# Merging Gravity with the other forces

VictorMedvil
How mathematically within the confines of mainstream physics would you experts in physics merge Einstein's Field Equations with Quantum Mechanics and Quantum Field Theory? I am looking for a different perspective on this subject usually I get the perspective of "Cranks".

Staff Emeritus
If there were an answer to your question we would already have a theory of quantum gravity.

• Richard Green, Dragrath, Heikki Tuuri and 2 others
VictorMedvil
If there were an answer to your question we would already have a theory of quantum gravity.
Okay, let me change my question then what are the known problems with merging the two and three, Mathematically.

• ohwilleke
HomogenousCow
Linearized GR can be quantized as an effective (non-renormalizable) QFT, where an infinite number of new terms in the Lagrangian are introduced to regularize the theory. So in principle as long as you're only interested in quantizing the weak field limit of GR, quantum mechanics doesn't protest.

• Richard Green
Gold Member
What if you quantized gravitomagneticfield in same way electromagnetic field is quantized?

HomogenousCow
You mean with a Kaluza-Klein theory? Alot of work has been done on this you can look it up.

Elias1960
How mathematically within the confines of mainstream physics would you experts in physics merge Einstein's Field Equations with Quantum Mechanics and Quantum Field Theory?
As an effective field theory, GR is essentially unproblematic. It is non-renormalizable, but this is a much less serious problem than one has thought in the past. Effective field theory means you have an explicit cutoff distance, and accept that you have no theory for distances below that cutoff. Then you assume that at this critical distance all that infinity of imaginable additional terms has some common upper bound of magnitude. Then you can consider the large distance limit. You will find out that the higher-order terms will decrease much faster so that the whole infinity can be safely ignored, and only the lowest order terms are worth to be considered at distances large in comparison with the critical length.

The straightforward candidate for the critical length would be Planck length.

A conceptual problem with this is that to transform GR into a usual field theory you have to break relativistic symmetry. This can be done by enforcing preferred coordinates, with harmonic coordinates as the straightforward choice. This would leave the Einstein EP intact and violate only the Strong EP. Thus, the preferred frame effects would influence only the gravitational field. These effects would, therefore, be similar to dark matter.

• Richard Green
Gold Member
You mean with a Kaluza-Klein theory?
I do not think it is what I meant. I meant quantisisng gravitomagneticfield same way electromagnetifield is quantized.

HomogenousCow
That’s not a different theory from GR

Gold Member
That’s not a different theory from GR
Maybe I misunderstood your wording, but quantized gravitomagneticfield is very different from general relativity.

VictorMedvil
Still seeking a mathematical description, this is all well and good but I wanted to see the math reasons, I always hear the QM,QFT, and GR cannot be fused I would like to see it with my own eyes. Yes, its not renormalizable but how so math please, is it the Reimann curvature of GR or what? Either way I would like to get to the bottom of the issue.

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Elias1960
... this is all well and good but I wanted to see the math reasons, I always hear the QM,QFT, and GR cannot be fused I would like to see it with my own eyes. Yes, its not renormalizable but how so math please, is it the Reimann curvature of GR or what?...
If you want the math with your own eyes, then such a forum cannot really help you. What you need is a serious textbook, which tells you how to do a Feynman diagram, how to write down the corresponding integral, which terms are the problematic ones. The only help you can hope for here would be a recommendation for a good textbook to learn all this, which is not easy because even if many handle the SM, essentially nobody will handle GR as a field theory. More generally, in textbooks, you will find what works, but will not find why other things don't work.

• Dragrath and weirdoguy
VictorMedvil
So you are telling me that the inability to merge GR and QM is mainstream however you cannot show how merging the two is impossible, Lame answer!

• weirdoguy
No one is going to write here a few textbooks for you. Get real.

• VictorMedvil
No one is going to write here a few textbooks for you. Get real.
This is why I don't like this forum, in any other forum there would be someone up to the task.

• • Gold Member
This is why I don't like this forum, in any other forum there would be someone up to the task.
Can you give me a link to some better forum?
But Iagree with your critisism, I have not got answers to many questions I have asked here. answering these would probably not be hard for someone who knows this stuff.

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• weirdoguy
weirdoguy
in any other forum there would be someone up to the task.

So why don't you ask someone on any other forum? Again, you are asking to write a whole textbook here, because this issue is technically very involved. Well, unless you have appropriate background in quantum field theory and general relativity, but then you would find the answer long time ago in textbooks you were using...

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castrogiovanni
This is why I don't like this forum, in any other forum there would be someone up to the task.

Try MIT, Harvard, Oxford, Cambridge, etc. They may be able to help. Although, as previously mentioned, if they knew how to do it they would have done, and you wouldn't be here asking the question.

VictorMedvil
Whatever this is going nowhere someone close this thread.

