Saturday, May 01, 2021

Dark Matter: The Situation Has Changed

[This is a transcript of the video embedded below]

Hi everybody. We haven’t talked about dark matter for some time. Which is why today I want to tell you how my opinion about dark matter has changed over the past twenty years or so. In particular, I want to discuss whether dark matter is made of particles or if not, what else it could be. Let’s get started.

First things first, dark matter is the hypothetical stuff that astrophysicists think makes up eighty percent of the matter in the universe, or 24 percent of the combined matter-energy. Dark matter should not be confused with dark energy. These are two entirely different things. Dark energy is what makes the universe expand faster, dark matter is what makes galaxies rotate faster, though that’s not the only thing dark matter does, as we’ll see in a moment.

But what is dark matter? 20 years ago I thought dark matter is most likely made of some kind of particle that we haven’t measured so far. Because, well, I’m a particle physicist by training. And if a particle can explain an observation, why look any further? Also, at the time there were quite a few proposals for new particles that could fit the data, like some supersymmetric particles or axions. So, the idea that dark matter is stuff, made of particles, seemed plausible to me and like the obvious explanation.

That’s why, just among us, I always thought dark matter is not a particularly interesting problem. Sooner or later they’ll find the particle, give it a name, someone will get a Nobel Prize and that’s that.

But, well, that hasn’t happened. Physicists have tried to measure dark matter particles since the mid 1980s. But no one’s ever seen one. There have been a few anomalies in the data, but these have all gone away upon closer inspection. Instead, what’s happened is that some astrophysical observations have become increasingly difficult to explain with the particle hypothesis. Before I get to the observations that particle dark matter doesn’t explain, I’ll first quickly summarize what it does explain, which are the reasons astrophysicists thought it exists in the first place.

Historically the first evidence for dark matter came from galaxy clusters. Galaxy clusters are made of a few hundred up to a thousand or so galaxies that are held together by their gravitational pull. They move around each other, and how fast they move depends on the total mass of the cluster. The more mass, the faster the galaxies move. Turns out that galaxies in galaxy clusters move way too fast to explain this with the mass that we can attribute to the visible matter. So Fritz Zwicky conjectured in the 1930s, that there must be more matter in galaxy clusters, just that we can’t see it. He called it “dunkle materie” dark matter.

It’s a similar story for galaxies. The velocity of a star which orbits around the center of a galaxy depends on the total mass within this orbit. But the stars in the outer parts of galaxies just orbit too fast around the center. Their velocity should drop with distance to the center of the galaxy, but it doesn’t. Instead, the velocity of the stars becomes approximately constant at far distance to the galactic center. This gives rise to the so-called “flat rotation curves”. Again you can explain that by saying there’s dark matter in the galaxies.

Then there is gravitational lensing. These are galaxies or galaxy clusters which bend light that comes from an object behind them. This object behind them then appears distorted, and from the amount of distortion you can infer the mass of the lens. Again, the visible matter just isn’t enough to explain the observations.

Then there’s the temperature fluctuations in the cosmic microwave background. These fluctuations are what you see in this skymap. All these spots here are deviations from the average temperature, which is about 2.7 Kelvin. The red spots are a little warmer, the blue spots a little colder than that average. Astrophysicists analyze the microwave-background using its power spectrum, where the vertical axis is roughly the number of spots and the horizontal axis is their size, with the larger sizes on the left and increasingly smaller spots to the right. To explain this power spectrum, again you need dark matter.

Finally, there’s the large scale distribution of galaxies and galaxy clusters and interstellar gas and so on, as you see in the image from this computer simulation. Normal matter alone just does not produce enough structure on short scales to fit the observations, and again, adding dark matter will fix the problem.

So, you see, dark matter was a simple idea that fit to a lot of observations, which is why it was such a good scientific explanation. But that was the status 20 years ago. And what’s happened since then is that observations have piled up that dark matter cannot explain.

For example, particle dark matter predicts a density in the cores of small galaxies that peaks, whereas the observations say the distribution should be flat. Dark matter also predicts too many small satellite galaxies, these are small galaxies that fly around a larger host. The Milky Way for example, should have many hundreds, but actually only has a few dozen. Also, these small satellite galaxies are often aligned in planes. Dark matter does not explain why.

We also know from observations that the mass of a galaxy is correlated to the fourth power of the rotation velocity of the outermost stars. This is called the baryonic Tully Fisher relation and it’s just an observational fact. Dark matter does not explain it. It’s a similar issue with Renzo’s rule, that says if you look at the rotation curve of a galaxy, then for every feature in the curve for the visible emission, like a wiggle or bump, there is also a feature in the rotation curve. Again, that’s an observational fact, but it makes absolutely no sense if you think that most of the matter in galaxies is dark matter. The dark matter should remove any correlation between the luminosity and the rotation curves.

Then there are collisions of galaxy clusters at high velocity, like the bullet cluster or the el gordo cluster. These are difficult to explain with particle dark matter, because dark matter creates friction and that makes such high relative velocities incredibly unlikely. Yes, you heard that correctly, the Bullet cluster is a PROBLEM for dark matter, not evidence for it.

And, yes, you can fumble with the computer simulations for dark matter and add more and more parameters to try to get it all right. But that’s no longer a simple explanation, and it’s no longer predictive.

So, if it’s not dark matter then what else could it be? The alternative explanation to particle dark matter is modified gravity. The idea of modified gravity is that we are not missing a source for gravity, but that we have the law of gravity wrong.

Modified gravity solves all the riddles that I just told you about. There’s no friction, so high relative velocities are not a problem. It predicted the Tully-Fisher relation, it explains Renzo’s rule and satellite alignments, it removes the issue with density peaks in galactic cores, and solves the missing satellites problem.

But modified gravity does not do well with the cosmic microwave background and the early universe, and it has some issues with galaxy clusters.

So that looks like a battle between competing hypotheses, and that’s certainly how it’s been portrayed and how most physicists think about it.

But here’s the thing. Purely from the perspective of data, the simplest explanation is that particle dark matter works better in some cases, and modified gravity better in others. A lot of astrophysicist reply to this, well, if you have dark matter anyway, why also have modified gravity? Answer: Because dark matter has difficulties explaining a lot of observations. On its own, it’s no longer parametrically the simplest explanation.

But wait, you may want to say, you can’t just use dark matter for observations a,b,c and modified gravity for observations x,y,z! Well actually, you can totally do that. Nothing in the scientific method that forbids it.

But more importantly, if you look at the mathematics, modified gravity and particle dark matter are actually very similar. Dark matter adds new particles, and modified gravity adds new fields. But because of quantum mechanics, fields are particles and particles are fields, so it’s the same thing really. The difference is the behavior of these fields or particles. It’s the behavior that changes from the scales of galaxies to clusters to filaments and the early universe. So what we need is a kind of phase transition that explains why and under which circumstances the behavior of these additional fields, or particles, changes, so that we need two different sets of equations.

And once you look at it this way, it’s obvious why we have not made progress on the question what dark matter is for such a long time. There’re just the wrong people working on it. It’s not a problem you can solve with particle physics and general relativity. It a problem for condensed matter physics. That’s the physics of gases, fluids, and solids and so on.

So, the conclusion that I have arrived at is that the distinction between dark matter and modified gravity is a false dichotomy. The answer isn’t either – or, it’s both. The question is just how to combine them.


  1. It would be amusing to me if it turned out that string theory mathematics via condensed matter physics provides the explanation for dark matter.

    I have a strange sense of humor...

  2. Brilliant post!
    A possible pathway through the mire after all!!?

  3. Is the reference to condensed-matter physics a node to Justin Khoury’s superfluid dark matter?

    1. That's the so-far most studied option. I didn't mention this specifically because it could be some other phase transition, or made of different stuff entirely.

    2. It would appear that there's a significant difference between whether dark matter is an emergent property of existing matter (MOND), or the result of additional, normally invisible matter, right?

  4. Some cosmological papers describe the important role of Dark matter in the early universe (the “fuel” to create matter). If it is true the existence of Dark matter violates the Standard cosmological model. Because Dark matter must have a direct relation with the evolution of the amplitudes of the electric field in our non-local universe. In other words, the amplitudes were higher in the early universe in relation to the present situation. The consequence is the red shift of the non-absorbed light of distant galaxies during the evolution of the universe. Gravity is the force that concentrate matter, but the electric field at the macroscopic scale concentrates mass. Thus Dark matter is just mass, local concentrations of quanta.

  5. While in some sense there is an equivalence of particles and fields, it really doesn’t help to say that they are the same thing with respect to the debate between dark matter and modified gravity. It’s like the title of Physical Review D: Particles and Fields; doesn’t that include everything studied by physics?

    Also, dark matter doesn’t have to be a particle in the conventional sense. Apart from superfluid dark matter, there could be primordial black holes, and so on. Even if they are somehow made of particles, the important point is that the typical dark-matter—detection experiment wouldn’t detect them.

    1. Microlensing puts some constraint on DM as black holes. It would also create more anisotropy in the CMB. I remember reading a few months ago this meant black holes were at best a minor contributor to dark matter.

    2. Check out any of many recent (and not so recent) papers by Bernard Carr and collaborators on this topic. Yes, microlensing does set some constraints (I’m an author on a paper claiming that), but there are ranges of mass not ruled out (very light (say, asteroid-mass) and very heavy, and of course there can be a range of masses. Quantitative analyses shows that they are still in the running, even for being all of the CDM.

    3. And these primordial black holes are distributed in a way that, as a result, 4th power of rotational velocity of eliptical galaxies is proporcional to their visible mass (BTFR)? Because this empirical observation isn't compatible with Newtonian gravity assuming only visible matter, so something is producing this deviation.

    4. Related to this microlensing I would think the anisotropy of the CMB would be greater. This is a measure of the entropy of the universe or early universe, and if there were many primordial black holes the entropy of the universe would be much larger. Appealing to Penrose's Weyl tensor theorem or hypothesis, the larger entropy is the more local curvatures there are and the CMB anisotropy should then appear much greater.

      It seems difficult to think all DM could be black holes. Other candidates are out. WIMPS is on life support, and I read a few weeks ago on how the axion is probably out. That was based on expected spin down of black holes absorbing tiny mass scalar field particles. It does appear all candidates for DM are failing.

    5. Read Carr’s papers to see why they are still viable. A long, well researched, well referenced, mathematically precise paper counts for more than “well, it seems unlikely to me”.

      As to the distribution of dark matter, if it is to explain MOND phenomenology then yes a certain distribution is required, whatever the dark matter is. Whether MOND or DM is the better explanation (and MOND might be in some situations and DM in others) is independent of the question what the best DM candidate is.

  6. Would it be possible that it's dark matter that is modifying gravity, and that they're acting on galaxies together?

    1. I don't even know if that's a useful question.

  7. It’s interesting how often nominally data-driven theorists have railed against the introduction of more complexity than initially anticipated. A recent example from biology is genetic clocks, which were assumed to be simple but have massively diverse rates.

    Regarding baryonic Tully Fisher relation and Renzo’s rule, one powerful but radical approach would be to assume the universe is tens of orders of magnitude less detailed and information-dense than is typically assumed. The nearly universal source of high-information-density assumptions is not experimentation but the unlimited and often wildly asymmetric implied precision from the resolution-indifferent application of real and complex matrix models to natural phenomena. In a low-res model, the existence of ordinary fermionic matter would generate and define the precision limits of gravity and general relativity. Such ordinary matter would generate spacetime as relationships between actual particles. Infinite-precision spacetime, in contrast, exists only as an unreachable calculation limit in precision-indifferent matrix models.

    As a modeling concept, baryon-generated spacetime would mean general relativity is incomplete in the sense of failing to capture the full complexity of baryonic relationships at the extrema of particle counts and distance metrics. My best assessment of the literature is that exploration of this path is at best tangential and incomplete. Space and gravity as entanglement (the brilliant work of Verlinde comes to mind) certainly touch on it. However, any holographic approach that first assumes the near-infinite information densities of Planck-scale entanglement also eliminates any possibility of deeper insights by forcing spacetime to behave as infinite-precision matrix models imply it can. The only way baryon-generated spacetime models could participate in the dark matter problem would be to permit the relative concentrations of baryons in space to play a direct role in determining when and how spacetime frays and loses resolution in cases such as deep voids between supercluster filaments.

    Oddly, the identity of the maximum resolution limit in such fundamentally blurry, Planck-foam-free models is easy to identify. It is identical to the uncertainty relationships of quantum mechanics, that is, to the holographic limit of a dual-holographic interpretation of quantum mechanics. In the dual holographic interpretation, an electron orbital wave function is the electron, not a wave hiding it. When played out over astronomical scales, such quantum imprecision has consequences by limiting the ultimate resolution of even the most massive entities.

