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Comment by trhway | Hacker News Reader

A spiral/disk galaxy's mass is proportional to the square of the radius:

Mg = C1 * Rg * Rg

where C1 depends only on shape and is basically the same across all the spiral/disk galaxies.

Orbital speed of stars in the disk is proportional to the square root of the galaxy's mass (the observed absence of the other otherwise must-have orbital velocity equation component - ie. 1/SQRT(r) - is what causes crack pot theories like dark matter) :

Vdisk = C2 * SQRT(Mg) = C2 * SQRT(C1) * Rg

where C2 also dependents only on shape and is basically the same across all the spiral/disk galaxies.

Thus Vdisk = C * Rg where the C is pretty close to being the same across all the spiral/disk galaxies.

Angular speed of a star in the disk at the distance "r" from center is

Vdisk / (2pi * r) = (C * Rg) / (2pi * r)

which at the edge of the galaxy, ie. where r = Rg, becomes

(C * Rg) / (2pi * Rg) = C / 2pi

ie. the same constant across all the spiral/disk galaxies. The end.

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> "...crack pot theories like dark matter"

Out of genuine interest, do you have any citations from reputable physicists who agree dark matter is a "crack pot theory"?

I think he was being sarcastic. The point is the basic law of gravitation is being violated here, and it's like, zero point energy or something.

not really. All the works postulating dark matter from the flat speed curve that i've seen so far are using basic orbital speed formula (sqrt(M/R)) which is only applicable to either spherically-simmetric masses and/or large (compare to the mass containing radius) distances between the interacting masses. Such simplification is just not valid for disk star orbital speed calculation because 1. disk galaxies are far from being spherically symmetric and 2. distance between a star and the galaxy center is of the same scale as the galaxy's radius. Very detailed Newton based calculation of those orbital speeds taking into account the shape of the galaxy mass distribution produces much flatter curve and, for example, for Milky Way to get a flat curve matching observations i needed to speculate only additional 20%-30% of galaxy mass to be present in the galaxy halo (like gas and dark dwarfs of all kinds which some works suggest there are and even that may be unnecessary - need to find and check some additional observational data for that) instead of additional 900% of dark matter that typical "dark matter" works speculate for.

What are your credentials, if you don't mind my asking?

He can do the math himself.

All the math?

Whereas professional physicists can't and haven't taken those maths into account?

That would be correct. I wondered if the problem was me reading things like Wikipedia which says the expected galactic rotation curve should follow something based on Kepler's laws. Then someone got me a subscription to Nature... You know the prestigious "peer reviewed" journal where the serious stuff is. Don't get me wrong Nature had some really awesome content. But there was a paper about a galaxy found in the early formative stages and the authors measured a rough rotation curve and felt the need to compare it to something Kepler would predict. Ugh.

If anyone can tell me why Kepler applies galaxies (vs 2-body systems with certain constraints), I'd be happy to show where the error in that analysis is. Kepler doesn't apply to galaxies. It's really that simple.

Credentials are irrelevant here as what I'm talking about is high school level integration of Newtonian forces.

And you, personally, correctly calculated the actual expected rotation?

I can't imagine the amount of superiority you must feel to assume that physicists don't know high school level integration of Newtonian forces.

I used to work in a well-regarded Astronomy and Astrophysics department at a research university. Every few months, I would go through the department "crackpot folder" when I was especially bored.

Every couple days the department chair or some well-known professor would get a letter (this was before most of the crackpots had email accounts, I guess) claiming that some theory--particularly general relativity--was wrong and all it took was a simple application of high school arithmetic to see it.

One of our faculty happened to coin the phrase "dark energy" while I was there, and man did the letters start coming in after that. Of course, the only absolutely universal commonality among all of the letters was that they were all nonsense, like the above.

