Hidden dimensions
We know of the world in three dimensions.
We visualise space in three dimensions.
We conceptualise and understand in three dimensions.
To explain some of the mysteries which are yet unsolved,
scientists have contemplated additional dimensions.
The quest is still ongoing.
From Newton to Einstein scientific thinking was dominated by one single idea.
The world is made of nothing but matter.
Fields were not understood in a basic way.
Two kinds of fields was known.
The gravitational field and the electromagnetic field.
Scientists wondered whether gravity in electromagnetism were aspects of a single phenomena.
This led to a search for a unified field theory.
One scientist called Gunnar found that, by using four dimensions of space,
and one of time, he was able to unify gravity and electromagnetism.
But, it was difficult to explain the extra dimension, of space.
To do so, we had to shrink it to such a small size,
that it was impossible to see.
For example, the wave length of light determines,
how small a thing we can see with it.
We cannot detect the existence of something,
smaller than the wave length of light, we use to see it.
Hence one cannot detect the existence of an extra dimension,
smaller than the wave length of light one can perceive.
This makes it difficult to prove the theory.
Einstein at this point was thinking about acceleration.
He realised that the effects of acceleration were indistinguishable,
from the effects of gravity.
Imagine a person is standing in an elevator.
If the cable is cut, the elevator along with the passenger, begins to fall.
The passenger feels weightless.
This is the same thing that astronauts feel, when they are in orbit.
The acceleration of the falling elevator exactly cancels out the effect of gravity.
He called this the principle of equivalence.
Einstein succeeded in unifying all kinds of motion.
Uniform motion is the same thing as rest.
Acceleration is being at rest, with the gravitational field turned on.
This concept had major implications.
For example it predicted that clocks will slow down, in a gravitational field.
This prediction was confirmed by experiment.
He also predicted that light bends, when it passes through a gravitational field.
Before this particular insight, there has been two different kinds of things, in the world.
The things that live in space, and space itself.
Space has three dimensions.
It also has a particular geometry, called Euclidean geometry.
According to Maxwell's theory of electromagnetism,
light rays move in straight lines.
Light rays are bent by gravitational fields,
which turn, response to the presence of matter.
The presence of matter affects the geometry of space.
In Euclidean geometry, two parallel lines can never meet.
If two parallel light rays pass on each side of a star,
they will be bent towards each other, and they will meet.
The geometry of space is not like a flat infinite plane.
It is like the surface of the ocean.
It is incredibly dynamic, with small ripples and great waves in it.
The geometry of space is the same as the gravitational field.
Einstein unified space and time in the special theory of relativity.
Space and time together makeup a four dimensional entity called space time.
Let us imagine a straight line in space.
One particle travels along it, at a uniform speed.
Another particle travels along it with constant acceleration.
As far as space is concerned, both the particles travel in the same path.
In space time, the particle with constant speed, travels in the straight line,
but the accelerating particle travels in a curved path.
Einstein's equivalence principle states,
that the effects of gravity cannot be distinguished from the effects of acceleration.
By telling which trajectories are accelerated, and which or not,
the geometry of space time describes the effect of gravity.
The geometry of space time, is thus the gravitational field.
The double unification given by equivalence principle,
becomes a triple unification.
All motions are equivalent, once the effect of gravity is taken into account.
Gravity is undistinguishable from acceleration.
The gravitational field is unified with the geometry of space and time.
This is the essence of Einstein's special theory of relativity, published in 1915.
Einstein's theory predicted, that gravity must bend light rays.
This was tested in 1919 during a total solar eclipse.
It was possible during the eclipse to see some stars, directly behind the sun.
This was due to the sun's gravity bending the star light.
Einstein's theory was proved by experiment.
For Newton, space and time constituted an absolute background.
It gave meaning to the things that change,
like the position and motion of particles.
But the background of space and time never changed.
We call this as a background dependent theory.
Einstein's general theory of relativity is completely different.
There is no fixed background.
The geometry of space and time evolves.
Different geometries of spacetime describe the history of different universes.
We do not have fields moving in a fixed background geometry.
We have a bunch of fields, all interacting with one and another.
All of them are dynamic and influence one another.
One of them is the geometry of spacetime.
We call such a theory a background independent theory.
Einstein's general theory of relativity,
satisfied all the tests required for successful unification.
There was profound conceptual consequences.
They led to predictions of new phenomena,
like the expanding universe, the Big Bang, gravitational waves, and black holes.
There is good evidence for all of them.
General relativity was just the start.
If gravitational force could be understood as a manifestation of geometry in space,
why couldn't this be also true of electromagnetism.
Many scientists grappled with this idea.
Some proposed this unification by adding a hidden 5th dimension.
But this failed.
For it to be true, the extra dimension is curled up into a circle,
whose radius is too small to see.
To get electromagnetism out of the theory,
the radius of the circle must be frozen.
It must not change with space or time.
This was the weak point, which caused its failure.
Scientists were now aware of more forces than gravity and electromagnetism.
They knew about strong and weak nuclear forces.
Scientists now had to search for a theory to unify all of them.
Many tried to resolve this by adding new dimensions.
Scientists got to understand that nature lacked a certain symmetry.
That is the parity between left and right.
Neutrinos are referred as left handed.
That is the direction of spin is always opposite to their linear momentum.
When we look at the world in a mirror, we see a false world.
In this world, the neutrinos would be right handed.
This was difficult to explain.
Theories which had higher dimensions, had to impose conditions on the higher dimensions.
The more dimensions you include,
the higher the price you pay for freezing their geometry.
When there are more dimensions, there are more degrees of freedom.
This makes the problem of instability worse.
When there is more than one hidden dimensions, there are many different ways to curl them.
Rather than being just one, which is a circle,
there are infinite number of ways the higher dimensions can be curled up.
This results in a infinite number of possible versions of the theory.
We do not know which one to choose.
After quantum theory was formulated,
scientists had different approaches to unification.
Many scientists ignored unification, and concentrated on applying quantum theory,
to vast variety of phenomena.
A few including Einstein persisted in looking for a unified theory,
while ignoring quantum theory.
Einstein sparked the quantum revolution, with his realisation that the photon was real.
But he did not believe in it.
He continued to search for a unified field theory.
This did not succeed.
No one knew on how to make general relativity consistent with quantum theory.
When more dimensions are added things got worse.
None of these theories could make relativity consistent with quantum theory.
The search is still continuing.