# Describing The World Dynamics So Far

According to the current understanding of Physics, there is as yet no uniform field theory.  No all-encompassing well-rounded theory that would enable all the known fundamental forces and elementary particles to fit neatly into one simple model, and to be expressed in terms of a single field.

And since there is no accepted unified field theory, it remains an open line of research.  Canadian graduate student Timothy Blais decided to explore the idea and promote his findings in a way that really rocks…  ♫

“Bohemian Gravity” may be the only physics-themed version of Queen’s “Bohemian Rhapsody” ever recorded.  And yet, that doesn’t detract from the fact that it is very VERY smart.  Infectious and geeky.  Clever and funny.  Musically excellent.  I can see it fast becoming an educational favourite in many Physics classrooms and labs.

♫♫  Molecules and atoms.  Light and energy.  ♫  Time and space and matter.  All from one united theory… ♫♫♫

# Searching for a Unified Field Theory

Fundamental forces are not transmitted between objects in a direct manner.  Instead, they are described by intermediary entities, called fields.  All four of the known fundamental forces are mediated by fields, described in the Standard Model of Particle Physics.

## The Fundamental Forces of Nature

Specifically, the four interactions that remain to be unified are the:

• Strong interaction is responsible for holding quarks together to form neutrons and protons, and holding neutrons and protons together to form nuclei.  The exchange particle that mediates this force is the gluon.
• Electromagnetic interaction acts on electrically charged particles.  The photon is the exchange particle for this force.
• Weak interaction is a repulsive short-range force, responsible for some forms of radioactivity, that acts on electrons, neutrinos, and quarks.  It is governed by the W and Z bosons.
• Gravitational interaction is the long-range attractive interaction that acts on all particles.  Based on theory, the exchange particle has been named the graviton.

A modern Unified Field Theory attempts to bring these four interactions together into a single framework.

Initially, Albert Einstein coined the term in his search to unify the General Theory of Relativity with the Theory of ElectromagnetismHowever, his precursor James Clerk Maxwell had already developed a first successful ‘classical’ unified field theory.

# Towards Unification…

In 1820, Hans Christian Ørsted discovered that electric currents exerted forces on magnets.  In 1831, Michael Faraday made the observation that time-varying magnetic fields could induce electric currents.  Until that time, electricity and magnetism had been thought of as two distinct natural phenomena.

Following on their footsteps, Maxwell published his famous paper on a dynamical theory of the electromagnetic field in 1864.  The very first example of a theory that encompassed previously separate field theories (namely, electricity and magnetism) to provide a unifying theory of Electromagnetism.

By 1905, Einstein had used the constancy of the speed of light in Maxwell’s theory to unify our notions of space and time into a single entity, called spacetime.  In 1915, he expanded his theory of Special Relativity to a broader description of gravity, General Relativity, using a field to describe the curving geometry of a four-dimensional spacetime.

In the years following Albert Einstein’s discovery, many physicists and mathematicians enthusiastically participated in the attempt to unify the then-known fundamental interactions.  Hermann Weyl’s theories of 1919 are worthy of particular interest, because Weyl introduced the concept of an electromagnetic gauge field into the classical field theory.  Two years later, Theodor Kaluza’s own theory extended General Relativity to five dimensions.

### Eventually, this goes on up to 10 dimensions!

And there is more to it.  “Bohemian Gravity” touches on Feyman diagrams, the Nambu-Goto and Polyakov actions, the concept of a world-sheet, the incompleteness of Einstein’s theory, Kähler manifolds and supersymmetry, and the abstract notion of extended 1-D objects with no mass…

I am not an expert on the subject.  When I think of string theory, as for many other physical processes (many of which I still find baffling!  :-o), I do my best to try and picture it in as simplified a way as possible.  So, here goes…

# Imagine a Piece of String…

Imagine a guitar string that has been tuned by stretching it under tension across a guitar.  Depending on how the string is plucked and how much tension is in the string, different musical notes will be created by the string.

These musical notes could be said to be ‘excitation modes‘ of that guitar string under tension.  But what does this have to do with Particle Physics?

Well…  In string theory, the elementary particles observed in particle accelerators could be thought of as the “musical notes” or excitation modes of elementary strings.  As in guitar playing, the string has to be stretched and placed under tension in order to become excited.

The difference is that the strings of string theory are floating in spacetime, instead of being tied to a guitar.  Nevertheless, they do have tension.  The string tension in string theory is described by the quantity $\frac {1}{2 p a'}$, where $a'$ is equal to the square of the string length scale.

