A Natural Law for Rotating Galaxies: What Does This Mean for Dark Matter?
physicscentral.com
physicscentral.com
https://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtr...
"The Friedmann–Lemaître–Robertson–Walker (FLRW) metric is an exact solution of Einstein's field equations of general relativity; it describes a homogeneous, isotropic expanding or contracting universe that is path connected, but not necessarily simply connected."
> No one has ever observed any dark matter
http://chandra.harvard.edu/press/06_releases/press_082106.ht...
"NASA finds direct proof of Dark Matter"
> or dark energy so far.
This is probably the only part of your post that actually came close to the truth. Dark energy is far more of a placeholder than dark matter at this point.
2. I am quoting from the article.
"In addition to the Chandra observation, the Hubble Space Telescope, the European Southern Observatory's Very Large Telescope and the Magellan optical telescopes were used to determine the location of the mass in the clusters. This was done by measuring the effect of gravitational lensing, where gravity from the clusters distorts light from background galaxies as predicted by Einstein's theory of general relativity."
Since they are calculating the mass by using General Theory of Relativity (indirect measurement, you have to trust the theory for this), I don't see how this can be called direct detection.
3. We don't seem to disagree on this :)
'The most serious problem facing Milgrom's law is that it cannot completely eliminate the need for dark matter in all astrophysical systems: galaxy clusters show a residual mass discrepancy even when analysed using MOND.'
'Besides these observational issues, MOND and its generalisations are plagued by theoretical difficulties. Several ad-hoc and inelegant additions to general relativity are required to create a theory with a non-Newtonian non-relativistic limit, the plethora of different versions of the theory offer diverging predictions in simple physical situations and thus make it difficult to test the framework conclusively, and some formulations (most prominently those based on modified inertia) have long suffered from poor compatibility with cherished physical principles such as conservation laws.'
Basically, people have tried to fiddle with the laws as you suggested, but none of actually managed to fit the data better than GR + dark matter, plus the fiddling often just looked like curve-fitting without any good theoretical justification. Of course, the jury's still out.
Exactly. The whole basis for belief in "dark matter" and "dark energy" is basically: "our theories on how the universe works don't compute, so there must be some invisible things (dark matter & energy) we cannot detect since our theories can't be wrong."
We're going with them because all the other new theories end up requiring fractional dimensions or some similarly bizarre space time and still don't end up explaining things as well as "I dunno guys maybe there's just some stuff we can't see". We already know there's a bunch of stuff we can't see, dark matter is just some other kind of stuff we can't see. Dark matter is on the correct side of the razor.
https://en.wikipedia.org/wiki/MACS_J0025.4-1222
https://en.wikipedia.org/wiki/Dragonfly_44
We have had direct detection of dark matter since the 50s https://en.wikipedia.org/wiki/Neutrino
And the generally successful standard model predicts several possible additional forms of dark matter e.g. https://en.wikipedia.org/wiki/Neutralino
I mean no shit there are in answered questions. We aren't omniscient. this is how it works.
People seem think think this allows our current theories to be wrong.....
Perhaps there might be small issues with Einstein theories, personally I doubt it, but, to me, I really don't think small fixes to the theory will explain this stuff away.
I am a physicist (well, I studied as one, before going technology entrepreneur), and have always sat in the "dark matter is bullshit" camp - so my opinion is likely tainted.
I think a far more likely explanation, as this paper could suggest, is that something far more mundane is happening.
For instance, we already understand tidal forces - that bodies can become tidally locked, that there is an inertial frame shear that drags bodies along around a rotating centre of mass, and exchanges energy between an orbiting body and the centre.... So why is it infeasible that galaxies are tidally locked, and the lack of fall-off in radial velocity is down to the gravitational shear from the galactic core being far more intense than we anticipate, causing the behaviour we see. It doesn't require a rewrite of relativity, "just" of galactic evolution.
Either that, or galaxies are sprites, and lazily rendered ones, at that.