  8. You have mentioned many independent observations that need an explanation. Is it a simple binary choice between a) some form of particle, and b) some modification of gravity? What strikes me is that particle physics usually involves particles together in the same location, whereas gravity usually involves objects separated by enormous distances. After dismissing the obvious crank ideas, are there no plausible alternative hypotheses put forward by competent scientists?

  9. I agree, the gravitational field is made up of particles,
    but the problem of dark matter modified by the theory of gravity MOND does not solve,
    because in fact, by solving dark matter, you will solve the energy of the gravitational field, that is, the real essence of why gravity exists.

    Albert Einstein was on the trail, but the two world wars destroyed his brain :( that is, the atrocities that happened)

    Unfortunately, my hypothesis of how gravitational energy arises is just a hypothesis :( but again it has the potential to break the Big Bang theory,

    in such a way that, in fact, space does not expand, but on the contrary, the gravitational energy decreases, all the more the more matter is created in the universe from this gravitational field ...

    this, of course, gives other predictions:
    a) the effect of dark matter decreases with time,
    b) the gravitational force is finite, ie the gravitational potential is the same from a certain density,
    c) black holes have no singularity,
    d) black holes are older than the universe (stars, plaids) around us,

    Tomas TRNiK, EU, Slovakia, Bratislava
    sorry, translate google translator :)

  10. Very nice summary of current situation. Do you have references on condensed matter approach to the problem? Thanks.

  11. Do you think that improving our understanding of Gravity (a modified Gravity) is a required step towards a theory of Quantum Gravity?

  12. By "modifying gravity" I think Dr. Hossenfelder means modifying our model of gravity--changing the equations. Another alternative is to keep the same model/equations and assume there is more mass (which we can't otherwise detect, hence dark mass). So what seems to be possible are:

    1) Our model of gravity needs to be modified (at long distances, well beyond what we can observe in our solar system).

    2) There is more mass than we can observe by telescope, spectral analysis for dust, estimates of planetary mass per star, etc..

    3) Or a combination of the above, which is what Dr. H is leaning toward. Her recent web seminar discussed an example. In that example the modification was due to a different sort of interaction of condensed dark matter which could combine with gravity at very low temperature, if I understood it correctly.

    4) Or something else we haven't thought of.

    So far none of the above are known for certain. See the blog "Triton Station" for lots of technical data.

    1. Aside from his blog "Triton Station" Prof. McGaugh has also given a Golden Webinar recently (i hope the link is ok, still waiting for Dr. Hossenfelders one to be uploaded, but it's the same series) where he details his thoughts on the matter:
      Also, related to that, there is work trying to reconcile MOND like theories with the CMB power spectrum (see e.g. A new relativistic theory for Modified Newtonian Dynamics).

    2. Errata: My comment above was meant to be a direct reply to C. Thompson's question above, but I managed to get the wrong posting box. As a stand-alone it looks like I am imposing my opinion unasked, which I did not mean to do.

    3. Hi JimV,
      thanks for clarifications and recommendation for further information, I don't think I've read or watched anything by McGaugh yet.
      I think I've had different concepts slightly muddled through no fault of Dr Hossenfelder's.
      I watched the last couple of interviews Dr H did, I should review them.
      Your comment comes across as a general contribution to the topic.

      @G Bahle Thanks also for your information.

  13. Sabine, could you recommend a technical-level paper that would go through some of these issues? Review would be great.

    I'd also be curious if there are any robust predictions for what you might see in a terrestrial experiment in a mixed particle-modified gravity model. E.g. can you have a typical particle-style signature but the number density is changed relative to the usual expectation, or is it is something more complex?

  14. I think it is possible that DM and something similar to Verlinde gravity or MOND are different phases of a field. I though found the comment about the Bullet Cluster puzzling. The Bullet Cluster result found the Einstein lensing regions separated from the luminous matter. This pointed to how DM was noninteracting and by momentum conservation continued moving along its merry way, while the two regions of luminous matter being interacting stuck more in the collision. This was declared a major defeat for MOND as a modification of F = -GMm/r^2 for small accelerations.

    1. It's true that there appears to be non-visible matter in the Bullet Cluster. However, that does not mean that such is non-baryonic, i.e. dark matter. In fact, both LCDM and MOND require that there be some degree of non-visible baryonic mass, as much as 30% of the overall mass!

    2. To be honest I increasingly entertain the prospect that ΛLCM and MOND are both simply wrong.

    3. As I've said many times before, we know that MOND is "wrong". To begin with because it' s a Newtonian limit. We're looking for the complete relativistic theory which has MOND as a limit.

    4. The odd thing about cosmology is that much of it is very Newtonian. The FLRW for k = 0 is Newtonian. Then for galaxies, all except the central region near the black hole, is pretty much Newtonian. For average velocities of stars v = 200km/sec or so there is not a lot of relativity involved.

      Of course to connected MOND to GR one has to consider a covariant formulation of MOND or the Verlinde gravity.

  15. Radical Panpsychism
    postulates that universes and their particle offspring evolve by natural selection to become better at being homunculi because the ideal type of body depends on the environment which is very diverse and always changing. Higher quality smart conscious homunculi result in more successful reproduction of universes.

    The more massive and electrically charged a particle, the more time perception and cognitive ability the particle has according to radical panpsychism.

    A very massive particle of dark matter would be an excellent candidate to be a homunculus in brains using radical panpsychism theory. Normally dark matter has miniscule electric charge of about one millionth that of an electron and would be in a sleep state but if it is a homunculus then a brain would have a way to wake it up and its positive charge would increase which would cause it to be surrounded by a great number of electrons that can enable large transfers of information in and out and vastly increase its time perception allowing for a high bandwidth of electromagnetic homuncular code in and out.

    The electromagnetic homuncular code is a language or code for dark matter serving as homunculus to send coded streams of photons to the brain for free will actions and decisions and receive codes for sounds, images, ideas, emotions and other qualia.

    If people have a dark matter particle homunculus then an artificial body industry would arise which allows for people to have unlimited lifespans and choice of bodies such as bodies suitable for the moon or mars!

    1. The idea that elementary particles have consciousness is incompatible with evidence. I explained this here.

    2. I am surprised Dr. H condescended to respond to this post. I want to speak up because I also endorse a form of panpsychism but I stick with the rigorous treatment given by A.N. Whitehead. For Whitehead, any real entity, called an 'actual occasion', or 'actual entity', in his metaphysics, has a self-referential experience of being, that is to say, a subjectivity. It has both a physical and a mental pole, but his use of the term 'mental', is not synonymous with consciousness. He even writes that in the case of very basic 'actual occasions', like an electron, the mental pole, while present, is an almost negligible component of it´s constitution. For Whitehead, consciousness is a very rarified form of subjectivity found only in more complexly integrated systems of actual occasions.

      Whitehead writes in Process and Reality (1929), "The principle that I am adopting is that consciousness presupposes experience, and not experience consciousness. It is a special element in the subjective forms of some feelings. Thus an actual entity may, or may not, be conscious of some part of its experience."

      I think Whitehead would reject the notion that a simple particle, mysterious dark matter or otherwise, can embed the full complexity of animal consciousness like this idea of a 'homunculus particle' suggests, and I certainly do as well. I think its irresponsible to apply the term 'consciousness' to elementary particles and is not what Whitehead's form of panpsychism supports. It also gives the otherwise venerable tradition of panpsychism in the philosophy of mind the status of a crack-pot theory that people like myself are trying to overcome. Its not just a wrong idea, but counterproductive.

      As a former neuroscientist, I also find it distressing that the 'homunculus' idea is still being invoked today. There is no 'little person inside a bigger person'! Consciousness is much more likely a feature of the brain system as a whole, rather than contained as a kernel of dark matter within the living brain. It is an integrated multitude of actual occasions Whitehead would call a 'nexus'.

      My apologies to the group for this tangential comment that is WAY off-topic on a discussion of dark matter! I just wanted to rebuke this abuse of the panpsychism tradition and its attempt to co-opt the uncertainties around dark matter for ill-conceived ideas.

    3. The scientific way is for experiments to determine the truth or falsity of a theory. Do you own experiment such as the following and I will listen more to what you say:

      You would need to first break the electromagnetic homuncular code to discover the location of the homuculus because then you could send tones or colors to the homunculus with a electromagnetic emitter to quickly triangulate the location.

      It is sort of like SETI, but instead of searching for extraterrestrial intelligence by searching radio waves, you are searching for an homunculus by looking for electromagnetic codes associated with sensory input and voluntary actions. Call it, SICH, Search for an Intra-Cranial Homunculus.

      The microtubules are good candidates for antennas because they are long, rigid and thin and some researchers like Penrose and Hameroff have already associated them with consciousness.

      With SETI, a lot of thought is given to which frequencies to search, with SICH, the job is easier. If microtubules are the main antennas you can search the frequencies the microtubule absorbs and emit for that part of the brain using a spectrum analyzer. You can then use neural net AI to discover codes the microtubules are transmitting or receiving. If the AI can tell what color you are looking at or what tone you are listening to from EM radiation emitted from microtubules alone you may be on your way to cracking the electromagnetic homuncular code!

    4. Let me assume for the moment all elementary particles have consciousness. Maybe it is some quantum number. If every particle has the same unit of consciousness then how do we measure it? It is not possible to do so from some domain without it, because consciousness is everywhere. Only if there are particles without consciousness or at least differences in this "quantum number" called consciousness can we ever hope to measure anything.

      The only thing worse than a theory that explains everything is one that explains nothing. A theory that posits consciousness is "ALL" has the effect of not being able to explain anything, or much of anything. Explaining consciousness by saying it is universal in all particles and objects really does not explain consciousness.

    5. If a particle is a baby universe then it would really be very complex even if they externally behave in very simple ways -- a sleeping person has very simple external behavior but internally a lot of very complex things are occurring both physically and mentally (dreaming).

      If particles are sleeping then their external behavior might just revert to default mode which is simple and mostly predictable (quantum mechanics). It is only with high mass particles or quantum coherent molecules that quantum mechanics can transition to libertarian free will physics.

      A higher mass particle would have more time perception as suggested by the de Broglie frequency mc^2/h. Close to the speed of light, time perception would slow down so it becomes m0c^2/(h gamma).

      There is another problem for high mass particle Alice to send a lot of information to high mass particle Bob electromagnetically -- bandwidth. Both Alice and Bob would need to be a positively charged particle or a nucleus surrounded by many electrons to send/receive coded streams of photons.

      If particle Alice is not in the presence of awake particles sending valid photon streams of homuncular code then there is no need for a lot of bandwidth so a standard number of electron antennas are sufficient. But if chatty Bob comes by, Alice might need to up her electrons by decreasing her fine structure constant and therefore increasing her electric charge. Normally the fine structure constant would limit a particle or nucleus to about 137 electrons at most. Both Alice and Bob would both need to up their bandwidth if they both expect to communicate large amounts of information. If upon detecting valid homuncular code, Alice and Bob were able to decrease their own fine structure constant, their electric charge would go up and they would be surrounded by more electrons which would dramatically increase bandwidth.

      Homuncular particles are like little holodecks, the particle feels like a certain body moving around in a VR space. Particle Alice would experience particle Bob as an avatar in her VR space, same as Bob. Particle Alice, having no brain or body would know little about the real world and would live in a VR world but would still be able to experience sights and sounds and think and communicate with other intelligent particles that would appear as avatars in her VR space.

      When a homuncular particle has a brain and body attached, the VR world can correspond to the real world at least when you are awake. You would also be awake much more when you have a brain and body because you (a homuncular particle) are being bombarded with valid homuncular code which would increase time perception.

      If the presence of valid homuncular code increases time perception, then the equation for conscious time perception becomes qm0c^2/(h gamma) where q would be the ratio of valid code to noise which results in an increase of positive charge to increase the bandwidth by increasing the number of electrons.

    6. In reading the linked post ("Electrons Don't Think") and some of its comments I got a vague notion of what some of the panpsychists seems to be saying. What we call consciousness is made up ultimately of the interactions of elementary particles--because everything in this universe is. Without those interactions there would be no consciousness. However they seem also to go beyond this to think that there is some hidden-variable spiritual aspect involved. I take somewhat the opposite lesson (as I have argued previously), that consciousness is a mechanical/physical process available whenever particle interactions are complex enough to provide (with much development over billions of years, in our case) computational ability, memory, sensory ability, and some ability to manipulate the external environment. In our case that is accomplished (discretely) by huge numbers of neurons and synapses, triggered by accumulations of discrete electron charges, which can process sensory nerve impulses from the environment and control muscles to manipulate the environment. With that as a basis, I see no issue in principle with the development of machine intelligence/consciousness. (However, a big one in practice. It is currently not feasible and will never be easy to build the machine equivalent of 100 billion neurons, which is roughly what a typical adult human has.)

