Insights A Principle Explanation of the “Mysteries” of Modern Physics

[PeterDonis]

The phrase "matter can simultaneously possesses different values of mass when it is responsible for different combined spatiotemporal geometries" doesn't seem correct to me

After further perusal of the paper, I think the choice of words here is misleading. What is being described in the paper is simply the fact that the externally measured mass of a gravitationally bound system in GR is not equal to the "naive" sum of the masses of its constituents--where "naive" sum means we just add up the locally measured masses of the constituents instead of actually doing a proper integral with a proper integration measure that takes the spacetime geometry into account. The difference between the "naive" sum and the externally measured mass of the system as a whole is usually referred to as "gravitational binding energy".

All of that is fine, but the phrase "different combined spatiotemporal geometries" is misleading. There is only one spacetime geometry in any given spacetime in GR. What I called the "locally measured mass" of a constituent of a gravitationally bound system above is the mass that would be measured by an observer co-located with the constituent, in a local inertial frame in which spacetime curvature can be ignored. But the fact that spacetime curvature can be ignored in such a local measurement does not mean it isn't there; the actual spacetime geometry is still curved, and doesn't change when we go from a local measurement on a single constituent to an external measurement of the system as a whole.

I also don't think "contextuality for mass" is an appropriate term in this context. All of the measurements being described are invariants; they don't depend on who is measuring them or what other measurements are being done in combination with them. So I don't see any valid analogy with contextuality in QM.

 

[RUTA]

After further perusal of the paper, I think the choice of words here is misleading. What is being described in the paper is simply the fact that the externally measured mass of a gravitationally bound system in GR is not equal to the "naive" sum of the masses of its constituents--where "naive" sum means we just add up the locally measured masses of the constituents instead of actually doing a proper integral with a proper integration measure that takes the spacetime geometry into account. The difference between the "naive" sum and the externally measured mass of the system as a whole is usually referred to as "gravitational binding energy".

The two different values of mass for one and the same matter are obtained properly using the local metric.

All of that is fine, but the phrase "different combined spatiotemporal geometries" is misleading. There is only one spacetime geometry in any given spacetime in GR.

One solution obtained by combining two other solutions. Standard GR, nothing misleading here.

What I called the "locally measured mass" of a constituent of a gravitationally bound system above is the mass that would be measured by an observer co-located with the constituent, in a local inertial frame in which spacetime curvature can be ignored. But the fact that spacetime curvature can be ignored in such a local measurement does not mean it isn't there; the actual spacetime geometry is still curved, and doesn't change when we go from a local measurement on a single constituent to an external measurement of the system as a whole.

Again the meaning of "mass" in the two solutions is unambiguous and intuitive. In the cosmology part, it is just dust density times co-moving volume. In the Schwarzschild part, it is obtained by rotational dynamics. In both cases, the observers are in inertial frames (following geodesics). Again, standard GR, nothing unusual.

I also don't think "contextuality for mass" is an appropriate term in this context. All of the measurements being described are invariants; they don't depend on who is measuring them or what other measurements are being done in combination with them. So I don't see any valid analogy with contextuality in QM.

Thus, one and the same matter has two different values of mass -- one obtained by inertial observers inside the matter and one obtained by inertial observers in orbit around the matter. This differs from the usual notion of binding energy, e.g., a free neutron has one mass and a bound neutron has another mass. In that case, the mass is different at different times, the context changes temporally. Here the mass is different in different regions of space, it is the same in each spatial region at all times. Either way, the mass of matter is clearly a function of the context, thus the phrase.

There is nothing "crank" about this result, it's not like this idea slipped past referees and editors at different journals. No referee or editor has ever questioned the result or the terminology because it comports with GR.

 

[PeterDonis]

one and the same matter has two different values of mass -- one obtained by inertial observers inside the matter and one obtained by inertial observers in orbit around the matter.

I see what you mean, but I still think your language is misleading. An inertial observer in orbit around an object made of matter is not measuring the "dynamic mass" of individual small pieces of matter in the object; he's mesauring the "dynamic mass" of the whole object. He has no way of separating that into individual pieces.

The inertial observer inside the matter, OTOH, is measuring the "proper mass" of the individual piece of matter with which he is co-located. He cannot directly measure the mass of the whole object. He can only calculate it using observations and assumptions.

