There’s plenty of evidence for dark matter, ranging from velocity dispersion, flat galactic rotation curves, and gravitational lensing. The evidence for dark matter is so good we can even map it out:
Image credit NASA, ESA and R. Massey (California Institute of Technology), see spacetelescope.org
There’s also plenty of papers and articles about dark matter candidates. Maxim Khlopov refers to WIMPs, axions, neutrinos, mirror-world particles, extra-dimensional particles, and black holes. Andreas Ringwald refers to neutralinos, gravitinos, sterile neutrinos, and axions. Kim Griest refers to MACHOs, molecular hydrogen, MOND, axions, WIMPs, and neutrinos. And to something else. To “the ‘none-of-the-above’ possibility which has surprised the Physics/Astronomy community several times in the past”. However why that should be a surprise is something of a mystery to me.
One of our candidates is missing
That’s because one of our candidates is missing, and it’s right there in the foundation of the general theory of relativity. That’s where in 1916 Einstein said “the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy”. Gravitational field energy causes gravity, and it isn’t made up of WIMPs, or axions, or sterile neutrinos. It’s none of the above. Whilst some might claim this field energy could be quantized as some kind of particle, that’s the wrong approach. That’s not how gravity works. There are no actual photons flying back and forth between the proton and the electron in the hydrogen atom. The virtual photons of QED are virtual, as in not real. They aren’t the same thing as vacuum fluctuations, they only exist in the mathematics of the model. Photons are real electromagnetic waves, but hydrogen atoms don’t twinkle, and magnets don’t shine. In similar vein you might say gravitons are real gravitational waves, but there are no virtual gravitons flying around in the room you’re in. Instead there’s gravitational field energy in the room you’re in.
Field energy is spatial energy
In his 1929 essay on the history of field theory, Einstein described a field as a state of space. He was talking about gravitational fields and electromagnetic fields, and he said this: “it can, however, scarcely be imagined that empty space has conditions or states of two essentially different kinds”. The crucial point to appreciate is that a field isn’t something that exists in space, it’s a state of space. As to what sort of state, Einstein talked about that in his 1920 Leyden Address. That’s where he referred to a gravitational field as a place where space was “neither homogeneous nor isotropic”. He finished up saying this: “recapitulating, we may say that according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an ether”. See the Wikipedia aether theories article and note the quote by Robert B Laughlin: “it is ironic that Einstein’s most creative work, the general theory of relativity, should boil down to conceptualizing space as a medium when his original premise [in special relativity] was that no such medium existed”. Laughlin also said the empty vacuum of space is more like a piece of window glass than ideal Newtonian emptiness. He finished up saying “the modern concept of the vacuum of space, confirmed every day by experiment, is a relativistic ether. But we do not call it this because it is taboo”. Einstein is supposed to have done away with the ether or aether, but in the end, he didn’t. He thought of space as a something rather than a nothing. Something elastic.
Space is modelled as an elastic solid
This is why general relativity is related to continuum mechanics. And why if you google on Einstein elastic space, you can find articles such as evicting Einstein. It was written in 2004 by NASA’s Patrick Barry and Tony Phillips. It says this: “relativity explains gravity and motion by uniting space and time into a 4-dimensional, dynamic, elastic fabric of reality called space-time, which is bent and warped by the energy it contains”. This is why we have the stress-energy-momentum tensor, which “describes the density and flux of energy and momentum in spacetime”:
Public domain image by Maschen, based on an image by Bamse see Wikipedia
Note the shear stress term on the right. That tells you space is modelled as some kind of elastic solid. Also note the energy-pressure diagonal. Space is modelled as an elastic solid that’s subject to pressure. For an analogy, imagine you have a large block of gin-clear elastic jelly, with grid lines in it so you can see what’s going on. You slide a hypodermic needle into the centre of the block, and inject more jelly. This represents a concentration of energy bound up as the matter of a massive star. It creates a pressure gradient in the surrounding jelly. Stress is directional pressure, the pressure is outwards, and Einstein’s equation Gμν = 8πTμν is modelling the way gin-clear elastic space is conditioned by the energy you added. But note that you added jelly to represent energy, and that the jelly is also representing space. Space doesn’t just have some kind of innate intrinsic vacuum energy. At some deep fundamental level, energy and space are the same thing. A solid thing.
