# Loop Quantum Gravity: The Answer to What Space is

Chesham, London

Subatomic particles, how do we link such a small thing with planets, galaxies, and the entire universe? We need to connect Einstein's theory of general relativity with quantum physics. We have long searched for a theory of quantum gravity, the lead contender for this would be string theory, which includes tiny little wriggling strings in coils that includes extra dimensions. String theory is considered to be a theory of everything, the other theory that opposes it and tries to find quantum gravity is loop quantum gravity which only focuses on trying to bring together quantum mechanics and the theory of general relativity.

Einstein stated that the laws of physics apply the same to every individual regardless of the speed that they are moving at, or the place they are at. The point of this is, if you see an object, let's say an electron moving from one point to another, you can't determine whether it is the electron that is moving or the observer. We can thus infer that speed is relative. Another principle was that the speed of light is finite and constant, supporting evidence of this would be the Michelson-Morley experiment conducted at the end of the 19th century on top of a mountain. It concluded that the speed of light is a constant independent of the speed of the source of the light.

If you agree with these two statements above, let's pose a scenario: Person A has seen two twin lightning bolts strike simultaneously. Whilst these are striking the ground, person B moves from left to right (this would have to be very quickly, about a fraction of the speed of light), due to this, person B sees the right-hand bolt strike first. If you accept the two principles stated in the previous paragraph, you come to the conclusion that there is no such thing as absolute simultaneous, and eventually, that leads to the concept that there is no absolute time. Out of this comes special relativity, this was a theory made by Einstein while he was working as a patent Clerk in 1905. He suggested that time dilates, space contracts, and energy and mass are the same things.

Special relativity was however not a complete theory. Acceleration, for one, did not have the same status that it did in Newton's laws of motion, and it could not account for gravity. In 1907, Einstein had “his happiest thought”: If a person falls freely he will not feel his own weight. This led Einstein to the equivalence principle, that gravity and acceleration are the same things. Einstein then worked out that spacetime itself is something that can be curved, this led to Einstein's theory of general relativity. In this, Einstein thought that space and time were intertwined in an infinite “fabric,” like an outstretched blanket.

Separate from this, Einstein published a paper in 1905 saying that monochromatic radiation behaves discontinuously and is made up of energy quanta; we then later figured out that the energy quanta were photons. So He basically stated that a light wave can be made up of particles. Later on, Louis de Broglie said that particles can also be waves, this caused a lot of arguments, but these ideas were the basis for what we call quantum mechanics. The standard model was then underpinned by this and it tells us how the universe is built in a way(like the physics version of the periodic table). For example, to build a proton you would need 2 up quarks and a down quark, these would need to be forged together by gluons.

Now to relate general relativity, which is used for massive things in the universe, but quantum mechanics which is used for minuscule things which we have not even seen. Physicist Lee Smolin published a book called “Three roads to quantum gravity”. We could start with quantum field theory and make it background independent, we could start over, or we could quantize general relativity which is the goal of loop quantum gravity. It sounds easy but mathematically is incredibly hard.

Back to the standard model, QCD is the quantum field theory that binds quarks together inside neutrons and protons, however, the equations used for QCD are way too complex to do analytically, you would need a computer. Lattice QCD is a technique used to solve these equations, but you end up getting a loop of gluons without any quarks. One of the reasons that this is possible is because gluons have a color charge so they interact with themselves as well as quarks. Kenneth Wilson thought that it may be possible to create a situation without quarks and the lattice, and all we have left are loops of force which can be used as models for gravitational force instead of gluons. This was the inspiration for loop quantum gravity.

Loop quantum gravity kicked off in the 80s and was initially focused on the loops and how they intersect. Then the possibility of them knotting came into play, so then physicists began focusing on knots and then how they would weave together. This then leads to the Penrose spin networks. When we look at these pictures we imagine these loops existing in space but in loop quantum gravity these loops make up space, they are space. Loop quantum gravity implies that space itself is quantum in nature. If you look at a spin network, you look at the nodes and links, Smolin and Rovelli realized that the nodes are where you will find quanta of volume in space, and along the links, you will find the quanta of the area of space.

What about time? In this road to quantum gravity, time seems to disappear, it's called the problem of frozen time. In these quantum states of space, they are quantum states so they fluctuate, they don't stay still, this is due to the Heisenberg uncertainty principle. To put time back into the picture, we imagined that the fluctuations create the appearance of time. So as you change the number of nodes in a spin network, time advances.

Another thing about loop quantum gravity is that instead of treating gravitons as force particles, they are treated as pseudo particles. Particles like electrons can then be modeled as open loops which puncture the spin network. This means that particles from the standard model can be put into the model of space-time from loop quantum gravity. The theory can also be used to calculate the entropy of black holes, but this is still controversial.

Back to Einstein’s theory of general relativity, it was presumed that space is continuous, naturally, you would expect to get many infinities when working this out but since there really is no such thing as infinity in nature, there must be something wrong. Loop quantum gravity indicates that space is granular and once you get to a certain size you can not go any smaller. For example, you can't get any smaller than an electron or a photon. This means that there can not be any singularities because the quantum nature of space won't allow it. Based on this, it is theorized that the universe had not begun with a bang but a bounce. This could mean that there may have been a universe that condensed, contracted, compressed and once it ran up against the ultimate invincible quantum of space, it bounced.

To conclude, loop quantum gravity is a theory that space is made up of loops. It attempts to find a theory for quantum gravity and has no proof and research is still going on regarding it. Time seems to be non-existent in it, whereas in general relativity it is treated as a dimension. It tries to unite quantum mechanics with general relativity by quantizing general relativity and is the main opposition to string theory however it is not a theory of everything.

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