I think the time has come for another update on wide binaries. These were intensely debated at the conference in St. Andrews, with opposing camps saying they did or did not show MONDian behavior. Two papers by independent authors have recently been refereed and published: Chae (2023) in the Astrophysical Journal and Hernandez (2023) in Monthly Notices. These papers both find evidence for MONDian behavior in wide binaries.
If these new results are correct, they are the smoking gun for MOND. I’ve been trying to avoid that phrase, and think of how we would explain this with dark matter. I haven’t come up with any good ideas. This doesn’t preclude others from coming up with bad ideas, but the problem this result poses is profound.
The basic idea is that galaxies reside in dark matter halos. These are diffuse entities with a particular mass distribution that must contribute the right gravitational force to explain observations on galactic scales. On local scales, like the solar neighborhood, this leads to a very low space density of about 0.007 solar masses per cubic parsec, or 0.26 GeV/cm3. For comparison, the local density of stars and gas is about 0.11 solar masses per cubic parsec. Adding up all the dark matter in the solar system within the orbit of Pluto amounts to the equivalent mass of a one km-size asteroid. That doesn’t do anything noticeable to solar system dynamics, especially when it is spread out as expected rather than concentrated in an asteroid.
Wide binaries should encompass more dark matter than the solar system by virtue of their greater size, but the enclosed mass remains too tiny to affect the orbits of the stars. There could be the occasional lump of dark matter, but those should be few and far between: the conventional expectation for binary stars is purely Newtonian, with no hint of a mass discrepancy. In contrast, the expectation in MOND is that every system that experiences the low acceleration regime should show a discrepancy of predictable amplitude. I simply don’t see how to imitate that with any of the usual dark matter suspects.
Here is the results from Chae’s paper. There are many figures like this that explore all sorts of permutations on sample selection and other effects. The answer persistently comes up the same. There is a systematic deviation from Newtonian behavior that is consistent with MOND, and in particular with the nonlinear theory AQUAL proposed early on by Bekenstein & Milgrom.
This figure subsumes many astronomical details, like the distribution of orbital eccentricities and the frequency of triple systems. Chae has simulated what to expect as a result of all these effects, with the results in the top panel distinguishing between the Newtonian expectation in blue and the data in red. At high accelerations, the red histogram is right on top of the blue histogram. These distributions are indistinguishable, as they should be in both theories. As one looks to lower accelerations, the red and blue histograms begin to part. They stand clearly apart in the lowest acceleration bin. This is as expected in MOND. In contrast, the histograms should never diverge in the Newtonian case, with or without dark matter.
A similar result has been obtained by Hernandez (2023), who emphasizes the importance of obtaining a clean sample for which one is sure that the binaries are genuinely bound and have radial velocities as well as proper motions. The data follow the Newtonian line until they don’t. The deviation is consistent with MOND.
Again, there are many figures like this in the paper to explore all the possible permutations. These all paint the same picture: MOND. The published result Hernandez obtains is consistent with the result obtained by Chae, relieving a small tension that was present in the preprint stage.
Still outstanding is why Chae and Hernandez get a different answer from Pittordis & Sutherland (2023), who utilize many more binaries. This is a tradeoff that frequently arises in astronomical data analysis: numbers vs. quality. The risk with numbers is that the signal you’re searching for gets drowned out in a sea of noise. The risk in defining a high quality sample is that you unintentionally introduce a selection effect that causes a signal to appear where there isn’t one. It seems unlikely that this would result in MOND-like behavior – it could do any number of crazy things – but I don’t know enough about this specific subject to judge. Note that I’m willing to say when I’m out of my expertise; I expect it won’t be hard to find faux experts who don’t acknowledge the limitations of their qualifications and are perfectly happy to find flaws with studies they dislike but don’t understand.
What I hope to see in future is some convergence between the different groups, or at least for some understanding to emerge as to why their results differ. In the meantime, I expect most of the community will duck and cover.
Triton Station 
Very nice blog post.
It sounds like MOND is getting one more powerful argument….
Duck and Cover:
I went to the Oppenheimer movie with my younger son.
It was too loud for me. I should have put on the noise-canceling headphones.
But the historical details were well reflected.
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There’s been some coverage of wide binaries in the scientific and mainstream media:
https://www.vice.com/en/article/ak3jwb/unbelievable-astronomer-claims-direct-evidence-of-gravity-breaking-down
https://www.popularmechanics.com/space/deep-space/a44776417/study-contradicts-newton-einstein-theory-gravity/
https://thenextweb.com/news/einstein-newton-gravity-gaia-telescope-space
https://interestingengineering.com/science/new-study-challenges-einstein-and-newtons-theories-of-gravity
https://physicsworld.com/a/binary-star-study-favours-modified-gravity-over-dark-matter/
https://phys.org/news/2023-08-smoking-gun-evidence-gravity-gaia-wide.html
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That’s good. I am not a fan of science by press release, but that seems to be necessary to get the attention of scientists these days. (I’m old enough to remember when scientists read their own journals without needing such prompting.)
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“old enough to remember…”
And, I am old enough to remember when actual researchers wrote the articles which had appeared in Scientific American outlining their research for a more general audience.
With all due respect for concientious science writers who try to get “the science” right, much science writing devolves to an unquestioning science promotion.
“Coolness” overshadows “correctness.”
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Not a word in Quanta Magazine, while another preprint appearing roughly the same week about Dark Matter gets some big coverage. Lots of nice astronomer pictures. Ah, well, nobody is perfect.
