Today we will talk about what ideas physicists have come up with to quantize gravity.

But before I get to that, I want to tell you why it matters.

That we do not have a theory of quantum gravity is currently one of the biggest unsolved problems

in the foundations of physics.

A lot of people, including many of my colleagues, seem to think that a theory of quantum gravity

will remain an academic curiosity without practical relevance.

I think they are wrong.

That’s because whatever solves this problem will tell us something about quantum theory,

and that’s the theory on which all modern electronic devices run, like the ones on which

you are watching this video.

Maybe it will take 100 years for quantum gravity to find a practical application, or maybe

it will even take a 1000 years.

But I am sure that understanding nature better will not forever remain a merely academic

speculation.

Before I go on, I have to be clear that quantizing gravity by itself is not the problem.

We can, and have, quantized gravity the same way that we quantize the other interactions.

The problem is that the theory which one gets this way breaks down at high energies, and

therefore it cannot be how nature works, fundamentally.

This naïve quantization is called “perturbatively quantized gravity” and it was worked out

in the 1960s by Feynman and DeWitt and some others.

Perturbatively quantized gravity is today widely believed to be an approximation to

whatever is the correct theory.

So really the problem is not just to quantize gravity per se, you want to quantize it and

get a theory that does not break down at high energies.

Because energies are proportional to frequencies, physicists like to refer to high energies

as “the ultraviolet” or just “the UV”.

Therefore, the theory of quantum gravity that we look for is said to be “UV complete”.

Now, let me go through the five most popular approaches to quantum gravity.

First, String Theory.

The most widely known and still the most popular attempt to get a UV-complete theory of quantum

gravity is string theory.

The idea of string theory is that instead of talking about particles and quantizing

them, you take strings and quantize those.

Amazingly enough, this automatically has the consequence that the strings exchange a force

which has the same properties as the gravitational force.

This was discovered in the 1970s and at the time, it got physicists very excited.

However, in the past decades several problems have appeared in string theory that were patched,

which has made the theory increasingly contrived.

You can hear all about this in my earlier video.

It has never been proved that string theory is indeed UV-complete.

Second, Loop Quantum Gravity.

Loop Quantum Gravity is often named as the biggest competitor of string theory, but this

comparison is somewhat misleading.

String theory is not just a theory for quantum gravity, it is also supposed to unify the

other interactions.

Loop Quantum Gravity on the other hand, is only about quantizing gravity.

It works by discretizing space in terms of a network, and then using integrals around

small loops to describe the space, hence the name.

In this network, the nodes represent volumes and the links between nodes the areas of the

surfaces where the volumes meet.

Loop Quantum Gravity is about as old as string theory.

It solves the problem of combining general relativity and quantum mechanics to one consistent

theory but it has remained unclear just exactly how one recovers general relativity in this

approach.

Third, Asymptotically Safe Gravity

Asymptotic Safety is an idea that goes back to a 1976 paper by Steven Weinberg.

It says that a theory which seems to have problems at high energies when quantized naively,

may not have a problem after all, it’s just that it’s more complicated to find out what

happens at high energies that it seems.

Asymptotically Safe Gravity applies the idea of asymptotic safety to gravity in particular.

This approach also solves the problem of quantum gravity.

Its major problem is currently that it has not been proved that the theory which one

gets this way at high energies still makes sense as a quantum theory.

Fourth, Causal Dynamical Triangulation

The problem with quantizing gravity comes from infinities that appear when particles

interact at very short distances.

This is why most approaches to quantum gravity rely on removing the short distances by using

objects of finite extensions.

Loop Quantum Gravity works this way, and so does String Theory.

Causal Dynamical Triangulation also relies on removing short distances.

It does so by approximating a curved space with triangles, or their higher-dimensional

counterparts respectively.

In contrast to the other approaches though, where the finite extension is a postulated,

new property of the underlying true nature of space, in Causal Dynamical Triangulation,

the finite size of the triangles is mathematical aid, and one eventually takes the limit where

this size goes to zero.

The major reason why many people have remained unconvinced of Causal Dynamical Triangulation

is that it treats space and time differently, which Einstein taught us not to do.

Fifth, Emergent Gravity

Emergent gravity is not one specific theory, but a class of approaches.

These approaches have in common that gravity derives from the collective behavior of a

large number of constituents, much like the laws of thermodynamics do.

And much like for thermodynamics, in emergent gravity, one does not actually need to know

all that much about the exact properties of these constituents to get the dynamical law.

If you think that gravity is really emergent, then quantizing gravity does not make sense.

Because, if you think of the analogy to thermodynamics, you also do not obtain a theory for the structure

of atom by quantizing the equations for gases.

Therefore, in emergent gravity one does not quantize gravity.

One instead removes the inconsistency between gravity and quantum mechanics by saying that

quantizing gravity is not the right thing to do.

Which one of these theories is the right one?

No one knows.

The problem is that it’s really, really hard to find experimental evidence for quantum

gravity.

But that it’s hard doesn’t mean impossible.

I will tell you some other time how we might be able to experimentally test quantum gravity

after all.

So don’t forget to subscribe.