Spatial energy is vacuum energy
But this thing is not a solid like silicone rubber is a solid. Space is a continuum, it isn’t made of matter particles, or dark matter particles. We say matter is made of energy, but we don’t say energy is made of matter. Particularly spatial energy, which is vacuum energy, because that’s what’s left when you’ve taken the matter away. It is what it is, it isn’t made of something else. Au contraire, as far as I can tell it’s fundamental: everything else is made of it. For example a gravitational field is a place where space is inhomogeneous. A wave is a dynamical non-uniformity. A photon is a transverse wave propagating linearly at c. An electron is where a 511keV photon is going around and around in the guise of a spin ½ standing wave. Standing wave, standing field. But even if the electron isn’t there, or the photon, or the gravitational field, the vacuum energy is. There’s no discernible gravitational field in a gedanken void at the centre of a planet. That’s where space is homogeneous and there’s no gradient in gravitational potential. But it’s also a place where gravitational potential is low because the vacuum energy density is high.
As for how high, we don’t know. But we do know that the energy density is higher in a black hole where gravitational time dilation is infinite. The energy density is lower in free space well away from the black hole. In between there’s a density gradient. It’s similar for the room you’re in, which is why your pencil falls down. And where the Moon is, which is why the Moon orbits the Earth. And where the Earth is, which is why the Earth orbits the Sun. And where the Sun is, which is why the Sun orbits the centre of the galaxy. But unfortunately the FLRW metric “starts with the assumption of homogeneity and isotropy of space”. This is not a good assumption. Not when Einstein said a gravitational field is a place where space is “neither homogeneous nor isotropic”. Not when modern authors say the same thing and write papers like inhomogeneous vacuum: an alternative interpretation of curved spacetime. Or papers like inhomogeneous and interacting vacuum energy.
The contrast between aether and matter would fade away
Especially since Einstein said if we could understand the gravitational and electromagnetic fields “as one unified conformation”, the contrast between ether and matter would fade away. He was saying the contrast between space and matter would fade away. So the contrast between space and dark matter should fade away too. See does matter differ from vacuum? by Christoph Schiller. The answer is no. Because this space, this quintessence, doesn’t just have energy, it is energy, and matter is made of energy. So it’s perhaps rather prescient that “medieval scholastic philosophers granted aether changes of density, in which the bodies of the planets were considered to be more dense than the medium which filled the rest of the universe”. It would seem that Newton granted that too:
Fair use excerpt from Newton’s views on aether and gravitation by Léon Rosenfeld 1969
When it’s inhomogeneous, space has a mass equivalence and a gravitational effect. But it doesn’t interact with photons in the usual sense. It’s gin clear. It’s invisible to the entire electromagnetic spectrum. It doesn’t change a photon’s E=hf energy, because energy is conserved. Space merely bends a photon’s path when space is inhomogeneous. When it isn’t, like in the void at the centre of the planet, you wouldn’t know it was there. Because light goes straight and pencils don’t fall down. It’s similar for electrons and protons. Space only affects them gravitationally when it’s inhomogeneous. It’s also dark, and it’s cold because it doesn’t consist of fast-moving particles, so it fits the bill in every way you can think of. Particularly when you think of black holes and the early universe. Because as Stephen Hawking said, the universe is like a black hole in reverse. We’ll come back to that another day.