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Thanks for collecting the data and presenting it easily understandable!
Great to see MOND confirmed. Which kind of MOND, we might see someday. I’m wondering if the scatter of points comes from accuracy problems or from something deeper. In any case the data show clear deviations towards MOND on average exactly where it should show this, which certainly means it’s worth it to get a closer look at MOND.
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The scatter is expected and inevitable from the unknown distribution of orbital eccentricities and viewing angles wrt the orbital plane. Chae’s paper has a nice illustration of this.
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Would a confirmation of a MOND-like theory mean, to question General Relativity?
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The MOND-like theories under the most serious consideration are all relativistic. But if you mean ‘exactly GR’ then yes, any modified gravity theory is a challenger to that by definition.
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Thanks for your reply. What I mean is the curvature of space-time, which causes gravity in GR. I thought it would be verified by the discovery of gravitational waves, as the ´last puzzle-piece´. Would it come on the test bench again, if MOND is the solution?
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There are many theories with gravitational waves that are not precisely GR, e.g., AeST: https://arxiv.org/abs/2109.13287
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I would be interested in how far MOND-variations of GR affect the gravitational lensing of light compared to standard GR. This is typically used as a means to detect/measure DM and referenced as ‘proof’ for DM. Is there also some enhanced lensing as with additinal (dark) matter? If there is some non-standard lensing, would it show specific dynamics?
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The binary data come close to constituting what Karl Popper called a “crucial experiment”: an experiment that confirms a novel prediction of one theory (MOND) while at the same time refuting the competing theory (dark matter+GR).
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Indeed. Wouldn’t be the first time.
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Excellent evidence! Would be great to get a breakthrough on the next problem, which is presumably the need for cosmological DM.
Is getting the 3rd peak right really something that a MOND-based theory needs to do, i.e. apparently AQUAL may not do it right?
If there is another explanation for it, that would really make things interesting.
Anyone familiar with the study below about “angular correlations on causally-coherent inflationary horizons”? Are they reproducing the CMB spectrum based on an evolving causality structure? I got a little lost trying to follow, but it is coming out of the University of Chicago.
https://iopscience.iop.org/article/10.1088/1361-6382/ace608
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The third peak does appear to require some form of cosmic dust. This is a technical term in cosmology for pressureless gravitating mass, and has nothing to do with interstellar dust. CDM is one possible form of cosmic dust, but other things are possible, like the “ghost condensate” in AeST. This just seems like dark matter by a different name, but the theory at least produces MOND effects.
Of course, it could be something we don’t understand at all.
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As much as this is a smoking gun, I’m afraid it just won’t matter. The truth is we’re doomed to suffer through an entire generation or two of Axion experiments with null results before the majority begins to suspect something is awry. Even if we explore the entire possible parameter space of masses, people like Ethan Siegel will just fall back on some dark sector particle that’s undetectable even in principle, just so they can’t be proven wrong.
I’ve lost all faith that there’s a way out of this mess.
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Yes, I share that feeling. If it’s not WIMPs, it’s axions. If not axions, we can make something else up, ad naseum. That’s why I wrote https://tritonstation.com/2023/01/05/question-of-the-year-and-a-challenge/ – they can’t legitimately claim to be doing science if they can’t identify a way out, i.e., a test that would tell us we’ve been barking up the wrong tree with dark matter. As you note, we’re very far from that ideal. The notion of falsifiability doesn’t darken the imaginations of most people who are building dark matter models, much as they labor in apparent ignorance of what those models need to explain – https://tritonstation.com/2023/08/17/required-dark-matter-properties/
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For me, two things are important:
Selecting a good sample has the risk of introducing a systematic error. But why should such a systematic error reproduce MOND! (Stacy in this Blogpost)
Suppose someone loves dark matter above all. Even then, dark matter theories in disk galaxies must reproduce MOND. (Stacy in this Blog) I don’t get the impression that the PBS influencer is aware of this.
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Nope. Most scientists fail top grasp this. Which is kinda weird; when I published the mass discrepancy relation in 2004 the reaction was that it couldn’t be true, since it obviously conflicted with the dark matter picture. Since then people seem to have learned to ignore the obvious, a la the Emperor’s New Clothes.
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Stacy
do you plan to publish a paper on Wide Binary Results since Banks rules it out
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I do not plan to publish a paper on wide binaries as its not a topic I feel I can add meaningfully to.
I presume by Banks you mean Banik. Yes, he has said that; I linked to one of the talks in which he said that in a previous post. People say (and publish!) a lot of things that turn out to be incorrect. I have yet to see a paper from him on the topic, so I can’t judge in the way I can attempt to do for the refereed publications discussed here. So I find the framing of your question strange. Chae and Hernandez have already published the papers you seem to be asking me to write.
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I presume by Banks you mean Banik.
yes I was thinking specifically a paper on Banik vs Chae and Hernandez, with your own conclusions
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Meanwhile the dark matter aficionados are trying to save the phenomenon by looking for structure in the putative dark matter haloes: https://www.quantamagazine.org/in-a-monster-stars-light-a-hint-of-darkness-20230829/
With observing time on JWST being so precious, it is sad to see it being used for something that looks like a wild-goose chase.
