Can someone please explain how dark matter, which can’t be directly observed, is mathematically any different than adding an arbitrary parameter to the equation and tuning it to fit? I can’t help but think of von Neumann’s elephant.
This isn’t me trying to be clever, I’d really appreciate some clarity on this.
It's probably worth considering this question from the perspective of how we know most subatomic particles are real. They can't be directly observed either - the LHC and other particle accelerators only ever observe electrical disturbances in their sensors following a pattern of results from decay product interactions. No one sits down with a microscope and says "yep that's a gluon".
EDIT: Consider that the Higgs boson wasn't "directly" observed till very recently but was assumed to exist for decades prior for the exact same reasons - you needed to add an additional term to the equations to break the symmetry and cause particles to have mass, which in turn implied a pervasive field throughout the universe we hadn't observed yet. Which in turn implied it should exist discreetly under high energy conditions as a particle, which became the Higgs.
I thought the extra term was added so the equations didn't result in probabilities outside the 0-1 range.
> "The Higgs boson gives mass to other elementary particles such as quarks and electrons, and its existence is necessary for the theory to give sensible results (i.e., the probability of processes to occur cannot be greater than 100 percent)."
https://www.albany.edu/news/87798.php
It’s not much different. That doesn’t mean DM is wrong, though! Logically, there’s two possibilities: laws of gravitation are 100% correct at all scales and the discrepancies we see at level of galaxy rotations, etc, are due to matter we can’t yet observe in other ways (hypothesized dark matter). Other option is gravity dynamics are in need of further refinement, much like GR refined Newtonian gravity. Or some combination... maybe GR isn’t the full story but dark matter is also a real thing.
I think there’s often sloppiness in how things are stated - dark matter is inferred based on observation of X (edges of galaxy rotate too fast) and an assumption that GR is 100% correct. X is then said to be “evidence for DM”, but there’s that unstated premise.
Cold (as in moving slowly compared to the speed of light) dark matter has yet to be directly observed. We have certainly observed relativistic dark matter in the form of neutrinos, including streams of them we can produce in labs like Super-Kamiokande [1], where we can watch the flow of momentum exceed that available from electromagnetic interactions. "Relativistic" here means moving as speeds closely approaching the speed of light.
It took almost a decade to go from experimentally demonstrating a momentum-deficit in certain nuclear interactions, to proposing a self-consistent and consistent-with-observations theory of an electron-neutrino carrying the "missing" or "surprise extra" momentum in examining clouds of nuclear decay products. There were many theoretical false-starts, where the behaviours of the momentum deficit in the bulk did not match up with microscopic details of the theory. This is in spite of direct in-laboratory repeatability at accessible energies with then-modern equipment. Worse, it took a further twenty years to directly observe the anti-electron-neutrino (consequently also proving the existence of the electron-neutrino) in a controlled experiment.
Although neutrinos individually carry low momentum, and individually interact only rarely with atomic nuclei, there are an awful lot of them carrying momentum out of stars, and even more out of supernovae and other violent phenomena, so a bit more than sixty years after the first detection of a neutrino, laboratories are pretty good at detecting them. Theory has had to adapt to laboratory discoveries, adding in two other types of neutrinos, and neutrino oscillation. Along the way, the theory has become relativistic (allowing for accurate prediction of observations by differently-moving observers) and generally covariant (allowing for accurate prediction of observations by differently-accelerated observers or equivalently observers near different sources gravitation, including neutrino interactions in stellar cores or near the surfaces of neutron stars).
Neutrinos enter into the energy-density of the universe in the standard model of cosmology; they are there and they make a difference to the arrangement of visible matter in the sky.
In the 1880s (yes, nineteenth century!) a momentum-deficit was detected at the scales of clusters of stars in our own galaxy, with a radial relation being proven for the Andromeda galaxy in the 1930s, which was about the same time that the first self-consistent theory for the (neutrino) momentum-deficit for beta decays was produced. Sky-observing technology development did not quite keep up with particle-observing technology over the intervening decades, so it was not until the 1970s that a momentum-deficit in galaxies is extremely commonplace.
