Relative energy of a black hole.

[TrickyDicky]

A counterexample would look like this: "Here's an actual physical observable that the standard EFE/SET method doesn't predict or explain .

Does dark matter qualify?

 

[PeterDonis]

Does dark matter qualify?

No. "Dark matter", from the standpoint of the EFE/SET, is just ordinary "matter" (i.e., it has the same kind of SET as the matter we observe every day) that doesn't interact with anything else non-gravitationally, so we have no way of observing it the way we observe ordinary matter, by EM radiation or any other type of non-gravitational radiation or interaction; the only way we know it's there is indirectly, through its gravitational effects.

I realize that there is an ongoing debate in astronomy as to whether the standard interpretation of observations (like galaxy rotation curves) as signifying the presence of "dark matter" is correct. There are alternate theories that modify the way gravity works (i.e., they are *not* standard GR) in order to account for the observations without postulating dark matter. I am not saying those alternate theories have been proven wrong; they haven't (I consider them all much more unlikely than the standard interpretation, but that's just my opinion). I'm just saying that the observations, by themselves, are not counterexamples to standard GR: standard GR can account for them perfectly well, by just adding the dark matter to the total SET that is being used in the EFE.

I realize also that the above is open to another objection: well, sure, you can make any set of observations compatible with standard GR by [Edit: fixed typo, was "but"] just fiddling with the SET. First of all, that's not quite true; mathematically, it can be done, yes--you can postulate any tensor you like as an "SET", put it on the RHS of the EFE, and solve for the metric it will produce--but the results may not be very reasonable physically (for example, they may violate energy conditions or other constraints that are widely accepted). Dark matter doesn't do that: the dark matter SET, as I said, is just like that of ordinary matter, so it's perfectly reasonable physically.

Second, dark matter fits into the picture in multiple places, not just one; for example, the current "best fit" big bang model requires cold dark matter, in roughly the same proportions ("roughly" because all of these calculations have significant "error bars" at our current level of knowledge) as are required to explain the galaxy rotation curves and other "local" observations. So dark matter is not just being put in ad hoc to fit one piece of data; it has a reasonable place in a comprehensive model, and that comprehensive model uses the standard EFE/SET of GR. (That's one reason, btw, why I think the alternate theories that modify gravity are unlikely to be right; they all monkey with the overall dynamics of the universe in a way that messes up the correspondence with other cosmological observations, so they then have to make other ad hoc assumptions to fix things up. I admit I am not very up to date in this area, so there may be recent developments that I'm not aware of; but that's my understanding of where things stand.)

 

[Q-reeus]

Peter, appreciate that in #105 you have tackled in your own inimitable style the specifics I raised earlier. There is a sense of deja vu to it all. Collectively we have created a a lengthy record of exchange for any looking on to make their minds up from. Guess you can figure what I'm saying. I will end my participation with a slightly edited cut-n-paste from #57 which turned out to be just intermission. End of the show here for me, and I trust no hard feelings between us: From #57:

Peter, thanks for your clarification and with that I agree with [some of] the above. On the broader picture, while I respect you are an accomplished master of GR maths and it's application, sad to say there is no final consensus. Bravo though for putting in a lot of effort in trying to evaporate my scepticism. At the least it has given me a clearer understanding on how this issue is seen by the GR community. Have a nice day.

 

[PeterDonis]

I trust no hard feelings between us.

No hard feelings at all. It was a fun discussion.

 

[TrickyDicky]

No. "Dark matter", from the standpoint of the EFE/SET, is just ordinary "matter" (i.e., it has the same kind of SET as the matter we observe every day) that doesn't interact with anything else non-gravitationally, so we have no way of observing it the way we observe ordinary matter, by EM radiation or any other type of non-gravitational radiation or interaction; the only way we know it's there is indirectly, through its gravitational effects.

I realize that there is an ongoing debate in astronomy as to whether the standard interpretation of observations (like galaxy rotation curves) as signifying the presence of "dark matter" is correct. There are alternate theories that modify the way gravity works (i.e., they are *not* standard GR) in order to account for the observations without postulating dark matter. I am not saying those alternate theories have been proven wrong; they haven't (I consider them all much more unlikely than the standard interpretation, but that's just my opinion). I'm just saying that the observations, by themselves, are not counterexamples to standard GR: standard GR can account for them perfectly well, by just adding the dark matter to the total SET that is being used in the EFE.

