Extraordinary claims require extraordinary proof

[GreyICE]

In general "mathematical models" are created to model actual reality. Therefore they have both credibility and usefulness.

Mathematicians though do not just do mathematical physics. The mathematical models used to describe reality are just a small part of mathematics. Thus there are things in mathematics that can’t be validated by actual reality because they do not occur in actual reality.

Example: Klein Bottle, the mobius strip's older brother.

 

[Taffer]

Abstract mathematical models may or may not accurately represent actual reality. The abstract mathematical models themselves are only abstract realities, not actual realities.

If you read carefully the post I liked, you will notice that actual real things, such as energy fields and various properties of reality, follow a structure related to a Mobius strip. How is that not validation of "abstract" math?

 

[m_huber]

ynot, I think the way you are defining what is "concrete" vs. "abstract" makes everything we know fall into the category of "abstract."

Math accurately models what we can experience empirically. Math also makes predictions of things that we do not or can not experience empirically. The Mobius Strip is one such example. What we know about Black Holes gives us another example.

If you want to say that math is not "real," then you need to define what you think is "real." If you really want to go into the discussion, we will get into DesCartes and "I think, therefore I am."

While I'm posting I might as well mention: The evidence for time being a dimension is basically as strong as the evidence for width being a dimension.

 

[ynot]

Food for thought - thanks

 

[Dancing David]

The mobius strip mathematical model has no actual existence. It’s not real. The paper model is the thing that’s real.

I am beggining to think that we need to label this line of argumentation, this is very similar to Zeuzzz and the magnetic reconnection thing. The reverse finger/moon argument just doesn't sound cool.

Sorry Ynot, just making a side bar here.

 

[robinson]

Will this sidetrack ever return to the expanding Universe? Stay tuned, pictures at 11.

 

[m_huber]

Will this sidetrack ever return to the expanding Universe? Stay tuned, pictures at 11.

As I recall, this discussion is all about whether or not dark matter/energy should fall into the "woo" category or the "science" category.

This is the same as asking if mathematics is "real." The models for physics that we have are based on empirical observation. If we extrapolate from the math of what we observe, then we are left with problems. These problems are fixed with a correction factor. We call this correction "dark matter." As the article in the OP points out, testing for this gives positive results (insomuch as we can test for it).

Thus the relevancy of this discussion.

 

[robinson]

The sidetrack about models and reality started with a raisin muffin being used to explain the expanding Universe. I'm not kidding.

It had little to do with dark matters, but did relate to dark energies.

 

[Dancing David]

No, it is a bran muffin or burrito which leads to the expanding universe, and the Big Poot.

 

[robinson]

I think there was also some discussion about the "real" shape of the Universe. Which led to this incredibly convoluted conversation which boils down to the claim that a mathematical model is more real than a strip of paper.

Or something like that.

 

[DeiRenDopa]

WARNING! WARNING! WARNING!!

This thread's last post was 26 March, 2008 ... I am raising it from its slumber ...

First, I want to correct something that was said about the middle of the thread: the first evidence of DM came NOT from galaxy rotation curves, but from application of the virial theorem by Zwicky, way back in the 1930s, to the Coma cluster of galaxies.

Second, the history of DM is by no means a nice, clear, straight line - as befits a story in which the players are human, there is jealousy, ego, arrogance, and much more; there are mistakes, wrong turns, misunderstandings, and so on. For example, Zwicky had a very strong personality, perhaps even a quite unattractive one, while Oort was the perfect gentleman (yet Zwicky was right and Oort wrong); Vera Rubin was a young, female, grad student (so her 'contrarian' findings on galaxy rotation had to await a senior male scientist's corroboration before they were accepted; note too the irony of her Princeton honorary degree); and so on. There are several good books which cover both the history and the evidence, the one by Ken Freeman for example.

Third, galaxy halos contain a trivial amount of DM, in the grand scheme of things; in (rich) galaxy clusters, the mass in between the galaxies is far greater than that in the galaxies, so even if, somehow, it turns out galaxies have little or no DM (highly unlikely), the large-scale ('universal') implications would be essentially nil. In fact, 'dark' baryonic matter (the kind of stuff stars, planets, gas, plasma, and dust are made of) considerably overwhelms the stuff that you can see with your eyes (or telescopes).