Gold Member
Still seeking a mathematical description, this is all well and good but I wanted to see the math reasons, I always hear the QM,QFT, and GR cannot be fused I would like to see it with my own eyes. Yes, its not renormalizable but how so math please, is it the Reimann curvature of GR or what? Either way I would like to get to the bottom of the issue.
I gave my answer to this question at Physics Stack Exchange a few years ago. The highest-voted answer there may also help.

• • Dragrath, Heikki Tuuri, Auto-Didact and 1 other person
Still seeking a mathematical description, this is all well and good but I wanted to see the math reasons, I always hear the QM,QFT, and GR cannot be fused I would like to see it with my own eyes. Yes, its not renormalizable but how so math please, is it the Reimann curvature of GR or what? Either way I would like to get to the bottom of the issue.

The real calculation as you will see is quite difficult, but it was done here for the first time:
http://www.numdam.org/article/AIHPA_1974__20_1_69_0.pdf

• • Dragrath, VictorMedvil, Lord Crc and 1 other person
VictorMedvil
The real calculation as you will see is quite difficult, but it was done here for the first time:
http://www.numdam.org/article/AIHPA_1974__20_1_69_0.pdf

Thanks that was very helpful, they are not that difficult to read but I am sure actually doing the calculation itself is.

Heikki Tuuri
Some people claim that string theory has successfully merged gravity and quantum mechanics. However, I have understood that there is no proof of that fact. String theorists seem to have a problem describing the de Sitter universe or the FLRW universe. String theorists have become frustrated in the past two decades.

Loop quantum gravity is another effort. I have the impression that it is almost impossible to calculate anything in their network model, and that Lorentz covariance is a problem.

The non-renormalizability of gravity is often quoted as a problem in a straightforward inclusion of gravity as just one force in QFT.

Another problem is that QFT is formulated in an inertial frame of the Minkowski space. It is not easy to generalize that to the curved spacetime of General relativity.

A black hole is something we do not have in standard QFT. How to handle it?

• Dragrath and cosmik debris
cosmik debris
Another problem is that QFT is formulated in an inertial frame of the Minkowski space. It is not easy to generalize that to the curved spacetime of General relativity.

QFT can be formulated in curved spacetime OK, they cannot generate it.

Cheers

• olgerm
Heikki Tuuri
QFT can be formulated in curved spacetime OK, they cannot generate it.

Cheers

Classical fields seem to work ok in curved spacetime if we do not take into account the backreaction. If we do, then the problem is to find a solution for the Einstein equations with an arbitrary matter field, and that problem has been open since 1915.

In the semiclassical regime without a backreaction, there is the dispute: does Unruh or Hawking radiation exist?

QFT in curved spacetime would require gravitons, or some completely new insight. Some string theorists claim that they can handle it, but many people are sceptical.

I am right now doing research on this: what is the relationship between classical fields in curved spacetime and QFT.

weirdoguy
I don't see the incompatibility of QM with GR...

Don't take it personal, but what you wrote there shows that you have no idea what you are talking about. ##R## is not a radius, and Einstein equation is not an algebraic equation, it's tensorial so you can't just simply divide by ##g_{\mu\nu}##.

VictorMedvil
Don't take it personal, but what you wrote there shows that you have no idea what you are talking about. ##R## is not a radius, and Einstein equation is not an algebraic equation, it's tensorial so you can't just simply divide by ##g_{\mu\nu}##.

Then what is that R?

weirdoguy
Scalar curvature. You should know that if you try to manipulate this equation.

VictorMedvil
but isn't scalar curvature just the two principal radii? where are the principal radii of the surface. For example, the scalar curvature of the 2-sphere of radius r is equal to 2/r2.

weirdoguy
Not in four dimensions. General definition is ##R=R^\mu_{\phantom{\mu}\mu}##. You should really study some textbook on very basics before you try to learn about quantum gravity.

VictorMedvil
Not in four dimensions. General definition is ##R=R^\mu_{\phantom{\mu}\mu}##. You should really study some textbook on very basics before you try to learn about quantum gravity.
The parameter r is a geometrical invariant of the hyperbolic space, and the sectional curvature is K = −1/r2. The scalar curvature is thus S = −n(n − 1)/r2. Explain this to me, from what I understand it is just a radius.

weirdoguy
from what I understand it is just a radius.

Then your understanding is flawed. As I said before ##R=R^\mu_{\phantom{\mu}\mu}##, that is ##R## is a trace of Ricci tensor. Please get some textbook on general relativity and learn everything properly, not from random articles on the internet.

• Matter Times
Matter Times
Why is this a "hot thread"? It is basically someone quoting from Wikipedia who demands an answer to something he is not capable of handling.

VictorMedvil
Why is this a "hot thread"? It is basically someone quoting from Wikipedia who demands an answer to something he is not capable of handling.

No, I am perfectly able to handle the information, it is just me and weirdoguy have differing opinions about this.

Matter Times
Okay :)