# Unifying gravity and quantum mechanics

• I
• kent davidge
In summary: This is a common issue with quantum theories that try to include both quantum mechanics and classical mechanics: they can't always agree on the rules for how the two systems should interact. This is usually resolved by imposing a classical limit on the quantum system, or by incorporating some kind of quantum corrections into the classical theory.
kent davidge
I was sitting at my bed when I suddenly have an idea.

The unification of electromagnetism and gravity was made with General Relativity. For this to happen, one just need to write the energy due to electromagnetic field in "differential geometry" form, through the Electromagnetic tensor, in a way that it matches with the right hand side of the Einstein equation.

Then I wonder, for quantum-mechanics one just need to write the "quantized" energy of a particle in a manner to combine it with the stress-energy tensor and... uu-uhhh, we could FINALLY know what happens to particles in the singularity of a black hole.

Why would it not work?

I'm sorry for my bad poor English.

kent davidge said:
for quantum-mechanics one just need to write the "quantized" energy of a particle in a manner to combine it with the stress-energy tensor

More precisely, you need to write the particle's energy, taking into account all of its quantum properties, in such a way that it is part of the stress-energy tensor.

However, this doesn't fix the key issue with unifying QM and GR, which is that in QM, the particle will not, in general, be in an eigenstate of energy--it will be in a superposition of states that have different energies. But each of these states will have different gravitational effects, i.e., different stress-energy tensors; so the particle will be in a superposition of stress-energy tensors. That will lead to different effects on the curvature of spacetime; so spacetime itself would need to be in a superposition of different curvatures. But GR is a classical theory: it only works if you have a single stress-energy tensor, not a superposition of different ones.

kent davidge said:
Then I wonder, for quantum-mechanics one just need to write the "quantized" energy of a particle in a manner to combine it with the stress-energy tensor and... uu-uhhh, we could FINALLY know what happens to particles in the singularity of a black hole.
People tried that as long as QFT exists. It is easy to write down such a theory, but it does not work. At least no one knows how it would lead to finite, meaningful results.

PeterDonis said:
More precisely, you need to write the particle's energy, taking into account all of its quantum properties, in such a way that it is part of the stress-energy tensor.

However, this doesn't fix the key issue with unifying QM and GR, which is that in QM, the particle will not, in general, be in an eigenstate of energy--it will be in a superposition of states that have different energies. But each of these states will have different gravitational effects, i.e., different stress-energy tensors; so the particle will be in a superposition of stress-energy tensors. That will lead to different effects on the curvature of spacetime; so spacetime itself would need to be in a superposition of different curvatures. But GR is a classical theory: it only works if you have a single stress-energy tensor, not a superposition of different ones.
Where is the problem if we accept that the curvature of spacetime is probabilistic in small scales, such as near the singularity of a BH? And say that spacetime behave like a classical entity in larger scales, so that we can ignore ?

mfb said:
People tried that as long as QFT exists. It is easy to write down such a theory
I would like if you could show me some no-too-complicated equations.

kent davidge said:
Where is the problem if we accept that the curvature of spacetime is probabilistic

The problem is that we don't have a workable theory that includes this. The obvious, and even not so obvious, ways of constructing such a theory don't work. That is why finding a workable theory of quantum gravity is still a hot research topic, more than half a century after the need for one was recognized.

PeterDonis said:
The problem is that we don't have a workable theory that includes this. The obvious, and even not so obvious, ways of constructing such a theory don't work. That is why finding a workable theory of quantum gravity is still a hot research topic, more than half a century after the need for one was recognized.
Is it like the Coulomb force problem? That it predicts a infinite electric field strength at zero distance from the punctual source, but the reality is that quantum forces start acting up to repeal the two charges when they come close together, so the field is not infinite there, and if we try to put quantum equations in the problem, we get wrong predictions, because the Coulomb theory has a classical nature?

kent davidge said:
Is it like the Coulomb force problem?

No. Quantum electrodynamics doesn't have the same issues as quantum gravity.

kent davidge said:
quantum forces start acting up to repeal the two charges when they come close together

Where are you getting this from?

kent davidge said:
if we try to put quantum equations in the problem, we get wrong predictions, because the Coulomb theory has a classical nature?

I don't know where you're getting this from either.

PeterDonis said:
No. Quantum electrodynamics doesn't have the same issues as quantum gravity.
Where are you getting this from?
I don't know where you're getting this from either.
Well, suppose the two charged particles happen to be fermions. Then a repealing force would not allow the two fermions to occupy the same place.

kent davidge said:
suppose the two charged particles happen to be fermions. Then a repealing force would not allow the two fermions to occupy the same place.

First, this is oversimplified. The correct statement is that fermion wave functions are antisymmetric under particle exchange. The wave functions include spin as well as position, so two fermions with opposite spins will not experience the "repelling force" you are talking about (thinking of it as a "repelling force" is also an oversimplification).

Second, saying that the antisymmetry of fermion wave functions "makes the field finite" at zero radius is not correct. The "infinite field at zero radius" problem still exists for fermions in QED. It is solved by renormalization. But that fix, which works for QED, doesn't work for quantum gravity, because unlike QED, quantum gravity is not renormalizable.

