People often ask me of how “perfect” MOND has to be. The short answer is that it agrees with galaxy data as “perfectly” as we can perceive – i.e., the scatter in the credible data is accounted for entirely by known errors and the expected scatter in stellar mass-to-light ratios. Sometimes it nevertheless looks to go badly wrong. That’s often because we need to know both the mass distribution and the kinematics perfectly. Here I’ll use the Milky Way as an example of how easily things can look bad when they aren’t.
First, an update. I had hoped to stop talking about the Milky Way after the recent series of posts. But it is in the news, and there is always more to say. A new realization of the rotation curve from the Gaia DR3 data has appeared, so let’s look at all the DR3 data together:
The new Gaia realization does not go very far out, and has larger uncertainties. That doesn’t mean it is worse; it might simply be more conservative in estimating uncertainties, and not making a claim where the data don’t substantiate it. Neither does that mean the other realizations are wrong: these differences are what happens in different analyses. Indeed, all the independent realizations of the Gaia data are pretty consistent, despite the different stellar selection criteria and analysis techniques. This is especially true for R < 17 kpc where there are lots of stars informing the measurements. Even beyond that, I would say they are consistent at the level we’d expect for astronomy.
Zooming out to compare with other results:
Overall, I would say the data paint a pretty consistent picture. The biggest tension amongst the data illustrated here is between the outermost Gaia points around R = 25 kpc and the corresponding results from halo stars. One is consistent with the model line and the other is not. We shouldn’t allow the model to inform our interpretation; the important point is that the independent data disagree with each other. This happens all the time in astronomy. Sometimes it boils down to different assumptions; sometimes it is a real discrepancy. Either way, one has to learn* to cope.
The sharp-eyed will also notice an apparent tension between the DR2 data (black squares) and DR3 around 6 and 7 kpc. This is not real – it is an artifact of different treatments of the term in the Jeans equation for the logarithmic derivative of the density profile of the tracer particles. That’s a choice made in the analysis. The data are entirely consistent when treated consistently.
Putting on an empiricist’s hat, I will say that the kink in the slope of the Gaia data around R = 18 kpc looks unnatural. That doesn’t happen in other galaxies. Rather than belabor the point further, I’ll simply say that this is how things mostly go right but also a little wrong. This is as good as we can hope for in [extra]galactic astronomy.
In contrast, it is easy to go very wrong. To give an example, here is a model of the Milky Way that was built to approximately match the rotation curve of Sofue (2020).
Fig. 1 from Dai et al. (2022). Note the logarithmic abscissa. Their caption: The rotation curve of the Milky Way. The data (solid dark circles with error bars) for r < 100kpc come from [22], while for r > 100kpc from [23]. The solid, dashed and doted lines describe the contribution from the bulge, stellar disk and dark matter halo respectively, within a ΛCDM model of the galaxy. The dashed-dot line is the total contribution of all three components.The parameters of each component are taken from [24]. For comparison, the Milky way rotation curve from Gaia DR2 is shown in color. The red dots are data from [34], the blue upward-pointing triangles are from [35], while the cyan downward-pointing triangles are from [36].
This realization of the rotation curve is very different from that seen above. Note that the rotation curve (black points) is very different from that of Gaia (red points) over the same radial range. These independent data are inconsistent; at least one of them is wrong. The data extend to very large radii, encompassing not only the LMC but also Andromeda (780 kpc away). I am already concerned about the effects of the LMC at 50 kpc; Andromeda is twice the baryonic mass of the Milky Way so anything beyond 260 kpc is more Andromeda’s territory than ours – depending on which side we’re talking about. The uncertainties are so big out there they provide no constraining power anyway.
In terms of MOND-required perfection, things fall apart for the Dai model already at very small radii. Dai et al. (2022) chose to fit their bulge component to the high amplitude terminal velocities of Sofue. That’s a reasonable thing to do, if we think the terminal velocities represent circular motion. Because of the non-circular motions that sustain the Galactic bar, they almost certainly do not – that’s why I restricted use of terminal velocities to larger radii. We also know something about the light distribution:
This is essentially the same graph as I showed before, but showing only the Newtonian bulge-bar component, and on a logarithmic abscissa for comparison with the plot of Dai et al. The two bulge models are very different. That of Dai et al. is more massive and more compact, as required to match the terminal velocities. There may be galaxies out there that look like this, but the Milky Way is not one of them.