# The Low-Down on String Theory

If string theory is to be the ultimate theory, the theory of Quantum Gravity, then the average size of a string ought to be somewhere in the region of the length scale of quantum gravity, called the Planck length (about 10-35 m).  That is about a millionth… of a billionth… of a billionth… of a billionth… of a centimetre!

Unfortunately, this is far too small to make strings observable by any current or upcoming particle physics technology.  String theorists must then devise more clever methods to test the theory, rather than just looking for little strings in particle experiments.

# Quantum Loops and Fermions

String theories are classified according to whether or not the strings are open or closed loops, and whether or not the particle spectrum includes fermions.  Including fermions in string theory involves a special kind of symmetry called ‘supersymmetry’, which means that for every boson (the particle that transmits a force), there is a corresponding fermion (the particle that makes up matter).  Supersymmetry relates the particles that transmit forces to the particles that make up matter.

### For every boson, there’s a fermion.

Supersymmetric partners of currently known particles have not been observed in particle experiments, but theorists believe this is because supersymmetric particles are too massive to be detected at current accelerators.  Particle accelerators could be on the verge of finding evidence for high energy supersymmetry in the next 10 years or so.

Evidence for supersymmetry at high energy would be the compelling evidence that string theory was a good mathematical model for Nature at the smallest distance scales.

If the theory of supersymmetry could be summarised in just three words, remember this line:

Vibrations become particles!

# Bohemian… what?

McGill University Masters candidate Timothy Blais posted this link to his recently submitted thesis, along with the video.  The track touches on some of the more confounding elements of string theory.  From a compositional point of view, it also turns out to be a rather outstanding cover version of “Bohemian Rhapsody”.

Take a cappella, string theory and Queen.  Throw in an Einstein sock puppet into the mix.  And you get perhaps the greatest physics-themed cover of the rock classic ever heard.  A masterpiece.  The ultimate geeky rendition of… “Bohemian Gravity”…

Here are the lyrics:

Is string theory right?

Is it just fantasy?

Caught in the landscape,

Out of touch with reality

Compactified On S5 or T*S3

Space is a pure void

Why should it be stringy?

Because it’s quantum not classical

Nonrenormalizable

Any way you quantize

You’ll encounter infinity

You see

Quanta…

Must interact

Via paths we understand

Using Feynman diagrams

Often, they will just rebound

But now and then they go another way

A quantum Loooooop

Infinities will make you cry

Unless you can renormalize your model

Of baryons, fermions

And all other states of matter

Curved space:

The graviton

Can be thought of as a field

But these infinities are real

In a many-body

Loop diagram

Our results diverge no matter what we do…

A Quantum Soup (any way you quantize)

Guess Einstein’s theory wasn’t complete at all!

I see extended 1-D objects with no mass

What’s their use?  What’s their use?

Can they give us quark plasma?

What to minimize?

What functional describes this String?

Nambu-Goto! (Nambu-Goto)

Nambu-Goto! (Nambu-Goto)

How to quantize I don’t know

Polyakov!

I’m just a worldsheet, please minimize me

He’s just a worldsheet from a string theory

Reparametrized by a Weyl symmetry!

Fermi, Bose, open, closed, orientable?

Vibrations Modes!

They become particles (particles!)

Vibrations

They become particles (particles!)

Vibrations

They become particles (particles!)

Become particles (particles!)

Become particles (many many many many particle…)

Modes modes modes modes modes modes modes!

Oh mamma mia mamma mia,

Such a sea of particles!

A tachyon, with a dilaton and gravity-vity-VITY

(rock out!)

Now we need 10 dimensions and I’ll tell you why

(anomaly cancellation!)

So to get down to 4D we compactify!

Oh, Kahler!

(Kahler manifold)

Manifolds must be Kahler!

(Complex Reimannian symplectic form)

If we wanna preserve

Any of our super-symmetry

(Superstrings of type I, IIa and IIb)

(Heterotic O and Heterotic E)

(All are one through S and T duality)

(Thank you Ed Witten for that superstring revolution and your new M-theory!)

(Maldecena!)

(Super-Yang-Mills!)

(Type IIB String!)

Dual!  Dual!

(Holography!)

Molecules and atoms

Light and energy

Time and space and matter

All from one united

Theory

Any way you quantize…

Lyrics and arrangement by Tim Blais and A Capella Science.

Original music by Queen.