This differs from the usual notion of binding energy

In the sense that, in your description, the spacetime is not stationary (since the FRW region cannot be stationary), yes, this is true. However...

e.g., a free neutron has one mass and a bound neutron has another mass.

...this is stated incorrectly, IMO. A correct statement would be that a system containing bound neutrons (such as an atomic nucleus) has a mass that is smaller than the sum of the free masses of its constituents (for example, the mass of a deuteron is less than the mass of a free proton plus the mass of a free neutron). A measurement of the mass of the bound system cannot be separated into a measurement of the "bound mass" of individual constituents: you can't separate the measured mass of a deuteron into "mass of a bound proton" and "mass of a bound neutron".

 

[PeterDonis]

One solution obtained by combining two other solutions.

Just to be clear, you mean that the spacetime in this solution has a region which is Schwarzschild and a region which is FRW, with a boundary between them, correct?

[Edit: This is in reference to the example in ref. 24 in the article.]

 

[RUTA]

Just to be clear, you mean that the spacetime in this solution has a region which is Schwarzschild and a region which is FRW, with a boundary between them, correct?

[Edit: This is in reference to the example in ref. 24 in the article.]

Correct.

In order that the DM fits are compelling, we would need to derive theoretical predictions for the fitting factors currently found empirically (for galactic rotation curves, galactic cluster mass profiles, CMB anisotropies) using contributions from those boundary terms. Again, that's just a simplification, but no one is ever going to solve Einstein's equations for a real galaxy. What we need to do is at least motivate the fitting factors via other measurements (luminosity, temperature, etc.). Then check the theoretical (approximated) predictions for the fitting factors against those obtained empirically. The work done to date was simply to find out whether or not the inverse square law functional form is reasonable (the answer there is clearly affirmative), so we know what we're looking for in the GR formalism. Have you done the fits for these data using MOND, various modified gravity theories, and the different DM models? If so, you'll see that our result is on par with all of those (I did all those and showed the comparisons in our papers). Anyway, finding theoretical predictions for the fitting factors should be possible, but I've been working on other questions in foundations that I find more interesting :-)

What I find more interesting than finishing the "no-DM-GR-is-correct model" is showing how the whole of physics is coherent, contrary to popular belief. And, I found a big piece of that by answering Bub's question, "Why the Tsirelson bound?" So, I've been busy these past two years working on the consequences of that answer.

 

[PeterDonis]

Correct.

Ok. One thing about that example that makes it inappropriate for modeling something like galaxy rotation curves is that the "interior" FRW spacetime region cannot be stationary, whereas to model something like a galaxy, you would need an "interior" spacetime region that was stationary. This would also be true for modeling an individual star in a galaxy, but a stationary model for a star is easy: a spherically symmetric blob of matter in hydrostatic equilibrium with a constant surface area. A galaxy is not a continuous distribution of matter, although a really rough approximation could perhaps model it as such; but a better model would be a system of objects orbiting their common center of mass under their mutual gravity. I don't know how much models of that sort have been constructed in the literature; the only one that I can bring to mind at the moment is the one in a paper by Einstein in the 1930s where he was trying to prove that black holes were impossible (of course he didn't use the term "black hole" since it hadn't been invented yet) by showing that no such stationary system of mutually orbiting objects could have an "areal radius" smaller than $3 G M / c^2$, where $M$ is the externally measured mass of the system. A galaxy of course has a much larger "areal radius" so that wouldn't be an issue for such a model.

 

[PeterDonis]

Have you done the fits for these data using MOND, various modified gravity theories, and the different DM models?

I'm not approaching this from the perspective of trying to do empirical curve fits. Your basic contention is that, if we properly model something like a galaxy using GR instead of a Newtonian approximation, we can explain the discrepancy between the mass inferred from observed galaxy rotation curves and the mass inferred from observed total luminous objects in the galaxy without having to use dark matter. I'm trying to figure out if I agree that some kind of GR model could be constructed that would do that.