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They’re just using data from public surveys, so no JWST time was harmed in enabling this work. This is a great example of when physicists perch on the wrong peak of the Dunning-Kruger curve. There is a vibrant field concerning the formation of stars, and a sub-field of that dedicated to the formation of the first stars. The work that you refer to is what happens when a particle physicist starts by thinking in terms of dark matter halos, and imagines in a simple-minded way that a whole bunch of baryons therein collapse to form a single object – not a galaxy, but a single massive star – without bothering to check that others have considered this collapse and simulated the heck out of it and find that chunks always fragment because it is never as simple as one isolated DM halo forming one single star at its very center.
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Dark matter has low density within the wide binary range. Only this is not the point. Wide binaries are surrounded by halo of normal matter of normal galaxy. This normal matter will act similarly for wide binaries as hypothetical dark matter would do for galaxy according to the official understanding.
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Yes, the density of normal matter is greater than that of dark matter in the solar neighborhood, but no, the analogy you’re making does not work. There has to be mass interior to the orbit of the binaries for it to have the desired effect. If there was that much normal mass enclosed, it wouldn’t be a binary. It’d be a trinary or a whole star cluster or a gas cloud with stars in it, depending on what the normal matter was.
In MOND, the surrounding matter is important; this is what gives the external field effect. That arises through the nonlinearity of MOND and is not a think in Newtonian mechanics, which is blissfully linear.
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Close to MOND behavior for wide binaries simply means that rotation of wide binary stars are at speed greater than Newtonian. Interior mass can have effect on it. After all in galaxies it is nothing but just the interior mass that determines it and external halo of dark matter is just a fiction. After all real thing for galaxy is only the interior mass. But for wide binaries, there is no real interior mass. That’s why they are binaries and not trinaries or anything superior. If MOND has already considered the “external field” (of normal matter) and the rotation speed close to MOND behavior is determined by duly considering that external field effect then exact that was my point. MOND like behavior is simply due to the presence of external field effect. If there is no normal surrounding galaxy then it will simply be a normal Newtonian behavior.
I suggest a simple simulation. Take a simulated isolated wide binary with behavior according to MOND formula.
Now add interior mass to this system and convert it into a galaxy like distribution of mass. Now again apply MOND formula. Net result will not be MOND like behavior.
For actual galaxies where actually there is no external field (of hypothetical dark matter) then MOND like behavior, in terms of Newton Theorem XXXIII, simply comes from distribution of interior mass.
By applying MOND formula on a simulated distributed mass system, we will get like double the MOND effect.
Then if we say that other half thing of that double thing is the hypothetical thing dark matter which is accounted for by MOND then we can stay in our illusion that Galaxy also follows MOND behavior.
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I think the man in black answered this one: https://www.youtube.com/watch?v=wwIFMCKlVK8
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not Johnny Cash ? dissapointed.
the question is also answered by the song ‘Stacy’s MOND has got it going on’
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Every opposition is trolling. This is not a strong argument that can stop opposition. If isolated binary gives MOND like result and adding interior mass and converting it to a galactic system will also give MOND like result then MOND is totally ignorant of dynamics of interior mass. MOND is in need to study Newton Theorem XXXIII
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I was trying to gently, with humor, point out that what you say makes no sense. There are words, in English, but their combination does not succeed in expressing a coherent thought.
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It is unfortunate thing for the science itself that baseless MOND makes perfect sense just because it can be made to work for galaxies. But Newton Theorem XXXIII makes no sense despite that it is the actual solution to the problem.
At least now there is one improvement. Now believers of counterintuitive theories have started taking care of what makes sense and what not.
My point is that MOND makes no sense. Newton Theorem XXXIII makes perfect sense.
If a very wide binary is aligned with flat rotation curves and then adding interior mass to it and making it into complete galactic disk will also give flat rotation curves then it is making perfect sense that MOND is totally ignorant about the dynamics of interior mass. MOND is actually in need to study Newton Theorem XXXIII.
Saying that flat rotations are true for isolated wide binaries and also for complete galactic disk is equal to saying that MOND is also true and Dark Matter WIMPs also have been found.
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Can Newton’s theorem XXXIII be stated? Newton said a lot of things, so rather than refer to an obscure number, can you put it in words? The statement I find in a search is
If for some given sphere, equal centripetal forces attract particular points decreasing in
the square ratio of the distances from the points : I say that a corpuscle within the sphere
constituted is attracted by a force proportional to its distance from the centre.
This just says that the centripetal force is directed towards the center, and decreases as the inverse square law. But it doesn’t in galaxies – that is the whole entire problem. To paraphrase Newton, everything happens as if MOND is the effective force law. I don’t claim to know why any more than he understood at the time why the inverse square law worked. But it must mean something, and nothing you’ve said remotely explains it.
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“Magellanic Cloud”, if you would like to explain more about your analysis, please leave a comment under the wide binaries post at
https://quantizinggravity.blogspot.com/
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Ask Ethan: Do binary stars prove modified gravity?
Bad science
The problem that all of these studies face is that although Gaia data may be the absolute best thing that we have for the systems we’re trying to measure, the data itself is still extremely limited in a number of very important ways.
One important limitation is simply that of observing time. If you look at our own Solar System, for instance, you can tell whether an object is within the inner Solar System, a member of the Kuiper belt, or is even farther out (in the Oort cloud, for example, assuming we could measure objects that far away) simply by tracking its motion over time. Measure it today, measure it tomorrow, measure it six months from now, etc., and you’ll be able to reconstruct a part of its orbit: eventually, you’ll have enough data to characterize its entire past-and-future trajectory.
