# Quantum Gravity

## Main Question or Discussion Point

I watched a seminar in particle physics and they mentioned that it was difficult to reconcile general relativity and Quantum field theory, I was just curious as to why it was so difficult considering quantum field theory is already reconciled with special relativity and gauge symmetry. what mathematical anomalies keep this feat away from us? I'm truly interested in this myself, its sort of a goal of mine to figure out quantum gravity, best to know what I'm getting into.

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malawi_glenn
Homework Helper
well, renormalizability. The graviton must/should be a rank-2 tensor and massless, i.e. transform as a spin-2 particle with 0 rest mass. The theorem by Weinberg and Witten states that a Quantum Field Theory with massless gauge bosonswith spin greater than 1 can not be both Lorentz invariant and renormalizable.

weren't they able to solve a similar problem with W and Z bosons having mass? by inventing the higgs field concept, so perhaps there is a solution in a similar way in this case?

malawi_glenn
Homework Helper
weren't they able to solve a similar problem with W and Z bosons having mass? by inventing the higgs field concept, so perhaps there is a solution in a similar way in this case?
But they are spin-1.

And they are massive in nature -> i.e. short range force.

Theory with massive gauge bosons can only be renormalizabile iff they aquire mass from spontanteos symmetry breaking.

So what is left for you is to introduce graviton with current mass into the Lagrangian, but that will not save you since, as I said, a theory where the gauge boson have mass is also renormalizable.

The logic you are suggesting is that one should have a spontaneous symmetry breaking mechanism which makes the graviton massless, or what? I can not follow you here =/
Then the graviton still have spin-2.. so?

The problem is NOT similar at all.

Have you consulted textbooks on this? Have you done classes in QFT and GR?

well, I didn't really know much of anything about the complexity of the problem. No I haven't consulted any textbooks, I barely understand relativity and quantum field theory, I would really enjoy learning this sort of thing. perhaps there could be some sort of mechanism that accounts for spin-2?

perhaps there could be some sort of mechanism that accounts for spin-2?
Yeah, they are called strings: string theory successfully reconciles quantum mechanics and general relativity.

robphy
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Gold Member
Yeah, they are called strings: string theory successfully reconciles quantum mechanics and general relativity.
successfully ??

malawi_glenn
Homework Helper
perhaps there could be some sort of mechanism that accounts for spin-2?
define "mechanism that accounts for spin-2"

One has to forget about "classical" quantum theory - that particles are point-like in space-time. That is what string theory is about, and indeed, it "works" but I would not say that it work "successfully" since it is still under large development ;-)

Well my advise is to take one step at the time :-)

Also, make sure to study MUCH math (topology, differential geometry, groups, rings etc.)

robphy
Homework Helper
Gold Member
I watched a seminar in particle physics and they mentioned that it was difficult to reconcile general relativity and Quantum field theory, I was just curious as to why it was so difficult considering quantum field theory is already reconciled with special relativity and gauge symmetry. what mathematical anomalies keep this feat away from us? I'm truly interested in this myself, its sort of a goal of mine to figure out quantum gravity, best to know what I'm getting into.
Standard QFT presumes a fixed background Minkowski spacetime.
However, in general relativity and, presumably, in a quantum theory of gravity, spacetime is also dynamical.
This dual role of spacetime makes "gravity" different from the "other fundamental forces".

Here's a more elaborate description of that point of view:
http://www.perimeterinstitute.ca/Outreach/What_We_Research/Quantum_Gravity/ [Broken]

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Now I get it, yeah. don't worry about the math, math is my first love, I would love to learn topology and linear algebra, differential geometry, groups, rings. I enjoy just about every kind of math accept, possibly, statistics. I suppose if there was another field if gravitons skimmed it they might gain extra spin, but their point so I guess that doesn't work. hmm, I do have another question are gravitons equivalent to gravitational waves the same way Photons are light waves?

malawi_glenn