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FURTHER STUDY
Quantum gravity, mathematical explanation: https://youtu.be/NsUm9mNXrX4
String theory vs. loop quantum gravity: https://youtu.be/3jKPJa-f3cQ
How QM Ruins GR: https://youtu.be/S3Wtat5QNUA
General relativity explained: https://youtu.be/tzQC3uYL67U
CHAPTERS
0:00 How gravity models evolved
2:22 Is quantum gravity even necessary?
6:23 3D Bronstein cube
7:56 Why can't we quantify gravity?
11:19 Ways we can quantify gravity
12:59 Why don't we fit the other forces into general relativity?
14:26 String theory and Loop quantum gravity
16:52 Why should we worry about quantum gravity?
RESUME
The universe appears to be quantum and not classical. But general relativity is classical. When we try to use Einstein's theory to create a quantum model of gravity, we get nonsensical results. Why is quantum gravity the hardest problem in physics? Is a quantum model of gravity even necessary? why can't we fit the other three forces into the framework of general relativity?
Reasons to Quantize Gravity: All other fields in nature are quantized. Why would nature make an exception only for the gravitational field? General relativity also fails at the singularity at the Big Bang and in black holes. A zero-sized singularity seems absurd and probably unphysical. It probably means there is a break in the theory.
We can see a problem just by looking at the equation for general relativity. The left side describes the curvature of spacetime, which is classical. But the right side is matter, and that is quantum. So we have two incompatible types of mathematics.
A 3D Bronstein cube can illustrate what a quantum gravity theory would look like. We either have to take general relativity and quantize it, or take quantum field theory and integrate gravity into it.
All Standard Model quantum theories take classical theories and make them quantum by turning certain variables, such as momentum, into operators. However, this procedure doesn't seem to work with gravity, because we get all kinds of infinities that can't be corrected or normalized.
What makes general relativity unique is that it is a theory about space-time itself, and not about things that happen in space-time, as is the case with the other three fundamental forces. Gravity is the result of the geometry and curvature of space-time. The other forces describe events that occur within this background geometry, not the background itself.
Another factor that makes quantifying gravity difficult is because it is very weak, making it almost impossible to conduct experiments. Coming up with a quantum theory of gravity will therefore mainly be a thought experiment.
We can try to treat gravity as a field, just like other fields. An excitation in this area would be the graviton. The exchange of gravitons between two particles would lead to attraction. This is what string theory is trying to do, because a graviton comes up in the mathematics of string theory.
The second way is to quantize spacetime itself. This is what Loop quantum gravity is trying to do. But this would mean that spacetime could exist in a superposition of several different geometries. This is problematic because spacetime would be dynamic in quantum gravity. So, for example, we can't ask what the probability is of finding an electron at a particular location, because there is no objective way to specify which location we are talking about. This is because spacetime itself would be in a superposition.
Instead of trying to fit general relativity into quantum mechanics, why not try to fit everything into the framework of general relativity? This has been tried. In 1919, Theodore Kaluza invented the general theory of relativity with five dimensions instead of four. He found the laws of classical electromagnetism in his five-dimensional equations. But it was clearly wrong, because we live in a four-dimensional universe, three dimensions of space and one dimension of time, not five.
Swedish physicist Oskar Klein suggested that the newly hypothesized fifth dimension might be very small, so small that it could not be detected. This idea was put on the back burner because at the same time he published his paper, quantum field theory was taking off.
#quantumgravity
One of today's most popular approaches to quantizing gravity is String Theory and Loop Quantum Gravity. This video discusses the difference between these two theories, and their pros and cons.
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