Because someone has indubitably already ran the numbers. The tidal force only has a non central, orbit changing influence on spatially extended bodies, and its effects even on objects as large as our solar system are completely negligible, as it doesn't seem to have a measurable effect on the orbits of the planets. The rotation curves are way off, which is a huge chunk of excess angular momentum that no tidal force can conjure. Where would it even come from, the rotational angular momentum of component stars?
As to running the numbers - agreed - but one can get an answer which is correct but incorrect if your premises are incorrect.
At a galactic scale the perturbations are likely tiny, but a tiny force applied over enough time adds up.
Anyway. It's a poor example that's almost certainly wrong but my point was more about how a single incorrect assumption can wreck a model.
I'd rather call it a paradigm shifting revolutionary idea ;)
However, it is not correct to call this a "small improvement." Relativity was a radical change to our understanding of how the universe behaves. In a Newtonian universe, information (including gravitation, electrical attraction, and light) travelled instantaneously. This does not happen in relativity, and nor does it happen in the universe we live in. Einstein did not merely improve upon Newton's work; Einstein proposed a theory which explained the ways in which we do not live in a Newtonian universe. Thomas Kuhn goes into this concept in detail in "The Structure of Scientific Revolutions."
While I agree with definition of dark matter that you provided, keep in mind that there are hypothesis that try and explain it as something that exists. For example: WIMPs.
Both of these have been tried, but there are many reasons why the majority of astrophysicists prefer the dark matter approach. Firstly, there are observations which suggest large regions of mass that are not aligned with the visible mass (e.g. the bullet cluster). Secondly, dark matter can explain the statistical properties of the Cosmic Microwave Background radiation in a way that can not be achieved with ordinary matter alone. Thirdly, when we include dark matter in simulations, we get results that are a very good match for the universe as we observe it. etc. etc. If that weren't enough, we know that there are plenty of types of matter that are dark - e.g. neutrinos, early black holes etc. Whilst none of these have yet satisfied the conditions for dark matter as we understand it, it's perfectly possible that we have already identified some of the constituent parts, and there is a list of potential candidates as long as my arm that the particle physicists are working their way through.
Finally, the biggest annoyance is the intimation that we are all just one big cabal. Let me put it like this: if you could provide indisputable evidence that dark matter was wrong, you would be a superstar in our field and everyone would be phenomenally excited, because it would demand the hunt for new physics. Scientists are a rational bunch, however, so any evidence must be weighed against the existing evidence already observed (which, as above, is substantial).
Dark energy is slightly different. No one know's what this is, but models with a dark energy component do very well at modelling the universe. The question is, why? No one is pretending that this is a solved question, but what we do know is that whatever is driving the universe's accelerated expansion has properties that are very similar to what dark energy is.
tldr: There are loads of great reasons for thinking dark matter exists, contrary to many posters here, and it is well accepted that dark energy is a mathematical term that represents something of unknown physical origin.
[1] https://arxiv.org/abs/1011.3495
Number one is the continued references to Keplers laws. Kepler only applies to 2-body systems where the mass of one is dramatically larger than the other. This works well for the solar system, where the sun is huge compared to the planets and the planets have little effect on each other. But do note that some planets were predicted to exist based on their effect on the orbits of other planets, so even in this sparse system the effects do make a difference. My point is that Kepler has no place in galactic dynamics but is often referenced - if that were the model that doesn't match observation then DUH! But the physicists are smarter than that.
Second, I occasionally see mis-application of the divergence theorem and/or gauss's law. Some folks seem to treat a portion of a galaxy out to a radius R as a point mass by using this theorem. The problem of course is that to make that leap you must have a uniform spherical distribution of matter inside the spherical boundary. In other words, a disk-like distribution of matter does not have a uniform gravitational pull at all points of distance R from its center. You'll find it is stronger near the edge of the disk than at the same distance perpendicular to it.
Third, this particular article keeps making reference to the "radial velocity" or speed of stars where I believe they are actually talking about the orbital or tangential velocity.