There is a self-consistent relativistic, generally covariant theory for this momentum-deficit in the bulk, but the microscopic details are not yet known from experiment. That is, the equivalent of the electron-neutrino has not been shown, and there may be more than one microscopic component, roughly similarly to how there are three types of neutrinos (and three anti-neutrinos), and of course there may be dynamics (similar to neutrino oscillation).
That's why there are so many detection experiments. There are lots of possible microscopic contributions to dark matter in the bulk, but they are all even more difficult to detect in principle than the neutrino, because (being cold in the sense above) interactions will nudge atomic nuclei with much less momentum than neutrino interactions with the same atomic nuclei. Also, we don't have a way to build a source like Super-Kamiokande that lets us study a stream of excess non-neutrino, non-electromagnetic momentum.
However, there is no serious doubt as to the momentum-deficit at scales of galaxies and galaxy clusters. It's not just galaxy rotation curves. There is also a momentum-deficit clearly visible in the cosmic microwave background, and it is an extremely close match to that seen in the more recent universe at galaxy cluster scales. The only non-self-contradictory theories to date suggest an entry into the Einstein Field Equations in the stress-energy tensor. The entry need not be much like a neutrino or any other particle of the Standard Model of Particle Physics, and in principle might not even interact with them except gravitationally. Those possibilities will necessarily be studied later, if and as technology develops.
> I'd really appreciate some clarity on this
The mathematics of dark matter in the bulk has generally followed from observations of mass-deficit. However, the mathematics of various proposals for the microscopic details of the composition of that bulk has outpaced observation and experiment. A number of proposals were motivated by other issues essentially unrelated to gravitation, so the mathematical structure was there in a modification of the Standard Model of Particle Physics, and experiments would simultaneously test such extensions and the possibility that bulk dark matter is (at least partially) such particles.
Thus, on the one hand, annoying observations that won't go away led to "hot" dark matter (neutrinos) ultimately, there are annoying observations that won't go away that are consistent with "cold" dark mater (details not yet known). Known types of neutrinos and their dynamics proliferated once they were directly detectable in a laboratory setting, leading to updated theories. However, there is as yet no direct detection of a "cold" dark matter candidate, and no especially strong reason to believe that an initial laboratory observation of one such candidate will be all there is to discover in the dark matter sector.
It seems like the title should be something like "Dark Matter Sighting Get Reprieve". Dark matter is pretty well established, it's just a supposed direct sighting that now seems to be getting a second look.
Well, I think this supposed "sighting" of dark matter rests on an assumption that this version of dark matter actually decays via particle-anti-particle annihilation. If that is true, then one could begin to describe or speculate on it's quantum and electromagnetic properties and look for other places these properties manifested. IE, the matter would be no longer literally dark but could be fit within our broader understanding of atomic particle ... or might force us to expand this understanding. Either way, it seems like a significant advance.
This is basically impossible unless someone has figured out a way to break the laws of thermodynamics. And if that's true a whole bunch of stuff goes out the window.
Basically a Dyson Sphere is about the least subtle thing a civilization could do and would be detectable from hundreds of millions of light years away. All energy ends as heat. The only way to get rid of heat in space is to radiate it away. It radiates away in a predictable way based on the temperature of the object. At any sort of temperature we're talking about this would be a massive glowing infrared cloud with the energy output of a star. It'd be hard to miss that.
Think about this: a Dyson sphere here would be absorbing the energy output of a star. That energy has to go somewhere.
Another point against it is the Elapsed Time Argument, which can be used to effectively disprove many such hypotheses. The argument goes like this: if a given phenomenon is artificial it should be less common the more distant you look. At the edge of the observable universe we're looking at a universe significantly younger than ours. Because of this something artificial should be less common further away because less time has elapsed there. If that's not the case it's almost certainly not artificial.
