and we cant look this deep into space – such a small scale in fact that they are indistinguishable from our 3D dimensions. So they’d have no effect on us, so why bother?

So why does this matter? (get it?)

The Big Bang:

String theory states that ‘The Big Bang’ is caused by the collision of two universes or fissioning of one universe into two universes. This gives an opposing hypothesis to the ‘Big Crunch’ in that we could actually survive the end of our universe since we’d just end up in another one – a new one; whether it be from another universe colliding with us or our universe splitting in two is impossible to predict. It also opens up the idea to multiple parallel universes that, again, we could instantaneously collide with, sounds pretty science fiction!

Black Holes:

Black Holes have always been trouble for scientists, especially for Einstein as both Black Holes and The Big Bang cause a singularity (a point where the mathematics breaks down) in his General Theory of Relativity, as both require the curve of space-time to be infinite. The Black Hole singularity is due to the gravitational collapse of a body, and here there’s gravity so we can apply String Theory! In general relativity, a Black Hole is defined as ‘a region of space-time where the gravitational field is so strong that neither particles nor radiation can escape; Black Holes are also important for theoretical reasons, as they also cause profound problems for physicists understanding quantum gravity. String theory has been a useful tool for investigating the theoretical properties of black holes, since it allows a framework in which one can study their thermodynamics.

Qubits: — (“Quantum Bits”)

In a 2010 study, Duff used the mathematics from string theory black holes to try and compute a new way to describe four entangled qubits, and these statements were precise and experimentally provable. The fact that string theory magically works in vastly different areas of science only lead to a greater possibility that one day it could potentially be a theory of everything.

But can it ever be proven?

Can String theory ever be proved/disproved?

The only way it can be proved at the moment is to accelerate particles with similar energy to that of the first milliseconds of the universe, and to see how the results of the experiment, as this is one of the only areas that string theory differs from the other quantum mechanical hypotheses.

Unfortunately, the Large Hadron Collider isn’t really possible for this, we need much more powerful colliders, but evidence can come from experiments at the LHC that can tend to suit certain versions of string theory better than others, which can help us to modify our theories.

Also, because the extra dimensions are on such a small scale, we haven’t been able to create photons with high enough frequencies to detect these extra dimensions yet, as they exist on the Planck scale (with a wavelength less than 1.62 x 10?³? m).

c = f? 300,000,000 = f x ?P ?P = the Planck length = 1.62 x 10?³? m

f = 300,000,000/(1.62 x 10?³?) f = 1.85 x 10?³ Hz

As seen here, this would require a frequency of at least 1.85 x 10?³ Hz – as the wavelength would have to be a maximum of the diameter of the extra dimension in order to detect it – and so far the highest frequency photon made or even detected is nowhere near this; as this photon would have an energy of 12.3 GigaJoules!

Yet, if John Wheeler’s concept of quantum foam (hypothesised in 1955) is correct, then a photon of such a small wavelength would disappear in the quantum foam, so it appears that we’ll never be able to prove String Theory with light.

However, recently a paper has claimed that gravitational waves (gravitational waves are basically ripples in the fabric of spacetime reverberating from a source of gravitational disturbance) could actually prove string theory, in that extra dimensions, could be hidden within the ripples of gravitational waves. Gravitational waves are similar to electromagnetic waves but EM waves travel in spacetime, whilst gravitational waves are an actual disruption in spacetime. The paper goes on to predict that gravitational waves should ripple through each extra dimension at a specific frequency.

Scientists at CERN have so far have had inconclusive results as to energy vanishing into these hypothetical extra dimensions. Possibly the dimensions are coiled up so tightly that they are unnoticeable?

But at the moment String Theory is our closest attempt to a final Theory of Everything, well either String Theory or its closest competitor – ‘Loop Quantum Gravity’ – but that’s for another project.