      Also, as Dr. Crowell says, to think this solves the made-up problem of qualia is an exercise in tautology. Qualia and electrons (or any other particle or field) are the same problem philosophically, it seems to me. We know electrons exist and what their properties are and ways to make use of them, but we will never know why they exist. (Unless more fundamental sub-particles are discovered.) They are among the properties this universe has. The experiences called qualia are the same. Their necessity and use is also tautologous: they are how we experience what our nerves and chemical impulses are telling us; it is impossible to experience something without a signalling experience.

      Computers already have some signals they can detect (keypresses, mouse-clicks). What does it "feel" like for them? I have no idea of course, but a detection is an experience, so they too can have qualia. Not the same as ours, but as useful.

      Pain is one of those signals, telling us to alter our behavior. Computer programs have analogous mechanisms, such as virus-detection, and Ctrl-Alt-Delete in Windows.

      So ultimately, the major disagreement I have with panpsychists is that the existence of (specific) qualia (or of fundamental particles and fields) is a problem which needs to be or can be solved, by the use of different labels or in any other form of rug-sweeping-under.

    7. I think pansychism and the attribution of consciousness and communication abilities to non-living particles and systems is unnecessarily overcomplicating how matter and energy interact.

    8. @JimV: I see little about quantum mechanics or QFT that suggests anything conscious. We might further consider the photon. The photon does not even have a proper time. I cannot think of anything more unconscious than a photon.

    9. Dr. Crowell (thanks for the reply), I agree that there is no evidence or logical reason for particles governed by QM to be conscious. However, there is a link between that and what some panpsychists seem to be saying, in that those particles and QM mechanisms are the elements by which consciousness is achieved. Because as far as I know, there isn't anything else involved in brains. There certainly isn't anything else in the computers we make, and the capabilities they have already demonstrated convince me that they can, in principle, achieve intelligence and consciousness.

      I agree with Dr. Hossenfelder that intelligence and consciousness are emergent properties, and that panpsychism makes the fallacy of not seeing the forest for the trees. I am trying to explain that to panpsychists in these comments. For example, nuts and bolts and other parts make up automobile engines. The panpsychism thesis seems equivalent to saying that since cars can move, their individual nuts and bolts must also have the innate power to move.

      They (in the linked post comments) claim this fallacy, if while not true in general happened to be true in the claimed case, would help explain qualia, so I tried to explain the fallacy in that claim also. Philosophy would like to explain everything, but that is a hopeless task, as I think Socrates understood.

    10. P.S. to Dr. Crowell: excellent point about photons!

    11. A theory can be criticized as being incompatible with evidence. But I don't characterize panpsychism as a theory; it's just an idea. I fully realize it has no explanatory power in a scientific sense. But neither does any other idea about consciousness, at this point. Elevating panpsychism to the status of a theory, just so it can be shot down as such, strikes me as a bit unfair.

    12. Ideas can be bad, and most are. Science (including math and logic as part of math) is the only way I know of that we have to tell good ones from bad ones. Believing as I do that all progress is made by trial and error, I don't intend to fault people for having bad ideas, but trial and error only work if the selection process (for success and failure) is rigorous. So I feel some duty to try to contribute to it.

      People who are getting paid to teach and practice philosophy showed up in the comments of the linked post to advocate for panpsychism. It seemed fair to me to give my views also, although nobody is (or should be) paying me for them.

      I certainly don't mean to elevate panpsychism to the status of a theory. I think it is just a bad idea. (Of which I have had plenty myself.)

  16. Hello, thank you for the clear video!

    How do the observations of dwarf galaxies that appear to have no dark matter factor into your opinion?

    From my limited understanding, it seems like it would be hard to explain this with modified gravity, because there don't seem to be any parameters that would let some galaxies interact differently with gravity than all the others.

    1. I believe this issue has been discussed at one or more posts at "Triton Station". For one thing, this proposed explanation using dark matter illustrates the extreme plasticity of the dark matter hypothesis, in that proponents are free to adjust the amount of dark matter to match as many observations as they can, without any explanation for the variations. Secondly, I think Dr. McGaugh at Triton Station has calculated those galaxies using MOND and found agreement with observation to a fair degree. MOND has a single parameter, a0, that acceleration level at which gravity begins to decrease as 1/r with distance rather than 1/(r^2) and a single value for that parameter fits basically all the well-observed galaxies. A small (dwarf) galaxy would be likely to be entirely within the 1/(r^2) domain, which would be interpreted under the DM hypothesis as no dark matter.

      (Don't take my word for it, go to "Triton Station" for the actual data.) (Again, MOND itself is not a complete theory, it is just a shortcut which seems to be trying to tell us something about our gravity model.)

    2. JimV,

      The transition from 1/(r^2) to 1/r would seem to suggest, that the effective gravitational mass contribution, from that point outward, has transitioned from the central bulge to the distributed mass of the disk. MOND avoids the difficulties of calculating the gravitational effects of such a distributed mass by couching its math in a second order derivative, the resultant acceleration. That isn't a bad thing, but it means that MOND does not explain the cause of the effects it is good at calculating.

  17. As Sabine checked off one successful prediction of MOND after another, I reflected on the remarkable precision with which this phenomenological theory was able to match the data as delineated in many charts imbedded in numerous blog posts at Stacy McGaugh’s tritonstation website. One chart in particular illustrates Renzo’s Rule, which states: “For any feature in the luminosity profile there is a corresponding feature in the rotation curve and vice versa”. In his blog post: “It Must Be So. But which Must?”, under the “MOND” category, there is a rotation curve chart of the galaxy NGC 1560. One can see in this chart that the MOND prediction (blue line) tightly tracks the luminosity profile of the galaxy. As Stacy points out in that article MOND requires only one parameter to achieve this tight correlation versus a minimum of three for the Cold Dark Matter paradigm.

  18. Good morning Sabine,

    thank you very much for the blogpost.
    I enjoyed the video very much.

    The connection of Dark Matter and Modified Gravity looks very engineer-like to me.
    But it is 10 times better than extra dimensions in space or time.
    These guys treat extra dimensions like a joker in a deck of cards or a fairy godmother who fulfills them all their wishes.
    But I think it's a mortgage they have to pay for.

    I distrust the particle field concept. It leads us or one must say lures us
    to quantum mechanics and all its contradictions. I dropped it many years ago.
    The only acceptable reason for its use is: we have no other concept.
    But that is not a good reason.
    More on that when you talk about our mutual friend.

    Many thanks for Tully-Fisher and Renzo.
    Many greetings and have a nice Sunday

    1. Hi Stefan,

      Good morning to you too :o) Yes, you are right, it's very engineer-like. Which is why most astrophysicists don't like it, I think. They've all become used to what we call a "top-down" approach. That basically means you guess a theory from higher principles and try to show it fits with data. It works incredibly badly because there are just too many "pretty" theories you can guess. Milgrom's ideas are the exact opposite, they're "bottom-up" - looking at the data and trying to find patterns in it. I think we have to build on that bottom which Milgrom has laid.

      I am not sure in how much one actually needs the quantum effects in cosmology. Yes, in principle one needs them to create the superfluid in the first place. But in practice you can treat it like a classical field. Wish you a good Sunday too,


  19. could mond plus black hole remnants explains everything ?

  20. When you say "dark matter creates friction" are you referring to dynamical (gravitational) friction or hydrodynamic friction? Hydrodynamic friction explains the separation between the optical and X-ray images in the cluster collisions, but why would dark matter experience more dynamical friction than the optical sources?
    Also, what kind of MOND theory could explain why the dark matter sticks with the optical components in the collision rather than the bulk of the baryonic mass (the X-ray sources)?

    1. Yes, dynamical friction. Dark matter doesn't have more than normal matter, but more than no matter.

    2. Let me make my question more precise. If the dark matter lensing signal is MOND, why is it not with the main concentration of ordinary matter, that is, the hot gas. Instead it is with the much smaller optical matter (galaxies) signal.

    3. I wasn't talking about MOND, why are you?

    4. My mistake. You talk repeatedly about modified gravity in six or so paragraphs. I thought that was a synonym for MOND. Let me modify my question: "If the dark matter lensing signal is modified gravity, why is it not with the main concentration of ordinary matter, that is, the hot gas. Instead it is with the much smaller optical matter (galaxies) signal."

    5. Hi CIP,

      No, modified gravity is not a synonym for MOND. Modified gravity is the relativistic completion that must give rise to MOND in some limit. We already know that MOND is wrong, to begin with, because it's not generally covariant.

      ""If the dark matter lensing signal is modified gravity, why is it not with the main concentration of ordinary matter, that is, the hot gas. Instead it is with the much smaller optical matter (galaxies) signal."

      Why should it be? It's a dynamical system. It has a time dependence. And as I explained in my video, modified gravity works by introducing new fields. These fields have their own time-dependence. The lensing signal can be off-set from the baryonic matter in modified gravity for the same reason as in dark matter models: more degrees of freedom.

  21. I was going to add one more observation to my earlier comment, but was rather tired after our local cycling club’s inaugural season ride yesterday and pizza/beer party afterwards. That was to point out that both MOND and LDCM have their particular deficiencies. For MOND it is a lack of a mechanism to explain its empirical success in galactic structures, so far, not to mention its inability to accommodate larger astrophysical structures as Sabine pointed out. For LCDM it is the lack of detection of a suitable particle, so far, to fill the role of the missing mass in galaxies and galactic clusters, though it readily can account for cosmological features of the Big Bang paradigm like the CMB power spectrum, etc., as Sabine explained.

    Greatly impressed by MOND’s ability to predict fine details in galactic dynamics, I wondered, like, undoubtedly, many other armchair, non-professional ‘theorists’, what might lie behind this unique success. Having had an interest in condensed matter anomalies for years and noting the common denominator of “acceleration” in both phenomena, made me wonder if their might be a causal link between the two despite their vastly different scales. But there was a major concern in this toy model, which was whether it might overstep the bounds that quantum mechanics imposes on the fleeting existence of negative energy densities, as the model requires such densities. If it doesn’t, the model can potentially provide a mechanism to not only explain MOND’s remarkable success in anticipating the kinematics of galaxies, but extend its domain to early universe cosmology. I say “potentially”, as it’s a rough-hewn idea and there’s a lot of data that it would need to agree with for any chance of this model to solve the outstanding puzzles in cosmology.

  22. Thanks! Great summary. Renzo's rule is particularly interesting.

  23. Thank you for this recent review. In the past, I have read that black holes or the right handed neutrino versions etc.. all cannot account for dark matter due to certain observational bounds.

    When taking a scenario of MOND for part of the observations into account, would such known candidates suffice to explain the observations that MOND cannot account for ?

  24. "Dark matter creates friction"? Now I know the MOND proponents are grasping at straws to keep their theories alive. Is there an actual reason that dark matter should cause friction? I don't see one; please explain. (I don't think there's any reason it shouldn't, either – it depends on the details of the dark matter, about which we have no clue.)

    1. Peter,

      I think you should read this before documenting that you are extremely biased against MOND out of ignorance.

    2. Dynamical (Chandrasekhar) friction:,with%20surrounding%20matter%20in%20space.

      However, this friction is usually proportional to the mass^2 of the body moving through the matter distribution, so I would naively expect stars and galaxies to be more affected than dark matter particles. Sabine may know better, though.

    3. As I already explained above, I did not say dark matter is more affected than normal matter. I merely said that dark matter is more affected than no matter.

  25. Yes, if you think science's explanatory power comes from statistics instead of storytelling, there would be no reason to prefer introducing a 10 parameter pure dark energy model or pure modified gravity model to explaining the data with two 5 parameter models.

    It's curious to me that the folks who ascribe very human notions of 'beauty' to different bits of math don't tend to so with statistics as often. But it's really quite nice!

    I'm going to blame prioritizing the explanatory power of coherent-sounding storytelling over the power of statistics on the persistent baggage of Aristotle ;)

    1. "I'm going to blame prioritizing the explanatory power of coherent-sounding storytelling over the power of statistics on the persistent baggage of Aristotle"

      But then explanatory power is the essence of science while statistics, and math generally, have no explanatory power, only descriptive abilities. Those descriptive abilities function as useful, essential, modeling tools within science, but they are not science, in and of themselves.