And lastly, if the dark matter obeys the same laws of gravitation, there must be a reason for its distribution to be different than the other matter. At that point, I don't see any need for "strange dark matter" or new particles or physics. You really can't have it both ways - it's fundamentally different, yet it obeys the same rules. Having said that, I could see how exploding stars would spread non-visible matter (remnant material) in a way that might be very different from the stars themselves.
But stars (and gas clouds) orbiting in a disk are essentially always "near the edge" of the disk (that is, the disk defined as matter interior to the orbit in question), so the approximation is usually pretty good.
reference to the "radial velocity" or speed of stars where I believe they are actually talking about the orbital or tangential velocity.
The (understandable!) confusion originates because "radial" and "tangential" refer, in an observational sense, to velocities along or perpendicular to the line-of-sight vector. To simplify a bit: for observations of astronomical objects, velocities along the line of sight from you to the object (detectable from Doppler shifts in its light) are "radial", while velocities perpendicular to the line of sight (which require that you wait long enough to see things change position on the sky) are "tangential". For edge-on spiral galaxies, the orbital motions that we can observe are those producing Doppler shifts along the line of sight (which are, in the frame of the galaxy, "orbital or tangential", as you suggest).
And lastly, if the dark matter obeys the same laws of gravitation, there must be a reason for its distribution to be different than the other matter.
The usual argument is that dark matter is "non-dissipative" -- that is, it can't lose orbital energy via things like radiation, the way ordinary matter in the form of gas can. (And, unlike gas, it doesn't feel pressure forces.) Stars are also non-dissipative, but stars form out of gas, so their distribution reflects the effects of dissipation in ways that dark matter can't.
Not sure we're on the same page. For a star orbiting at radius r on a disk of radius R, some folks will lump all mass inside r into a point and apply keplers laws. They will reject all the mass between r and R because of the same surface integral theorems. The problem is that neither of those assumptions are anywhere near correct. The pull from the interior <r mass is not the same as though it were a point, and the pull from the outer mass >r is very much non-zero. For an example using electric charge instead of gravity:
http://www.phys.uri.edu/gerhard/PHY204/tsl34.pdf
Note that the field is non-zero at most places inside the ring, however it would be zero over the entire volume if it were a spherical distribution.
Yes, the orbits within the inner part of a galaxy don't follow a Keplerian curve. However, at large radii most of the visible matter is well inside the orbit and very little is outside (galaxies are quite centrally concentrated), so the rotation curve should approach the Keplerian limit as you go to larger and larger radii. The fact that it doesn't is one of the primary pieces of evidence for dark matter in galaxies (though not the only one).
(I'm not sure why you linked to that slide, since it's not calculating the field in the plane of the ring, nor is it dealing with a continuous charge distribution. Regardless, you'll note that E_x goes to 1/x^2 for x >> a, which is a "Keplerian" limit.)
I don't agree. If we treat the galaxy as a bunch of concentric rings, many of them are nowhere near far enough away to reach that "Keplerian" limit.
As an experiment I modeled a flat disk of uniformly distributed stars. Without doing a dynamic simulation one can do the n-body calculation to determine the total pull on each star and determine what its orbital velocity must be to go in a circular orbit. You find that the "galactic rotation curve" will have a velocity that actually increases all the way to the edge. Of course a uniform distribution is not what a real galaxy looks like, but I think we can all agree reality is somewhere between the uniform flat disk and the highly concentrated central mass. And the actual rotation curves are somewhere between Keplers and mine. I'd expect people to work backward from the rotation curves to determine the mass distribution and then try to understand why that isn't what is observed. I suppose that's just a different way to get at the same mystery.
I raised my hand and asked "how do the galaxies maintain their spiral shape? Shouldn't the inner stars rotate much more quickly than the outer ones?"
The teacher didn't understand my question (this was one of my first inklings that teachers didn't tend to be that bright).
The last 10-15 years with headlines in the popular press about dark matter, MOND, etc. are quite satisfying - 10 year old me is thrilled that my question is mainstream now!
The spiral arms maintain their shape not because of an anomaly in orbital velocities, but because they are density waves[1]. Kepler doesn't work because the arms themselves and the rest of the disk exerts significant gravity.