It takes about two-to-four years of high-quality data, today, to characterize the orbit of a typical object in our Kuiper belt: an object with a several hundred year orbit. For the wide binary stars in the Gaia catalog, although we have several years of data, it would literally require centuries or even millennia of data to make the same precision characterization of their orbits. As it turns out, there isn’t even one single system among the Gaia wide binaries that we can point to and say, confidently, “This is what the long-term orbit of this system looks like.”
https://bigthink.com/starts-with-a-bang/binary-stars-prove-modified-gravity/
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Yes, now that’s truly doubting everything we know even about Newtonian gravity. There’s new data and you can use it or wait a few years to have even more data, but that doesn’t make the initial new data useless.
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This misrepresents the present results. Sure, we always want better data, and it’d be great to have a millennia-long baseline so we could see complete orbits. But we don’t need complete orbits to work them out; we do that all the time for newly discovered comets with only a few observations a few nights apart even though the orbits might be centuries long, or longer if they’re fresh arrivals from the Oort Cloud. We’re not looking at a single wide binary; we’re looking at the statistics for many of them. The same reasoning applies to the supermassive black hole at the center of the Milky Way. The dynamical timescale is short enough there that we have now seen individual stars complete full orbits. But we knew full well long before then that there was a concentration of several million solar masses there just from the statistics of the velocities of stars in the vicinity, with no orbit reconstructions at all. It works the same way for wide binaries: are they, as a statistical ensemble, moving at the speed we expect from Newton, or from MOND? Whether the data are adequate yet is always a concern, but we don’t need to wait for thousands of years.
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If we apply Ethan Siegel’s reasoning to Newton’s or Einstein’s theory of gravity, then there is no reason to believe that Newton’s or Einstein’s theory of gravity is correct at the scale of wide binaries either until the full trajectory of the wide binaries have been measured. This means that everybody has been doing bad science by assuming that general relativity applies at all scales.
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He needs to step away from the “Whack-A-MOND” game, because it’s getting the best of him.
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Ethan has always been a hater. Don’t know why he hates MOND, but he has made it very clear over the years that he is completely blinded by that animosity.
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Hardly. You have a theory which is general – it’s even in its name 😉 – so until you have hard evidence to the contrary the null hypothesis is that it applies.
MOND died 6 years ago, but I guess such facts doesn’t matter for it. [ https://www.quantamagazine.org/troubled-times-for-alternatives-to-einsteins-theory-of-gravity-20180430/ ]
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Torbjorn, but nothing in the data discussed in that article falls in the low-acceleration MOND regime, so as far as we know, MOND predicts the same results. True, no one (that I know of) has a complete theory which agrees with GR in the high acceleration regime and with MOND in the low acceleration regime, but no one has such a theory involving GR and dark matter either. (Not one which fits all the data, that is.)
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This article in Quanta dates from 2017 and could say nothing of C. Skordis, T. Złośnik, Aether Scalar Tensor Theory: Linear stability on Minkowski space, Phys.Rev.D 106, 2022 (first version June 2020 https://arxiv.org/abs/2007.00082). This theory predicts that gravitational waves propagate at the speed of light. It’s now 2023, or so it seems to me. I hope Mr Larsson that you will enjoy the reading !
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And the work of C. Skordis and T. Złośnik had been mentioned in Quanta https://www.quantamagazine.org/modified-gravity-theory-passes-a-critical-test-20200728/ Enjoy your reading, Mr Larson.
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Well, he was quite active in there so he should already know, but he chose the older news as it suits better his narative.
I noticed that there are several voices here which do not engage in the arguments, or if they are, they don’t actually listen to the other side.
I wonder what would they do if the consensus shits away fron LCDM. I’m couroius about Ethan Seigel, for instance – will he admit that all science communication that he did with respect to this was biased? And not only him…he’s just a visible figure (and he can do a lot of damage with that – but also random users on the net, like T. Larsson, can)
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MOND is not about giving a specific new theory of gravity. It’s about acknowledging that dark matter gives too much problems and predicts too little coincidences that are too good to be true. It gives a general direction of how gravity should be modified such that the situation is better, but it is not about a single theory that can die. It’s about admitting that the data was surprising to you too (regardless of if MOND predicted it).
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As others have already noted, T. Larsson is confused. The observation to which he refers shows that gravitational waves propagate at the speed of light (within tiny uncertainties). That excludes any theory that predicts a difference, like TeVeS. TeVeS is not MOND. It’s embarrassing to confuse the two while asserting that facts don’t matter.
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Posted a long reply that wordpress vanished into the aether. But as others have also pointed out, this is a silly perspective. Sure, it’d be great to see a complete orbit, but we haven’t seen that for stars around the Milky Way, so by this standard we cannot infer the existence of dark matter (or MOND) from rotation curves. We have seen a couple of individual stars orbit the central supermassive black hole, but we already knew it was there long before that had been accomplished. How? Because we can measure speeds without complete orbits and distinguish statistically between how fast they move in the presence or absence of a supermassive black hole. That’s the essence of the wide binary test: are the measured speeds consistent with MOND or pure Newton? This can be done without a thousand year baseline; the legitimate question is whether or not it has already been done.
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What more is necessary for answers on the wide binary test?
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I think the most important thing at this point is for the various groups to figure out why they get a different answer when interrogating the same database. The methodologies are very different, and at least one approach must be giving a misleading result.
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is the data sufficient for the wide binary test or more is needed ?
if the wide binary test could prove MOND, at least for galaxies, isn’t that a Nobel Prize ?
