Modifications in General Relativity

[aditya ver.2.0]

Decades have passed since the first idea of General Relativity arose in the mind of einstein. Surely development of the GR must have taken place during these years. May anyone one update me about these development that took place since the late past.oo):w

 

[martinbn]

You are talking about a hundred years of work. Surely you don't expect someone to update you on all of it! Did you try to find out some of the developments by yourself?

One of the famous things that happened in the 60's and 70's was the development of the global techniques by Penrose and the others.

 

[stevendaryl]

You are talking about a hundred years of work. Surely you don't expect someone to update you on all of it! Did you try to find out some of the developments by yourself?

One of the famous things that happened in the 60's and 70's was the development of the global techniques by Penrose and the others.

The original post title said "Modifications..." Development of new techniques is not a modification of the theory.

As far as modifying the equations, it's actually pretty remarkable how well they have stood up over the years. In contrast, quantum theory has been modified a bunch of times, to take into account relativity and intrinsic spin and particle creation, etc.

One modification of GR that I think most people believe is necessary for consistency, although it's not going to make much difference to most observational consequences of GR is to allow nonzero torsion. This is necessary (as I understand it) to take into account particles with intrinsic spin, such as an electron. It's also clear that GR will have to be modified in some ways to accommodate quantum mechanics. For the latter, there has been a tremendous amount of work done, although there is no definitive theory yet.

 

[Mentz114]

You should find out about Eli Cartan's theories and differential geometry. Also more recently Thamu Padmanabhan and others on holographic gravity.

 

[VantagePoint72]

In contrast, quantum theory has been modified a bunch of times, to take into account relativity and intrinsic spin and particle creation, etc.

I don't agree with this. Many new applications of quantum theory have been developed, such as those you mention. None of them represent a modification of the basic axioms of quantum mechanics, but rather the application of quantum mechanics to increasingly more interesting choices of Hamiltonians. The underlying structure of quantum mechanics has not changed since the previous mish-mash of heuristics usually called "old quantum mechanics" was formalized by Dirac, von Neumann and others. Indeed, we've found that mathematical structure of quantum mechanics is even more resilient than that of general relativity. There are theories similar to GR, like Brans-Dicke theory, which are still compatible with experimental data though GR is generally the simpler choice. On the other hand, as Weinberg noted, it's so far not been possible to find something "close to" quantum mechanics in some sense that doesn't have some extremely undesirable properties and isn't quantum mechanics itself.

 

[stevendaryl]

I don't agree with this. Many new applications of quantum theory have been developed, such as those you mention. None of them represent a modification of the basic axioms of quantum mechanics, but rather the application of quantum mechanics to increasingly more interesting choices of Hamiltonians. The underlying structure of quantum mechanics has not changed since the previous mish-mash of heuristics usually called "old quantum mechanics" was formalized by Dirac, von Neumann and others. Indeed, we've found that mathematical structure of quantum mechanics is even more resilient than that of general relativity. There are theories similar to GR, like Brans-Dicke theory, which are still compatible with experimental data though GR is generally the simpler choice. On the other hand, as Weinberg noted, it's so far not been possible to find something "close to" quantum mechanics in some sense that doesn't have some extremely undesirable properties and isn't quantum mechanics itself.

I sort of agree. "Quantum mechanics" is broad enough that all the various theories, Schrödinger's equation, Dirac's equation, the Klein-Gordon equation, QED, QCD, Weinberg-Salam model, etc., are all instances of the general axioms of quantum mechanics. However, it's only the instances of quantum mechanics that make testable predictions. I don't think that the general framework makes any predictions at all--only the specific theories. Or the specific choice of Hamiltonian, state space, etc.

In contrast, the Einstein Field equations are a very specific theory--they are more comparable (in my opinion) to a specific theory such as QED than to the broad category of quantum mechanics.

QM is a framework for theories, rather than a theory in itself. It's sort of like Special Relativity in that sense (there are many theories that are capable of being put into Special Relativistic form), but not like GR.

That's just a matter of opinion.

 

[VantagePoint72]

I sort of agree. "Quantum mechanics" is broad enough that all the various theories, Schrödinger's equation, Dirac's equation, the Klein-Gordon equation, QED, QCD, Weinberg-Salam model, etc., are all instances of the general axioms of quantum mechanics. However, it's only the instances of quantum mechanics that make testable predictions. I don't think that the general framework makes any predictions at all--only the specific theories. Or the specific choice of Hamiltonian, state space, etc.

The general framework makes falsifiable predictions about things like how strong non-local correlations in nature can be (via the CHSH inequality and related Bell inequalities), what kinds of physical processes should not be possible under any particular realization (via the various no-go theorems, e.g., no cloning of states), etc. I do see what you're saying and agree that "quantum theory" is best understood as a constraint on theories (though I'd argue its a much, much tighter constraint than, say, "classical theory") especially compared to general relativity. But the general structure of it does make concrete predictions on its own without appealing to any particular realization.

 

[pervect]

Decades have passed since the first idea of General Relativity arose in the mind of einstein. Surely development of the GR must have taken place during these years. May anyone one update me about these development that took place since the late past.oo):w

I can't provide a comprehensive update, (and I don't quite see how it can be an update unless you already know GR as it arose in the mind of EInstein. Which I rather doubt.)

A few points which are not a comprehensive update do come to mind though. We now have a better theoretical understanding of black holes than Einstein did. We have a rather larger number of alternate theories of gravity besides GR as well. Most (and perhaps even all) of these alternate theories of gravity are either equivalent experimentally to GR to the best of our ability to measure with currrent technology, or have been proven false by observation.

I'm not quite sure what you're fishing for here. I'm sure there has been a lot more done than I mentioned, these are a few of the main developments that come to my mind.

 

[aditya ver.2.0]

I can't provide a comprehensive update, (and I don't quite see how it can be an update unless you already know GR as it arose in the mind of EInstein. Which I rather doubt.)

A few points which are not a comprehensive update do come to mind though. We now have a better theoretical understanding of black holes than Einstein did. We have a rather larger number of alternate theories of gravity besides GR as well. Most (and perhaps even all) of these alternate theories of gravity are either equivalent experimentally to GR to the best of our ability to measure with currrent technology, or have been proven false by observation.

I'm not quite sure what you're fishing for here. I'm sure there has been a lot more done than I mentioned, these are a few of the main developments that come to my mind.

Good One