- #1
Thrice
- 258
- 0
I've done college courses on both & it's not clear yet how they conflict. I'm looking for a more technical account. Have I done enough to understand it, or do I have to do wait till QFT?
I don't know if there are any situations where they both make clear predictions that contradict each other, but see here for a discussion of one of the main problems in figuring out how to reconcile them, having to do with the fact that the uncertainty principle would seem to allow for huge uncertainty in energy at sufficiently small scales, but in GR big energies cause significant curvature of spacetime, and my understanding is that physicists only know how to make predictions in quantum field theory if they have a specific known background spacetime.
I guess another more general conflict is that quantum field theories treat the other set of forces using a common set of rules, but if you try to apply these rules to gravity you get infinities which can't be "renormalized" as in the case of the other forces.
This argument seems a bit sketchy, since without knowing more there's no obvious reason they couldn't be combined--after all, Maxwell's laws of electromagnetism don't incorporate the principle of superposition on a Hilbert space, and yet they were successfully combined with QM to make the theory of quantum electrodynamics.masudr said:The fundamental principle of QM is the Principle of Superposition on a Hilbert space.
The fundamental principle of GR is the Principle of General Covariance on a 4-dimensional Lorentizian differentiable manifold.
Really they are about two completely different things. How should one go about combining/relating them?
JesseM said:This argument seems a bit sketchy, since without knowing more there's no obvious reason they couldn't be combined--after all, Maxwell's laws of electromagnetism don't incorporate the principle of superposition on a Hilbert space, and yet they were successfully combined with QM to make the theory of quantum electrodynamics.
Not true; it depends on the particular quantum theory under consideration.in QM time is "absolute" (all the observers seem to have the same time)
Karlisbad said:A question not mentioned..and another problem.. in GR time is just a coordinate of the curve ..whereas in QM time is "absolute" (all the observers seem to have the same time) since for every observer you have that they share the same Hamiltonian and [tex] H\rightarrow i\hbar \partial _{t} [/tex] which is not the spirit of GR.
the most direct quantization method (in my opinion) would be using Poisson Bracket then:
[tex] \dot g_{ab}=[g_{ab} , H] [/tex] [tex] \dot \pi_{ab}=[\pi _{ab} , H] [/tex]
where gab and pab are the metric and the conjugate momenta to the metric...however i believe this can be done since Poisson approach only works well whenever H=T+V and L=T-V (lagrangian), by the way...¡¡the Hamiltonians in SR and GR are H=0¡¡ then there's no possible quantization.
QM stands for quantum mechanics and GR stands for general relativity. Quantum mechanics is a branch of physics that explains the behavior of particles on a very small scale, while general relativity is a theory that explains the behavior of gravity on a large scale.
QM and GR are incompatible because they have different principles and equations that do not work together. QM works on a microscopic level, while GR works on a macroscopic level. The two theories have not been able to be unified into a single theory.
The main differences between QM and GR are their fundamental principles and equations. QM is based on the principles of uncertainty and superposition, while GR is based on the principle of general relativity and the equivalence of mass and energy. QM uses the Schrödinger equation, while GR uses the Einstein field equations.
The incompatibility of QM and GR affects our understanding of the universe because they both play important roles in our understanding of different aspects of the universe. QM helps us understand the behavior of subatomic particles, while GR helps us understand the behavior of gravity and the structure of the universe. Without a unified theory, there are still many unanswered questions about the universe.
Yes, there have been many attempts to reconcile QM and GR, but none have been successful so far. Some proposed theories include string theory, loop quantum gravity, and quantum field theory. However, these theories are still in the early stages of development and have not been widely accepted by the scientific community.