Timeline for May the gravitational constant $G$ be a *functional* of all fields on spacetime?
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20 events
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| Jul 22, 2017 at 12:31 | history | edited | Cham | CC BY-SA 3.0 |
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| Jul 18, 2017 at 20:57 | comment | added | Cham | @BenCrowell, I don't think there's a problem with the equ. principle, even if $G$ depends on the metric or curvature, because you still can find locally a reference frame in which the metric is the Minkowski metric, and the partial derivatives of $g$ (or the conection) are 0, wathever what value is $G$. This is the true meaning of the qu. principle. You still can eliminate gravity localy. $G$ has nothing to do with this, if it's a constant. My idea doesn't change anything here. | |
| Jul 18, 2017 at 16:47 | comment | added | user4552 | In what aspect there's a problem with the equivalence principle ? Does g in the action has a problem with the equ. principle ? Yes. One way of stating the equivalence principle is simply that only curvature (2nd derivatives of the metric) is observable, not the metric or its 1st derivative. The 1st derivative of the metric is basically the gravitational field, which you obviously can't detect according to the e.p. The metric itself is basically the gravitational potential, and there are even more obvious reasons why a potential is not directly detectable. | |
| Jul 18, 2017 at 13:22 | answer | added | Alex Nelson | timeline score: 1 | |
| Jul 18, 2017 at 12:23 | comment | added | Cham | I agree the time correlation may feel weird. It would be better if it was total energy instead : $G = G(E)$. Is there a way to define invariant topological constants from the metric and fields on the space section only ? | |
| Jul 18, 2017 at 3:02 | comment | added | Bob Bee | Anyway, Isn't your proposal a proposal for a pet theory? I think those are excluded from this site. | |
| Jul 18, 2017 at 3:01 | comment | added | Bob Bee | It's not only no local in space, it is also acausal in time. The metric in a future 'cosmological' time would affect today's G. The present would be affected by the future. And how does it know? There are theories of G being a field, but teventhough those can be written to preserve causality they still have a hard time jiving with observations. And yes, I can see why pseudo Machian, G depends on spacetime, and the extra scalar field. But it doesn't help any. | |
| Jul 18, 2017 at 0:26 | history | edited | Cham | CC BY-SA 3.0 |
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| Jul 18, 2017 at 0:01 | comment | added | Cham | @BenCrowell, yes $g$ refer to the metric. In what aspect there's a problem with the equivalence principle ? Does $g$ in the action has a problem with the equ. principle ? And $\phi$ (from $G$) can't be absorbed into $T$ because $G[g, \phi]$ is a functional (not a function) of $g$ and $\phi$ (like in the action $S[g, \phi]$). Again, the idea is that $G$ is not a function of $x$ via the fields, it's a global constant defined from the fields over all of spacetime. | |
| Jul 17, 2017 at 20:05 | comment | added | user4552 | Is the notation $g$ supposed to refer to the metric? If so, then you have a problem with the equivalence principle. Is $\phi$ referring to matter fields? If so, then why can't this just be absorbed into $T$? | |
| Jul 17, 2017 at 19:17 | comment | added | Cham | I agree it's highly non-local, but since $G$ is still just a constant, we could in principle solve for any $G$, then compute it after we know the dynamics of the fields. This is viable only for analytical solutions, I guess (like the Schwarzschild solution), which is pretty limited. This non-locality would be essentially the same for any machian theory. Or maybe it's viable for successive approximations, if we already know the functional dependance of $G$. | |
| Jul 17, 2017 at 18:48 | comment | added | Alex Nelson | As per arguments against this, it's horribly nonlocal... | |
| Jul 17, 2017 at 18:35 | history | edited | Cham | CC BY-SA 3.0 |
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| Jul 17, 2017 at 18:35 | comment | added | Alex Nelson | Doesn't condensed matter physics do stuff like this, introduce a new matter field $\phi$, then pretend $\langle\phi\rangle$ is a coupling constant of some sort? | |
| Jul 17, 2017 at 18:13 | history | edited | Cham | CC BY-SA 3.0 |
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| Jul 17, 2017 at 18:02 | history | edited | Cham | CC BY-SA 3.0 |
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| Jul 17, 2017 at 17:58 | comment | added | Cham | And what about the possibility that our problems with dark matter - which happens at some large scale - may be explained by a different $G$ at that scale ? | |
| Jul 17, 2017 at 17:54 | history | edited | Cham | CC BY-SA 3.0 |
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| Jul 17, 2017 at 17:44 | history | edited | Cham | CC BY-SA 3.0 |
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| Jul 17, 2017 at 17:34 | history | asked | Cham | CC BY-SA 3.0 |