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Define sufficient. Extraordinary claims require extraordinary evidence. But when do we know this threshold has been met?
And yes, that would warrant a Nobel Prize. Indeed, there should already be multiple Nobel Prizes here. Milgrom has identified a new constant of nature, a0. Nevermind what it means; that it is a new scale of nature is enough. Flat rotation curves are a law of nature, analogous to Kepler’s first law for planets. That should have been a Nobel Prize for Vera Rubin and Albert Bosma, but it got mixed up with the larger dark matter issue. Discover a new law of nature was enough. Likewise, Tully-Fisher and the radial acceleration relation are laws of nature. Those are all Nobel Prize worthy – certainly no less so than all the prizes handed out in the ’60s for the discovery of various new particles. If someone discovers the dark matter and/or writes down the right theory that contains GR and MOND, that would also be prize worthy. We’re putting the cart before the horse by expecting this final development without acknowledging all the things that have been building towards it.
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Stacy said:
> … Flat rotation curves are a law of nature, analogous to Kepler’s first law for planets. <
Why Kepler's "first law"? I'd have thought flat RC's are analogous to Kepler's 3rd law. (?)
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Hmmmm… Was that Ethan Siegel or Steven Seagal? The quality of the answer sure points to Steven…
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Becky Smethurst covered the wide binary results in today’s video:
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Not only that, she linked to the Triton Station blog with strong recommendation…
IIRC, Dr Becky has been very dismissive of MOND previously, and it still shows that she would like it to be falsified, but now at least she has to take it seriously.
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Dr Becky mentioned Triton Station, but seems not to have included a written url. She also seems not to have read even a few of Stacy’s other recent posts, in particular the recent one checking in on troubles with dark matter. She also omits to say that, although GR has been proven correct, blah-blah-blah, those tests were not done down in the deep-MOND acceleration regime, which is the whole point of MOND. She also omits to note the *evidence* for a universal acceleration scale a_0, and nothing about how the *observed* spacetime scaling invariance in outer GRCs motivates the MOND formulas. In short, she clearly has not done much serious homework on MOND (sigh). But heh, that’s unnecessary for youtube, as is shown by the avalanche of crackpot/ill-informed comments saying how much they adore her. Brandolini’s law needs to be modified from “an order of magnitude” to “many orders of magnitude”.
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My reaction was negative to Dr. BS’s statement that “General Relativity, which has passed every experimental test, says that dark matter exists” (or something like that). It seems to me (possibly incorrectly) that the truer statement would be “the Newton’s Law approximation to GR, applied in a rough way to galaxies, says that dark matter exists.” That is, I doubt that any simulation of the motion of 100 billion (or even much fewer) stars in a galaxy based directly on GR rather than the Newton’s Law approximation has been done. My point there being that approximations are based on simplifying assumptions, which might be wrong in some cases.
Maybe she felt she had explained the “missing mass” problem in a previous video and didn’t need to repeat it in detail, or maybe it is in fact her opinion that GR directly implies missing galactic mass. But without more explanation her statement seemed misleading to me.
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Dear Stacy, does Verlinde’s sort of MOND also fit the results?
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I don’t know, but I doubt it. Verlinde’s emergent gravity predicts a force around a0 in excess of that predicted by MOND. That would almost certainly be too much.
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MOND is attractive (lol).
I would like to point out that we have evidence for gravity (be it GR or similar) working on the whole universe. We only _know_ quantum mechanics works on baryons – about 5% of the Universe. Since quantized dark matter hasn’t worked out, we may need to look for ‘non quantum fields’.
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(I mean I like MOND)
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Palmer Andersen said:
> We only _know_ quantum mechanics works on
> baryons […]
Rubbish. Quantum Theory also works on leptons, photons, and the W,Z bosons. Quantum Electrodynamics is one of the most accurate theories of physics in existence.
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Dark matter within radius of Pluto is higher than Stacy says in this blog post, I’m wondering if he meant ‘near the ecliptic’ or similar. (as in effective mass for orbit purposes).
27.5km radius asteroid mass
https://www.wolframalpha.com/input?i=4%2F3*pi*%2827500m%29%5E3*3000kg%2Fm%5E3
dark matter in sphere around the sun inside pluto at 34 au
https://www.wolframalpha.com/input?i=%2834.11au%29%5E3*4%2F3*pi*%280.007+solar+masses%2F%28pc%5E3%29%29+in+kg
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Technically you are correct. From the links you provide, the asteroid results as 2.613×10^17 kg and the dark matter as 2.64×10^17. That’s 1% error.
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There is a new preprint out on arxiv in which the authors use GAIA data to find that the Milky Way rotation curve has Keplerian decline. I am inclined to be skeptical given the SPARC data that shows flat rotation curves for a number of spiral galaxies. The abstract notes a decline in the radial velocity of ~30 km/s between 19.5 and 26.5 kpc.
Click to access 2309.00048.pdf
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Nice find in that it’s related. Although figure 5 looks not very far from asymptotically flat to me. If I look up keplerian decline the graphs are way more steep.
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These data are consistent with a Keplerian decline, but they’re also consistent with the RAR-based Milky Way model I’ve discussed in previous posts – albeit at the upper end of the error bars. On the other hand, they only discuss Gaia data out to 26 kpc, where even Gaia is dodgy. There are other types of data that go still further out; those are not consistent with a Keplerian delcine.