Indeed, Newton’s prediction for the rotation curve of the bulge-bar component – the line labeled bulge/bar based on what the Milky Way looks like – is in good agreement with the effective circular speed curve obtained from stellar data. It is not consistent with the terminal velocities. We could increase the amplitude of the Newtonian prediction by increasing the mass-to-light ratio of the stars (I have adopted the value I expect for stellar populations), but the shape would still be wrong. This does not come as a surprise to most Galactic astronomers, because we know there is a bar in the center of the Milky Way and we know that bars induce non-circular motions, so we do not expect the terminal velocities to be a fair tracer of the rotation curve in this region. That’s why Portail et al. had to go to great lengths in their analysis to reconstruct the equivalent circular velocity, as did I just to build the bulge-bar model.
The thing about predicting rotation curves from the observed mass, as MOND does, is that you have to get both the kinematic data and the mass distribution right. The velocity predicted at any radius depends on the mass enclosed by that radius. So if we get the bulge badly wrong, everything spirals down the drain from there.
Dai et al. (2022) compare their model to the acceleration residuals predicted by MOND for their mass model. If all is well, the data should scatter around the constant line at zero in this graph:
Things are not well.
The interpretation that is offered (right in the figure caption) is that MOND is wrong and the LCDM-based EAGLE simulation does a better if not perfect job of explaining things. We already know that’s not right. The alternate interpretation is that this is not a valid representation of the prediction of MOND, because their mass model does not follow from the observed distribution of light. They get neither the baryonic mass distribution and its predicted acceleration ab nor the total acceleration a right in the plot above.
In terms of dark matter, the model of Dai et al. may appear viable. In terms of MOND, it is way off, not just a little off. The residuals are only zero, as they should be, for a narrow range of accelerations, 2 to 3 x 10-10 m/s/s. That’s more Newton than MOND, and appears to correspond to the limited range in radii over which their model matches the rotation curve data in their Fig. 1 (roughly 4 to 6 kpc). It doesn’t really fit the data elsewhere, and the restrictions on a MOND fit are considerably more stringent than on the sort of dark matter model they construct: there’s no reason to expect their model to behave like MOND in the first place.
And, hoo boy, does it ever not behave like MOND. Look at how far those red points – the Gaia DR2 data – deviate from zero in their Fig. 4. Those are the exact same data that agree well with the model line I show above – the data that were correctly predicted in advance. This model is a reasonable representation of the radial force predicted by MOND, with the blue line in my plot being equivalent to the zero line in theirs.
This is how things can go badly wrong. To properly apply MOND, we need to measure both the kinematics and baryonic mass distribution correctly. If we screw either up, as is easy to do in astronomy, then the result will look very wrong, even if it shouldn’t. Combine this with the eagerness many people have to dismiss MOND outright, and you wind up with lots of articles claiming that MOND is wrong – even when that’s not really the story the data tell. Happens over and over again, so the field remains stagnant.
*This is a large part of the cultural difference between physics and astronomy. Physicists are spoiled by laboratory experiments done in controlled conditions in which one can measure to the sixth place of decimals. In contrast, astronomy is an observational rather than experimental science. We can’t put the universe in a box and control all the systematics – measuring most quantities to 1% is a tall order. Consequently, astronomers are used to being wrong. While I wouldn’t say that astronomers cope with it gracefully, they’re well aware that it happens, that is has happened a lot historically, and will continue to happen in the future. It is a risk we all take in trying to understand a universe so much vaster than ourselves. This makes astronomers rather more tolerant of surprising results – results where the first response is “that can’t be right!” but also informed by the experience that “we’ve been wrong before!” Physicists coming to the field generally lack this experience and take the error bars way too seriously. I notice this attitude is creeping into the younger generation of astronomers; people who’ve received their data from distant observatories and performed CPU-intensive MCMC error analyses, so want to believe them, but often lack the experience of dozens of nights spent at the observatory sweating a thousand ill-controlled but consequential details, like walking out to a beautiful sunrise decorated by wisps of cirrus clouds. When did those arrive?!?
**The data that define the radial acceleration relation come from galaxies spanning six decades in stellar mass, so this one decade range from the simulations is tiny – it is literally comparing a factor of ten to a a factor of a million. What happens outside the illustrated mass range? Are lower masses even resolved?
Good morning Stacy, I follow your impressive blog and try, since a while, to find a quantum gravity mechanism for MOND. The person nearest to achieving this was Verlinde, in my personal view. But why does the entropy of de Sitter space increase the gravitational force towards the central mass? dS entropy has no direction… I wrote to Verlinde, but he never answered. Do you know any papers on the microscopic basis from MOND?