The raisin loaf analogy
So, we have our vacuum energy. When it’s inhomogeneous it has a gravitational effect. Meanwhile the contrast between space and matter is fading away, and space is dark. It sounds promising. But there’s something else we need, starting with a raisin loaf:
Image by NASA, see Universe 101 by Britt Griswold and Edward Wollack
The raisin-loaf analogy likens the expanding universe to a loaf in an oven. The loaf rises and expands. It gets bigger, but the raisins don’t. They represent the galaxies, and the thing to remember is space expands between the galaxies but not within. That’s because each galaxy is gravitationally bound. Something else we need to accompany the raisin loaf is conservation of energy. Do you know of any situation in which energy is not conserved? I don’t. I don’t know of any over-unity free-energy perpetual motion machines. So when space expands, conservation of energy tells me the spatial energy density must reduce. Not stay constant.
Space expands between the galaxies but not within
This is important because there’s more than one way to skin Schrödinger’s cat. To recap, Einstein modelled space as a continuum, akin to some kind of gin-clear ghostly elastic jelly. Let’s make that a dark jelly, with white grid lines. When you inject more jelly in the middle you create a pressure gradient in the surrounding jelly. Curved spacetime is essentially a plot of this pressure gradient. It isn’t the curvature of the grid lines. Like John Baez said, curved spacetime is not curved space. Space isn’t curved where a gravitational field is. Instead, like Einstein said, it’s inhomogeneous. Then when the inhomogeneity is non-linear such that a plot of it is curved, the result is what we call curved spacetime. So, is there another way to make space inhomogeneous? What happens when space expands between the galaxies but not within? Let’s start with two galaxies close together. Let’s take a look at some grid lines, but let’s also take a slice through the middle to avoid getting confused by the curvature of the galaxies. Then we can depict each galaxy’s gravitational field as inhomogeneous space, like so:
Galaxy images by NASA
When space expands between the galaxies but not within, the energy density of space between the galaxies reduces by virtue of conservation of energy. So the inhomogeneity increases. Like so:
Galaxy images by NASA
And what’s a gravitational field? Like Einstein said it’s a place where space is “neither homogeneous nor isotropic”. So when the universe expands, when space expands between the galaxies but not within, those galaxies end up with deeper gravitational potentials. You can liken it to an upside-down rubber sheet analogy. A gravitational field is normally shown as a bowling-ball depression, but turn it over so it’s a mountainous hump in a plain. Injecting that gin-clear ghostly elastic jelly makes the mountain bigger. But expanding the universe is like lowering the whole plain. The mountain gets bigger in a roundabout way. So do the gravitational fields of our galaxies. Each and every galaxy, unless it’s bright and shiny and new, is of necessity surrounded by a region of inhomogeneous space. Caused by the non-uniform expansion of space. And inhomogeneous space is what a gravitational field is. So each and every galaxy has rather more gravity than you might expect.
The situation is similar for clusters of galaxies. The space within the galaxies doesn’t expand, and nor does the space between the galaxies of the cluster. So the galaxies end up embedded in a region of denser space, surrounded by a density gradient. A place where space is neither homogeneous nor isotropic. A gravitational field. In our upside-down rubber sheet analogy, the cluster is a massif. Expanding the universe is like lowering the surrounding plain so the massif gets more massive:
Dark matter map by Priyamvada Natarajan et al, see mapping substructure in the HST Frontier Fields figure 28
See the NASA article galaxy clusters reveal new dark matter insights. It dates from 2016, and concerns a study of 8,648 galactic clusters by Hironao Miyatake and 6 other authors. The article says the internal structure of a cluster is linked to the dark matter environment it’s in. It quotes co-author David Spergel saying this: “our work has shown that ‘age matters’: Younger clusters live in different large-scale dark-matter environments than older clusters”. Yes, age matters. Because an old cluster is going to look like its embedded in more dark matter than a young cluster. Because the surrounding space has expanded more. Hence you can read articles such as dark matter less influential in galaxies in early universe on PhysOrg dating from March 2017. It concerns a paper by Reinhard Genzel and 31 other authors on strongly baryon-dominated disk galaxies at the peak of galaxy formation ten billion years ago. What they found was intriguing: “unlike spiral galaxies in the modern Universe, the outer regions of these distant galaxies seem to be rotating more slowly than regions closer to the core – suggesting there is less dark matter present than expected”. There’s an accompanying illustration which also appears in the Scientific American reportage. I’ve flipped it horizontally to make fit better with the excellent animation by Ingo Berg in the Wikipedia galaxy rotation curve article:
CCA 4.0 image by ESO/L Calçada see ESO public images CCASA image by Ingo Berg, see Wikipedia
The early spiral galaxies have “normal” rotation curves wherein velocity diminishes with distance, like you’d expect if there was no dark matter. The contemporary spiral galaxies have flat rotation curves. Something has clearly changed whilst space has been expanding. What can it be? Why I rather think it might be something called space.