You're not exhibiting any such model in the paper; you're just using an ansatz that "looks reasonable" to you and doing empirical curve fitting with it. To me that's backwards. First you would need to construct a GR model--an actual spacetime geometry--that was a viable simplified model for something like a galaxy (i.e., stationary, which, as I have pointed out, the "interior" FRW region in the example you give is not), although obviously it would not be able to capture all the details of a real galaxy. Then you would need to show that this model exhibits the effect you are looking for--that there is a discrepancy between the mass inferred from rotation curves in the model and the mass inferred from observed total luminous objects in the model--and that the size of the effect is of the right rough order of magnitude. Only once you have done that would it be justified, IMO, to extract an ansatz from such a model and use it for empirical curve fitting.

What I'm trying to do for myself is the first two steps I just described: to see if I think there could be a simplified GR model that exhibits the effect in question of the right rough order of magnitude, based on your general description of a difference between "proper mass" and "dynamic mass", but a model whose "interior region" is stationary.

 

[RUTA]

All of these are really good points, Peter, and I agree with them. The place I would look first would be interior solutions for the rotating Kerr solution exterior. I would look at that numerically, since no such interior solutions are know as yet. I would do that exercise to develop a feel for how hydrodynamical cases marry up to vacuum exteriors. Doable, but nontrivial :-)

If you look at what else is being done in this area, you'll see for example the dark matter models are nothing more than searches for functional fitting forms (in that case, a search for the distribution of dark matter). And, as we point out in one of our papers, our ansatz is just as motivated as MOND's. I think modified GR is better theoretically, but even there one can ask, why those particular additions to the Lagrangian? The bottom line is always the same, because they work to fit the data. Of course, if you deviate from GR, then you lose its divergence-free nature, i.e., you violate local conservation laws (which they readily admit). That's why I wanted to find something in GR proper.

 

[PeterDonis]

The place I would look first would be interior solutions for the rotating Kerr solution exterior.

I'm actually starting with something simpler, a Schwarzschild exterior around a spherically symmetric matter distribution. To add angular momentum to the system, which is the primary reason for using a Kerr exterior, it might be sufficient to just add small correction terms to the interior and exterior metric, rather than trying to use the full-blown Kerr exterior metric, which, as you note, is significantly more complicated. That is how, for example, an experiment like Gravity Probe B is analyzed, as I understand it.

However, I'm not actually convinced that it is necessary to add angular momentum to the system, because the effects that doing that would be required to account for, such as the Lense-Thirring precession that Gravity Probe B was testing, are much too small to be what you are looking for. If the effect you are looking for is actually present in a GR model, it should be present in a model in which the angular momentum of the gravitating system overall can be ignored. So a Schwarzschild exterior with a stationary interior matter distribution should be enough.

dark matter models are nothing more than searches for functional fitting forms

Yes, but what is being fitted in that case is simply a distribution for the stress-energy tensor, which is already a free parameter in GR. In other words, the assumption is that the actual stress-energy tensor distribution is different from the one that would be inferred solely from the observed distribution of luminous matter, and the fitting is done to see how much different the actual stress-energy tensor distribution has to be to account for the observed rotation curves, using standard assumptions about the effects of spacetime geometry.

That's not what you're doing; you're assuming that the stress-energy tensor distribution is fixed by the distribution of luminous matter, and proposing that the spacetime geometry created by that stress-energy tensor distribution will have effects that differ from the standard assumptions, and that this effects will include a mismatch between the mass inferred from rotation curves and the mass inferred from the distribution of luminous matter. There are no free parameters to fit in such a model. The "fitting" you are doing is based on assumptions about what effects will be present in such a model, without actually constructing it to see if those assumptions are correct.

if you deviate from GR, then you lose its divergence-free nature, i.e., you violate local conservation laws (which they readily admit). That's why I wanted to find something in GR proper.

I agree that this is a very good reason to want to find a model that works within standard GR.

 

[RUTA]

But, there is a tacit assumption of the DM models that is just as speculative because they have no candidates for what they're placing in the stress-energy tensor. It's easy to wave your hand and say, "Well, someday maybe we'll discover a missing particle." But, the properties that particle would have to possesses are highly dubious. See this article by Sean Carroll.

 

[RUTA]

BTW, Peter, if you'd like another pair of eyes on your paper before submitting it, send me the arXiv link when you get it done. I'm VERY interested in what you find!

 

[PeterDonis]

there is a tacit assumption of the DM models that is just as speculative because they have no candidates for what they're placing in the stress-energy tensor

Yes, that's true. DM models have to assume that there is some non-baryonic kind of matter that will give rise to the stress-energy tensor they need, even though we have not found any such kind of matter in any experiments.