Hi Klaus, first being mostly a solid state experimentalist I know nothing. But I am also very interested in MOND as some manifestation of quantum gravity. I know of no papers, my favorite idea is that there is Bose-Einstein condensation of gravitons that somehow leads to MoND… don’t ask me how. But I get stuck trying to even do a back of the envelope type calculation. What’s the graviton density? And is it Plank’s constant that relates graviton energy to it’s wavelength?
George, massless bosons cannot form condensates…
Hmm OK. So maybe a tiny bit of mass for the graviton? Or maybe condensate is the wrong term. Photons inside a laser cavity can all get into the same state. Gravitons in the lowest state of the universe taken as one big spherical resonator. I know all my images are much too simple.
But perhaps we mostly agree that MOND could be a big hint towards some quantum gravity theory.
I do not.
It seems to me that the MOND phenomenon must be an important clue on the path to quantum gravity, but it is beyond my expertise. Most workers in that field (with some exceptions) seem to be blissfully unaware of it, so they continue to play solitaire with an incomplete deck of cards.
The difficulty in finding a mechanism for MOND is that the outer masses orbit *faster* than expected by Newtonian gravity. Inventing an additional interaction that produces this effect looks almost hopeless. In my reading, Verlinde’s explanation does not allow deducing this. There is a mistake in his derivation. And I do not find any alternative in any theory of quantum gravity in the literature.
The difficulty in finding a mechanism for MOND lies in the fact that we do not know the mechanism for the gravitational effect – unless you subscribe to Wheeler’s empirically-baseless, causally-interacting-spacetime conjecture.
Maybe another question. We know that outer stars orbit faster than their Newtonian speed. Now, is the measured orbital speed measured for the outer stars of a galaxy lower than their Newtonian predicted escape velocity v_e^2=2GM/R or is the orbital speed higher? Surely, this has been measured?
In other words, is the measured orbital speed larger than sqrt(2) times the Newtonian orbital speed (which is the Newtonian escape velocity for that orbit)?
The Newtonian escape speed depends on the radius, so it depends on how far out one measures. Rotation curves are generally not traced so far out that this occurs. Other tracers (like gravitational lensing) imply that the effective potential remains logarithmic arbitrarily far out.
Thank you Stacy. At radius r, the (circular) orbital speed is sqrt(GM/r) and the escape speed is sqrt(2GM/r), which is 41% higher. It seems that the measured star speeds are even higher than this latter value – am I correct? So, without MOND (or drak matter), the galaxies would have to eject stars all the time, am I correct?
It seems obvious to me that MOND is an important clue to the nature of quantum gravity, and that anyone wanting to build a quantum gravity theory should look for as many such clues as possible before starting work. Apart from anything else, the observations that lead to MOND can rule out a lot of attempted QG theories before you waste too much time on them.
If you need entropy to have a direction, then you (only) need a particle to carry information in or out. If you don’t want to invent new particles, then neutrinos are your best bet. The three generations of neutrinos then allow you to carry directional information from a source, in an arbitrary (i.e. independent) direction. I assume this is why many people have considered that neutrinos are the key to developing a plausible quantum theory of gravity.
In particular, it allows a theory of gravity to convey not only mass information, using the neutrino energy, but also rotational information, using the neutrino flavours, so that the gravity of a spinning disk is quite different from the gravity of an amorphous sphere.
The two main reasons why you might not want to do this are (1) if you believe in GR and DM you might be convinced that a graviton must have spin 2, rather than spin 1/2, and (2) if you believe in Yang-Mills theories of particle physics you might be convinced that gravitons must have integer spin, even if it is not spin 2. So the theoretical reasons against it are strong, but perhaps the observational reasons in favour of it are even stronger.
At first I thought that the paper going wrong (from Dai et al.) had not been published, but in fact it is. Given your explanations (very appreciated), I find that a little disturbing. Either the review process is far from thorough, or the general quality of submitted papers is much worse, and this is one of the best…
Lots of obviously wrong things get published. Part – only part – of what is going on here is the sociology of astroparticle physics (see https://tritonstation.com/2018/10/04/the-arrogance-of-ignorance/ ). This relatively new field is largely concerned with dark matter, but from the particle physics side – the “astro” is entirely aspirational. Indeed, when I first started meeting people at conferences who described themselves as astroparticle physicists, I quickly recognized tremendous gaps in their knowledge – this was one of the motivations to develop an entire semester course on dark matter. That was a decade ago, but only helps local students, so what you see here are people who are not really trained in the field thinking they are competent to do this work. They can do the math, but they don’t have the background to know that the Galactic bar is important or to recognize misleading data (though you might think that the discrepancy between Sofue and Gaia DR2 might have been a clue). One of these authors is on my campus and is personally known to me, but why consult with an actual expert on the subject when you consider yourself to be one?