In which case these types of discoveries are to be expected as we fill in the missing blanks.
If so then I am happy to see progress being made.
If I am wrong about my assumptions about Dark Matter and Dark Energy I wouldn't mind some starters :) Thanks!
OTOH, maybe everything in science is a kind of a placeholder, but that sort of thing can get unpleasantly philosophical.
(Really, I was objecting to the use of the word placeholder, because I found it unfair.)
What it comes down to, and this paper doesn't change this at all, is that either there's a bunch of matter we can't see or force carrying particles don't obey basic geometry (or the universe has much weirder geometry than we think). Most of us are a lot more comfortable with basically invisible matter.
https://en.wikipedia.org/wiki/Bullet_Cluster
My understanding is that our Universe is endless in all 4 dimensions and in scale. Every point of Universe contains infinite number of small, even infinite small, particles. These particles are forming large objects, even infinite large objects. And these objects are oscillating endlessly: condensing and evaporating, so whole Universe cannot be sink into singularity, even in endless time.
IMHO, we are in large bulb of plank-scale particles, which are called "physical vacuum", which are forming medium for all other particles and forces to travel. This medium is not regular: it denser in center (so it causes red shift), it denser around massive objects.
> Every point of Universe contains infinite number of small, even infinite small, particles.
https://www.youtube.com/watch?v=gEKSpZPByD0 (really worth it! Watch at 1.5 times speed)
and
https://news.ycombinator.com/item?id=12377393 (reading the discussion is useless though without understanding at least what is presented in the above lecture)
So there no particles, only fields OR there is no fields, only particles.
And MOND is an interesting theory that's been explored but hasn't gone anywhere.
[1] https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics
The actual paper also says that but then ignores the fact that they just said it so they can suggest MOND.
Perhaps the phenomenon is the result of new relativistic dynamical laws instead of dark matter, e.g. "All large-scale rotating structures appear to be indistinguishable from a single rotating object when viewed from any observer's frame of reference" for some definition of "large-scale".
"The Duhem–Quine thesis, also called the Duhem–Quine problem, after Pierre Duhem and Willard Van Orman Quine, is that it is impossible to test a scientific hypothesis in isolation, because an empirical test of the hypothesis requires one or more background assumptions (also called auxiliary assumptions or auxiliary hypotheses). In recent decades the set of associated assumptions supporting a thesis sometimes is called a bundle of hypotheses." https://en.wikipedia.org/wiki/Duhem%E2%80%93Quine_thesis
For example, when predicting the rotation curves you can instead assume the mass is log-normally distributed and get the flat curves:
"The generation of the 37 galaxy velocity profiles presented in this paper assumed that most of the galactic mass is in the disk, and gravity is Newtonian. A best-fit algorithm was used to generate the curves of Figures 1 and 3 – 38 using a truncated log-normal surface density distribution function. The log-normal models closely matched the shape of observational rotation velocities, and the predicted masses for these curves fitted a baryonic Tully-Fisher relation reasonably well over a wide range of galaxy sizes, from LSB galaxies to massive high-luminosity disks." https://arxiv.org/abs/1502.02949
It isn't that I think that must be the correct solution, but why was no one publishing the results of investigating that assumption until 2015?
Can you expand on that post? The paper you linked appears to assume the very thing being questioned here...
Dark matter has always in my eye so similar to the God hypothesis that we conjure something that is mysterious with undefined but whatever necessary to explain away the discrepancy or mystery.
Acknowledging that we don't know -- not even assume it is matter that fits our current understanding -- is the start of understanding.
Now it appears we do know it fits some mathematical equation ...
PS: the God hypothesis could well be correct, but that should be the last resort -- It is not really an explanation, so it is not necessary until the explanation is needed for reasons of other than explaining.
e: I'm agreeing with you that putting "matter" in its name is fairly misleading. Fortunately, that doesn't confuse physicists.
It's as baseless as the ether of the 19th century and as ubiquitous in its invocation.
But mention this and get downvoted.