 

[PeterDonis]

if you'd like another pair of eyes on your paper before submitting it, send me the arXiv link when you get it done

I wasn't referring to any potential paper I am working on; I'm not an academic. If I find the time to make any calculations along the lines I was describing, I will post them here.

 

[PeterDonis]

Btw, @RUTA, if you are able, it would be helpful if you could comment on whether the understanding of your papers (refs. 23 and 24 in the Insights article) that I have described in the following thread is correct:

https://www.physicsforums.com/threads/is-there-a-simple-dark-matter-solution-rooted-in-gr.994526/

I ask because it seems to me that one of the papers (ref. 24, the one we have been discussing here) is using standard GR, while the other (ref. 23) is not--it is proposing a model in which the GR assumption of spacetime as a continuous manifold is only an approximation. If I am correct about that, discussion of those two papers should be in separate threads; the thread I linked to above, which is in the Beyond the Standard Model forum, would be appropriate for ref. 23, since it is proposing a model that goes beyond standard GR, but discussion of ref. 24, if it were to go anywhere other than this thread, should properly be in the relativity forum, since that paper is using standard GR.

 

[ohwilleke]

Yes, that's true. DM models have to assume that there is some non-baryonic kind of matter that will give rise to the stress-energy tensor they need, even though we have not found any such kind of matter in any experiments.

Equally important, DM particle model makers are increasingly concluding that they need either a self-interaction force (SIDM) or a 5th force between DM and ordinary matter, to make the distributions of DM inferred fit to the properties of the BSM DM particle. True collisionless cold dark matter, or warm dark matter particle doesn't, produce halos of the shapes observed from observation and doesn't mimic features in the baryonic matter distributions in a galaxy or cluster in the way that is observed.

So, one needs not just a new DM particle, but also a new force mediated by another new dark sector particle.

Once you need a new force anyway, the benefit of a DM particle theory over a modification of an existing force disappears, in terms of an Occam's Razor type analysis.

 

[RUTA]

I wasn't referring to any potential paper I am working on; I'm not an academic. If I find the time to make any calculations along the lines I was describing, I will post them here.

If you do find something that's not suitable for PF (since it's not been properly refereed), please notify me! Let me say specifically what I hope someday to have the time to explore.

The way the momentum-energy content of the matter-occupied region of spacetime affects the geometry of the vacuum region surrounding it is via the coupling between regions as expressed in the extrinsic curvature K on the spatial hypersurface boundary. The goal would be to find the cumulative functional form for nested embeddings, i.e., K1 to K2 to ... . How does the mass M in a vacuum geometry vary from "shell" to "shell" as a function of the K's? You can see why I was considering a Kerr solution, since I don't have hydrodynamic support and I don't want radially expanding or collapsing shells.

 

[PeterDonis]

The way the momentum-energy content of the matter-occupied region of spacetime affects the geometry of the vacuum region surrounding it is via the coupling between regions as expressed in the extrinsic curvature K on the spatial hypersurface boundary.

This is one way of viewing the connection, but not the only one. A drawback of viewing it this way is that the extrinsic curvature you describe depends on how you slice up the spacetime into spacelike slices. In the simple examples you discuss, there is a "preferred" slicing given, roughly speaking, by the "rest frame" of the central body in the asymptotically flat vacuum region. But there won't always be any way to pick out a slicing from any symmetries in the problem.

Also, if we're talking about something like galaxy rotation curves, what we're really interested in is how the stress-energy in the interior region affects the geometry in the interior region. The rotation curves we measure for galaxies are not measurements of objects outside the galaxy orbiting it; they are measurements of objects inside the galaxy, responding to the local spacetime geometry in the galaxy's interior. The geometry in the exterior vacuum region only comes into play to the extent it affects the trajectories of the light rays we see coming from the galaxy, and that effect is going to be small, and is not the kind of effect you're looking for in any case.

I don't have hydrodynamic support and I don't want radially expanding or collapsing shells.