Hello, speaking of things that can go mostly wrong, thought I’d report on something that seems to be going mostly right. As found with the stellar component, disk gas can offer other tantalizing clues also deserving of discussion. Employing SPARC data, Korsaga https://iopscience.iop.org/article/10.3847/2041-8213/ace364/meta found a robust correlation between M200 halo mass and HI gas mass, a unexpected relation coming out of LCDM galaxy formation and evolution.
We use Korsaga’s newly minted M200-MHI relation to help understand another peculiar scaling relation recently identified by Chan (also employing SPARC) https://www.sciencedirect.com/science/article/abs/pii/S2212686422001157. Chan linked baryon and halo mass in a M200-Mbar scaling relation described as “mysterious” although acknowledging some form of DM and baryon interplay beyond gravity may be involved.
In a short straightforward article, Chan constructed a simple but relatively tight M200-Mbar relation sporting an unbroken log slope 0.74. Here, an attempt is made to connect the dots between Chan’s relation and galaxy properties employing Korsaga’s NFW halo M200-MHI relation in a unique way.
First, the (MHI/M*)-Mbar data provided in Korsaga Fig. A1 is reconfigured into the equivalent MHI-Mbar relation (where Mbar=M*+MHI). With this change in basis, the MHI-Mbar scaling relation has a log slope 0.75, very close to Chan’s M200-Mbar mystery relation. By extension, this provides a successful pressure check for both analyses. Can we now say the mystery behind Chan’s relation has been adequately explained? Probably not, but now we have new information that points to possible local effects rather than cosmological constraints in driving halo mass functionality.
Another unanticipated outcome of Korsaga’s work is a constant (baryon independent) galactic HI gas-halo mass ratio averaging 1.25% having ‘minimal’ scatter and residuals. This is a bold claim that can also be tested as the one above.
Above it has been shown that the M200-Mbar and MHI-Mbar relations are essentially parallel. Therefore, the gas fraction is simply the zero-point ratio. For the case of total galaxy mass obtained from SPARC data and Li’s 2020 NFW halo fits (see Fig 2. arXiv 2307.03975 for detail), the average MHI/Mtot fraction is ~0.95%, consistent with Korsaga and the Chan mystery relation.
As a caveat, this is not to say that NFW M200 halos represent the true virial/total mass of any galaxy. Nearly all of Li’s halo fits in Fig. 2 are heavily overestimated compared to their physical/dynamical requirements. For low mass galaxies, halo mass can “exceed” these requirements by a factor of six or more making total mass estimates highly suspect. So, the correlation may merely reflect least massive galaxies harbor the highest HI gas fractions (and nothing more).
But…Korsaga results also carry a couple significant implications. The first is the M200-MHI relation is consistent with the BTFR which can severely constrain halo model selection and fits moving forward. The second was best summed up by author, “Our result reveals that isolated galaxies with regularly rotating extended HI disks are surprisingly self-similar up to high masses, which hints at mass-independent self-regulation mechanisms that have yet to be fully understood.” Stepping onto the soapbox, “Could this governance be causally linked to the virial theorem?” Thanks for the opportunity to comment on these intriguing discoveries. Best regards, Jeff
I thought the Radial Acceleration Relation (RAR) was exclusive to galaxies, so was surprised to read the papers linked by jeffreymlafortune where researchers attempted to apply it to galaxy clusters. But there were mixed results in two separate cluster samples; one supportive of such a relation, the other not.
Somehow I lost my automatic login, possibly because my computer rebooted with a power outage.
Dear David,
The literature shows galaxy cluster ‘RAR internals’ are different than disk galaxies with both adhering to the BTFR. One study by Tian produces the slope, but with a much higher characteristic acceleration than a0. Most studies show higher accelerations and steeper slopes than their galactic counterparts. Several results have been compiled in Fig. 3 https://arxiv.org/pdf/2210.08264.pdf along with the kinematic disk galaxy RAR for comparison. Hope this helps. Best regards, Jeff
PS to all -> a must read paper by Mistele, McGaugh, Lelli, Schombert, and Li https://arxiv.org/pdf/2310.15248.pdf.