It's also worth pointing out that dark matter out-masses regular matter by 10-to-1 or more. That's a lot to attribute to Dyson Spheres. That would make the universe an extremely populated place where we somehow still can't detect anyone.
Hmmm, your response is amazing. I was just sort of pondering a far out idea. But the amount of time and energy you put into your response is awesome. So cool that you thought about my dumb idea that much. Not trolling just thinking about far out ideas. I like your response a lot.
You'd need an awful lot of Dyson Spheres, and they'd all be in places you wouldn't expect suitable stars at all, and then you'd have to hide them from searches for brown dwarfs and black holes as components of Dark Matter. See https://en.wikipedia.org/wiki/Massive_compact_halo_object for a brief overview.
The killer problem is that stars bright enough to gather up energy via Dyson Sphere mechanisms aren't seen around any of the many thousands of galaxies we've looked at. Moreover, in order to account for an appreciable fraction of the halo masses, there would have to be at least hundreds of millions of Dyson Spheres for every galaxy in the sky. The Dyson Spheres would also have to be very very old because, thanks to gravitational lensing by foreground galaxy clusters, we have decent enough views of galaxies billions of light-years away that we would see large numbers of not-yet-Dyson-Sphered stars well outside galaxies. The most distant spiral-type galaxies in particular would look very different than much closer ones, and that is not the case. Have a look for yourself: http://legacysurvey.org/viewer#IC%203556
Bright stars only form in regions where the dust and gas is sufficiently dense to collapse gravitationally; those regions are generally found only within galaxies or in "low points" of gravitational potential within clusters of galaxies (the dust and gas gathering in such points may form a new galaxy). Dust that doesn't fall into galaxies or into cluster "low points" becomes too diffuse to form even the dimmest stars.
By comparison, dark matter tends not to fall into galaxies or cluster low points because collisions between dark matter particles, or between them and ordinary matter, does not produce radiation. Radiation from particle collisions carries off the angular momentum that keeps the particles on higher orbits. Ordinary dust and gas collisions release light (and radio and so on) which enables gravitational collapse into stars. We can see the light (and radio and microwaves and so on) with telescopes.
This tendency of dark matter to stay on high orbits well above the luminous matter in galaxies leads to a greater angular momentum than expected in the outer reaches of the luminous matter. That angular momentum excess is how dark matter was discovered. Why don't the fast-moving stars and dust fly away from their galaxies? Because dark matter throughout the galaxy adds more mass than is seen electromagnetically, so there is a sufficient tendency to fall inwards counteracting the excess momentum. Why doesn't the fast-moving luminous matter collide more often, throw off more radiation, and collapse into the centres of galaxies more rapidly? Because the shell of dark matter well outside the bright parts of galaxies holds it up, somewhat like a scaffold. It's a balance, but not an especially fine one; it seems to be pretty generic for a collisionless, cold, non-self-interacting (except by gravitation), non-radiating, microscopic dust in which the visible components of galaxies are immersed.
Let's ignore the other responders' concerns about not being able to keep the Dyson Spheres as cool as the background to all observers (how would a Dyson Sphere builder in a galaxy 100 million light years away know that we might be looking from our galaxy, and so decide to cloak themselves only from us?). Let's also ignore whether such things would be transparent, or would occlude optical emissions from the galaxies they surround. We can't however ignore their gravitational influence: these Dyson Spheres have to "hold up" the non-Dyson-Sphered stars they surround, to stop their host galaxies from collapsing. You can't do that with only a few Dyson Spheres, and as you add more, you'd expect to see more small gravitational lensing distortions.
Although our telescopes aren't good enough to probe many galaxies, there are no such (gravitational lensing) distortions around our own galaxy, or Andromeda, and yet both galaxies' luminous matter's behaviour essentially requires an abundance of dark matter.