Third, the antisymmetry only applies to fermions, so your argument, even if it were correct for fermions, wouldn't explain why charged bosons (such as the weak bosons or the charged Higgs) can't produce an infinite Coulomb field.

PeterDonis said:
First, this is oversimplified. The correct statement is that fermion wave functions are antisymmetric under particle exchange. The wave functions include spin as well as position, so two fermions with opposite spins will not experience the "repelling force" you are talking about (thinking of it as a "repelling force" is also an oversimplification).

Second, saying that the antisymmetry of fermion wave functions "makes the field finite" at zero radius is not correct. The "infinite field at zero radius" problem still exists for fermions in QED. It is solved by renormalization. But that fix, which works for QED, doesn't work for quantum gravity, because unlike QED, quantum gravity is not renormalizable.

Third, the antisymmetry only applies to fermions, so your argument, even if it were correct for fermions, wouldn't explain why charged bosons (such as the weak bosons or the charged Higgs) can't produce an infinite Coulomb field.
Oh very interesting thing to know. Can you recommend me lectures/textbooks that covers that subject? Like, antisymmetry of wave functions, etc. All introductory books I've found does not contain such subjects.

kent davidge said:
All introductory books I've found does not contain such subjects.

For antisymmetry of wave functions, see, for example, Chapter 17 of Ballentine:

http://www-dft.ts.infn.it/~resta/fismat/ballentine.pdf

For the non-renormalizability of quantum gravity, you will probably need to look in the peer-reviewed literature.

kent davidge
kent davidge said:
Can you recommend me lectures/textbooks that covers that subject? Like, antisymmetry of wave functions, etc. All introductory books I've found does not contain such subjects.
There's a reason for that. This is quantum field theory, and there is no such thing as an "introductory" treatment of quantum field theory; it's something you encounter after you've started your PhD in theoretical physics. The closest to an introduction that I am aware of, accessible to someone who has completed a bachelor's degree in physics, is Lancaster and Blundell's "https://www.amazon.com/dp/019969933X/?tag=pfamazon01-20".

Or if you want to get an idea what you're letting yourself in for without buying a fairly expensive book, you can find a prepublication version of Mark Srednicki's textbook here; pay particular attention to the introduction where he describes the physics you already have to know to get into it. (I'm not recommending this book because I think it's better than the other QFT texts out there, but because there's a free and unpirated edition online).

Last edited by a moderator:
Fervent Freyja and kent davidge
Nugatory said:
pay particular attention to the introduction where he describes the physics you already have to know to get into it.
3/8.

Thanks

kent davidge said:
I would like if you could show me some no-too-complicated equations.
Something like this. You can write it down, but no one knows if that is reasonable, and even if it is, no one knows how to calculate things with that expression, because the tools developed for the other parts (everything apart from the "gravity" summand) don't work for the gravity part.

And as the others commented, you'll need a course in quantum field theory (and a lot of knowledge to understand this course) to understand what is going on in that equation.

mfb said:
Something like this. You can write it down, but no one knows if that is reasonable, and even if it is, no one knows how to calculate things with that expression, because the tools developed for the other parts (everything apart from the "gravity" summand) don't work for the gravity part.

And as the others commented, you'll need a course in quantum field theory (and a lot of knowledge to understand this course) to understand what is going on in that equation.
What is W in that equation?

## 1. What is the difference between gravity and quantum mechanics?

Gravity is a force that explains the attraction between objects with mass, while quantum mechanics is a theory that explains the behavior of particles at a subatomic level.

## 2. Why is it important to unify gravity and quantum mechanics?

Unifying gravity and quantum mechanics is important because it would provide a more complete understanding of the fundamental forces of the universe. It would also allow for a more accurate and comprehensive model of the universe.

## 3. What challenges are involved in unifying gravity and quantum mechanics?

The main challenge in unifying gravity and quantum mechanics is that they are currently described by two separate and incompatible theories - general relativity and quantum field theory. These two theories use different mathematical frameworks and have yet to be successfully integrated.

## 4. What are some proposed theories for unifying gravity and quantum mechanics?

Some proposed theories for unifying gravity and quantum mechanics include string theory, loop quantum gravity, and supersymmetry. These theories attempt to reconcile the differences between general relativity and quantum field theory by introducing new concepts and mathematical frameworks.

## 5. How close are we to achieving a unified theory of gravity and quantum mechanics?

While there has been significant progress in understanding the underlying principles of gravity and quantum mechanics, a complete unification of the two is still a subject of ongoing research and debate. There is currently no widely accepted theory that successfully unifies these two fundamental forces. However, scientists continue to work towards this goal and make new discoveries and advancements in the field.

Replies
3
Views
2K
Replies
2
Views
927
Replies
4
Views
2K
Replies
16
Views
1K
Replies
24
Views
4K
Replies
3
Views
597
Replies
1
Views
1K
Replies
1
Views
640
Replies
13
Views
2K
Replies
10
Views
1K