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Stacy, you recently remarked on the observations that vertical motions of stars in our galaxy did not show the expected MOND accelerations, while MOND behavior could be seen in expected radial accelerations. What are the ways something like that can make sense? How strongly does the data support that behavior?
Forgive me if this is either obvious or obviously wrong, but assuming no DM, would this observation then imply that orbiting bodies alter the spacetime curvature in the plane of motion differently enough from the spacetime normal to this plane?
If the orbital plane area-time was uniquely curved, could that be the source of MOND behavior?
I wonder if the annular area shrinks at low accelerations, then maybe the total amount of curvature required for the MOND effect is a lot less than currently presumed.
Not sure if the same notion might apply to collisions of clusters.
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well, if i knew, i’d say so! but i don’t so I won’t
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Ok. Well, what do you think about the ability to test MOND with the JWST maneuvering data, as it makes corrections to sit at the L2? Would it have to traverse regions of low acceleration near the stable point, in and out of plane, and is that worth a study?
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Scratch that idea. JWST is only orbiting L2, and not traversing it. I guess between any two rational thoughts, there really are an infinite number of irrational thoughts!
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Even if it did cross it, at this particular saddle point the radius where you can test MOND is only a few meters large. Also, trying to detect a change of course is not the right experiment to do, the effect is very small.
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I was thinking about the energy used over many maneuvers.
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there are a lot of such data for spacecraft other than JWST. Some anomalies are claimed, but I’ve never seen them combined into an analysis that makes sense – in terms of MOND or otherwise.
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Hooray, I’m back on the internet after hours of storms blocking the satellite signal. Sorry for being off topic, but I spent my time reading Milgrom’s “Ultra-diffuse cluster galaxies as key to the MOND cluster conundrum”. That was very informative, particularly regarding most of the unaccounted mass in clusters (from a MOND perspective) being concentrated in the vicinity of the core. I may not have stated that quite correctly, but I have to send this as thunder/lightning is drawing closer again and I want to check out Stacy’s new post: “Is the Milky Way’s rotation curve declining” before rain blocks the satellite signal again.
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@Stacy
<<<<<Can Newton’s theorem XXXIII be stated? Newton said a lot of things, so rather than refer to an obscure number, can you put it in words? The statement I find in a search is
If for some given sphere, equal centripetal forces attract particular points decreasing in
the square ratio of the distances from the points : I say that a corpuscle within the sphere
constituted is attracted by a force proportional to its distance from the centre.
<<<>>> that the centripetal force is <<>>>, and <<<>>>>>. But it doesn’t in galaxies – that is the whole entire problem. To paraphrase Newton, everything happens as if MOND is the effective force law. I don’t claim to know why any more than he understood at the time why the inverse square law worked. But it must mean something, and nothing you’ve said remotely explains it.>>>>>>
—————
Sir,
I thank you for giving the evidence that MOND actually doesn’t know anything about Newton’s Theorem XXXIII. MOND is not even able to simply read what Newton has actually stated here.
And … this MOND has “modified” Newton’s Theory without knowing what Newton theory actually is.
Following are your words:
<<<>>> that the centripetal force is <<>>>, and <<<>>>>>. But it doesn’t in galaxies – that is the whole entire problem.
—————
Sir, Newton Theorem DOES NOT say that force “decreases as the inverse square law”.
This theorem says that under given density situation as stated in the theorem, the force INCREASES LINEARLY.
Theorem XXXIII is NOT about INVERSE SQUARE force. It is about DIRECT LINEAR force.
I am sorry that you did find the correct wording of Theorem from google but since you had read it for the first time in life so you could not realize that it is NOT about inverse square law force from center. It is about DIRECT LINEAR force from center.
following are words from Theorem itself which are copied by you:
<<<<<<<I say that a corpuscle within the sphere constituted is attracted by a force proportional to its distance from the centre.>>>
As a matter of fact, Newton is very poorly understood even by the top tier scientists of today.
Theorem XXXIII is about sphere but galaxy is a disk. That is a secondary issue. I do have justifications for its applicability on disk.
But first thing first. first thing is that it is now a proven fact that MOND actually had wrong or faulty understanding of Newton law. And MOND has not actually modified Newton’s theory.
MOND has modified its own faulty understanding of Newton.
I am sorry to be so musch straight. This is not actually a diplomatic issue. If we will neglect the crucial facts then it will take centuries to correct the mistake.
I did not just use the term Theorem XXXIII without explaining it. I had sent you few emails before writing comments here. There I had explained the whole thing.
But either that email address should be incorrect or scientists in general do not actually read any opposing point.
Regards!
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Chill dude! If MOND is in nature’s laws, nobody is forcing it on you. Your posts are not how scientific discussions should progress, it feels more like you are extremely stressed and Stacy is trying to make the best of it.
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@stacy
Your words quoted in my previous comment missed in the quote formatting. Following were your comment:
——
Can Newton’s theorem XXXIII be stated? Newton said a lot of things, so rather than refer to an obscure number, can you put it in words? The statement I find in a search is
If for some given sphere, equal centripetal forces attract particular points decreasing in
the square ratio of the distances from the points : I say that a corpuscle within the sphere
constituted is attracted by a force proportional to its distance from the centre.
This just says that the centripetal force is directed towards the center, and decreases as the inverse square law. But it doesn’t in galaxies – that is the whole entire problem. To paraphrase Newton, everything happens as if MOND is the effective force law. I don’t claim to know why any more than he understood at the time why the inverse square law worked. But it must mean something, and nothing you’ve said remotely explains it.