      To prioritize statistics over "the explanatory power of coherent-sounding storytelling" essentially elevates abstract human reasoning over empirical reality (those things that can be directly observed (detected) and measured), which is the sole basis of all coherent, scientific "storytelling" with explanatory power.

      The results of that peculiar inversion, of abstract math over empirical reality, are incoherent, nonsensical stories (e.g. QM-QFT) that invoke entities and events for which there is neither direct empirical (scientific) evidence nor plausible explanation. That is the unfortunate, persistent baggage of Plato, if you like.

      The root of the problem is human hubris. The belief, of some humans, that their abstract, mathematical imaginations are more reliable sources of information about physical reality than physical reality itself, is scientifically and historically baseless. The standard models themselves are dispositive evidence that that dog don't hunt.

  26. I've wondered why dark matter coalesces in and around galaxies (making the outer stars orbit so fast), but apparently is diffuse (as in spread out evenly between the stars) and undetectable in solar systems and the orbits of planets. An I thinking about this correctly? Could dark matter be localized in normal matter, in proportion to every atom? If an apple were 80 percent dark matter and inseparable from the visible matter, how would we ever know? This may be unanswerable, as there are too many "unknown unknowns" about dark matter.

  27. Very interesting article, reminds me of the debate in the distant past whether light is a particle or a wave. Turns out its kind of both though I think the dark matter problem isn't really a problem of quantum superposition. What's your personal opinion about it, Prof. Hossenfelder?

  28. Suppose the problem is never resolved e.g, beyond human comprehension as we currently understand it on realistic time scales. What general fields of knowledge or technology would be made more difficult or impossible to gain as a consequence? If an explanation in fact does not appear in say 2-3 generations would it be then accepted to say well we just can't figure this one out so lets move on?

    1. Why and where would you have us move on to? How long do you think it took from first thought about how useful it would have been to be able to start a fire to somebody actually doing it? If then within [n,n+k] generations we fail to figure out whatever you would have us figuring out, we move on again? Who declares n, k and the thing we are moving on to?

      Imagine I render you unconscious and you wake up in a spherical room equipped like a modest apartment but w/o any communication with the outside except a field phone. You can order anything except exchange of information with anybody outside but me. Nor, obviously, anything that would breach the walls. How long would it take you to figure out what colour is the room on the outside?

      Would some contrived ability I'd rather not think about to make your effort multi-generational make any difference? And if at some point we agree you will never succeed could you also agree that you will never really know the room?

    2. Hi Morris and Olmo Sirk,
      I think it could well be generations if not centuries to resolve what dark matter is and how it works, that the technology, method of analysis, or even the right idea may take some time to be developed.
      I am reminded of how long it took for a working helicopter to be developed; Leonardo da Vinci drew up designs for such a machine, and Australian inventor David Unaipon came up with a concept of a machine that flew using the same flight principles as boomerangs, 20 years before a working helicopter was finally built in 1936. I mention this because it wasn't until ancient technology was bought into the mix that the concept saw rapid development, as I understand.
      I think that changing the paradigm of what dark matter could be is an important step.

    3. The example I like to use is the wheel and axle. Archeological evidence of modern human bone structure goes back about 200,000 years. Archeological evidence of the wheel and axle goes back about 6000 years. Of course from the wheel you get capstans, pulleys, gears, watermills, windmills, and lots of other things, including computer hard drives. So once some technology is found it tends to snowball, until finally we amaze ourselves with our genius. The basic method is trial and error and the secret of it is to keep trying. (It also helps to have memory of what did and didn't work in previous tries.)

      Dark matter was a first try, and it worked well on some things and poorly on others. (See the "Triton Station" blog for details.) MOND was another try, and it predicts the ratio of the heights of the first and second peak of the CMB power spectrum as well as a tremendous lot of astronomical data. With these strong hints it seems likely to me we will come up with better tries. What seems to be stopping us is that a lot of physicists seemed to be entrenched on the dark matter side, and dismiss MOND results as some kind of conspiracy theory. (Again, MOND needs to be expanded or merged or otherwise fit into a complete theory, and there have been some attempts at this, some failed, some ongoing.)

  29. Hi Sabine,

    I strongly disagree with the simplest explanation (for what it's worth :). Why would Lambda be a constant? In a second order differential equation, that does not make real sense: it should also be a differential. And that is already modified gravity in its simplest form... and it makes a lot of difference even in the Scherzschild metric. The impact in cosmology is huge.

    Just put Lambda = (2 pi*1.048)/(3 Ru^2) and check the numbers (that is not a coincidence but a theoretical result, 4.8% is matter density). You get MOND, inflation, and the difference between the short distant to long distance measurements of the Hubble parameter (except for a factor 2 for the Hubble parameter which is too long to explain here).


    1. akidbelle,

      "I strongly disagree with the simplest explanation (for what it's worth :). Why would Lambda be a constant? In a second order differential equation, that does not make real sense: it should also be a differential."

      Lambda is a constant in the action. It ends up in the equations because the volume element isn't constant. Also, there's nothing wrong with constants in differential equations. There's nothing to "disagree" with here, it's rather trivial math.

    2. Hi Sabine,

      thanks for your answer. Of course the math is correct, even trivial. What about the physics ? I am sure you know the math does not describes it completely... and what do you do? Add a new field and parameterize. Do you take the field for reality or just ad-hoc mathematical scripture made to fit some facts? In the first case you may be very wrong. In the second case what is the physical origin of the parameter? Can it be replaced by geometry? If so, this is minimal - and modified gravity. That is the meaning of the formula in my comment.

      I wonder if you can make sense of this. If not I am just sorry.

      Anyway thanks again, your answer is very instructive to me, at second order. I think you and your colleagues may be stuck in predefined concepts and mathematical requirements. There can be no way out of this without going back to physics down to foundations.


    3. akidbelle,

      Your questions make no sense to me. A good theory must describe observations, that's it. If you "take the field for reality" is a question for philosophers.

    4. And that was published where?

    5. And that was published where?

  30. If dark matter turns out to be some form of condensed matter, the may be a way to detect it. First there are some assumptions about this matter that are likely true. This matter most likely is coherent and as such it is also bosonic. There might be a condensed matter process that converts Baryons and fermions to bosons. and/or energy. A galaxy wide bose condensate of this superfluidic matter is likely. But the character of this matter is likely to be very obscure though it is very likely to be seen as a ubiquitous process seen on the microscopic level here on earth. The micro sized dark matter processes occurring here on earth would likely be highly unusual, not of usual run of the mill fair that would demonstrate unthinkable and unacceptable physical consequence. As an example of some possible weird condensed matter stuff that I like as a possible dark condensed matter candidate is the Edward Witten's bubble of nothing(exotic vacuum object (EVO)). This is a micro singularity embedded in anti de sitter space.

    How would such weird stuff be detected? If it is coherent, it is likely to be in superposition. But it would distort the index of refraction of any EMF as photons are passing through it. Photons slow down when passing through a Bose condensate. Dark matter may be making major contributions in the production of observed gravitational lensing. Dark matter may act in distorting light similarly as light that is passing through water. EMF passing through coherent matter would also likely become polarized.

    Instead of Thomson scattering of electrons, polarization of the Cosmic microwave background radiation might have been produced by a state change from coherent dark matter in plasma to decoherent baryonic matter in a Bosenova. In addition, observation of the possible polarization and refraction occurring in gravitational lensing might not be primarily caused by gravity but primarily generated by coherent dark matter effects on EMF passing through it.

    How would general relativity handle a galaxy sized entangled singular waveform generated by a population of micro singularities embedded in micro bubbles of anti de sitter space?

    1. Hi Axil,
      I did wonder what you'd make of this dark matter condensate. :)
      If you don't mind answering, where would the anti-de Sitter space be situated?

  31. Sabine,
    You gave us a great summary of the present state of DM. Bringing up the question: is the solution to DM a mix or a combination of a modified gravity and a specific particle? I know a model which is partially both, one could say.

    This model is based on the very simple but shocking assumption that gravity has nothing to do with mass (or energy). This is an unfamiliar approach but I do not know any observation or experiment which is in conflict with this assumption. (And I have discussed it with a prominent physicist/cosmologist not objecting to this statement.)

    If we follow this way then every elementary particle contributes similarly to the gravitational field irrespective of its mass. As a consequence, light particles like neutrinos and photons contribute similarly like e.g. quarks. And both types, mainly photons, are spreading out of the galaxy to all directions causing a corresponding gravitational field. I will list here the open problems of your list which are solved by this approach, in parts even quantitatively with good precision.

    First example is the rotation curves. I have a corresponding calculation for the well measured galaxy NGC 3198. The result of this view (i.e. the assumption of photons as DM) is not only the correct shape of the curve but as well the correct height of it within a tolerance of a factor 2, which conforms very well in view of the level of knowledge of this galaxy. (On the other hand, if this approach would be just phantasy, there should be a discrepancy of several orders of magnitude between calculation and observation).
    The situation at the galaxy clusters and gravitational lensing works similarly, however these were not evaluated quantitatively.

    Further consequence of this model is a flat distribution of DM in the center of a galaxy, as photons behave in this way.

    Also the observation of the Bullet Cluster conforms to this assumption as the speed of the photons is not affected by friction. So the observed distribution is explained.

    Renzo’s rule is a direct indication of the role of the luminosity (i.e. the photons) on the rotation.

    The Tully Fisher relation also shows the dependency of the gravitational influence of photons, and particularly the dependency of the wavelength shows the dependency on the *number* of photons in this relation. It further yields information about the structure of big galaxies which, however, has to be further investigated.

    “Small satellite galaxies are often aligned in planes”. The photons emitted by a galaxy are having a higher density in the plane, so the gravitational field is greater there and so its influence on the collection of matter.

    To the history of the model: This model of gravity was not developed in order to explain dark matter. The model followed from considerations about relativity; its relation to DM only appeared later on.

  32. A gravitational field is a configuration of Spacetime. The expanding Spacetime of a Void is a different type of Spacetime configuration. The two types abut each other right where observations indicate the presence of dark matter. It seems reasonable to ask if the dark matter paradigm is really an unexplored consequence of interacting Spacetime fields.

  33. I know what dark matter is. Dark matter is the pit around a sandcastle. Yes, when you build a sandcastle in a flat beach, there is always a pit formed around it. That means, the density of a vacuum in that gravitational pit is lower than expected. On average, the density of matter in the space between the stars of the Milky Way is 0.1 neutral hydrogen atoms per cubic centimetre. In a gravitational pit around a galaxy (or a cluster of galaxies) the density of matter is drastically lower than that value, so there we have what we call dark matter. The rapidly formed clusters of matter in outer space produce deeper gravitational pits around them. If the formation of clusters of matter is slow, their gravitational pits are shallow. That explains the reason why some galaxies, or cluster of galaxies, don't exhibit great amounts of that alleged dark matter, but others do. So, a gravitational pit is a gravitational "anti-well", If, by definition, we put the value of the gravitational potential of a flat area equal to zero, and any gravitational potential of baryonic matter as being lower than zero, at any point near its barycenter, then a gravitational pit is an area where the gravitational potential, at any spatial point inside it, is always greater than zero. Believed or not, that is what we call dark matter.

    1. Can you show quantitatively that your model of dark matter describes the observations correctly?

      There is a lot of nice ideas around but without quantitative proofs there is no judgement possible regarding their correctness in describing our physical world.

  34. Could it be as simple as gravity falls off even more at large distances? I’ve always been suspect of both infinities and continuous math in physics. The continuous equations are easier to work with, but math is not the universe, no matter how much mathematicians want it to be. If we could look inside a black hole, I suspect we’d simply see a highly compressed matter core, not a singularity.

    Why should gravity’s reach be infinite? Other than the maths look nicer when it is? I wonder if you could look at the universe as having a precision limit. Some hard limit maximum number of bits to describe phenomena, which would account for non infinite results.

    1. "Could it be as simple as gravity falls off even more at large distances?"

      No, because (a), it doesn't fall off, it gets stronger, and (b) the transition happens at a certain acceleration, not at a distance.


    2. “No, because (a), it doesn't fall off, it gets stronger, and (b) the transition happens at a certain acceleration, not at a distance.”

      Interestingly, the order of magnitude of that acceleration is the same as the order of magnitude of the accelerating expansion of the Universe....which may be a simple coincidence.

    3. " ... and (b) the transition happens at a certain acceleration, not at a distance."

      The transition happens - or becomes visible - at that distance from the center of the galaxy where the baryonic matter ends. This is at least true for the rotation curves of galaxies. Because at the rim of the galaxy the gravitational field caused by the baryonic matter decreases, but the shape of the curve does not reflect this decrease.