I realize also that the above is open to another objection: well, sure, you can make any set of observations compatible with standard GR but just fiddling with the SET. First of all, that's not quite true; mathematically, it can be done, yes--you can postulate any tensor you like as an "SET", put it on the RHS of the EFE, and solve for the metric it will produce--but the results may not be very reasonable physically (for example, they may violate energy conditions or other constraints that are widely accepted). Dark matter doesn't do that: the dark matter SET, as I said, is just like that of ordinary matter, so it's perfectly reasonable physically.

Second, dark matter fits into the picture in multiple places, not just one; for example, the current "best fit" big bang model requires cold dark matter, in roughly the same proportions ("roughly" because all of these calculations have significant "error bars" at our current level of knowledge) as are required to explain the galaxy rotation curves and other "local" observations. So dark matter is not just being put in ad hoc to fit one piece of data; it has a reasonable place in a comprehensive model, and that comprehensive model uses the standard EFE/SET of GR. (That's one reason, btw, why I think the alternate theories that modify gravity are unlikely to be right; they all monkey with the overall dynamics of the universe in a way that messes up the correspondence with other cosmological observations, so they then have to make other ad hoc assumptions to fix things up. I admit I am not very up to date in this area, so there may be recent developments that I'm not aware of; but that's my understanding of where things stand.)

Well explained, of course one has to wonder what kind of observation could serve as counterexample if we are always allowed to postulate some kind of SET source that fits our model but has never been detected or can't be directly observed.

 

[PeterDonis]

of course one has to wonder what kind of observation could serve as counterexample if we are always allowed to postulate some kind of SET source that fits our model but has never been detected or can't be directly observed.

I addressed this in my post (last two paragraphs). (Note: I just fixed a small typo in that post that may have caused confusion.) We are not "always allowed" to postulate whatever SET will match the data; there are other criteria we can use to judge whether the postulated SET is reasonable. Yes, that's a judgment call, but so is every statement about correspondence of theory with experiment.

 

[TrickyDicky]

I addressed this in my post (last two paragraphs). (Note: I just fixed a small typo in that post that may have caused confusion.) We are not "always allowed" to postulate whatever SET will match the data; there are other criteria we can use to judge whether the postulated SET is reasonable. Yes, that's a judgment call, but so is every statement about correspondence of theory with experiment.

Yes, you missed my point I guess, I meant the postulated SET in this case has no correspondence with experiment because no experiment has ever detected it and some claim it might never be.
Actually my questios was no rhetorical, what kind of observation would count as counterexample in your opinion?

 

[PeterDonis]

I meant the postulated SET in this case has no correspondence with experiment because no experiment has ever detected it and some claim it might never be.

It's not true that "no experiment has ever detected it"; the observations of galaxy rotation curves and the dynamics of the universe count as such experiments. A more accurate statement would be "no non-gravitational experiment has ever detected it, and some claim it might never be".

Actually my questios was no rhetorical, what kind of observation would count as counterexample in your opinion?

An observation that doesn't match the predictions of the standard EFE with a physically reasonable SET. Actually, for the cases we've discussed in this thread, the list of physically reasonable SET's is pretty short: perfect fluids just about covers it, with the proviso that the "dark energy" SET, which is a constant times the metric, counts as a "perfect fluid" where the pressure is equal to minus the energy density. For some of the cases (such as the case I gave of two objects that fall together and collide), we would also have to include non-zero kinetic energy and momentum components, and possibly shear stresses. This general category of SETs is used in numerical simulations in GR all the time; for example, the binary pulsar calculations that match up so well with the Hulse-Taylor observations, were done using this kind of SET. The animation of two black holes merging, which Q-reeus mentioned, also ultimately depends on the same kind of SET, since that's what's used to validate the initial form of the metric around each black hole due to the object that collapsed to form it. The rest of the evolution of the merger, AFAIK, follows simply from the vacuum EFE when you have two black holes separated in space.