Yes, that's indeed a problem, but it's a problem in the interior region; you need a stationary blob of matter that is not supported by hydrostatic equilibrium. That doesn't necessarily require the exterior region to be Kerr; in principle the total angular momentum of the whole blob could be zero, with various individual pieces of matter in the blob orbiting in different planes so their individual orbital angular momenta end up cancelling. (Or, more realistically, the total overall angular momentum could be very small compared to other parameters, so it could be ignored or approximated by small corrections to the zero total angular momentum case.) But in the interior, of course, each individual piece of matter has to be in a geodesic orbit about the overall center of mass, since there's no other way for the system to be stationary.

 

[RUTA]

I'm referring to the extrinsic curvature because that's the method I used to join solutions (metric on surface and K on surface are equal). It's obvious how that will map to empirical situations, so the invariance is not an issue.

 

[RUTA]

The mass inferred from galactic orbital kinematics (orbital mass) needs to grow with orbital radius faster than the luminous mass of the matter inside the orbital radius (proper mass). That's why I'm thinking about "shells" or "rings" of adjoined solutions. Since we know such adjoined solutions allow for larger orbital mass than proper mass, my intuition tells me that the "extra mass" is encoded in K. So, I'm simply building up those differences in the K's at the boundaries.

 

[RUTA]

I'm not taking about the effect of geometry on the light rays.

 

[PeterDonis]

we know such adjoined solutions allow for larger orbital mass than proper mass

Isn't the difference the opposite? The "orbital mass" is what you are calling "dynamic mass" in the paper, and it is smaller than the "proper mass".

 

[PeterDonis]

I'm not taking about the effect of geometry on the light rays.

Ok, good. I didn't think so, but thanks for confirming.

 

[RUTA]

Isn't the difference the opposite? The "orbital mass" is what you are calling "dynamic mass" in the paper, and it is smaller than the "proper mass".

The orbital mass obtained from galactic rotation curve data is larger than the locally-determined proper mass (obtained from mass-luminosity ratios for example). That's the "missing mass" problem.

 

[PeterDonis]

The orbital mass obtained from galactic rotation curve data is larger than the locally-determined proper mass (obtained from mass-luminosity ratios for example).

I understand what the actual data says. But the statement of yours that I quoted in post #51 does not seem correct as a description of the effect that is present in the model. In the model, "dynamic mass" is smaller than "proper mass", not larger. So if the "dynamic mass" in the model is supposed to correspond to the orbital mass obtained from rotation curve data, and the "proper mass" in the model is supposed to correspond to the mass obtained from luminosity data, then the model is obviously wrong, since the model says "dynamic mass" should be smaller than "proper mass" but the actual data says "dynamic mass" is larger than "proper mass".

So either the model is wrong or I've misunderstood how the "dynamic mass" and "proper mass" in the model are supposed to correspond to the "orbital mass" (from rotation curves) and the "proper mass" (from luminosity) in the data.

 

[RUTA]

I understand what the actual data says. But the statement of yours that I quoted in post #51 does not seem correct as a description of the effect that is present in the model. In the model, "dynamic mass" is smaller than "proper mass", not larger. So if the "dynamic mass" in the model is supposed to correspond to the orbital mass obtained from rotation curve data, and the "proper mass" in the model is supposed to correspond to the mass obtained from luminosity data, then the model is obviously wrong, since the model says "dynamic mass" should be smaller than "proper mass" but the actual data says "dynamic mass" is larger than "proper mass".

So either the model is wrong or I've misunderstood how the "dynamic mass" and "proper mass" in the model are supposed to correspond to the "orbital mass" (from rotation curves) and the "proper mass" (from luminosity) in the data.

I went back and looked at the paper and you're right, we flipped the terms there from what I said above. I was using the term "dynamical mass" as in astronomy where it corresponds to "orbital mass" (the larger mass). In the paper, the term "dynamical mass" corresponds to what we were going to take as the mass obtained from the mass-luminosity relationship, i.e., the "local" value, since that's how one ultimately obtains the ML relationship. Thus, the terms are flipped. See on p. 5 starting with "Suppose that the Schwarzschild vacuum surrounding the FLRW dust ball in our example above is itself surrounded ... ."