    4. Energy densities vary between planetary systems, galaxies and universe average a lot. Does this shed any light on problems with gravity theories? Newton good to Mercury and Einstein OK in our solar system but not in star forming galaxies. Coincidence, misunderstanding,or a clue?

    5. "The transition happens - or becomes visible - at that distance from the center of the galaxy where the baryonic matter ends."

      That's just wrong.

  35. I suggest that there is no such thing as Dark Matter, that we are experiencing a bleed over of gravity from a parallel universe through the brane that separates the universes. When there is enough mass in both universes in nearby spaces, they bleed together showing more gravity than either would normally have.

  36. What a delightful post. I completely agree and would add - there has been an unfortunate tendency in physics toward what I like to call "One ring to rule them all!". That is to say, coming up with the Big TOE - Theory of everything. I think it is important to think in these terms, but it becomes obsessive. Humility says we should come up with a theory to explain one small observation, and another theory to explain the next. Once you have a series of theories that explain various phenomena, you can then start to look for connecting tissues, simplifications. In the case of dark matter we don't have any theories to connect - or rather, people keep trying to connect theories that haven't yet been formulated for various observations. I think the solution is to scale down the theories to explain just the particular phenomena being studied. Integration and finalization can come later.

  37. Not an astrophysicist, so I could well be wrong, but I understand that all astrophysical measurements involved here (CMB temperature included) are light spectrum-based measurements. If you assume that light does something it does not do or miss something it actually does (at the quantum level), you might misinterpret large-scale distances, velocities, temperatures and so on, would not you? May this be another possibility (among many others, of course), in addition to combining dark matter and modified gravity? Thanks in advance.

  38. >> "The transition happens - or becomes visible - at that distance from the center of the galaxy where the baryonic matter ends."

    That's just wrong. <<

    Which way else can the rotation curves be explained?

  39. If only the observable universe is considered then galaxies near the latter’s periphery will be receding our galaxy at close to light speed. It occurred to me that the Fitzgerald/Lorentz contraction and the resulting relativistic huge increase in mass of such galaxy’s peripheral star systems might be so magnified that the gravitation effect thereof on our galaxy (with us as observers) would be vastly magnified. I am not capable of the mathematics involved but doubtless someone else could agree or disagree.

    If so then one result would be that the gravitational effect on a spiral or elliptical galaxy at right angles to its flat plane would be less from the peripheral gravitational effect of that distant observable sphere that it would be along its flat plane. Along the flat plane of such a galaxy the proximity of the other galaxies in that plane would be increased by their proximity in that one general direction but obviously not at right angles. Thus, the extra rotational effect of Newton’s mean square laws of gravitation would be enhanced in accord with Vera Rubin’s findings from more than about half a century ago. In short dark matter can be explained as a mainly gravitational effect: so simple really but it requires a physicist/cosmologist to condemn or agree the relativistic enhancement supposition.

    This would also be in accord with the fairly recent conformational findings of the astronomers that there is no such dark matter rotational effect observed in spherical globular cluster galaxies. A further conjecture to explain dark energy, as an added bonus, would be to consider the possibility of gravitation being a repulsive force using the same rationale, but with the further assumption that large quantities of mass (such as planets around a star) have a blanketing gravitational effect on each other, thus drawing them together via repulsion form the outer periphery. Counter intuitive of course, but it seems equivalent in principle to the blanketing effect in EM radiation of conducting materials obstructing signals from radiating transmitters. One further observation is that Mach's Principle could also be satisfied by such a rationale.

    1. "It occurred to me that the Fitzgerald/Lorentz contraction and the resulting relativistic huge increase in mass of such galaxy’s peripheral star systems might be so magnified that the gravitation effect thereof on our galaxy (with us as observers) would be vastly magnified."

      Objects at relativistic velocities do not increase their mass or their gravitational attraction.

      See explanation here:

    2. Severage wrote:
      "A further conjecture to explain dark energy, as an added bonus, would be to consider the possibility of gravitation being a repulsive force using the same rationale, but with the further assumption that large quantities of mass (such as planets around a star) have a blanketing gravitational effect on each other, thus drawing them together via repulsion form the outer periphery. "

      Farnes (2018, e.g. in 'Negative-Mass Dark Fluid' in Sci News) uses negative mass particles as the source of dark matter and dark energy, where in his model the negative mass particles gravitationally accelerate away from one another. In a previous blog topic Sabine holds that two negative mass particles would accelerate towards one another, so Farnes model has difficulties on this website.

      I have an earlier, naive, amateur paper agreeing with Farnes's results. Simply putting -m for negative masses in Newton's Laws gives negative masses accelerating away from one another. But Sabine says that she is relying on GR for the acceleration towards one another.

      Just a few extra ideas here. If the DM is made of repulsive gravitation then that might explain lack of friction? Not sure about density in cores which peak but, if the DM is predominently outside the galaxies, would there still be peaks predicted?

      Austin Fearnley

    3. Austin, wow, you've put an immense amount of thought and effort into your very interesting concepts, in the dozen submissions to the arXiv. I meant to post this downthread in response to your comment at 4:50 PM, May 06, 2021, but there doesn't seem to be a way to delete it here and post it there. I was actually fascinated by Jamie Farnes' model, and even toyed with shoehorning my own quite amateur ideas into his model. One thing that seems to mitigate against antimatter having negative gravitational mass is that when, for example, a positron and electron collide they produce two positive energy gamma rays of .511 MeV each. I’ve got to go over to the post on Jamie’s model to refresh my memory on what everybody was saying. It’s a bit early here in the northeast USA to do much deep thinking, but I’ll work on a longer response later, after checking out your papers on the arXiv.

    4. David, I am an amateur phyicist so my papers are online but not on arxiv. I only started working on physics after retiring and followed Leonard Susskind's excellent online physics courses. Farnes worked with unspecified negative mass rather than antimatter. So did I at first but later used antimatter. I have ideas about negative-mass antimatter and, as noted already, I feel there is no conclusion to be reached from up versus down results Aegis may produce. If I take that view, then it is not surprising that I am dubious about photon energies. I am over 70 and am actually trying to give up physics ...
      Austin Fearnley

  40. My small, non-scientific brain wonders if "Dark Matter" is something more basic - a sign of a framework or structure that was in some sense pre-existing. We're seeing the contours of the mold into which our universe's matter was poured. Galaxies naturally formed at some points in this structure, not others...

  41. The fundamental sciences have never accepted condensed matter science as a proper trustee of knowledge about reality. I think that the subconscious basis for this distrust revolves around the ingrained perception that the laws of nature are unchanging and immutable. But in condensed matter science the laws of nature are malleable and can be adjusted to satisfy just about any desire that mankind needs to be satisfied.

    Many practitioners of the fundamental sciences will not accept results from condensed matter science if those results violate those sacred immutable conservation laws and many others fear being branded as heretics if they tolerate any law breaking.

    In the delicate Kabuki of blending waveforms, with some quantum field theory here and a pinch of magnetism there, then add a portion of electron confinement with the dash of the uncertainty principle and a gentle application of some vibration, a new world begins to emerge. So condensed matter science can make electric charge disappear or assume a fractional value over a wide range of fractional states; electrical resistance can be disappeared through superconductivity; those fundamental immutable particles and fields can be modified so that a hundred different emergent particles are being created to meet any number of emerging needs.

    The more stiff necked and stubren practitioners of this modern day witchery are often outcast as pseudo scientists and crackpots. These conjurors usually respond to this flood of rejection and recremination by hunkering down within the protective confines of their own newly formed companies and withdraw into the secret world of practical product development where their magic is protected by non disclosure agreements and anti reverse engineering strategies. Their new masters are now the venture capitalists who could care less about the nature of reality as long as the projections of the margin percentages are good.

    As a fearless quintessential pragmatist after many years the situation for her has changed. Always at the vanguard of things, Dr. H now realizes that there could be more to reality then the immutable laws of fundamental science. There needs to be a reaching out so that some adjustments can be made to those fundamental laws in order that reality can be properly dealt with on its own terms. There very well might be some unrecognized magic floating around between the galaxies that make a difference to what actually happens in the universe.

  42. "because dark matter creates friction

    I read often and have never commented but I don't get this. To my layman's understanding, friction is entirely elections swapping photons with each other. Whether I'm sliding down the slippery slope or or just rubbing my my cold hands together, that's the friction I know.

    How would dark matter create friction?

    1. I think friction ultimately is matter bumping into matter. In baryonic matter with charged particles the bumping is resisted with EM effects, but take those away and two matter particles will still bump as they cannot both occupy the same place at the same time. (Some references were given in previous comments which probably explain it better. Search the thread for "friction".)

    2. If we accept that dark matter is in fact photons then there is no friction effective as the speed of photons is not affected by matter in the way as normal particles are. And the arguments for this assumption (photons as dark matter) I have explained earlier (see above).

  43. Wow, this is crazy exciting!! This is the most exciting video on dark matter in years since the WIMP miracle did not pan out! Still watching for axions, but watching your videos was getting the feeling there is some kind of phase change going on.
    That being said I wonder I wonder if thinking about 'buoyancy' might apply (i.e. you sink when a cold dense liquid, you float when a light gas). Consider that there is some field energy density (field energy density being energy+mass, I don't know, the Plank density which includes the vacuum energy?). Below it there is only gravity by Higgs field and space-time curvature of the Higgs field. You get to "float". Perhaps you are even always in superposition.
    But when above that density you now interact with each other and you have a centre of gravity. You are now a particle with realposition. You now have gravity by energy-bonds which is >> Higgs field gravity. Molecular bonds boost your energy density that large constructs have gravity.
    I think the kicker might be that when really hot you ionize and end up with a lower density even though you have a lot of energy (analogous to a sublimation).
    Also one thing I just do not get about gravity, if gravity is moving at the speed of light and all the planets are being drawn to where the centre of gravity was eight minutes ago then shouldn't the system be unstable? I asked on one forum and they said that the aberration of gravity is being cancelled out by velocity-dependent interaction which makes no sense to me! Help!! I wonder if just a phase change could be the better solution to this problem. Help!!

  44. Craig Pichach says:
    “ … Also one thing I just do not get about gravity, if gravity is moving at the speed of light and all the planets are being drawn to where the centre of gravity was eight minutes ago then shouldn't the system be unstable?”

    This is a good question which has kept physicists busy for a hundred years. It has a quite straight explanation:

    Fields like the gravitational field are not subject to aberration. That means in the case of gravitational attraction of two stars: The one star (A) does not see the direction of the field from the other one (B) where the other star was before (e.g. your 8 minutes) but where the star is at the time when the field is received. The reason is that the field vectors which leave the star A towards star B and later meet B are pointing to a different direction than along their of motion towards B.

    This sounds a bit confusing, but if we assume exchange particles mediating this field and follow their sequencing in their relativistic motion, it becomes obvious.

    This is BTW as well true for an electrical field, and here it is possible to check the lack of aberration in a laboratory.

    1. Antooneo,
      I thought the gravitational field is subject to aberration given it moves at the speed of light.
      Could we get a video explaining the difference and/or how that works? Also could you send me a link to a paper where there is no aberration in a laboratory?
      For some reason I cannot wrap my head around how the star can "see" the direction of where the star was before without information being passed along faster than the speed of light.
      I also don't get the lack of electrical field aberration. For lack of field aberration I used to think that it was because an electron moves an electron at the speed of light but pushes the next election that the whole system can move instantaneously across distance yet be constrained by the speed of light ("pressure").
      An added complication I have is some videos have shown that gravity is a result of time dilation, that space-time is curving inward due to gravitational time dilation. I don't see how this applies to photons of course.
      Could this be pointing to a phase change in which there is a gravity purely by Higgs field where particles exist in superposition that has NO aberration and then a gravity where bond energy is in place, you have position, and you have time dilation.
      Then you have it both ways, gravity experiences aberration/dilation in a gravity well with density but does not experience dilation when just the Higgs field resistance?

    2. Follow up thought experiment trying to figure out aberration (or lack of).
      If I have a nano-diameter rigid solid object (say a graphite rod) two (2) light years in length. I push on the graphite rod that it moves at a velocity far less than c (and assume it is of strength that it does not break). Two (2) Light years away would not one see the graphite rod move but at a velocity less than c?
      Wouldn't this movement be information received like years in advance of a photon moving at c?

    3. Dear Craig Pichach,
      the short answer is NO.
      The reason is this: "Rigid body" is a model. It fails in your thought experiment. The other end of the rigid body would experience from the "pushing" in the best case with speed of light or later.
      Many greetings
      By the way: Like you I don't understand Antooneo's argumentation. There are e.g. in the Wikipedia articles to the aberration of light...

