Nobel laureate perspective on the history, status and future of GR

[Chronos]

This paper offers a Nobel laureate perspective on the history, status and future of GR in the astrophysical regime - https://arxiv.org/abs/1609.09781, General Relativity and Cosmology: Unsolved Questions and Future Directions.

 

[Drakkith]

I only had time to read the first 15 pages, but they were a very interesting read. I'll try to read more later. Thanks for posting this, Chronos!

 

[Chalnoth]

This paper offers a Nobel laureate perspective on the history, status and future of GR in the astrophysical regime - https://arxiv.org/abs/1609.09781, General Relativity and Cosmology: Unsolved Questions and Future Directions.

I'm slightly annoyed that they claim that General Relativity can't explain cosmological observations without dark energy, as the cosmological constant has always been a component of the theory.

 

[vanhees71]

Indeed, the cosmological constant is a natural ingredient. Everything not forbidden by the symmetries nature has chosen to realize will happen. The only problem is that (perhaps) we don't know which symmetries these are ;-)).

 

[Chronos]

Not to split hairs, but, the cosmological constant was not a part of the original field equations paper by Einstein in 1915. He added the lambda term [CC] in 1917 because he realized the universe would otherwise be prone to collapse, in contradiction to the prevailing view of a static universe. He withdrew his support for lamda after Hubble discovered the universe was expanding in 1929. While It can be argued lamba technically belonged in the field equations from the beginning as it naturally arises as a constant of integration, the argument is historically inaccurate. Under the assumption that lambda is zero, the point was rendered moot until lambda was resurrected with the discovery of accelerated expansion by Reiss/Permutter in 1998.

 

[MathematicalPhysicist]

Indeed, the cosmological constant is a natural ingredient. Everything not forbidden by the symmetries nature has chosen to realize will happen. The only problem is that (perhaps) we don't know which symmetries these are ;-)).

Why there should be such symmetries?

 

[Chalnoth]

Not to split hairs, but, the cosmological constant was not a part of the original field equations paper by Einstein in 1915. He added the lambda term [CC] in 1917 because he realized the universe would otherwise be prone to collapse, in contradiction to the prevailing view of a static universe. He withdrew his support for lamda after Hubble discovered the universe was expanding in 1929. While It can be argued lamba technically belonged in the field equations from the beginning as it naturally arises as a constant of integration, the argument is historically inaccurate. Under the assumption that lambda is zero, the point was rendered moot until lambda was resurrected with the discovery of accelerated expansion by Reiss/Permutter in 1998.

To me, the history of what people thought of the cosmological constant is far less important than the math itself. It was always just assumed to be zero because its value in dimensionless units would have had to be so incredibly small for any structure in the universe to form.

 

[Chronos]

Why there should be such symmetries?

Feynman summed it up as follows here: http://www.feynmanlectures.caltech.edu/I_52.html "So our problem is to explain where symmetry comes from. Why is nature so nearly symmetrical? No one has any idea why." Humans are naturally gifted in the art of pattern recognition and symmetry is one of those patterns we have recognized in the laws of nature. While it is true that symmetry is essentially nothing more than a human abstraction, we might gain a deeper understanding by exploring the question of 'why not?' as opposed to 'why?' We might ultimately realize the universe cannot evolve into what it is without symmetry.

 

[Chalnoth]

Humans are naturally gifted in the art of pattern recognition and symmetry is one of those patterns we have recognized in the laws of nature.

I think symmetries are a good deal more important and fundamental than that. In particular, due to Noether's Theorem, we know that all conservation laws are a result of symmetries. Furthermore, the electromagnetic, weak, and strong nuclear forces are primarily defined by the symmetries they follow.

As for, "Why these symmetries?" that's a good deal more difficult to answer. Because symmetries are so intertwined with the natural of physical law, this question is essentially equivalent to, "Why these natural laws?" While that question may potentially have an answer, there's a good chance that there will never be any experiments that demonstrate what that answer is.

 

[MathematicalPhysicist]

Feynman summed it up as follows here: http://www.feynmanlectures.caltech.edu/I_52.html "So our problem is to explain where symmetry comes from. Why is nature so nearly symmetrical? No one has any idea why." Humans are naturally gifted in the art of pattern recognition and symmetry is one of those patterns we have recognized in the laws of nature. While it is true that symmetry is essentially nothing more than a human abstraction, we might gain a deeper understanding by exploring the question of 'why not?' as opposed to 'why?' We might ultimately realize the universe cannot evolve into what it is without symmetry.

I wasn't asking about the symmetries we already know of, but of the symmetries we haven't found yet, why should they exist?

 

[Chronos]

And what might those be? You cannot debate the question without posing one.

 

[MathematicalPhysicist]

Well, I quoted @vanhees71

Everything not forbidden by the symmetries nature has chosen to realize will happen. The only problem is that (perhaps) we don't know which symmetries these are ;-)).