A problem for structure formation
Take a look at the citations for the 2017 paper by Genzel et al. There’s corroboration in falling outer rotation curves of star-forming galaxies at 0.6 < z < 2.6 probed with KMOS3D and SINS/ZC-SINF. It’s by Philipp Lang and 27 other authors. They said “this outer fall-off strikingly deviates from the flat or mildly rising rotation curves of local spiral galaxies of similar masses”. That doesn’t sit well with dark matter’s supposed role in structure formation, where it’s said to form the “seeds into which the baryons could later fall”. Mark Swinbank is diplomatic in his 2017 Nature letter distant galaxies lack dark matter. He said “surprisingly, galaxies in the distant Universe seem to contain comparatively little of it”. Alexander Dolgov said new data strongly supports an inverted picture. Mordehai Milgrom wrote about high-redshift rotation curves and MOND in 2017, saying a0 may be varying with cosmological time. Andy Biddulph really spits it out in observational support for bottom up quantum gravity. He said it’s “contrary to the standard model of galaxy formation which supposes a dark matter halo about which baryons condense”. Quite. Which is why Genzel said it’s going to be an interesting time.
Old galaxies and clusters contain more dark matter than youngsters
That’s because older galaxies definitely appear to contain more dark matter than younger galaxies. The paper by Lang et al says star-forming galaxies at larger look-back times are more baryon-dominated, with the baryon fraction increasing with redshift. They refer to Förster Schreiber et al 2009, van Dokkum et al 2015, Burkert et al 2016, Wuyts et al 2016, Price et al 2016, and Stott et al 2016. Also see the 2009 NASA report Hubble provides new evidence for dark matter around small galaxies. That’s where Christopher Conselice said this: “these dwarfs are very old galaxies that have been in the cluster a long time. So if something was going to disrupt them, it would have happened by now. They must be very, very dark-matter-dominated galaxies”. The underlying paper is Hubble Space Telescope survey of the Perseus Cluster – I. The structure and dark matter content of cluster dwarf spheroidals by Samantha Penny, Christopher Conselice, Sven de Rijcke, and Enrico Held.
The Bullet cluster
Talking of clusters, the Bullet cluster is said “to provide the best evidence to date for the existence of dark matter”. You can find composite images such as the one on the Chandra X-ray observatory website, in the 2006 article NASA finds direct proof of dark matter:
Credit: X-ray: NASA/CXC/CfA/M Markevitch et al; Optical: NASA/STScI; Magellan/U Arizona/D Clowe et al; Lensing Map: NASA/STScI; ESO WFI; Magellan/U Arizona/D Clowe et al.
The picture is composed of an optical image showing orange and white galaxies, an X-ray image showing hot gas in pink, and a blue overlay of dark matter inferred from lensing observations. Most of the baryonic matter is in the form of gas rather than stars. This gas was slowed and heated to 160 million degrees in a 6 million mph collision. It was left behind, whilst the dark matter wasn’t. Hence the lensing is strongest in two separated regions near the visible galaxies. See the animation on the Chandra photo album. Strictly speaking the Bullet cluster is the one with the bow shock trailing behind it, but people tend to refer to both clusters as the Bullet cluster without thinking too much about it. It’s similar for MACS J0025.4-1222 which “provides independent, direct evidence for dark matter and supports the view that dark matter particles interact with each other only very weakly”. People presume dark matter consists of particles without thinking too much about it.
