- #1
Karmic Leprec
- 13
- 0
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?
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 [tex]g\sim g_0/\Lambda^d[/tex], where g_0 is dimensionless. Therefore, all vertices basically contain a factor [tex]E/\Lambda[/tex], 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.Fredrik said: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".
A singularity in GR is a "place" where the theory breaks down, it is not considered a fundamental part of the theory.bcrowell said: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 said: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.Passionflower said:A singularity in GR is a "place" where the theory breaks down, it is not considered a fundamental part of the theory.
Fredrik said: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.
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.Frame Dragger said:It's also possible that the singularities in question have a physical reality...
Fredrik said: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.
Passionflower said:A singularity in GR is a "place" where the theory breaks down, it is not considered a fundamental part of the theory.
bcrowell said: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.
Relativity and quantum mechanics are two different theories in physics that aim to explain different aspects of the universe. Relativity deals with the laws of gravity and how objects move in space and time, while quantum mechanics deals with the behavior of matter and energy on a very small scale.
Currently, there is no single theory that combines relativity and quantum mechanics. Scientists are still working on finding a unified theory that can explain all of the known laws of physics.
Both relativity and quantum mechanics have been extensively tested and have been found to accurately describe different aspects of the universe. However, they have different domains of applicability. Relativity is more accurate when dealing with large objects and gravity, while quantum mechanics is more accurate when dealing with small particles and their behavior.
Both relativity and quantum mechanics have revolutionized our understanding of the universe and have challenged some of our long-held beliefs about how the world works. These theories have shown that our traditional concepts of space, time, and causality may not apply at extreme scales, and that the universe is much more complex and mysterious than we may have previously thought.
While the effects of relativity and quantum mechanics may not be obvious in our daily lives, they are essential for many modern technologies. For example, GPS systems use both relativity and quantum mechanics principles to accurately determine location and time. Additionally, quantum mechanics plays a crucial role in the development of computers, electronics, and other advanced technologies.