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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.