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

[RUTA]

All undergraduate physics majors are shown how the counterintuitive aspects (“mysteries”) of time dilation and length contraction in special relativity (SR) follow from the light postulate, i.e., that everyone measures the same value for the speed of light c, regardless of their motion relative to the source (see this Insight, for example). And, we can understand the light postulate to follow from the principle of relativity, sometimes referred to as “no preferred reference frame” (NPRF). Simply put, if the speed of light from a source was only equal to $c=\frac{1}{\sqrt{\epsilon_o \mu_o}}$ (per Maxwell’s equations) for one particular velocity relative to the source, that would certainly constitute a preferred reference frame. Borrowing from Einstein [1], NPRF might be stated (see this...

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[Jimster41]

I enjoyed this, esp the image of other universal constants working the same as c.

it seems like a chicken and egg problem a little (QM superselection rules and NPRF physical constants) but at least they are both chickens.

 

[RUTA]

I enjoyed this, esp the image of other universal constants working the same as c.

it seems like a chicken and egg problem a little (QM superselection rules and NPRF physical constants) but at least they are both chickens.

Thnx. Would you mind expanding on that second comment for me? A referee said something similar, so I'm curious what exactly brought that to mind

 

[Jimster41]

Which comes first, the partition that provides the correct equivalence relation on average for (c,h,G, b?) or the equivalence relation that dictates partition?

 

[RUTA]

Which comes first, the partition that provides the correct equivalence relation on average for (c,h,G, b?) or the equivalence relation that dictates partition?

Which is the superselection rule as you see it?

 

[Jimster41]

I’m going to go with “partition”, and venture even further... that is what physical chemistry sort of is.

 

[RUTA]

I’m going to go with “partition”, and venture even further... that is what physical chemistry sort of is.

Let's look at SR. Here is the explanatory hierarchy as we present it in our paper:

NPRF --> everyone measures c --> time dilation and length contraction --> relativity of simultaneity (different partitions of spacetime).

So, NPRF is not the equivalence relation, but it is the ultimate basis for our equivalence relation, which is strictly speaking the synchronized proper time of the comoving observers for either Alice or Bob (or ... ). Here we have NPRF/equivalence relation leading to the partition. Now let's flip it:

Relativity of simultaneity --> time dilation and length contraction --> everyone measures c --> NPRF.

For QM we have:

NPRF --> everyone measures h --> average-only conservation and Bell state correlations --> relativity of data partition (different partitions of Bell state data).

Again, NPRF isn't the equivalence relation, but it is the ultimate basis for it. Now let's flip it:

Relativity of data partition --> average-only conservation and Bell state correlations --> everyone measures h --> NPRF.

If you go with the equivalence relation as fundamental, you have one and the same rule leading to two different consequences. If you go the other way, you have two different rules with the exact same consequence. I think physicists would prefer the former, since they tend to be reductionists (explain more and more with less and less" per Weinberg). The other way makes NPRF look like an amazing coincidence.

 

[Jimster41]

hmm. I sort of read the table in the article up and down and that's why "at least both are chickens" aha. And I guess I see NPRF as exactly that pretty neat coincidence between relativity of simultaneity and the discrete partitioning of information for Bell observers in different frames.

to me these sound like accurate historical accounts of "what happened"

Relativity of simultaneity --> time dilation and length contraction --> everyone measures c --> NPRF.

Relativity of data partition --> average-only conservation and Bell state correlations --> everyone measures h --> NPRF.

So, I guess I see NPRF as a statement of "connected fact" rather than pejorative "amazing coincidence".

 

[RUTA]

hmm. I sort of read the table in the article up and down and that's why "at least both are chickens" aha. And I guess I see NPRF as exactly that pretty neat coincidence between relativity of simultaneity and the discrete partitioning of information for Bell observers in different frames.

to me these sound like accurate historical accounts of "what happened"

So, I guess I see NPRF as a statement of "connected fact" rather than pejorative "amazing coincidence".

That could be true

 

[Jimster41]

Actually, I prefer

“Time dilation and length contraction --> Relativity of simultaneity -->everyone measures c --> NPRF.”