 

[PeterDonis]

the terms are flipped. See on p. 5

Yes, I see that part, but I don't think it's correct. On p. 2, the relationship between proper mass and dynamic mass is given by:

$$
dM_p = \left( 1 - \frac{2 G M}{c^2 r} \right)^{- 1/2} dM
$$

where $M_p$ is proper mass and $M$ is dynamic mass. This formula clearly says that proper mass is locally measured and dynamic mass is externally measured, and the text accompanying the formula agrees with that.

However, on p. 5, in the text you refer to, "proper mass" $M_p$ is now claimed to be "globally determined" and to be the mass that would be measured by an observer in the surrounding FRW region. That is inconsistent with the formula and text on p.2, and also with the standard GR treatment of the spacetime geometry the paper is describing.

In the text on p. 5, you are describing a collapsing FRW region, which I'll call the "interior region" (which, to properly model something like a galaxy, should really be a stationary region containing matter, as I have commented before, but making that change would not affect what I am about to say), surrounded by a Schwarzschild vacuum region, surrounded by an expanding FRW region, which I'll call the "exterior universe". The interior region and Schwarzschild vacuum region together I will call the "bubble".

In the Schwarzschild vacuum region, the mass of the interior region, as measured by orbital dynamics of objects in the Schwarzschild vacuum region, is $M$. The text on p. 5 agrees with that.

However, the mass of the interior region as measured by an observer in the exterior universe, will not be $M_p$. An observer in the exterior universe cannot even measure the mass of the interior region directly, using orbital dynamics, because any such orbit will be affected by the stress-energy in the exterior universe that is closer to the bubble than the orbit itself. And if we imagine correcting such a measurement to subtract out the mass in the exterior universe that is affecting the orbit, the remainder will be $M$, not $M_p$.

The simplest way to see this is to observe that the function $m(r)$, which gives the "mass inside radius $r$" ("mass" meaning the mass measured by orbital dynamics) as a function of the areal radius $r$ centered on the bubble, must be continuous, and its value in the Schwarzschild vacuum region is $M$. Call the areal radius of the exterior boundary of the bubble $R_0$. Then we have $m(R_0) = M$. Now consider $m(R_0 + dr)$, the value of $m(r)$ just a little way into the exterior universe. This value, by continuity, must be $M + dM$ for $dM$ infinitesimal. But the paper's claim would require it to be $M_p + dM$, where $M_p - M$ is not infinitesimal. So the paper's claim is inconsistent with continuity of $m(r)$.

 

[RUTA]

Yes, I see that part, but I don't think it's correct. On p. 2, the relationship between proper mass and dynamic mass is given by:

$$
dM_p = \left( 1 - \frac{2 G M}{c^2 r} \right)^{- 1/2} dM
$$

where $M_p$ is proper mass and $M$ is dynamic mass. This formula clearly says that proper mass is locally measured and dynamic mass is externally measured, and the text accompanying the formula agrees with that.

However, on p. 5, in the text you refer to, "proper mass" $M_p$ is now claimed to be "globally determined" and to be the mass that would be measured by an observer in the surrounding FRW region. That is inconsistent with the formula and text on p.2, and also with the standard GR treatment of the spacetime geometry the paper is describing.

In the text on p. 5, you are describing a collapsing FRW region, which I'll call the "interior region" (which, to properly model something like a galaxy, should really be a stationary region containing matter, as I have commented before, but making that change would not affect what I am about to say), surrounded by a Schwarzschild vacuum region, surrounded by an expanding FRW region, which I'll call the "exterior universe". The interior region and Schwarzschild vacuum region together I will call the "bubble".

In the Schwarzschild vacuum region, the mass of the interior region, as measured by orbital dynamics of objects in the Schwarzschild vacuum region, is $M$. The text on p. 5 agrees with that.

However, the mass of the interior region as measured by an observer in the exterior universe, will not be $M_p$. An observer in the exterior universe cannot even measure the mass of the interior region directly, using orbital dynamics, because any such orbit will be affected by the stress-energy in the exterior universe that is closer to the bubble than the orbit itself. And if we imagine correcting such a measurement to subtract out the mass in the exterior universe that is affecting the orbit, the remainder will be $M$, not $M_p$.