—–
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Stacy,
Magellanic Cloud evidently hasn’t read any modern expositions of the Shell Theorems in Newtonian gravity. The case he keeps ranting about seems to be the case of a homogeneous sphere (as in, e.g., section 3.4.2 of Jo Bovy’s online galaxy book https://galaxiesbook.org/). I.e., the case of constant mass density: rho(r) = const up to r<R. Interior to such a sphere, the shell theorem quickly shows that the force is proportional to r. (This is all well-known in modern textbooks, but Newton's original wording is so tedious and long winded I'm not surprised most people have trouble understanding what he was on about.) Moreover, Magellanic Cloud is evidently unable to do the simple math showing that if the radial force is proportional to r, this does NOT yield a flat rotation curve, but rather a linearly rising curve. I.e., v_orb propto r.
Regardless, this is all moot since the mass densities in typical galaxies are not radially constant (sigh).
(Btw, I'm impressed that you can patiently tolerate his misleading rubbish as much as you have, but his most recent effort was so excessively rude that I can't stay silent.)
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My point is not that modern textbooks do not know about xxxiii. They know. Their fault is that they do not apply it on galactic dynamics. In its fundamental form it is not about sphere. It is about density. Wherever there is interior density of mass involved, then basic principle of xxxiii is involved. For sphere of constant density it is pure direct linear. For non uniform density is is direct and close to linear. For disk, still the density is involved. Mr. Stancy had the actual responsibility to workout modified form of xxxiii which should be applicable to density of galaxy in disk shape. In my assessment it should be direct and slightly greater than linear law for galaxy. But to work out exact modified theorem for galaxies is the responsibility of scientists. Who are actually scientists.
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Your point that if radial force is proportional to r then it should not give flat curve.
Rather it should give linearly rising curve.
——
That is for uniform density. For bulge area of galaxy, density is uniform or greater than uniform for each concentric shell. That’s why for bulge area curve is is sharp rising. For main disk area, mass is almost same for each concentric shell. So density is lesser and lesser for each concentric shell. Flat rotations come from actual density profile of the main disk area.
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> Mr. Stancy had the actual responsibility to workout modified form of xxxiii which should be applicable to density of galaxy in disk shape.
References please?
> In my assessment it should be direct and slightly greater than linear law
In your “assessment”? Based on what? Have you studied the various analytical solutions of the Poisson equation relevant to disk-like geometry and physically reasonable mass density profiles?
> But to work out exact modified theorem for galaxies is the responsibility of scientists.
If you bother to read more of the Bovy book that I linked earlier, you will see that various, more realistic, cases for disk-like situations have indeed
been solved analytically. Only the “Mestel disk” profile yields flat rotation curves. Alas, the Mestel density profile does not correspond at all well with
realistic mass profiles, hence is little more than a curiosity.
If you would study more of Bovy’s book, which covers various more realistic cases, you’d be less reliant on (wrong) guesswork.
> So density is lesser and lesser for each concentric shell. Flat rotations come from actual density profile of the main disk area.
You’re just making more sweeping statements, unfounded in actual math.
Moreover, the modern method for studying a galaxy’s rotation curve involves building a radial mass density profile from actual measurements, and then solving the Poisson equation numerically for the gravitation potential. The potentials found this way do NOT, in general, yield asymptotically flat rotation curves, as shown in Stacy’s various papers on the subject in recent years.
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Before writing my book on dark matter (2019) I had duly gone through this Bovy Book and had concluded that this so-called all in one solution named “Poisson Equation” is also one of the culprits. It gives you illusion of knowledge of everything. In reality, this equation is devoid of the implications of Newton’s theorem XXXIII.
So disk like solutions in Bovy Book have nothing to do with the actual responsibility of scientits. They should have worked out the galactic disk counterpart of Theorem XXXIII which they never did.
Title of my book is “Philosophy Unscrambles Dark Matter”. Free PDF links should be easily found in google search. As I am not “scientist” so I openly accept that direct reading of my book is not recommended as there are certain mistakes or other aspects that were not clarified in the book. But fortunately I had discussion on an alternative cosmology group where those aspects of book have been clarified and I also duly accepted my previous mistakes. This is link to that discussion:
https://github.com/orgs/a-cosmology-group/discussions/111
In this forum my id is khuramonline
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> […] this so-called all in one solution named Poisson Equation is also one of the culprits. It gives you illusion of knowledge of everything.
Hardly a “culprit”. Given a mass density function, one solves the Poisson equation to find the potential. That’s a lot. Of course one needs also the Boltzmann and Jeans equations, and others, to solve the full dynamics of galactic formation and evolution.
> In reality, (Poisson) equation is devoid of the implications of Newtons theorem XXXIII.
Not so. From the Poisson equation one can derive the 1/r potential of a massive point source. From that, the shell theorems follow. IOW, the Poisson
equation is more fundamental than the shell theorems.
> So disk like solutions in Bovy Book have nothing to do with the actual responsibility of scientits. They should have worked out the galactic disk
counterpart of Theorem XXXIII which they never did.
Of course they did — and they found out that there is no direct analog of the spherical shell theorem in the disk case. There is no analogous “ring theorem”. However, by finding many exact solutions for various mass profiles, they found out a lot about the gravitational fields of disk-like
galaxies.
Anyway, I think this sub-discussion has polluted Stacy’s blog more than enough for now.
