Relativity vs Quantum Mechanics

[Karmic Leprec]

What are the main reasons why there is conflict between the theories of relativity and quantum mechanics? Specifically, why can't we explain gravity while adhering to the quantum explanation of particles?

 

[Fredrik]

I've seen several threads about this before. I suggest you try a search and let us know if the answers you find are satisfactory or not.

Considering the specific way you phrased the question, I would say that the main obstacle is that a quantum field theory of gravity isn't renormalizable, which essentially means that most interesting calculations just give you the answer "infinity".

 

[meopemuk]

The most fundamental statement of both special and general relativity is the symmetry between time and position. Such a symmetry is absent in quantum mechanics.

 

[saaskis]

Considering the specific way you phrased the question, I would say that the main obstacle is that a quantum field theory of gravity isn't renormalizable, which essentially means that most interesting calculations just give you the answer "infinity".

I guess this is true (I don't know anything about quantum gravity), but one has to notice that non-renormalizable theories are not useless as effective field theories. Since non-renormalizable vertices have a coupling constant with a negative mass dimension -d, the coupling constant is something like g\sim g_0/\Lambda^d, where g_0 is dimensionless. Therefore, all vertices basically contain a factor E/\Lambda, which is small for energies below the characteristic scale. If the desired accuracy is given before-hand, one only needs a finite amount of coupling constants to reach that accuracy.

Of course, a non-renormalizable theory would not be a good candidate for a fundamental theory, which probably was the topic here. But e.g. for E \ll m_e one can reduce QED to a non-renormalizable theory of self-interacting photons and make completely valid calculations.

 

[espen180]

I read that the foundations of quantum mechanics and general relativity are mutually exclusive, meaning that the validity of one implies invalidity of the other. Resolution of this is one of the inspirations for pursuiting a theory of quantum gravity. I suggest you read about Loop Quantum Gravity and String Theory.

 

[bcrowell]

One fairly straightforward argument is this. Quantum mechanics is supposed to have the property that information is never lost. (In technical terms, the evolution of a quantum state is described by a unitary operator.) In general relativity, you can dump information into a black hole, and it is gone forever. This is a fundamental incompatibility between the two theories.

 

[Passionflower]

One fairly straightforward argument is this. Quantum mechanics is supposed to have the property that information is never lost. (In technical terms, the evolution of a quantum state is described by a unitary operator.) In general relativity, you can dump information into a black hole, and it is gone forever. This is a fundamental incompatibility between the two theories.

A singularity in GR is a "place" where the theory breaks down, it is not considered a fundamental part of the theory.

 

[espen180]

A singularity in GR is a "place" where the theory breaks down, it is not considered a fundamental part of the theory.

The GR BH singularity, as far as I know, concerns the center of the body, where the enitre mass of the black hole is predicted to be concentrated in a single point in space. The theory is still valid inside the horizon. Heck, for an infaling observer there is no horizon.

 

[Fredrik]

A singularity in GR is a "place" where the theory breaks down, it is not considered a fundamental part of the theory.

I think that statement is too strong. This is what I would say instead: The singularity itself is not an event in spacetime or a subset of spacetime. It's just a mathematical property of some solutions of Einstein's equation. The fact that such solutions exist means that singularities are a fundamental part of the theory, and the fact that there are black holes out there means that those solutions are relevant in the real world. You are of course right that the agreement between the theory and reality is expected to get worse and worse the closer we get to the singularity, but that doesn't mean that the black hole information paradox isn't a major conflict between GR and QM. It is.

 

[Frame Dragger]

I think that statement is too strong. This is what I would say instead: The singularity itself is not an event in spacetime or a subset of spacetime. It's just a mathematical property of some solutions of Einstein's equation. The fact that such solutions exist means that singularities are a fundamental part of the theory, and the fact that there are black holes out there means that those solutions are relevant in the real world. You are of course right that the agreement between the theory and reality is expected to get worse and worse the closer we get to the singularity, but that doesn't mean that the black hole information paradox isn't a major conflict between GR and QM. It is.

It's also possible that the singularities in question have a physical reality and something like the Holographic principle is right. I doubt that, but it's a sign of how much wiggle room exists.

 

[Fredrik]

It's also possible that the singularities in question have a physical reality...

That's extremely likely, just like it's extremely likely that the smooth manifold structure doesn't have physical reality at small enough scales, but that doesn't really have anything to do with what we were talking about: Conflicts between two specific theories. Reality is irrelevant in that discussion. We don't have to bring reality into the discussion until we have a new theory that can reproduce all the predictions of the two that we have now.

 

[IceMan815]

The problem is both theories are based on different mats and they are the best two theories that explain the particle physics and astrophysics. They are working good but when it comes to gravity and black holes they have different definition. For exm:
-QM says it has particle called graviton that acts for the gravity
-GR says gravity is warping of space-time by the mass
and about the black hole its paradox about information in it

 

[Frame Dragger]

That's extremely likely, just like it's extremely likely that the smooth manifold structure doesn't have physical reality at small enough scales, but that doesn't really have anything to do with what we were talking about: Conflicts between two specific theories. Reality is irrelevant in that discussion. We don't have to bring reality into the discussion until we have a new theory that can reproduce all the predictions of the two that we have now.

I said it was possible, I don't make a claim that it is likely or not, and I am not qualified to do so. Really, the issue of what is beyond an event horizon of a BH is academic, and is overwhelmingly likely to remain so for the lifetime of our species in my barbarian's opinion. I was simply highlighting the possibility that GR does not "break down", but that our universe is strange. QM has similar issues which are yet to be resolved. As the OP did not seem to be overly concerned with formalism in either case, I don't see the harm in a bit of reality mixed with speculation and theory. QM and GR both present cases on different scales where their predictions cease to make any meaningful sense, and extreme gravity is a fairly typical place to find that conflict.

I am not offering a new theory, but merely accepting the partial nature of the ones we have.

 

[bcrowell]

A singularity in GR is a "place" where the theory breaks down, it is not considered a fundamental part of the theory.

If you look at my #6, I never said anything about a singularity. The argument depends only on the existence of a horizon, not a singularity.

 

[TCS]

One fairly straightforward argument is this. Quantum mechanics is supposed to have the property that information is never lost. (In technical terms, the evolution of a quantum state is described by a unitary operator.) In general relativity, you can dump information into a black hole, and it is gone forever. This is a fundamental incompatibility between the two theories.

If you think of a massive particle as a localized standing wave in three dimensions, where the standing wave is really a collecton of infinetly extended traveling waves, then some part of the particle is always going to exist outside of the black hole and its information still exists in the observable portion of the wave function.

You can have a quantized wave on a continuous string.