In general, I felt sort of bad because you could tell that a lot of these people were really not well, but it's still hard for me to see things from someone's perspective who genuinely believes that the entire astrophysics community (save a tiny handful of contrarian actual physicists) has somehow engaged in a massive conspiracy to ignore introductory physics in favor of some other vastly more complicated theory for absolutely no possible benefit. (Especially when these professors are literally teaching introductory physics to students while they're pursuing their research.)

I feel your pain :) Back then the most such fun we had were Fermat theorem proofs coming to the algebra department.

There was a time when the entire scientific community believed the entire universe was filled with a light-bearing medium (luminiferous aether) because they couldn't explain propagation of light in empty space; or that there was another planet between Mercury and the Sun (Vulcan) because they couldn't explain Mercury's orbit.

I'm not claiming it is the case now (though it does smack of luminiferous aether a bit) but the scientific community can and has been wrong sometimes in the face of as yet undiscovered principles.

I think you might have missed my point. I'm not saying that dark matter skeptics are crackpots because they don't believe in dark matter. I'm saying that if people think they can disprove the existence of dark matter because you can apply some high school arithmetic and claim that Keplerian law is violated, then you are a crackpot.

Someone else unwittingly suggested a parallel to Fermat, which I think hits the nail on the head exactly. If someone thinks they can prove Fermat's last theorem with some high school geometry, odds are pretty good they're a crackpot. If they're a well-regarded mathematician and they can build off new mathematics and make a few very complicated leaps by discovering new mathematics of their own, then people take them more seriously.

Scott Aaronson has a really great take on this here: https://www.scottaaronson.com/blog/?p=304

As an aside that's probably only interesting to me, I went to a Great Books college. It's one of those hippy dippy liberal arts schools where there are no electives, no textbooks, no lectures, just primary sources. You learn mathematics by reading Euclid, Ptolemy, Newton, etc.

At any rate, for first-year "Labratory" class, you trace the atomic theory from the Greeks to roughly Avogadro. Along the way you read papers by and replicate the experiments of many influencial scientists along the way. When I mention that the above crackpots are "wrong", I don't mean it in the sense of the aether or analogous theories along the way to the atomic theory, namely phlogiston or caloric, two previous theories of heat. Those theories did not explain new observations and were rightly discarded along the way. Priestly and Lavoisier were brilliant and tried to make theory match observation, so now even though their theories are discarded, their work still stands on its own for the time. I wouldn't call them wrong. There's a definite difference between them and theories that are just wrong.

Nobody's going to get a Nobel Prize when they just make the world believe that they have obviated the need for dark matter by pulling out some high school math and some Kepler proofs.

Someone will win it if they ever make an observation that proves a MOND theory in a way that shows conclusively that dark matter is not needed to explain all current observations and in fact cannot remain compatible with this new observation.

There's a big difference between the two, I think.

>"Someone will win it if they ever make an observation that... shows conclusively that dark matter ... cannot remain compatible with this new observation."

This requirement is impossible to meet for sufficiently flexible theories. Eg no one will ever "win" over "God did it" according to your metric.

Also, if you see how many people in high academic positions are obviously wrong about simple stuff they use every day like p-values, nothing will surprise you any more.

Regarding your first point, that's not what I meant and you know it. Dark matter is the current theory explaining many different astronomical observations. It explains quite a lot of observations, so something pretty conclusive will need to happen for people to abandon it. Either new observations will disprove it or a new theory will come about that makes some prediction that can be observed that cannot for with current theories. I hope something like that happens! New science would be so much cooler than dark matter, but at the moment it doesn't seem likely.

I'm not sure I see how your second point is relevant. You seem to imply that I think that academics are infallible in all areas not even related to their expertise. Do you truly see no difference between non-statistics researchers incorrectly calculating statistical values and dozens of unrelated experiments all leading to the same result?

Flexibility is a main feature of the dark matter explanation, so it is relevant. It amounts to putting otherwise undetectable halos of mass wherever is needed to explain deviations from the model. There are further constraints people put on it for now, but none are crucial and will be quickly discarded (or more dark matter added) if required.