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All you are saying is that one needs Mumbo and all other Jumbos. But one does not need XXXIII. Sir, if problem is 0.3 then solution should not be found in 3 billions.
For the exact solution to the actual problem, 0.3 is more important than 3,000,000,000
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Secondly, when Poisson Equation is devoid of the implications of Theorem XXXIII then obviously they will not find direct analog of the spherical shell theorem and other results also will be consistent with their dark matter illusion.
i repeat it again. Sphere shape is not the fundamental thing. Density is the fundamental thing. Wherever there is density of interior mass, then basic principle of XXXIII is also involved. Sphere is only shape. Shape only determines how much matter with given density can be contained in that shape. Sphere shape is just straightforward. Because with a uniform density, the matter within sphere is proportional to r cube. And gravity is inversly proportional to r square. By dividing r cube with r square, we simply get r that means gravity is directly proportion to r for a sphere of given density.
Same basic principle should have been applied for any shape. For any shape, XXXIII cannot be denied altogether. It will only give slightly different results. Actual rotation curves will be theoretically obtained by applying actual non-uniform density as actually exists in that shape.
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From last sentence of para 2 of above comment.
For sphere of given* density (incorrect)
For sphere of uniform density. (correct)
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And … OK. I hereby attempt to make a theorem for disk with width equal to the width of one unit of matter contained within it. For such a disk with uniform density of mass throughout the disk, total mass will be proportional to square of r.
And gravity is inversly proportional to square of r. By dividing r square by r square we get 1.
Therefore for a uniform density of mass there will be SAME gravity everywhere within the radius. Same gravity means flat rotations within the radius.
Any variation in the shape of curve will be due to variation in uniformity of density and actual width of the disk containing the matter.
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The New York Times published last week an article about how the current standard model of cosmology is falling apart and the possible need for a revolution in cosmology:
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Hi Stacy: Thank you for your latest post on “Is the Milky Ways’ rotation curve declining?”. I think I understand why you haven’t opened this new post up for comments.
If the rotation curve of a disk galaxy has a Keplerian decline, then
log(v) = -1/2 log(r) + constant
where v is the observed rotational velocity and the constant includes the galaxy mass and inclination. So, we can look for a Keplerian decline by simply plotting log(v) against log(r) and seeing whether or not the slope is around -0.5. We don’t need to know the inclination of the galaxy and we don’t need to know the mass distribution. Of course, we should look for the Keplerian decline in the outermost part of the rotation curve.
When I do this for the outermost 6 points of the Milky Way rotation curve from the recent paper by Jiao et al, I get a slope of -0.53 (ignoring the errors on the data points). So, I can conclude at a superficial level that our Milky Way galaxy appears to have a Keplerian decline.
I can repeat this procedure for the galaxies in the SPARC catalog. The only galaxy that comes close to showing a Keplerian decline is NGC 7793, with a slope of -0.43.
This is such a simple test to carry out that I suspect many people must have done so in the past, although I am not aware of any reference to it – (I am probably missing something.) Can MOND cope with declining rotation curves?
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> Secondly, when Poisson Equation is devoid of the implications of Theorem XXXIII …
“Devoid”? That’s rubbish. I already told you that the shell theorems can be *derived* from the Poisson eqn.
> Actual rotation curves will be theoretically obtained by applying actual non-uniform density as actually exists in that shape.
That is *exactly* what is being done when one solves the Poisson equation (which you call “Mumbo Jumbo”) for a particular distribution of mass.
> … Therefore for a (disk with) uniform density of mass there will be SAME gravity everywhere within the radius.
Rubbish. The gravitational potential of a uniform disk was calculated analytically by Krough, Ng & Snyder (Celestial Mechanics, April 1982). Pdf copies are available via Google Scholar. The result is surprisingly complicated, involving elliptic integrals.
Finally, by dismissing major equations of modern theoretical physics (such as the Poisson eqn) as “Mumbo Jumbo”, you reveal yourself to be a raving crackpot. Therefore, goodbye.
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I have presented the true and simpler theorem for disk. One thing I missed is just that gravity is directed towards the center of disk.
I have derived theorem for disk in exact same way as theorem xxxiii was derived. Only difference is that for sphere mass is proportional to radius cube. And for disk mass is proportional to radius square.
I have honestly presented this theorem despite the fact that it apparently contradicts with my stated positions in my book. But truth is more important than my previous stated positions.
I state it again. Poisson Equation is devoid of the implications of theorem xxxiii.
Shell theorem is different from theorem xxxiii. Shell theorem is for a setup where there is only a halo shell with no interior density. That is not the domain of theorem xxxiii.
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To be specific. The shell theorem which is about spherical halo shell. That is theorem xxx in Principia. I am talking about different theorem xxxiii and saying that Poisson Equation is devoid of the implications of this theorem xxxiii.
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Well, I have further thrashed the matter. Now there is hard evidence that Jo Bovy’s book and Poisson’s equation has not actually accounted for theorem xxxiii.
According to section 3.2 of Jo Bovy’s book, Newton had proved only two fundamental theorems for spheres. He has mentioned those two theorems as first shell theorem and second shell theorem. Basically they are theorems xxx and xxxi.
Clearly he totally ignored another fundamental theorem which is xxxiii.
According to Bovy, these two theorems that is xxx and xxxi have significantly simplified all work with spherical mass distributions and, in particular, that of solving the Poisson Equation.
Now root of the problem has come to clear limelight. Thanks.
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