(There also isn't a dust eclipsing distant sources of light, which we would expect for a very dim but not exactly invisible Dyson Sphere would; there also isn't a large number of pointlike sources of deep infrared or radio in our or Andromeda's galactic halos, which one would expect if a Dyson Sphere builder were extremely energy-efficient. We also don't see excited dusts and gas around galaxies suggesting accidental "painting" with lasers or the like being shot out of Dyson Spheres if their operators decided not to radiate unused energy in every direction).
Finally, there is a hierarchical problem here: not only does dark matter surround galaxies and affect their structure gravitationally, it also surrounds whole clusters of galaxies. Without lots of dark matter hanging around waaaaay outside galaxies within a galaxy-cluster, clustering would be very different from what we see in the sky. Moreover, we know from Einstein lensing that the bulk of the magnification done by clusters is not traceable to the luminous matter in the galaxy cluster.
So you'd need to have lots and lots and lots of invisible Dyson Spheres many tens of thousands of light years outside galaxies. By lots, for a cluster similar to ours, this would mean a few hundred trillion Dyson Spheres, all very carefully engineered and positioned to mimic cold dark matter in areas where stars are not naturally seen. Also all evidence of towing stars, or generating new stars from scratch, has to be hidden from view in tens of thousands of galaxies over a span of a billion or more years, and somehow no galaxies known are older than the completion of the Dyson Sphere project, or somehow undisturbed early galaxies look identical to much more recent galaxies.
The engineering challenges would be outright cosmological, not just astronomical.
Wanna scare yourself with sci-fi thoughts? If this type of engineering is all done by a single culture, what would make them want to hide so carefully?
PS: I wrote the long reply above because it's refreshing in these comments to see someone asking "crazy questions" honestly, rather than advancing some crazy idea as if it were fact.
Tangential to your point, but is there any particular reason a Dyson sphere must "radiate away in a predictable way" (like the black body you described)? Surely a civilization sufficiently advanced as to create a Dyson sphere might either (a) direct excess energy in a beam to some satellite civilization or (b) store excess energy as matter, rather than just jettison it into space?
It goes towards the energy needs of the civilization? I'm confused why you think they harnass a sun just to radiate it all into space. Sure, some percentage will leak, but not all..
MOND describes, it doesn't explain. By adding a simple function to Newton's law of universal gravitation, it does a very good job of describing the momentum-deficit in the bulk motion of large optical and radio sources in a variety of galaxies compared to the predictions from Newton's unmodified theory. That it does so, and with such a simple modification, is interesting. Milgrom's function in MOND is almost certainly the simplest post-Newtonian gravitational term extending Newton's theory consistent with observations. (There are other adaptations of Newton's theory to add post-Newtonian elements, for example to describe motions within the solar system. These are generally much more complicated than MOND [see [1] for a quick overview].)
In practically any post-Newtonian term expanding Newton's law of universal gravitation, one will discover a greater mismatch with observation as the relative speeds of material participating in Newtonian gravitation increase.
One has to "patch" with additional terms and counter-terms, resulting in something comparable to a Taylor Series. One generally experiences obvious failure with this approach as the relative speeds of the masses become comparable to tenths of the speed of light.
MOND doesn't describe the momentum-deficit in the motion of large clusters of galaxies, nor the momentum-anisotropies in the cosmic microwave background. It doesn't describe large mass-flows, or especially relativistic mass-flows as seen in Seyfert galaxies and a number of galaxy clusters. It doesn't describe fast binary objects. It doesn't accurately describe the fine details of the bulk sources that it describes very well. It also doesn't accurately describe our solar system; one has to "patch" MOND with additional terms, and it quickly becomes easier just to discard MOND as a contribution to solar system dynamics altogether. MOND also doesn't abolish the need to use General Relativity to describe the angle-brightness-redshift relationship of the reddest galaxies (and the supernovae within them) visible in the sky. MOND does not provide sufficient post-Newtonian correction for GPS and other orbiting satellites with very precise frequency generators on board, nor for the results of experiments in MESSENGER [3] and numerous other spacecraft.