>"I'm not sure I see how your second point is relevant. You seem to imply that I think that academics are infallible in all areas not even related to their expertise. Do you truly see no difference between non-statistics researchers incorrectly calculating statistical values and dozens of unrelated experiments all leading to the same result?"

This is series of strawmen... I'm saying widespread confusion can, and currently does, exist on a topic even amongst the experts. Therefore it is not unbelievable that it does on other topics as well.

Also, dark matter is an interpretation of a result, not a result itself, so an experiment cannot lead to it directly. Finally, I don't think there are any actual experiments that have supported dark matter, only astronomical observations. Correct me if wrong but I found this after a quick search: https://www.sciencenews.org/blog/science-ticker/results-slew...

>"non-statistics researchers incorrectly calculating statistical values"

Actually another point is that this is not the issue. The calculations are fine, they are just calculating something other than they think: p(Data | Hypothesis) when they want p(Hypothesis | Data).

That is very similar to what the OP claimed about calculating a model that assumes a sphere to describe a disc (no idea if they are correct on that).

Newtonian forces are a generalization anyway. Do they even apply to objects as large as galaxies?

Finally! Someone else made the same observation I did. All that "expected" rotation curve stuff is bullshit since it's based on Keplers laws, which don't apply to a flat disk.

They do that based on a misapplication of the divergence theorem. They assume that all the mass inside an orbital radius can be treated as a point-mass which is true for uniform spherical distributions. They also assume the mass outside the radius has no net infuence - which is true for uniform spherical shells. Neither of these is valid for non-uniform distributions - a flat disk in not symmetric in 3-space. If they'd just do some electrostatics problems they'd know the different formulas for disks and rings. I was going to google a sample page but there's too many to sift through and I gotta run an errand.

Welcome to the club - it's incredibly small...

Yet DM is so sexy and mysterious ... Even Sheldon couldn't resist the temptation.

I really encourage you if you are actually interested in the arguments to progress beyond the entry level explanations. Binney & Tremaine (https://press.princeton.edu/titles/8697.html) is the standard work - I highly recommend it. At the very least, it will put to rest your notion that astrophysicists only consider spherically symmetric potentials or fail to consider the effects of a disks etc., which is just patently untrue.

And here I thought Hacker News was going to get the Nobel Prize! I can't believe quickly deriving something from first principles also occurred to the people devoting their lives to this field.

Thanks for the link. They have a .pdf of chapter one which I gave a look. Right there on page 14 when estimating the mass of our galaxy inside our suns radius we have:

"The approximation that the mass distribution is spherical is reasonable for the dark halo, but not for the flat stellar disk. Better models suggest that this estimate is probably high by about 30%, since a disk requires less mass to produce a given centripetal acceleration"

And there you have it. While he notes that a spherical distribution is different than a flat disk, he estimates the error at about 30%. The problem is that the error is not one of a constant factor, it's a different function. This unspecified better model also doesn't seem to care about the matter outside the solar radius - which also affects our velocity in a disk, but not in a sphere.

There is a lot of math in chapter one, but also a lot of hand waving.

Of course you are completely wrong:

http://iopscience.iop.org/article/10.1086/508162/meta

There is a great deal of evidence for dark matter that does not depend on Kepler's laws, please stop spreading misinformation.

Source: assistant editor of a physics journal, know several astrophysicists personally, currently dealing with a MOND paper this very week...

I don't mean to just be a pedant when I say this, but the use of the word crackpot is missplaced here.

Crackpot theories are eccentric and not commonly believed.

I am interested in crackpot theories because sometimes they end up turning out right, and I think within that dynamic there are important lessons for humanity that we end up learning in very hard ways.

For example, the Great Depression paved the way for the acceptance of Keynesian economics--ideas previously written-off as crackpot theories. Another: NASA engineers warned of the exact dangers of a foam strike, under the exact conditions in which it took place, were at the time written-off by senior management. Social scientists that studied this described part of the problem as Groupthink.