The simplest way to see this is to observe that the function $m(r)$, which gives the "mass inside radius $r$" ("mass" meaning the mass measured by orbital dynamics) as a function of the areal radius $r$ centered on the bubble, must be continuous, and its value in the Schwarzschild vacuum region is $M$. Call the areal radius of the exterior boundary of the bubble $R_0$. Then we have $m(R_0) = M$. Now consider $m(R_0 + dr)$, the value of $m(r)$ just a little way into the exterior universe. This value, by continuity, must be $M + dM$ for $dM$ infinitesimal. But the paper's claim would require it to be $M_p + dM$, where $M_p - M$ is not infinitesimal. So the paper's claim is inconsistent with continuity of $m(r)$.

Sorry for the delay, I'm working on another paper now, let me get back to you with my thinking on this :-)

 

[Jimster41]

Correct.

In order that the DM fits are compelling, we would need to derive theoretical predictions for the fitting factors currently found empirically (for galactic rotation curves, galactic cluster mass profiles, CMB anisotropies) using contributions from those boundary terms. Again, that's just a simplification, but no one is ever going to solve Einstein's equations for a real galaxy. What we need to do is at least motivate the fitting factors via other measurements (luminosity, temperature, etc.). Then check the theoretical (approximated) predictions for the fitting factors against those obtained empirically. The work done to date was simply to find out whether or not the inverse square law functional form is reasonable (the answer there is clearly affirmative), so we know what we're looking for in the GR formalism. Have you done the fits for these data using MOND, various modified gravity theories, and the different DM models? If so, you'll see that our result is on par with all of those (I did all those and showed the comparisons in our papers). Anyway, finding theoretical predictions for the fitting factors should be possible, but I've been working on other questions in foundations that I find more interesting :-)

What I find more interesting than finishing the "no-DM-GR-is-correct model" is showing how the whole of physics is coherent, contrary to popular belief. And, I found a big piece of that by answering Bub's question, "Why the Tsirelson bound?" So, I've been busy these past two years working on the consequences of that answer.

So this T bound says there is some cutoff that makes the classical world have zero QM (neutral monistic) magic (no long-distance-large-object/ensemble-non-local ...ness), is that roughly right?

Is it related to “decoherence” which I sort of interpret as the Gaussian noise canceling effect of Lots of long distance large object/ensemble non-localness - which seems plausible but statistical and therefore unsatisfying (FYI that was a joke)... or is it somehow a clean unavoidable deduction?

And if it seemingly analytic and clean could that be due to the fact all Alice and Bob cases are toys (I.e they pretend there are these bounds on the lab to begin with)? Alternatively could it be that there are something more like Tsirelson “gaps” or troughs (waves) recurrence etc?

I know that’s a lot of question, so, just say I’m looking forward to learning about that one. Also, to me it bears on the discussion you and Peter were having about observes “inside the mass” vs “orbiting the mass”

 

[RUTA]

Here is the paper I was working on "Einstein's missed opportunity to rid us of 'spooky actions at a distance'". I'm posting the link here since it's relevant to this Insight. Hopefully I can get back to the pending questions above tomorrow.

 

[RUTA]

So this T bound says there is some cutoff that makes the classical world have zero QM (neutral monistic) magic (no long-distance-large-object/ensemble-non-local ...ness), is that roughly right?

Is it related to “decoherence” which I sort of interpret as the Gaussian noise canceling effect of Lots of long distance large object/ensemble non-localness - which seems plausible but statistical and therefore unsatisfying (FYI that was a joke)... or is it somehow a clean unavoidable deduction?

And if it seemingly analytic and clean could that be due to the fact all Alice and Bob cases are toys (I.e they pretend there are these bounds on the lab to begin with)? Alternatively could it be that there are something more like Tsirelson “gaps” or troughs (waves) recurrence etc?

I know that’s a lot of question, so, just say I’m looking forward to learning about that one. Also, to me it bears on the discussion you and Peter were having about observes “inside the mass” vs “orbiting the mass”

The Tsirelson bound is the most QM can violate the Bell inequality known as the CHSH inequality. Classical physics says the CHSH quantity must reside between $\pm 2$, but the Bell states give $\pm 2 \sqrt{2}$ (the Tsirelson bound). Superquantum correlations respect no-superluminal-signaling and give a CHSH quantity of 4. So, quantum information theorists want to know "Why the Tsirelson bound?" That is, why doesn't Nature produce superquantum correlations? Our answer is "conservation per NPRF." Of classical, QM, and superquantum, only QM satisfies this constraint.