Let's return to what MOND does do very well: describing the relative angular momentum of slow-moving inner and outer bulk bits of galaxies.
Attempts to adapt MOND so that it accurately describes relativistic galaxy/cluster components have generally resulted in adding a field to standard General Relativity [3], and it is mostly cultural history that keeps MOND from being properly promoted as a source contributing to the stress-energy tensor. That would put it on identical footing to dark matter in the bulk, focusing minds on the question: "what are the microscopic details of the beyond-the-Standard-Model-of-Particle-Physics contributions to the stress-energy tensor?".
> epistemologically far superior
What is Newton's explanation for his law of universal gravitation, which MOND slightly modifies in a very specific way? What is the modern explanation of gravitation, which can encode MONDian behaviour in various ways?
>"The galactic center shines too brightly, like the glow of a metropolis at night where maps show only a town.
[...]
The new study, along with two others that came out in March, reopens the possibility that space-based instruments have found the first direct evidence of the elusive “dark matter” thought to pervade the universe."
Please give an example of what dark matter cannot explain.
Galactic rotation curves exactly as predicted: explained by dark matter
Galactic rotation curves not as predicted: explained by dark matter
Area of sky brighter than predicted: explained by dark matter
Area of sky dimmer than predicted: explained by dark matter.
Not entirely sure what you'r referring to by area of the sky but as to rotation curves it's:
-Galactic rotation curve not as predicted by relativity: explained by dark matter
-Galactic rotation curve exactly as predicted by relativity: allowed by dark matter, not explained by theories that propose a different uniform law of gravity that also explains case A.
I never said it was contradictory. I think what they've done is set up a system to filter out all theories except those that are flexible enough to be consistent with all possible observations.
Specifically, they measure some value for each galaxy: x +/- e. Where e is calculated for a 95% (or whatever) statistical interval. In each paper they study another galaxy and check whether the prediction is within x +/- e, if they find one that is not there are two branches:
1) If it is a flexible theory: they adjust the theory, arbitrarily fit some parameters, etc.
2) If it is a very exact theory that cannot be adjusted: they reject the theory.
Obviously this practice is flawed because the 95% interval says if you look at 100 galaxies and the theory is correct you should expect 5 of them to be outside your interval.
This bothers me too. Theories with too many adjustable parameters aren't really testable. And so, following Popper, I don't see how they can actually be scientific.
No they're just potentially not particularly useful models.
To be a theory they have to be making some direct claim we can use to predict future results.
To be rejected we have to find evidence where one adjustment would invalidate previous evidence (bring the hypothesis into contradiction with itself).
Being a good scientist means being positivist about your models - if the model works, it works, and it's irrelevant in some respects what it says something actually is if the name is not part of an additional claim of how things should behave.
Check out Imre Lakatos. "Falsifiability" is too strict since "every model is wrong". Lakatos calls that Popper0, which is not what Popper ever advocated.
In a nutshell:
The real thing going on is you are supposed to use Bayes' rule, where you normalize how well your explanation explains the observations ( p(H[0])p(H[0]|D) ) to the sum of all known explanations ( p(H[0:n])p(H[0:n]|D) ).
Thus if you have a vague explanation that can fit anything, it won't be much better than a million other possibilities so who cares. We only care when someone comes up with an accurate prediction that would be otherwise surprising. There are many more interesting ideas too (eg, "degenerating research programmes").
Edit:
I should also emphasize that my main point above is that there is a misuse of statistics going on though.
> We only care when someone comes up with an accurate prediction that would be otherwise surprising.
Sure. But the problem is when predictions don't pan out, parameters just get tweaked. Or new perturbations are introduced. Theories just keep getting more and more complicated.
This isn’t me trying to be clever, I’d really appreciate some clarity on this.