Possibly naive question from a non-physicist... does this not follow from relativity as a natural a consequence of the effect gravity/mass has on spacetime?

By that I mean that the edges of galaxies experience a "reference" spacetime (e.g. constant period), while the interiors experience a stretched out version spacetime (i.e. inverse time dilation and length constriction)?

Also not a physicist. At the galactic scale gravity forces are too weak to take into account any non-Newtonian considerations. At least for myself, most things observed so far at galactic scale, like flat disk star orbital speed for example, can be easily explained by straight 6th grade Newtonian physics.

Another fun experiment is to write script to cover a disk with points, then do a full calculation of all N gravitational forces at a point along the radius. Calculate the acceleration of a mass at that point and back-calculate the velocity that would orbit with that inward force. Repeat this for many points along the radius and plot the rotation curve without doing any dynamic simulation. There can be some interesting numerical issues with this but a random set of points to "measure" the curve will still show it.

sigh I wouldn't have replied to this if you hadn't posted half a dozen comments. When I was 16 I thought special relativity was a hoax and I tried to demonstrate this with triangular diagrams scribbled in pencil in my notebooks. I ended up just rediscovering the Doppler effect. I never showed it to anyone, but when I think back, I still cringe a little. Relativity and time dilation are real things with real theory and real experiments.

You'd do well to do a little more research on the topic before posting so many comments on HN.

There is a ton of evidence for dark matter. We still don't know exactly what it is, but we do know lots about it (e.g. it is not baryonic matter because observation differs from theoretical models of how it would interact with ordinary baryonic matter). As for all that other evidence, the first hit on Google is for laymen: https://medium.com/starts-with-a-bang/five-reasons-we-think-...

TLDR: gravitational lensing, missing mass, and three other really good reasons that dark matter is a serious subject of study.

Disclaimer: I am not a physicist. And I'm trying not to represent myself as one on HN.

Talking about this stuff is fun, sure. It's great to learn! But please don't spread ignorance with such high confidence. As for "just" Newtonian physics, there's a whole research field called "Modified Newtonian Dynamics" (MOND). https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics

TLDR; there are lots of problems with MOND, and it doesn't explain gravitational lensing and other effects of dark matter that we see.

no, the point is that it follows from basic algebra, and high-school physics defitions of velocity.

Highschool definitions of velocity don't really apply once the distances involved grow beyond a couple light years. Atleast not without corrections for stuff like relativity (which has been measured and confirmed to exist by simply observing curvature of light over the sun.

Or did the entire community of astrophysics simply ignore high school physics in favor or something vastly more complicated because reasons?

Even at galactic scales the correction is not that great. I don't thing the OP's claim is that they are exact to say 3 sig figs but more like exact to within an order of magnitude

But how does the proposed model compare to the accuracy of the dark matter model?

In physics, how well your model can predict past and future states from the current state is rather important. Though future states more than past state but any model should be able to also somewhat agree with it's the past it generates.

dark matter is irrelevant. The speed law is empirical (whether or not you explain it with dark matter) and the first poster points out that the constant edge rotational rate falls out from that, and geometry.

It is relevant when you compare models. All I asked is how accurate both models are. If Dark Matter is more accurate in predicting how galaxies move and shape then it is obviously the better model even if a simpler one also exists but it's predictions are worse.

You can't simply say "this model also predicts that" without giving on how accurate it does predict and comparing to existing models. Otherwise we'd be using flat earth models for building bridges and planning ship routes.

The original poster's original comment didn't make claims about the validity of dark matter, it was only in a different subthread that he talked about dark matter directly, challenging it. The original comment's content is invariant on how you derive the distribution of stellar velocities.

For anyone interested in why there's a lot more to it than this argument, the first equation:

Mg = C1 * Rg * Rg

Is not a good assumption for the discs we observe in the universe, because they do not have a constant surface density. The picture is further complicated by the fact the many disc galaxies also contain a central bulge, large enough to effect the potential (to say nothing of Dark Matter).

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