Understanding the Compatibility of Relativity and Quantum Theories

[mathshead]

can something tell me what the theory of relativity and quantum are, and how they are not compatiable with each other?

 

[Hurkyl]

General Relativity is a theory about gravitation. It says that the universe has an intrinsic curvature which is generated by the location and flow of mass and energy, and our perception of gravity is really just the natural tendency of matter and energy to flow along the curves of space-time.


Quantum Chromodynamics is a theory about electromagnetism and the weak & strong forces. It says that the concept of "simultaneous knowledge of position and momentum" is gibberish.



When you put the two together, things blow up.

Basically, if I understand it correctly, what happens is that QCD tells you that you don't know both the position and the momentum of a particle. This means that GR doesn't know exactly how space-time should be curved. This uncertainty magnifies the uncertainty in our knowledge of the particle's position and momentum... thus we're even less certain how it bends space time...

This self-perpetuating uncertainty keeps feeding and growing, until uncertainties become infinite!

Now, Quantum Mechanics works with such loops; less naive techniques are used to "renormalize" equations to get rid of the infinities... however the infinities involved with gravitation have resisted all attempts at being normalized away.


Hurkyl

 

[drag]

Originally posted by Hurkyl
General Relativity is a theory about gravitation. It says that the universe has an intrinsic curvature which is generated by the location and flow of mass and energy, and our perception of gravity is really just the natural tendency of matter and energy to flow along the curves of space-time.

Yahoo ! 5.5 lines ! You're the man Hurkyl !

 

[lethe]

Originally posted by Hurkyl
General Relativity is a theory about gravitation. It says that the universe has an intrinsic curvature which is generated by the location and flow of mass and energy, and our perception of gravity is really just the natural tendency of matter and energy to flow along the curves of space-time.


Quantum Chromodynamics is a theory about electromagnetism and the weak & strong forces. It says that the concept of "simultaneous knowledge of position and momentum" is gibberish.



When you put the two together, things blow up.

this isn t quite accurate. first of all, QCD is a theory of the strong nuclear force only. the theory that encompasses the strong and electroweak forces is known as the standard model.

second, the standard model is a field theory, not a quantum single particle theory. as such, it says nothing about the observability of the position and momentum of a particle. the observables in a field theory are the field and is conjugate field momentum. so for example, the electric field amplitude of a photon and the magnetic field amplitude are not simultaneously observable. or the matter and antimatter components of a complex scalar field.

it doesn t even make a lot of sense to ask about the position of the photon, since it is a field, extended in space.

it might be possible to speak about position and momentum operators as observables in field theory, but i have never seen this done. then again, i m no expert in quantum field theory.

Basically, if I understand it correctly, what happens is that QCD tells you that you don't know both the position and the momentum of a particle. This means that GR doesn't know exactly how space-time should be curved. This uncertainty magnifies the uncertainty in our knowledge of the particle's position and momentum... thus we're even less certain how it bends space time...

This self-perpetuating uncertainty keeps feeding and growing, until uncertainties become infinite!

Now, Quantum Mechanics works with such loops; less naive techniques are used to "renormalize" equations to get rid of the infinities... however the infinities involved with gravitation have resisted all attempts at being normalized away.


Hurkyl

i haven t heard it described exactly that way, but i like the way it sounds.

let me offer the explanation as i have heard it.

firstly, it is not quantum field theory in general which blows up when you try to add gravity, it is quantum perturbation theory. it is currently unknown whether one can avoid the nonrenormalizability by avoiding perturbation theory (since perturbation is the only way we know how to use field theory).

ok, so perturbation theory involves expanding in a series that is polynomial in the coupling constant. higher order corrections contribute less to the interaction in say, QED, because of the small size of the coupling constant, the fine structure constant.

well, in gravitation, the field (the metric) couples to energy (remember: G_μν=8πGT_μν energy couples to metric)

so in quantum theory, when you do your perturbation, you must have a series that is polynomial in energy, and blows up for the UV limit.

 

[Hurkyl]

this isn t quite accurate. first of all, QCD is a theory of the strong nuclear force only. the theory that encompasses the strong and electroweak forces is known as the standard model.

Aha, thank you! I have been unsure for quite some time on this aspect of the nomenclature!


Hurkyl