Jeffrey, thanks for the links. I’ll print them out so I can read them while being a passenger on a drive to a regional casino.
Jeffrey, I managed to read partway through the two linked papers you provided – the 39 page paper by Mistele, McGaugh, Lelli, Schombert, and Li, and your paper: “The Global Escape Velocity Profile and Virial Mass Estimate of the Milky Way Galaxy from Gaia Observations”. But I also had earlier read the synopses of other papers that you had linked that were posted on ScienceDirect like: “Yet another test of Radial Acceleration Relation for galaxy clusters”, by S. Pradyumna et. Al. The full papers weren’t available on that platform, but the “Section snippets” and introductions did a pretty fair job of explaining their position and results.
I confess I’m pretty overwhelmed by all this literature, but I can see that you have put a tremendous effort into your own hypothesis regarding the Milky Way (MW) galaxy. Your thesis evidently is that neither Dark Matter or MOND is necessary to explain the MW’s dynamics. And, if I’m not mistaken, you utilize the kinematics of Hyper Velocity stars and Dwarf Galaxies, presumably in settled orbits about the MW, as the proper tracers to infer the MW’s mass, so as to agree with your thesis. What worries me is that using those for tracers is too restrictive. But I haven’t read your whole paper, so I may have missed some critical detail.
Also, it’s my understanding that the RAR and other regularities like the BTFR, observed in hundreds of galaxies, are a natural outcome of MOND’s phenomenology and were predicted well in advance by Milgrom. Now one thing I’m not sure of is whether the outermost galaxies in galactic clusters reach down to the MOND acceleration of a0. I assume that the aspect of MOND that allows that phenomenological model to predict the regularities observed in galaxies is the acceleration threshold of a0 and the consequent flat rotation curves. I did note that your either your model or one of the others indicates a higher acceleration threshold than does MOND.
To be honest, the mixed results of the six separate galactic-cluster samples evaluated in various studies doesn’t bode well for a galactic-cluster version of RAR. For example, the Pradyumna et al, paper I mentioned states in the abstract: “..we argue that the RAR is not universal” referring to galactic clusters.
Jeffrey, In paragraph 4 of the above I changed the sentence and forgot to delete the extra “your” in the last sentence. Also, the “higher acceleration threshold than does MOND.” in that last sentence was in reference to galactic clusters, which I believe you indicated to be the case in your paper. Would try to check that but want to get some chores done, so am in a rush.
Dear David,
Thanks for the comments. I’m a retired guy with an interest and passion trying my best to make sense of this (within the purview of standard physics). I enjoy problem solving and this is the ultimate challenge. Reflecting my background and philosophy, the models and math are basic, with heavy reliance on and interpretation of empirical scaling relations.
Tracers are an interesting subject and their behavior as related to gravitational potential (mass estimates) is now only being understood within our own Galaxy. Fir the MW, rather than focusing exclusively on a particular tracer set (say the stellar disk), an attempt was made to select data that directly probed the acceleration ranges (and radii) of interest. These were assembled into a global Vesc profile that is surprisingly Keplerian over an extended range. Per Dr. Hammer, this is under the assumption of equilibrium which is still in debate, but you need to start somewhere. Using accelerations from combined tracer sets, the estimated total mass of the Galaxy is a consistent 1E12 Mo, agreeing with nominal values in the literature. Are there are non-equilibrium effects ‘baked into’ in this and other previous estimates, I’m not sure.
With regard to galaxy clusters and the empirical data, Tian provided outermost or “last” radii and dispersions for a small HIFLUGCS sample https://iopscience.iop.org/article/10.3847/1538-4357/abe45c/pdf. For this dataset, the median cluster characteristic acceleration scale is only 30% below a0. The “RAR” plotter using these outermost points exhibits a cluster log slope 0.5 consistent with disk galaxies. As MOND has previously pointed out many times, this is unequivocal universal behavior for cosmic structure. You mentioned Pradyumna’s abstract: “..we argue that the RAR is not universal” referring to galactic clusters. Most generally, internal cluster and galaxy RAR profiles may not be universal, but the functionality at outermost radii between them agree per the BFTR, independent of what’s happening inside (i.e., higher interior cluster accelerations compared to galaxies).