“Average-only conservation and Bell state correlations --> Relativity of data partition --> everyone measures h --> NPRF.”

 

[RUTA]

I bought and am reading the book you recommended, "Universal Constants in Physics". Thnx for pointing that out, Jimster41.

 

[Jimster41]

And I just bought your book (Kindle) for morning coffee.

 

[ohwilleke]

I've started a thread in the BSM forum zeroing in only on the subtopic of a discussion of references [23] and [24] in the Insights article. https://www.physicsforums.com/threads/explaining-dark-matter-and-dark-energy-with-minor-tweaks-to-gr.994343/

 

[PeterDonis]

I've started a thread in the BSM forum zeroing in only on the subtopic of a discussion of references [23] and [24] in the Insights article. https://www.physicsforums.com/threads/explaining-dark-matter-and-dark-energy-with-minor-tweaks-to-gr.994343/

Moderator's note: That thread has been put in moderation for review. On an initial look, it is much too long and much too broad for a single thread discussion; a single thread discussion should be focused on one particular reference, and ideally on one particular question raised by that reference.

Also, that thread is asking for people's "gut check" opinions, which is off topic and doesn't lead to fruitful discussion.

 

[PeterDonis]

relativity of simultaneity (different partitions of spacetime)

Relativity does not partition spacetime into two regions with respect to a particular event. It partitions spacetime into three regions: the past light cone, the future light cone, and the spacelike separated region. This partitioning, for any given event, is invariant.

It seems to me that the above fact should be taken into account in any attempt to provide an explanation.

 

[Jimster41]

I only just started chapter two of the book. The chapter is titled “Block Universe from Special Relativity” looking forward to it. My gut reaction to your comments above (FWIW):

There is only ever Alice and Bob.
And
Invariant except for differential aging
(I get that both measure the same second... and yet their seconds aren’t the same)

the first thought leaves me wishing I had a clearer picture of some of the more complicated Bell experiments... ones with more than two detectors etc. What does the math even look like when you are trying to simultaneously resolve three of Schrodinger’s cats? I’m guessing it has to be done pair-wise?

 

[RUTA]

Relativity does not partition spacetime into two regions with respect to a particular event. It partitions spacetime into three regions: the past light cone, the future light cone, and the spacelike separated region. This partitioning, for any given event, is invariant.

It seems to me that the above fact should be taken into account in any attempt to provide an explanation.

That is a different partition altogether. I'm talking about partitions per surfaces of simultaneity for any given observer. The partition I'm talking about is therefore observer dependent, which is key to the entire explanation.

 

[PeterDonis]

I'm talking about partitions per surfaces of simultaneity for any given observer.

Yes, I know that.

The partition I'm talking about is therefore observer dependent

No, it's coordinate dependent. Which means that, according to the standard way that GR is interpreted, it has no physical meaning, since only invariants have physical meaning.

 

[RUTA]

No, it's coordinate dependent. Which means that, according to the standard way that GR is interpreted, it has no physical meaning, since only invariants have physical meaning.

The coordinates are associated with the observer here and they certainly do have physical meaning for the observer, they represent what that observer will measure.

 

[PeterDonis]

The coordinates are associated with the observer here

But there's no unique way of doing that. In SR, if the observer is inertial forever, there is at least a coordinate chart that is picked out by the observer's state of motion--but in our real universe spacetime is not flat and no observer is ever inertial forever.

they certainly do have physical meaning for the observer, they represent what that observer will measure.

Only on the observer's worldline. The coordinates picked by an observer on Earth don't represent what the observer directly measures in the Andromeda galaxy since the observer can't directly measure anything there.

 

[RUTA]

But there's no unique way of doing that. In SR, if the observer is inertial forever, there is at least a coordinate chart that is picked out by the observer's state of motion--but in our real universe spacetime is not flat and no observer is ever inertial forever.

Only on the observer's worldline. The coordinates picked by an observer on Earth don't represent what the observer directly measures in the Andromeda galaxy since the observer can't directly measure anything there.

We rarely have to worry about GR corrections. And we do use distant coordinates all the time in making measurements, e.g., probes around distant planets.