    4. Yes it is a model but I don’t see what physically would prevent it from moving two light years away at a velocity slower than the speed of light.... yet it must be restricted?
      This means that some inherent structure of the universe would impact Rheology to prevent this. How? There must be something.
      Or is there? Is molecular bonding by gluon field just there?
      And is there some kind of equivalence with gravity in a high density field explaining how the Earth can rotate the present, not aberrated position of the sun, lest our orbit be unstable?

    5. Let’s link the thought experiment to Einstein because all good thought experiments generally do. A person is on a train. The motor starts accelerating at the back moving the floor of the train the man is standing on. What speed did it take for the position of the floor above the motor to move in relation to the position of the floor under the person? Is it just me or does even Einstein have this as instant?

    6. Dear Craig,

      2 light years long crystal as an example for the rigid body
      A crystal consists of atomic nuclei and electrons between them.
      If you push the first layer of atomic nuclei towards the other end of the crystal,
      the atomic nuclei shift a little with their positive charge.
      This affects the electron cloud and shifts it.
      The second layer of atomic nuclei notices this and shifts it and so on.
      A pressure wave is formed.
      This propagates with the speed of sound
      and is much smaller than the speed of light.

      Maybe you read a little bit in the Wikipedia about crystals or chemistry.
      The cohesion is always realized by the electromagnetic interaction
      between electrons and atomic nuclei.
      Never mention gluons in this context!

      Thought experiments
      They are very cheap, but also dangerous.
      Wrong thoughts or wrong assumptions lead to wrong results.

      Einstein train
      With your train, the same thing happens as in the crystal above.
      The original Einstein train, i.e. the one in Einstein's thought experiments
      moves with constant speed. So things are different here.

      In my opinion we see the sun actually somewhat in flight direction
      and not 100% perpendicular to flight direction of the earth around the sun.
      Aberration results from the finiteness of the speed of light.
      Together with gravitation it is a question for general relativity.
      I am not an expert in it.
      I would expect something like the perihelion rotation of Mercury, but weaker.

      Many greetings

    7. Craig and Stefan
      This is my thought experiment to explain gravitational aberration. A g-field is a configuration of Spacetime. It must always interact with Spacetime. Alone, a self gravitating body in motion must, by way of its g-field, alter Spacetime along its direction of motion. By way of its g-field it ‘recognizes’ that alteration and always responds. Now imagine two similar mass self gravitating bodies nearing each other. The first inkling that each has of the other is when the two g-fields interact and alter the intervening Spacetime. Each responds to that alteration according to its own mass and momentum. If you wish to think of an exchange of gravitons you have to consider that gravitons are bosons and will congregate with the greatest congregation being where the two fields interact.

    8. Craig
      Ask yourself how two atoms of the floor which are next to each other communicate. Is any communication instant? Isn’t there always a space to traverse?
      Everything is built up atoms. Atoms in anything have large spaces between them. Any signal that begins at one end must traverse each finite space at the speed of light or less. By the time a signal reaches the other end it has traversed potentially, millions of finite spaces in some elapsed time. Nothing is instant.

    9. Brad and Stefan,
      My understanding is that the curvature of by mass of space-time is supposed to move at the speed of light. This makes sense to me, that we rotate around the past position of an object where it was the distance/speed of light ago with gravitation aberration.
      BUT this doesn't appear to be happening with respect to the Earth-Sun system. If the Earth is rotating around where the sun was eight minutes ago (keep in mind the sun is moving around the galaxy) our orbit should be wobbling and unstable.
      The best I could find to explain this was "Aberration and the Speed of Gravity" by S. Carlip, 1999 where he argues that it is cancelled out by velocity-dependent interactions.. velocity-dependent interactions that just EXACTLY cancel out the aberration in the sun-earth system. I don't pretend to understand how he arrived at it but my question to him is what if the sun suddenly was pulled in a different direction opposite the Earth, would the Earth REALLY have gravitated around the future predicted position of the sun that it never goes.
      Do you think that is true, if so amazing!!
      Also for moving things by pressure I think is indicating that when you move anything, your pencil, you are being countered by a lot of limitations in the transfer of information.
      But some how those contribute to a centre of gravity for an object. If I take a four light year rod and snap it in the middle, how does the universe communicate to the end of the rod that the centre of gravity has changed. I snap the rod in the centre, will the centre of mass at the end change? No, it must take two years right?

    10. I don't know if this has anything to do with the issue, but many years ago I saw a display in the Museum of Science in Chicago, consisting of a large bowl (around 2 meters in diameter, semi-circular) with a hole in the bottom, and a tube at the top that ejected a small ball at certain intervals, with a circumferential velocity. The ball traveled around the bowl in an orbit, until friction and gravity made it spiral down the bowl, going faster and faster circumferentially until finally it spun into the hole. It was supposed to illustrate a black hole, I think.

      My thought experiment is to have the bowl moving along some path as this was taking place--would the orbit be altered? But of course the bowl was moving along a complex path at high speed, just not moving relative to me. The bowl represented Einstein's theory of curved spacetime.

      My guess is the answer is that the bowl of our solar system is due to the mass of the sun, and hardly perturbed at all by the orbiting planets. Similarly, the bowl of a galaxy is hardly perturbed at all by individual star motions, especially if they tend to average out to the same center of mass as they move, and if the galaxy has a super-massive black hole at its center.

      Another factor is that I read somewhere about the orbits of this solar system being calculated for billions of years in the future (assuming a stable sun) and hardly deviating. The theory was that this is a result of evolution over billions of years in the past, as unstable orbits were ejected or fell into the sun. The same could happen in galaxies.

    11. I found this Feynman Lecture at
      Antooneo is this what you are talking about regarding lack of aberration in the lab regarding electric fields.

      It really does have it where an electrical field moving at a constant speed has it where using the Lorentz transformation that it will point at the present position instead of the retarded (abberated) position.... just like gravity in the Earth-Sun system.
      Figure 26-2 has it even where the field points to the "projected" position which is different from the actual "Present" position..
      I've got to sleep on what that actually means. Electromagnetic forces are pointing to projected positions instead of actual positions?
      Does this apply to gravity? Is it all pointing to projected positions instead of actual?!? And WHY?!? (And isn't that convenient, aberration just happens to cancel out).
      Also quote: "Then you imagine that the charge would keep on moving with this velocity during the delay time (t′−t), so that it would then appear at an imaginary position Pproj, which we can call the “projected position,” and would arrive there with the velocity v′. (Of course, it doesn’t do that; its real position at t is at P.) Then the potentials at (x,y,z) are just what equations (26.1) would give for the imaginary charge at the projected position Pproj. What we are saying is that since the potentials depend only on what the charge is doing at the retarded time, the potentials will be the same whether the charge continued moving at a constant velocity or whether it changed its velocity after t′—that is, after the potentials that were going to appear at (x,y,z) at the time t were already determined."
      So he is talking electromagnetic fields, but if this was like the space-time field and we are in an expanding accelerating space-time well, all of our gravity fields would be projected based on the velocity at the time and thus not pointing to actual locations??

    12. Craig Pichach:

      I think your reference describes it correctly. But understanding it may be easier by this:

      The nonexistence of aberration in case of an electrical field can be shown by the principle of relativity.

      Assume two charges A and B. A may be at rest and B moving along passing A at a certain distance. The charge B will see A always at the position where it actually is, because the field of A is static. This is of course particularly true when B is at the minimum distance to A. Now view this situation from B and take your frame so that B is at rest. In this frame the field of B is static and so A will see B always at its actual position.

      By the principle of relativity both frames are equivalent having the same physical rules. And this is only fulfilled if for both charges each on is seeing the other one continuously here it presently is.

      This is a formal consideration. If we want to look at it in the view of detailed physics rather than a principle, we have to follow the path of the exchange particles in a system of motion. A bit more complicated.

      This is of course similar for the gravitational field as it reacts in this respect similar to the electrical one.

      In descriptions like the one at Wikipedia the aberration problem of gravity is said to be explained by General Relativity. But it works similarly for electrical fields and those are not subject to GR.

      And for the electric field this has a consequence: Because photons are subject to aberration as we know, photons cannot be the exchange particles of the electric field.

    13. Antooneo,

      Isn't Feynman saying that there is aberration however it is offset by v′ (the velocity at the retarded time)?

      That is how I am reading "potentials depend only on what the charge is doing at the retarded time, the potentials will be the same whether the charge continued moving at a constant velocity or whether it changed its velocity after t′"

      Now since the sun is moving at a constant velocity I see how this would work in the Earth-Sun system.
      But strange if applied to gravity.
      This would mean that your gravity is being projected "forward" by velocity (or backwards by negative velocity) regardless of acceleration.
      I am going to read more on the Lorentz transformation to figure this out. I was trying to find some physical analogy but no luck (rigid frame doesn't help) - what would be projected only based on your velocity now without regard of acceleration independent of your realposition?
      Thinking about it I am going 0.3c, I slow down (negative acceleration), my gravity though is "projected" forward by my velocity at the time that I pull forward (inertia?) I am going 1km/s. I go forward to 0.3c, my center of gravity is projected backwards that I pulled backwards. Is that inertia?
      Also what happens then if you have two galaxies separated by expanding space. They are moving at an increasing acceleration due to expansion, but the projection is only based on velocity.. so gravity would be based on their uh, velocity-only projected positions behind them?
      All I know is there must be answer since the Earth is rotating around the sun without an unstable wobble.

    14. Craig Pichach:

      The situation is difficult in so far as textbooks only describe how the result of the interaction is but nothing about how the physical process works. Also Feynman is doing it in this way as you quote him.

      I understand the influence of a moving source charge on a test charge so that the field vector moving from the source to the test object is not parallel to the path of this vector but has from the beginning on a direction so as coming from the source to the destination where the source charge is at the time of the impact. That means that if the motion of the source is altered during this time of motion, the force onto the test charge will not change its direction.

      I feel that we need a better explanation and shall try to find this out.

  45. Yesterday I recalled another approach to explaining MOND’s empirical success within galaxy sized structures, which is the gravitational polarization of the vacuum, pioneered by Luc Blanchet at the Institut d’ Astrophysique in Paris. This idea was later taken up by Dragan Hajdukovic of CERN who developed his own version of this concept. I looked up their respective papers on the net. Blanchet’s paper is highly professional and deeply mathematical, while Hajdukovic’s paper is written in a style and comprehension level that is much easier to follow. Reading the first few pages of both papers it was clear that both authors had to carefully specify the properties of their hypothetical gravitational dipole Dark Matter to match MONDian phenomenology; Blanchet treating them as real particles, while Hajdukovic considered them to be virtual particles.

    I knew I had considered the possibility that a type of matter that I had dreamed up, entailing the hypothetical transposition of the electromagnetic and general relativistic gravity fields, might just fit the bill for the proposed particles in these theories. Scanning through half a dozen ‘ideas’ notebooks I found entries dating to late September, 2018, and early November of the same year relating my own amateur idea to their professional models. It looks like I didn’t pursue this possible connection too far before moving on to another speculative idea for Dark Matter and Dark Energy that encompassed a wider range of astronomical phenomena than just that seen at the galactic scale.

  46. no mention of radial acceleration relation

  47. "Odd radio circles" or ORCs have never been seen before and have left scientists baffled. An ORC is a very large unexplained astronomical object that, at radio wavelengths, is highly circular and brighter along its edges. As of 27 April 2021, there have been five such objects (and possibly six more) observed. The observed ORCs are bright at radio wavelengths, but are not visible at visible, infrared or X-ray wavelengths.Three of the ORCs contain optical galaxies in their centers, suggesting that the galaxies might somehow have formed these objects.

    The ORCs were detected in late 2019 after astronomer Anna Kapinska studied a Pilot Survey of the Evolutionary Map of the Universe (EMU), based on the Australian Square Kilometre Array Pathfinder (ASKAP) radio telescope array. Every detected ORC, about 1 arcminute in diameter, are some distance from the galactic plane, at high galactic latitudes. The possibility of a spherical shock wave, associated with fast radio bursts, gamma-ray bursts, or neutron star mergers, was considered, but, if related, would have to have taken place in the distant past due to the large angular size of the ORCs, according to the researchers. Also according to the astronomers, Circular features are well-known in radio astronomical images, and usually represent a spherical object such as a supernova remnant, a planetary nebula, a circumstellar shell, or a face-on disc such as a protoplanetary disc or a star-forming galaxy, ... They may also arise from imaging artefact around bright sources caused by calibration errors or inadequate deconvolution. The discovery of a class of circular feature in radio images that do not seem to correspond to any of these known types of object or artefact, but rather appear to be a new class of astronomical object.

