Quantum gravity
The main lesson of general relativity, is that the geometry of space is not fixed.
It evolves dynamically, changing in time as matter moves about.
Gravitational waves travel through geometry of space.
In traditional geometry, the angles of a triangle add up to 180 degrees.
But in general relativity the angles of a triangle can add up to anything,
because the geometry of space can curve.
There is no fixed geometry of space.
Can be anything, and it can evolve in time.
Newton's laws do not tell us about where objects are,
but tells us how they move, by specifying what effects force has on their motion.
Similarly, there is a law that governs how the geometry of space changes.
The geometry of space, is not part of the laws of nature.
This means that the laws of nature have to be expressed in a form,
that does not assume that space has any fixed geometry.
This is the core of Einstein's lesson.
We can encapsulate it in a principle called background independence.
The laws of physics are background independent.
Space and time does not provide an arena, for things to happen.
Space and time emerge from the laws.
In general relativity principle relationships have to do with causality.
One event may be in a chain of causes leading to another event.
Space is a secondary concept.
The concept of space is in fact entirely dependent on the notion of time.
General theory of relativity tells us how the geometry of space evolves in time,
not just for one definition of time, but for any possible definition of time.
Einstein had realised that there were gravitational fields and they carried energy.
He knew that the energy carried by gravitational waves,
would have to be described in terms of quantum theory.
He was the first to state the problem of quantum gravity.
At that point scientist did not know how to apply quantum theory, to general relativity.
The first big success of quantum field theory was QED.
This was the unification of Maxwell theory of electromagnetism, with quantum theory.
Scientists were thinking about the quantisation of the gravitational field.
When gravitational waves are very weak, they are like ripples in a small pond.
They hardly disturb the flat surface of the water.
It is easy to think, that the ripples move on a fixed background.
General relativity predicts that there are regions in the universe,
where the geometry of the space time evolves turbulently, like the waves crashing on a beach.
In this case, the fixed background is not suitable.
Gravitational waves interact with each other.
They interact with anything that has energy.
This does not occur in electromagnetic waves.
The photons interact with electrical and magnetic charges.
They themselves are not charged, so they go right through one and other.
This is the important difference between these two waves.
Once the gravitational waves interact with one and another,
they can no longer be seen as moving on a fixed background.
They change the background as they travel.
QED was developed in the late 1940's.
This success inspired scientists to take up the challenge of unifying gravity with quantum theory.
Some of them took the background independence of general relativity seriously.
Others ignored background independence.
They followed Heisenberg and Pauli's route,
their efforts to apply quantum theory to gravitational waves,
moving in a fixed background.
Many quantum gravity theorist still work on background independent approaches.
They constitute the most important alternatives to string theory.
After formulating QED, scientist knew a lot about background dependent quantum theories.
They did not know much about what a background independent quantum theory would be.
This route led to string theory.
Richard Feynman did good work on QED.
He wanted to see if he could quantise gravity.
He clarified a technical issue with probabilities.
Anything which is certain to happen will have a probability of one.
The probability that anything at all happens is one.
Feynman made the probability of various things to happen in quantum gravity,
to add up approximately to one.
Scientists first tried to quantise gravity, to understand the effect that quantum theory had on gravity.
They then tried to study what effects gravity might have on quantum phenomena.
To do that, they studied quantum particles moving in spacetimes, where gravity is important,
such as black holes or an expanding universe.
Some of the discoveries made led to puzzles that later approaches, such as string theory,
aimed to solve.
The first success was a prediction that when the gravitational field changed rapidly in time,
elementary particles would be created.
This idea could be applied to the early universe when it was rapidly expanding.
Some scientists tried to study the effect that black hole can have on quantum particles and fields.
Black holes have a region were the geometry evolves very rapidly.
This region is hidden behind a horizon.
The horizon is a sheet of light, that is standing still.
It marks the boundary of a region within which all light is pulled inwards,
towards the centre of the black hole.
No light can escape from behind the horizon.
Inside the horizon is a region where everything is pulled towards stronger and stronger gravitational fields.
The end is a singularity where everything is infinite, and time stops.
Scientist discovered that black holes have entropy.
Entropy is a measure of disorder.
The second law of thermodynamics states that the entropy of a closed system can never decrease.
Scientist worked out that the entropy of a black hole,
must be proportional to the area of the horizon.
They also found that the temperature of a black hole, is inversely proportional to its mass.
Normally to heat things up, we have to put in energy.
It is the opposite in black holes.
If we put energy or mass in, - the black hole becomes more massive -, and it cools off.
The findings let to a puzzle.
Because the black hole has a temperature, it will radiate like any hot body.
The radiation carries energy away from the black hole.
Given enough time all the mass in the black hole will turn into radiation.
It loses energy, and it gets lighter.
When it loses mass, it heats up, so it radiates faster and faster.
At the end of this process, the black hole would have shrunk down to a Planck mass.
One needs a quantum theory of gravity to predict the final fate of the black hole.
The puzzle concerns the fate of information.
During its life a black hole will pull in huge amounts of matter,
carrying huge amount of intrinsic information.
At the end, what is left is a lot of hot radiation, - which being random, carries no information -,
and a tiny black hole.
This is a puzzle for quantum gravity.
Quantum mechanics says that information can never be destroyed.
This leads to what is called as, - the black hole information paradox -.
Understanding quantum gravity requires answering the challenges posed by,
the entropy temperature and information loss in black holes.
Scientists proposed the idea of supersymmetry to explain quantum gravity.
We can think about the symmetries of space and time.
The properties of ordinary space remain unchanged if we ourselves rotate,
because there is no preferred direction.
They are also unchanged if we move from place to place.
The geometry of space is uniform.
Translations and rotations are symmetries of space.
The gauge principle states that in some circumstances, symmetry can dedicate the laws,
that the forces satisfy.
We can apply this principle to the symmetries of space and time.
The result is Einstein's general theory of relativity.
Supersymmetry can be seen as a deepening of the symmetries of space.
If you change all the fermions into bosons, and change them back again,
you get the same world as you had before, but with everything moved a little bit in space.
It tells us that supersymmetry is in some way fundamentally connected to the geometry of space.
Unification should start from a deep principle, like the principle of inertia or the equivalence principle.
From this one could gain a deep and surprising insight.
Two things that once seemed unrelated were actually at root the same thing.
Energy is mass.
Motion and rest are indistinguishable.
Acceleration and gravity are the same.
Many scientists gets complex mathematics based on supersymmetry,
and came up with a concept of super gravity.
However it is not enough to solve the problem of quantum gravity.
There is now two things to try.
Give-up methods based on fixed background geometry.
Give-up the idea that the things moving through the background geometry were particles.
Both approaches are being explored.
They would yield dramatic successes on the road to quantum gravity.