- #71
PeterDonis
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RUTA said:That fact alone is used heuristically
This is probably where I see the disconnect.
First, as I think I've said before, I don't think "heuristically" is enough. You can't just assume the effect you want to be there actually is there in a solution that is applicable to a galaxy and our observations of it. You have to show that the effect is there and of the right general order of magnitude. Just assuming it's there because it appears to be there in a different solution is not enough.
Second, the "fact" you are talking about, even in the solution you explicitly examine (collapsing FRW surrounded by Schwarzschild vacuum surrounded by expanding FRW), is not an effect that produces what you are looking for, as you are describing it later in your post. More on that below.
RUTA said:The correction we proposed is simply to replace ##M_L## in the Newtonian acceleration with a corrected value, since the mass of the matter responsible for the acceleration is being measured in two different ways and GR allows for simultaneously differing mass values for one and the same matter
This is simply invalid handwaving. "GR allows for simultaneously differing mass values for one and the same matter" is not a magic wand. It's a specific statement about a specific pair of measurements, and it has a specific effect, and that effect is not what you're looking for.
A correct application of "GR allows for simultaneously differing mass values for one and the same matter" would look like this:
The mass ##M_L##, because it is obtained from observed luminosities, is a sum of "locally measured" masses--masses that would be measured by an observer in the same local region of the galaxy as the stars whose luminosities are being observed. Those are the masses that appear in the mass-luminosity relationships that are being used.
The mass ##M_R##, because it is obtained from observed rotation curves, is a sum of "externally measured" masses--masses that would be measured by an observer in the vacuum region outside the system. (There are some technicalities to this, but I think it's reasonable for the case under consideration.)
GR allows "externally measured" masses to be different from "locally measured" masses for systems like galaxies, because the latter include the effects of gravitational binding energy while the former do not. But that effect, as I've already noted, is in the wrong direction: "locally measured" masses are larger than "externally measured" masses, not smaller. So if the only matter in a galaxy is luminous matter, we would expect a GR correction to make ##M_L > M_R##, which is the opposite of what we need. (Also, the magnitude of this correction is small; it is of rough order of magnitude ##G M / c^2 R##, where ##R## is some appropriate value for the radius of the galaxy. For all galaxies we know of, this correction is a tiny fraction of a percent at best.)
GR also includes spatial curvature, which is not included in the standard Newtonian models of galaxies, but as I've already said, this does not affect either ##M_R## or ##M_L##; it only affects our estimate of average density.
There is no other GR effect I know of that is applicable here. The only other thing you discuss in the paper that seems at all relevant is the claim on p. 5, after equation (7), that observers in the exterior FRW region will somehow measure ##M_p## instead of ##M##; I have already explained why I don't find that claim to be valid. The only thing I would add to that here is that, as far as I can tell, any such effect, if it were valid, would affect how we infer ##M_R## from observations, not how we infer ##M_L##; but you are saying in what I've quoted above that your claimed effect changes how we infer ##M_L##.
RUTA said:We found a functional form for correcting ##M_L## that rivals or beats all competitors across three different astronomical matter distributions -- galactic, galactic cluster, and cosmological
As an empirical finding, this is fine. But it does not support any claim that there is a valid GR correction that will produce such a functional form. I don't see how there can be one, for the reasons given above. And as I've already remarked, and you have agreed, you are not deriving your functional form from any underlying GR equations; you are just assuming it as an ansatz and seeing how it fits the data. So the fact that it fits the data well does not provide any support for the claim that there is in fact a valid GR correction that leads to your ansatz.
So if your functional form turns out to be valid (i.e., if it doesn't turn out to be just another way of representing the effects of dark matter), I think it will be because it is a reasonable approximation to some underlying effect that is not present in GR, but is present in some modified theory (possibly derived from quantum gravity) that includes effects that are not present in GR. (I personally think this is extremely unlikely, but that's just my opinion; once we actually have a working theory of gravity, possibly quantum gravity, that goes beyond GR, we'll see what it says.)