    The ORCs may have been produced by a Bosenova of a coherent dark matter bose condensate in which an instability in the condensate triggered a state change transition from a bosonic cloud of polaritons lock in a entangled lattice to an expanding cload of electrons expanding at near light speed. The radio waves might have been produces by Magnetobremsstrahlung.

    Condensed matter explosions of bose condensates are seen at the micro scale when the condensate becomes unstable. The tell tale indicator that the ORC is produced by exploding dark matter is the lack of any other radiation type other than radio waves that may have been produced by a huge cloud of electrons being propelled by their instantaneous wholescale transition from a bosnic state to a fermionic repulsive state.

    Being originated in a coherent system, the radiation profile of these ORC radio waves would be polarized possibly into a synchrotronic profile.

    Also the galaxies imbedded in some of these radio clouds could be surveyed for the absence of dark matter indicators that might now be missing from their rotational profiles.

  48. One thing I don't understand is why do you say that adding fields is modified gravity? It seems like some form of matter whether you call it dark or not.

    1. This was a genuine question. I expected some explanation. If Einstein's equations are G=T, where T is the stress-energy tensor and one considers G=T+T'. Then why would this be modified gravity, and not unmodified gravity plus additional matter fields with stress-energy tensor T'?

  49. It's normal but none the less disappointing to continually see a plethora of human emotions obfuscate the simplest and most probable approach to these problems. A purely scientific approach tells us to try and start over, first with strong empirical foundational axioms, including what we've experimentally verified from relativity. Take what is already inferred regarding the fabric of empty space but try to suppress ones past conjecture and intuition. Put great effort into only going where the evidence leads, without inflicting the many kinds of human emotions that constantly sway our judgments. I say this because I haven't seen any evidence this has been done without a huge amount of inflicted bias, thus we’ve been missing some of the most basic and verifiable truths about space time, that would give us a strong foundation to rebuild our theory’s.

  50. I think there may be even a third form or phase of dark matter, like ordinary matter

  51. The underlying assumption in postulating "dark matter" is that a complex star system will behave following the same laws that simpler systems follow, as planetary systems. But that is not different from the assumption that a very complex assembly of quantum objects will follow the same laws followed by simple quantum systems which is not the case. And condensed matter Physics deal with these situations.
    In this context Galaxies "rigid" rotational speeds is an obvious indication of an emergent property in the same way that the rigidity of a macroscopic solid is an emergent property.
    Postulating Dark Matter is superfluous.
    As P. W. Anderson said "More is different".

  52. Yesterday, I read Dragan Hajdukovic’s arXiv paper: “Is dark matter an illusion created by the gravitational polarization of the quantum vacuum?”, He postulates that the gravitational mass of anti-matter is negative and thus should fall up in a gravitational field. Now, I thought that the behavior of antimatter in a gravitational field had already been measured. So I was surprised on checking a CERN news release titled: “AEgIS on track to test the free fall of antimatter”, dated 11 February 2021, that technical issues are still being addressed, and these aren’t expected to be resolved till 2022. However, according to the article physicists do not expect antimatter to behave differently as most of the mass in antimatter comes from the strong force that binds quarks together.

    Another article, in the CERN Courier titled: “Does antimatter fall up?”, which I didn’t read yesterday, since it was dated 13 January 2017, and I was looking for the latest information, stated: “To date [2017], indirect measurements have set limits on the deviation from standard gravity at the level of 10^-6.” So it looks pretty doubtful that they will find antimatter behaving any differently from normal matter gravitationally.

    1. I wrote about negative gravitational mass above on
      ben6993 9:20 AM, May 04, 2021
      and there is a relevant previous thread somewhere else on this blog.

      Using Newtonian Laws with -m plugged in for negative mass (see: Wiki negative mass), one gets a negative mass accelerated towards a positive mass; and a positive mass accelerated away from a negative mass. Since the earth is a huge positive mass, a microscopic negative mass will, under gravity alone, fall to earth. So IMO the Aegis result will not prove that antimatter has positive mass simply by it falling to earth. Also, two negative masses under the same Laws will gravitationally accelerate away from one another.

      Farnes uses negative masses to explain both DM and DE in a professional paper. I have an amateur paper saying the same (Austin J. Fearnley, July 2018). Since then I attributed the negative mass to antiparticles (Aug 2018) and have a further paper on the nature of space and time inhabited by antiparticles (Jan 2021).

      Sabine holds that Newtonian calculations are not appropriate and that GR calculations would have two negative masses accelerating themselves gravitationally towards one another.
      IMO two negative mass particles would gravitationally accelerate each other towards themselves if they inhabited an overall space appropriate to negative masses. However the space of the universe is not the space of antiparticles. As an analogy, the space of the universe is dS while the space needed for antiparticles to demonstrate attraction is AdS, while in dS they will accelerate away. My Jan paper uses geometric algebra rather than GR or dS, based on a paper by Chappell et al, 2016.

      Some further speculations next.
      't Hooft has some lecture slides online, search: lecture2tHooft.pdf . I suspect that his slide 36/39 maybe making a similar point??? For a timelike Moibus strip ... "the external observer chooses the point where the Hamilton density switches sign as being on the horizon, gives us a good practical definition for the entire Hamiltonian."

      IMO The sign of universal curvature flips at infinity and until we reach infinity two negative masses will accelerate away. Or maybe equivalently (???) time's arrow holds its direction from here to infinity?

      Austin Fearnley

  53. Two galaxies, called NGC 1052-DF2 and NGC 1052-DF4, are ultra-diffuse dwarf galaxies located in proximity to the elliptical galaxy NGC 1052. Both of these dwarf galaxies are small, containing only about a hundred million stars. Both DF2 and DF4 rotate at rates that are identical to what astronomers would predict if Newton’s laws of both motion and gravity are correct, using only the mass of the galaxies found in stars and gas. In short, these two galaxies appear to have no dark matter in them.

    Here, the exception breaks the rule. These dwarf galaxies that exist without dark matter are evidence that dark matter, and not MOND, is a correct part of the theory that governs the universe.

    1. The blog "Triton Station" has a category "Dwarf Satellite Galaxies". I recommend reading those posts to see whether or not MOND does a good good predicting their observed velocity dispersions, based on normal matter only, without any need to decide how much dark matter would be required to post-dict the observed dispersion. How could one decide whether MOND or dark matter does a better job without looking at that data?

      Note that MOND certainly predicts that there are regions in which Newton's approximation holds to a high degree of accuracy in determining orbital velocity dispersion, our solar system being an example.

    2. Not really, the "dark matter" affect only is present/observable on very complex(large) star assemblies in the same way that the rigidity of an object only is present in very large(macroscopic) assemblies of quantum objects. A very strong indication of an emergent property.
      Postulating the reality of dark matter is superfluous exactly as postulating the reality of the Luminiferous aether was superfluous.

    3. Using an analogy:
      Even when each real number is a limit of rational numbers, you need a different set of irreducible properties(axioms) to describe the set of Real numbers.
      In the same vein even when classical objects can be considered as a limit of a large set of quantum objects, you need new irreducible properties to describe an assembly of classical objects; for example classical objects can be labeled uniquely but quantum objects can't be uniquely identified.
      Identity is a strong emergent classical property.
      So very complex sets of stars can exhibit properties that simple systems don't exhibit and some of these properties can only be discovered by observations since they are irreducible.
      Complexity breaks Naive Reductionism.

  54. Nineteen newly discovered dwarf galaxies seem to be missing their dark matter, and physicists aren't sure why. One theory explains that tital striping of dark matter by large nearby galaxies leave these naked dwarf galaxies in various stages of disintegration.

    But there is exceptions to that rule. For instance, dwarf galaxies in the middle of dense galaxy clusters have many other gravity sources around to strip away their dark matter. But some of the dark matter-free galaxies are solitary, far from any other gravity source.

    Here is when the transient nature of a condensed matter origins of dark matter might provide a explanation of these solitary naked galaxies.

    Condensed matter is emergent from more fundamental structures. Being emergent, dark matter could occasionally experience a change of state where dark matter decomposes and reverts back into it more fundamental foundations. This change of state will disperse the energy content of dark matter more broadly through the production of radio waves radiating in a sphere.

  55. On this topic, any opinion on this recent paper ( that claims models of this type (attempting to have MOND-like and DM-like behavior), when completed to be Lorentz invariant, tend to break locality? Curious if you think they did something wrong, or if you don't expect this to be a problem for the theory.

    1. hi 4gravitons,

      I saw the paper this morning but haven't read it. That MOND-like theories tend to have a superluminal mode isn't really new and there's a long discussion in the literature as to why this doesn't cause causality problems. But I'll actually have to read the paper to figure out whether they're just rediscovered the same thing or whether it's a new argument. I'm not sure what you mean by "break locality".

  56. A polariton condensate is weird stuff, but it punches the ticket for dark matter. To begin with, it has a dark mode where it is transparent to EMF. This effect is produced by a anapole field affected by a superfluid toroidal circulation of polariton spins(electron isospin quantum property). This spin circulation hides the condensate from any interaction with EMF.

    Next, the anapole field modifies gravity and is the likely cause of the MOND effect. I will post the math in an upcoming post.

    Next, the polariton condensate is a superfluid which can lay dormant indefinitely and can form entangled aggregations of any size.

    As a bosonic quasiparticle comprised of electrons and photons, it has zero charge and mass like a photon, but a huge magnetic potential made possible by its electron nature. The amount of anapole magnetism contained in a galaxy sized condensate of polaritons is unimaginably huge. This magnetism may be the source of dark energy.

    The polariton condensate is a supersolid which generates a lattice structure that confines the polaritons but at the same time allows the polariton spins to travel a toroidal anapole circulation.

    The polariton condensate may contain either a dipole or monopole toroidal circulation of spin with the dipole mode suppressed. The anapole fields that its spin circulation generates gives the polariton condensate its dark matter nature which includes MOND generation and EMF transparency.

  57. Related to the polariton condensate post above.

    How Current Loops and Solenoids Curve Space-time
    André Füzfa

    Namur Center for Complex systems (naXys),
    University of Namur, Belgium

    (Dated: December 15, 2015)

    The curved space-time around current loops and solenoids carrying arbitrarily large steady electric currents is obtained from the numerical resolution of the coupled Einstein-Maxwell equations in cylindrical symmetry. The artificial gravitational field associated to the generation of a magnetic field produces gravitational redshift of photons and deviation of light. Null geodesics in the curved space-time of current loops and solenoids are also presented. We finally propose an experimental setup, achievable with current technology of superconducting coils, that produces a phase shift of light of the same order of magnitude than astrophysical signals in ground-based gravitational wave observatories.

  58. Under the posit that dark matter is a polariton condensate, there is a connection between dark matter and dark energy. The polariton condensate would consist mainly of an isospin superfluid. The amount of magnetic potential that a galaxy sized bose polariton condensate would contain is immense. Recently, a simulation of the dark energy as magnetism hypothesis has been completed and is presented as follows:

    [Submitted on 15 Feb 2021]

    Consistency analysis of a Dark Matter velocity dependent force as an alternative to the Cosmological Constant

    Karoline Loeve, Kristine Simone Nielsen & Steen H. Hansen1
    1Dark Cosmology Centre, Niels Bohr Institute, University of Copenhagen, Jagtvej 128, 2100 Copenhagen, Denmark

    A range of cosmological observations demonstrate an accelerated expansion of the Universe, and the most likely explanation of this phenomenon is a cosmological constant. Given the importance of
    understanding the underlying physics, it is relevant to investigate alternative models. This article uses numerical simulations to test the consistency of one such alternative model. Specifically, this model has no cosmological constant, instead the dark matter particles have an extra force proportional to velocity squared, somewhat reminiscent of the magnetic force in electrodynamics. The constant strength of the force is the only free parameter. Since bottom-up structure formation creates cosmological structures whose internal velocity dispersions increase in time, this model may mimic the temporal evolution of the effect from a cosmological constant. It is shown that models with force linearly proportional to internal velocities, or models proportional to velocity to power three or more cannot mimic the accelerated expansion induced by a cosmological constant. However, models proportional to velocity squared are still consistent with the temporal evolution of a Universe with a cosmological model.

  59. There is a significant body of research dealing with Anapole dark matter.

    Among this research, professor Robert Scherrer and post-doctoral fellow Chiu Man Ho authored an article published by the journal Physics Letters B.

    "There are a great many different theories about the nature of dark matter. What I like about this theory is its simplicity, uniqueness and the fact that it can be tested," said Scherrer.