If we don't know which symmetries nature has chosen to realize how do we know that it even decided on such symmetries?

 

[Chronos]

Natural constants do not choose symmetries anymore than natural constants choose their values. We must accept some things are simply what they are. It might be useful to explore what might be were things otherwise. I expect the universe will emerge unscatheed.

 

[vanhees71]

Well, I quoted @vanhees71

If we don't know which symmetries nature has chosen to realize how do we know that it even decided on such symmetries?

Well, of course it could be that there are no further symmetries than the already known at all.

 

[houlahound]

Totally above my pay scale but could symmetries have an anthropomorphic basis cos that's just how we see things and how we have assembled the pieces?

 

[MathematicalPhysicist]

Well, of course it could be that there are no further symmetries than the already known at all.

It also depends if we define new physical quantities to measure in the future, they might be invariant or not.

 

[PeterDonis]

of the symmetries we haven't found yet, why should they exist?

If we haven't found them yet, we have no way of answering this question.

If we don't know which symmetries nature has chosen to realize how do we know that it even decided on such symmetries?

We don't.

Well, of course it could be that there are no further symmetries than the already known at all.

Or it could be that there are. In other words, we don't know.

Everyone, please keep the discussion focused on things we can at least potentially test by experiments, and try not to get sidetracked on questions that aren't answerable.

 

[strangerep]

Totally above my pay scale but could symmetries have an anthropomorphic basis cos that's just how we see things and how we have assembled the pieces?

No. Here's one "proof": rotational symmetry, implemented as unitary operators on a Hilbert space, implies that quantum angular momentum comes in half-integral steps. That's crucial to the structure of all matter and fields. Add a little more symmetry details (Poincare + causality) and one gets the Pauli exclusion principle for fermions, without which atomic shell structure would not be what it is (and hence "we" wouldn't exist at all).

 

[Jimster41]

I'm a little confused why the green line in the first diagram isn't a green cone - albeit a super narrow one?

 

[Jimster41]

I'm just trying to clarify my confusion

on pg 10 he writes

"Every other theory introduces auxiliary gravitational fields, or involves prior geometry.
Prior geometry is any aspect of the geometry of spacetime which is fixed immutably, that is, it cannot
be changed by changing the distribution of gravitating sources."

Is is correct to say that Bell pairs depend on the geometry of space-time? My conclusion was that they must - since GR asserts that everything does.
So is there a solution to the GR theory that can support Bell pair correlations? I thought the answer was no. That would have to be a version of GR that supports non-locality. The fact that GR must also support non-locality if it is to fit EPR strikes me as a constraint on GR, or an implied "prior geometry". In other words does EPR imply an auxiliary that is immutable in the sense he states?

Maybe this gets answered later in the paper... I am still reading.

 

[PeterDonis]

is there a solution to the GR theory that can support Bell pair correlations?

GR is a classical theory, not a quantum theory, so this question isn't really well posed; no classical theory can be expected to predict violations of the Bell inequalities.

A better way of phrasing the question I think you are asking is: can a quantum theory which predicts violations of the Bell inequalities be formulated with a dynamic spacetime geometry, i.e., one which depends on the distribution of gravitating sources, which would include the gravitational effects of any quantum objects which are present? Or does such a theory require that the background geometry of spacetime be fixed?

The answer to this question right now is "we don't know". Most discussions of the Bell inequalities use non-relativistic quantum theory, so they don't even address the issue at all. Standard quantum field theory, which does include the effects of relativity, is formulated on a fixed background spacetime (usually Minkowski spacetime although not always, it can be done on a curved background as well). However, most physicists appear to believe that a theory of quantum gravity, if we ever discover one, will remove this restriction and allow the dynamics of the spacetime geometry to be treated using the same quantum framework as everything else. If that turns out to be true, such a theory would not have any "prior geometry". But we don't know (yet) if it will turn out to be true.

 

[Jimster41]

can a quantum theory which predicts violations of the Bell inequalities be formulated with a dynamic spacetime geometry, i.e., one which depends on the distribution of gravitating sources, which would include the gravitational effects of any quantum objects which are present? Or does such a theory require that the background geometry of spacetime be fixed?

I see why that is more precise - QM is not derived from GR (is that what you mean?).

allow the dynamics of the spacetime geometry to be treated using the same quantum framework as everything else.

Does it go too far (logically) to then say that a theory of dynamics of space-time geometry if it supports such a formulation of QM has to support non-locality?

I am wondering here (very vaguely) about fractal geometry and lattice formulations (still reading the paper)

 

[PeterDonis]

QM is not derived from GR (is that what you mean?).

Partly, yes. More generally, GR is not a quantum theory.

Does it go too far (logically) to then say that a theory of dynamic of space-time geometry if it supports such a formulation of QM has to support non-locality?

Any theory that reduces to our current theory of QM in the appropriate limit/approximation would have to support non-locality, since that is a (verified) prediction of our current theory of QM.