David, I hope this answers your questions and a sense of the direction taken. Although now, it’s the latest low acceleration study by Mistele, et al, consistent with the RAR (constant Vc) out to ~Mpc distances that’s got me scratching my head. From a modified gravity standpoint, this is what has been predicted. You’d think DM adherents should be spearheading this kind of work to demonstrate the veracity of their halo models. But no, they have outsiders tell them how they are not the answer (or what I term “non-value added” work). The current concerns with LCDM and the flood of contradictory data pouring in presents a good opportunity for alternative galaxy theories to gain traction. Regards, Jeff
Jeffrey, thanks for your extensive and scholarly reply, which I only just read and haven’t fully digested. I have to say that your modeling ideas are far more sophisticated than my own ideas in this field. I plan to finish reading your paper and will try to understand your vision of how the kinematics work in our Milky Way galaxy. I’m especially interested in the link you provided authored by Tian, as I’m not real familiar with the kinematics of galactic clusters. I’ve long been aware that clusters present a two to one disparity for MOND, but never really looked into how that assessment was made. Hopefully, the paper by Tian will help to clear that knowledge deficiency up.
David, the two-to-one baryon disparity for MOND occurs in the central regions in galaxy clusters where the calculated characteristic accelerations which can be up to 20x greater than a0. Is this disparity due the internal “thermal” kinetic energy content of the X-ray gas component compared to the kinetic energy of rotation of galactic disks? Perhaps. Regards, Jeff
It would be nice to have an open access computer program that shows the changes over time of a given 1D, 2D or even 3D distribution, so that researchers can check the stability and credibility of their rotation curve
Jeffrey, the thread above has apparently reached its response limit, so I’m posting a response to your 12:47 PM, Nov. 1 post here on a new thread. It’s interesting that you bring up “the internal “thermal” kinetic energy content of the X-ray gas” as a possible source of the remaining 2-to-1 discrepancy for MOND, at least that’s how I interpreted what you wrote. Luckily, I just came across a paper by Professor Pavel Kroupa: “Galaxy clusters: no problem for MOND after all?”, and was delighted that it highlights: “A first problem is related to the offset between X-ray and weak-lensing distributions, like in the case of the Bullet Cluster.” (2nd sentence of 2nd paragraph). I’d long been aware of the Bullet Cluster, which advocates of LCDM regard as the ‘smoking gun’ of dark matter’s existence. When I first came across this Bullet Cluster issue it seemed to be an intractable problem for MOND. However, from reading Dr. Kroupa’s paper, it seems that applying the “virial theorem” to clusters is a possible solution to MOND’s incompatibility with the Bullet Cluster and other clusters like it, so it may no longer be an issue.
But, getting back to your mention of the X-ray gas; I had toyed around with finding an underlying mechanism for MOND’s phenomenology. It’s wildly speculative and very likely wrong, but here it is: Between about 1996 and 2006, and sporadically thereafter, there were claims of acceleration signals being detected from high temperature superconductors, as well as conventional superconductors. To make a long story short, these claims made me wonder if momentary fluxes of gravitons; the hypothetical quanta of the gravitational field, were emanating from these superconductors. If so, then could such graviton fluxes be a factor in astronomy’s dark sector? Now, of course, the vast bulk of the universe does not harbor matter in the superconducting state. But in standard physics when two stars (black holes) pass in proximity to one another their gravitational fields undergo distortion leading to the generation of gravitational waves (gravitational bremsstrahlung). Such waves can be considered coherent states of gravitons. Alternatively, a quantum system like an atom may have a transition between a d-orbital and an s-orbital, emitting a spin-2 graviton.
Of these two processes the former requires huge masses that quite rarely collide or interact, and the latter phenomena is greatly suppressed by the rules of QM. But I had come up with a very speculative idea that might lead to gravitational bremsstrahlung on the atomic scale and/or greatly amplify the 2nd process. The kicker is it would require bi-energy graviton emission, which gets into negative energy and the supposed vacuum instability that would engender. However, a theory developed by John Cramer (University of Washington) called the “Transactional Interpretation of Quantum Mechanics” (TI) which entails bi-energy photon production and absorption, leads to exactly the same predictions as standard QM. So, effectively, this bi-energy graviton emission/absorption idea, would be an extension of TI. Anyway, the thinking was that bi-energy graviton emission from the intensely ionized gas in the collision zone of the Bullet Cluster might account for the offset in baryon concentration indicated by lensing.