    In the article, titled "Anapole Dark Matter," the physicists propose that dark matter, an invisible form of matter that makes up 85 percent of the all the matter in the universe, may be made out of a type of basic particle called the Majorana fermion. The particle's existence was predicted in the 1930's but has stubbornly resisted detection.

    A number of physicists have suggested that dark matter is made from Majorana particles, but Scherrer and Ho have performed detailed calculations that demonstrate that these particles are uniquely suited to possess a rare, donut-shaped type of electromagnetic field called an anapole. This field gives them properties that differ from those of particles that possess the more common fields possessing two poles (north and south, positive and negative) and explains why they are so difficult to detect.

    Particles with familiar electrical and magnetic dipoles, interact with electromagnetic fields even when they are stationary. Particles with anapole fields don't. They must be moving before they interact and the faster they move the stronger the interaction. As a result, anapole particles would have been much more interactive during the early days of the universe and would have become less and less interactive as the universe expanded and cooled.

  60. So it looks like everything is connected: from the beginning of time, after billions of years the cosmic connections are as tight as ever. The CMB, the percentages of dark matter and dark energy and visible matter are all tied together and have never changed since time began. But how can that be? How does dark matter control how much visible matter is allowed to exist in the universe? What is the fundamental controlling mechanism? But more importantly, how can humankind access and manipulate that fundamental controlling mechanism.

    Can we learn how to rip galaxies apart, or make visible matter disappear, or even better make matter appear. Can we control gravity and the very fabric of space and time? And are we now mature enough to use such power wisely?

  61. Given how humans have used knowledge of manipulating atoms to build nuclear weapons, I hope that ways of manipulating dark matter on that scale are never found. I still want to know what it is and how it works, though.

  62. Had some dead time today at the laundromat, so I brought along a printed out copy of Sabine’s and Tobias Mistele’s 2018 arXiv paper “Strong lensing with superfluid dark matter”. It didn’t take long to realize that if one wants to be taken seriously in the physics community, that you need to research a subject to the depth and thoroughness as exemplified in this paper, not that I didn’t know that already. The math is challenging, and it would take me quite a bit of effort to fully understand, if I ever could. For sure this is what real science is all about, so it behooves me to understand the symbiosis between physics and math, as thoroughly as possible, to provide the grounding for any ideas that I might come up with in any area of physics.

  63. My recent exploration of the EVO in its possible role as dark matter and the associated source of dark energy now informs my newly developed opinion that the EVO serves as a major regulatory mechanism that keeps the cosmos from unraveling.

    From the earliest times in the formation of the universe, dark matter maintains a 5 to 1 ratio between visible matter and dark matter on a galaxy by galaxy basis. If this ratio is not maintained, the galaxies would decompose.

    The galaxy structure is the basic organizing principle that underpins the overall structure of the universe. Like atoms provide the organizing structure of matter, so too, galaxies form the organizing structure of the universe.

    Galaxies merge and reorganize frequently on cosmic timescales but at the end of these epochs of galactic reorganization, the galaxies always stabilize with the 5 to 1 dark matter/visible matter ratio.

    It seems to me that the universe formed from a miniscule seed of minimus energy that was embryonic in nature; a structure that is just a few planck lengths in size. This seed had the blueprint for future formation of an ever expanding universe. This seed also had a self regulatory mechanism engendered in the nature of dark matter.

    From the earliest times even when the cosmic background formed, dark matter imposed on the cosmos the 5 to 1 ratio rule.

    When the universe began, the primordial kernel did not contain in a compressed format all the unlimited matter and energy that would eventually appear in an ever evolving and expanding universe. Like an embryo, the blueprint for a fully formed and mature universe was ingrained from the very first instance of its cosmic inception, the galactic based structure of the cosmos. From the beginning within the embryonic form, a dark matter seed would guarantee the adherence to a proper future formation of a galaxy centered mature expanding universe.

    This constancy in the nature of the universe must involve a self regulatory mechanism that both creates and reformulates matter and energy.

    With this self regulatory principle in mind, the rules that dark matter expresses are easy to deduce.

    First, dark matter creates matter and energy as an ongoing never ending self perpetuating activity.

    If visible matter happened to be expressed above the 5 to 1 ideal galactic ratio, then dark matter would automatically recalibrate that visible matter/dark matter ideal relationship to reacquire and adhere to the ideal galactic ratio. But on the other hand, if the percentage of dark matter to visible matter were to dropped below the 5 to 1 ratio, then visible matter would be created until the 5 to 1 ratio visible matter to dark matter ratio was reached again.

    The evidence for this self regulating dark matter process which has been enforced from the very earliest times in the history of the universe is seen in the nature of the easily recognized nature of the first galaxies that came to exist some 13 billion years ago. This unremarkable organization of the earliest matter and energy as well as associated unchanged physical laws that comprised this early universe is no different than exists today; it is the same natural laws, matter, and energy makeup that we see today in our current universe.

  64. When we think of the EVO as the organizing principle of dark matter and dark energy, the behavior of the EVO comes into sharp focus.

    In our recent experimental observations we should expect that dark matter is ubiquitous in nature and will show up in our observations as reflected in how micro scale EVOs behave. We see EVOs eating their way through matter so that visible matter is made to be rearranged into dark matter, but on long duration tunnel digging, the EVO deposits a ball of matter periodically inside the tunnel. It is my observation that this matter distribution to matter creation ratio is observed to be 5 to 1, where the disappearance of visible matter is reformed into newly generated dark EVOs and dark energy appears as magnetic energy and the 5 to 1 ratio is maintained by the depositing of visible matter within the 5 to 1 self regulatory universal mandate.

    The visible matter that the EVOs produce conform to the elemental proportions that appear in the elemental mix that is found throughout the universe as prima materia.

    We might expect that the final product of the EVO operation produces a situation where It turns out that roughly 68% of the EVO final product is magnetic based dark energy. Dark matter as newly formed EVOs makes up about 27%. The rest that we observe is reformed normal matter - adds up to less than 5% of the energy equivalent product.

    We also see gravity modification EVO based behavior that conforms to our expectations about how modified newtonian dynamics (MOND) works which is the basic force that confines visible matter in galaxies. This MOND effect is affected by the toroidal circulation of magnetic spins of the polariton which forms an anapole.

  65. The matter-antimatter asymmetry problem

    The EVO as a source of matter creation presents a solution to the matter anti-matter annihilation dilemma. The EVO is an exotic vacuum object in that its vacuum potential is derived from the superconductive seed of its formation. It demonstrates the Mexican hat vacuum potential like the Higgs field. This potential breaks electroweak symmetry as a false Higgs vacuum. The EVO only creates matter as a consequence of CP electroweak symmetry breaking.

    The assumption is that superconductive dust such as metallic hydrogen and other superconductive molecules such as water is found in large quantities near the outer reaches of galaxies. This unique dust type is formed by energetic stellar events inside galaxies. These superconductive seeds provide an ideal cavity in which photons and electrons can mix to form a metastable coherent polariton condensate with a Higgs potential which is the EVO.

  66. We must ask ourselves, what is the reason that transmutation of elements that we have observed exist? What purpose does transmutation serve the cosmos? Is transmutation just some fluke of nature, or does transmutation act in some way to regulate cosmic forces and structures?

    Tully–Fisher relation

    In astronomy, the Tully–Fisher relation (TFR) is an empirical relationship between the mass or intrinsic luminosity of a spiral galaxy and its asymptotic rotation velocity or emission line width.

    To begin with, Tully and Fisher used optical luminosity, but subsequent work showed the relation to be tighter when defined using microwave to infrared (K band) radiation (a good proxy for stellar mass), and even tighter when luminosity is replaced by the galaxy's total baryonic mass (the sum of its mass in stars and gas). This latter form of the relation is known as the Baryonic Tully–Fisher relation (BTFR), and states that baryonic mass is proportional to velocity to the power of roughly 3.5–4.

    In the dark matter paradigm, a galaxy's rotation velocity (and hence line width) is primarily determined by the mass of the dark matter halo in which it lives, making the TFR a manifestation of the connection between visible and dark matter mass. In Modified Newtonian dynamics (MOND), the BTFR (with power-law index exactly 4) is a direct consequence of the gravitational force law effective at low acceleration.

    In planer language, this relationship between total baryonic mass in a galaxy and the dark matter that keeps the galaxy from falling apart says that baryonic matter creates dark matter so that galaxies as we know them can exist.

    What Sveinn Ólafsson is seeing in its most basic formulation is dark matter which is being created from ultra dense hydrogen. We know that the corkscrew path of an as of yet unidentified particle that Sveinn is seeing in his cloud chamber particle detector is an EVO and that this particle is also dark matter.

    Ultra dense hydrogen is being continually produced by baryonic processes at a rate proportional to the amount of baryonic matter within a galaxy. The ultra dense hydrogen is then transformed into dark matter via photons.

    Dark matter(EVO) is also creating baryonic matter via transmutation. This is how the cosmos continually expands from a minicul cosmic seed created at the big bang to an never ending and an ever expanding universe that we live in today.

    Sveinn Ólafsson is a Research Professor at the School of Engineering and Natural Sciences at University of Iceland. Along with teaching young PhDs, Dr. Ólafsson worked in hydrogen storage research. His interest in Rydberg matter led him to Dr. Leif Holmlid's work with ultra-dense hydrogen.

  67. Over at Stacy McGaugh’s recent thread “Despondency” a poster cited a recent paper “Tree-ring structure of Galactic bar resonance”, authored by Dr. Ralph Schoenrich and Ph.D. student Rimpei Chiba, which reaches the conclusion that the Milky Way’s galactic bar has slowed down in rotation by more than 24 percent due to angular momentum transfer to the Milky Way’s dark matter halo. Their apparently novel way of determining this slowdown was via a gradient of metallicity of stars within the cross-section of the galactic bars at different radii from the bars central (longitudinal) axis and various distances from the central region of the galaxy. At least that’s what I think was what they meant, as this would correspond to the wording of the paper’s title “Tree-ring structure…”, where a tree trunk corresponds to a galactic bar, and tree rings to the orbits of stars around the bar’s longitudinal axis.

    In any case the authors point out that the slowing of the Milky Way’s bar via the gravitational drag of the dark matter halo is incompatible with modified gravity (MOG) theories but supportive of the LCDM concept. So this new paper will no doubt stimulate much discussion within the LCDM and MOG communities.

  68. Sabine,
    I saw a picture of you online wearing that sweater sitting on a bench next to Albert Einstein. It's a very cute photograph. It should be captioned with Einstein's quote, “When you sit next to a pretty girl for an hour it seems like a minute, but when you sit on a hot stove for a minute it seems like an hour.”

  69. This is a belated comment on dark matter which I find essential.

    I just got the CLASH report on the dark matter in the galaxy cluster A2261. The collaboration has built a density map of the dark matter (particles?) in it. They used the gravitational lensing (strong and weak lensing) to detect the dark matter.

    The surprising result comes from the possible comparison with the density of the photons in this cluster (which is not difficult to determine). And the result is that this density distribution of photons matches the density distribution of the dark matter.

    What can we learn from it?

    1. The density distribution of ? photons ? Can you post a reference?

    2. It sounds vaguely like another instance of the old "the distribution of baryonic matter" (the stuff we see due to its photons) matches everything else we see, including velocity gradients. Which is to say, MOND strikes again.

      While I'm being suspicious, I wonder if the report cites any of the studies on lensing effects simulated with MOND variants, or any MOND work at all. I apologize in advance as my suspicions are not well-founded, having not seen the report.

    3. I cannot post a reference. But the calculation is simple. Take some galaxy. It has some luminosity, which is in general known. Or look for the luminosity of our sun. You can convert the energy emission into the rate of photons. Or simpler: Look into Wikipedia and you find this rate. Now multiply this rate with the number of “suns” in the galaxy. Then you have the rate of photons passing the surface of the galaxy. Now the interesting part: Think of some volume around this galaxy. What is the number of the photons in this volume? It is the rate at the surface of the galaxy multiplied with the dwell time in this volume. The dwell time is radius of this volume divided by the speed of light. So we have the number of photons in this volume and from the volume also the density. You can differentiate this density by the radius and you get the differential density at a radius.

      Now look into the CLASH report “CLASH: PRECISE NEW CONSTRAINTS ON THE MASS PROFILE OF THE GALAXY CLUSTER A2261”. Here you find in the results the “mass” of the dark matter and the differential density of the dark matter in dependence of the radius of the volume, which is just tangentially passed by the lensed light beam. Look at figure 6 for the mass of dark matter and figure 10 for the differential density, this for a certain range / volume. And you find that this dependency is the same for photons as for dark matter.

      I hope that this is understandable. But if you want it, I can present you the detailed calculation.


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