 

[PeterDonis]

We rarely have to worry about GR corrections.

Perhaps in a practical sense this is true for many problem domains. But you are talking about foundations. For foundations, the fact that GR is more accurate than SR is critical.

we do use distant coordinates all the time in making measurements, e.g., probes around distant planets

We use coordinates to describe the results of measurements. We do not use coordinates to make measurements. Measurement results are invariants. Coordinate values are not.

 

[RUTA]

Perhaps in a practical sense this is true for many problem domains. But you are talking about foundations. For foundations, the fact that GR is more accurate than SR is critical.

We use coordinates to describe the results of measurements. We do not use coordinates to make measurements. Measurement results are invariants. Coordinate values are not.

The comparison I'm talking about is the relativity principle of SR as applied to c with its application in QM to h. The theoretical structure of GR in no way undermines that relationship and does not add anything to the analysis. The coordinate values can (and usually do) correspond to or directly relate to measured values, e.g., SG magnet angles. The point of a coordinate system is, as the name states, to "coordinate."

 

[PeterDonis]

The theoretical structure of GR in no way undermines that relationship and does not add anything to the analysis.

To me, that's because your analysis is limited in scope, which, as I said, doesn't seem viable if you are talking about foundations. For example, your analysis doesn't cover gravity.

 

[RUTA]

To me, that's because your analysis is limited in scope, which, as I said, doesn't seem viable if you are talking about foundations. For example, your analysis doesn't cover gravity.

The relationship between SR and QM that we point out is valid, so de facto it is independent of gravity. Indeed, the principle relating them (relativity principle) and dd = 0 hold across all theories of physics, Newtonian and modern. Thus, it is clear that we don't need a theory of everything to do foundations of physics.

 

[PeterDonis]

The relationship between SR and QM that we point out is valid, so de facto it is independent of gravity.

You can't possibly know this without a theory of quantum gravity that has been experimentally confirmed. All you can know without that is that the relationship is valid under conditions where gravity can be ignored.

we don't need a theory of everything to do foundations of physics.

As long as your definition of "foundations of physics" is ok with the fact that claims based on theories that are known to have a limited domain of validity cannot be asserted as valid outside that domain.

 

[RUTA]

You can't possibly know this without a theory of quantum gravity. All you can know without that is that the relationship is valid under conditions where gravity can be ignored.

Not as long as your definition of "foundations of physics" is ok with the fact that claims based on theories that are known to have a limited domain of validity cannot be asserted as valid outside that domain.

We can possibly know what is shown deductively in the paper. It's not a matter of opinion, we are stating mathematical and empirical facts. Now, it may be the case that what we are observing and describing mathematically in current experimental situations does not extrapolate to other experimental situations. But, that's the point of physics -- to articulate empirically discovered principles/laws/regularities/constraints, extrapolate them theoretically, and test the extrapolations. What we point out in https://www.mdpi.com/1099-4300/22/5/551/pdf is that dd = 0 and the relativity principle that held for Newtonian physics and E&M are still holding in modern physics. We then outline how one might extrapolate to theories of quantum gravity based on those principles. That's one way to use foundations of physics.

 

[PeterDonis]

We then outline how one might extrapolate to theories of quantum gravity based on those principles.

Ok, I need to read that part of the Insight more carefully. 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, but perhaps I'm misunderstanding what it's intended to mean.

 

[ohwilleke]

References [23] and [24] make some very bold claims (namely that dark energy and dark matter are chimeras of improper application of GR thus explaining the CMB, galaxy rotation curves, clusters, and dark energy phenomena). Are there any other groups that have concurred in that conclusion?

 

[RUTA]

References [23] and [24] make some very bold claims (namely that dark energy and dark matter are chimeras of improper application of GR thus explaining the CMB, galaxy rotation curves, clusters, and dark energy phenomena). Are there any other groups that have concurred in that conclusion?

There are lots of other fits, we share some in those papers. No one has anything compelling at this point. I’d like to get back and develop the physics, but I’ve been too busy working on foundations stuff

 

[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.