They don’t think too much about Abell 520 either. See the 2012 Chandra article dark matter core defies explanation in NASA Hubble image. The associated press image and caption says “the result could present a challenge to basic theories of dark matter, which predict that galaxies should be anchored to dark matter”. Again the galaxies are orange and white, the pink is hot gas which is evidence that a collision has occurred, and the dark matter is shown in blue:
Credit: X-ray: NASA/CXC/UVic/A Mahdavi et al; Optical/Lensing: CFHT/UVic/A Mahdavi et al, see the Chandra photo album
Like the Bullet cluster there’s a bow shock, but pointing 45° down to the right rather than straight left to right. However unlike the Bullet cluster there’s dark matter in the middle, and apparently no dark matter around a group of bright galaxies on the left. See the Canada-France-Hawaii telescope website for a good write up in their article dark matter core defies explanation. It says this: “the team has proposed a half-dozen explanations for the findings, but each is unsettling for astronomers. “It’s pick your poison,” said team member Andisheh Mahdavi”. The article refers to a study of the dark core in A520 with Hubble space telescope: the mystery deepens. It’s by Myungkook James Jee, Andisheh Mahdavi, Henk Hoekstra, Arif Babul, Julianne Dalcanton, Patricia Carroll, and Peter Capak. They offer a variety of possible causes, namely a compact high mass to light group, a contribution from neighbouring substructures, a distant background cluster, the ejection of bright galaxies, the collisional deposition of dark matter, and a line-of-sight filament. In a later paper in 2014 the first four authors favour collisional dark matter. What they don’t offer is a none of the above possibility. The possibility that dark matter is as smooth as hell. That it’s more smoothly distributed throughout space than previously thought. So much so, that it doesn’t consist of particles.
Filaments of the large scale structure
I think we’ll get there in the end. But meanwhile take note of the 2008 paper Cluster Abell 520: a perspective based on member galaxies. A cluster forming at the crossing of three filaments? It’s by Marisa Girardi, Rafael Barrena, Walter Boschin, and Erica Ellingson. Their results suggest that “we are looking at a cluster forming at the crossing of three filaments of the large scale structure”. Also note that the observable universe is comprised of “galaxy groups, galaxy clusters, superclusters, sheets, walls and filaments, which are separated by immense voids, creating a vast foam-like structure”. This structure isn’t just made of galaxies, just as a raisin loaf isn’t just made of raisins. The raisins are only a small fraction of the whole. Take away the raisins, and you still have a loaf. A foam-like inhomogeneous structure that’s a something rather than nothing. In similar vein there are no galaxies in the centre of Abell 520. But there are lensing centres. Because space itself is not homogeneous, and nor is its expansion.
Space is dark and there’s a lot of it about
I suppose this non-uniform expansion of non-uniform space means gravity is “modified”. Which in a way means Milgrom was always half right. The same goes for the people who talk about dark matter in non-specific terms. But not for the particle physicists. They’ll never find those supersymmetric WIMPs. They’re out on a limb because they don’t understand the nature of the electron or why there are no magnetic monopoles, or how gravity works. They can’t see what’s hiding in plain view because they haven’t listened to what Einstein said. Their general relativity is an ersatz secondhand general relativity that doesn’t even acknowledge that light curves because the speed of light is not constant. Or that Einstein said space is neither homogeneous nor isotropic, that it’s the aether of general relativity, and that the contrast between space and matter would fade away. What’s a quantum field? A state of space. How many states of space are there in any one place? There can only be one. What’s the state for a gravitational field? Inhomogeneous. So after forty years of no-show exotic particles, what’s left? What’s the none of the above possibility? Inhomogeneous space. That’s what dark matter is. Inhomogeneous space with its inhomogeneous spatial energy which has a gravitational effect. Because space is dark, it has its vacuum energy which has a mass equivalence, and there’s a lot of it about.