Fourth, no one in this thread has even sketched just how extraordinary the evidence for DM actually is ... and the marketing types who write breathless Press Releases (or articles in New Scientist), which robinson has so enthusiastically quoted, seem to have no interest in trying to explain this.

Take rich clusters, as just one example.

From measurements of the line of sight motion of galaxies, you can use high school physics to estimate the total mass in the clusters in which they reside; this is what Zwicky did, and has been done thousands of times since. That estimated mass is far, far greater than what you get if you simply add up the light from all those galaxies and estimate the mass of stars that must be producing it (adding in dust and gas/plasma in the galaxies makes no difference worth commenting on).

Fast forward many decades, and you learn that these same (rich) clusters of galaxies emit lots of x-rays. Apply textbook physics, undergrad level this time, and you discover that most of the (baryonic) mass in these clusters, again hundreds or thousands of them, is in the thin gas/plasma between the galaxies, not the galaxies themselves.

... and you learn that the total mass of the clusters is the same (to within the various uncertainties) as that you estimate from Zwicky-type observations!

... and that this total mass is ~5 times greater than the estimated baryonic mass.

Do not skip lightly over this; two completely independent methods of observation, using quite different parts of the physics textbook produce the same result! How extraordinary.

But wait! There's more!!

By painstakingly analysing the shapes of galaxies behind rich clusters, you can estimate the total mass in those clusters using yet another, completely independent method - gravitational lensing.

... and the results are, once again, the same: within the various uncertainties, the estimated mass of these clusters is the same as that derived from the virial theorem and from the x-ray observations (though there are, to date, only a handful of clusters analysed using this method).

... and that mass is, once again, ~5 times greater than the total estimated baryonic mass.

How extraordinary.

But wait!! There's more!!!

(to be continued)

 

[zosima]

It's more like you walking into my house and saying,

You: "Your dog has fleas."
Me: "Hang on, I've lived with this dog for ten years, I'm a doctor of veterinary medicine, and I did three separate flea tests over the past week."
You: "I dunno, lots of dogs have fleas, I bet your tests were wrong."
Me: "Shall I show you my test results?"
You: "Meh. Fleas are invisible anyway, you're probably missing them. You're going to have a hard time convincing me that your dog doesn't have a single flea."
Me: "Um? Fleas are not invisible."
You: "Oh yeah? How do you know? Someone who doesn't know that fleas are invisible and can teleport has no business making wild claims about flealess dogs."

Arrrrrrgh!

lololol
I just started reading the thread from the beginning and this is just hilarious!

 

[DeiRenDopa]

(continued; an interlude)

One neat thing about gravitational lensing is that it can be used to independently test the results of studies on DM in (normal) galaxies based on quite different physics, galaxy rotation curves for example.

And here's one paper reporting such a result: "Weak Lensing with SDSS Commissioning Data: The Galaxy-Mass Correlation Function To 1/h Mpc"; there are many more (this paper alone has 117 citations, not all of the to do with weak lensing of galaxy halos).

With something as intriguing as DM, many researchers are keen as mustard to study it ... and some are also extremely keen to find a way to explain DM via some new physics, perhaps a new aspect of gravity for example, or some quirk of textbook physics that everyone has so far overlooked.

And so you would expect to find lots of papers with interesting ideas on what DM might be (other than some 'cold', very weakly interacting particles with mass), like the Cooperstock and Tieu one robinson cited earlier, for example.

And a few enjoyable minutes (or hours) browsing arXiv quickly confirms your expectation ... but also shows you that no one has come at all close yet to finding an explanation that does as good a job as DM in accounting for the observations ... except, perhaps, just maybe, some relativistic extention of MOND.

But wait!!! There's (even) more!!!!

(to be continued)

 

[DeiRenDopa]

doppo

 

[DeiRenDopa]

Suppose you simulate the evolution of a chunk of the universe, from a time astronomers call 'z = 127', to now, using textbook physics and cold dark matter (CDM) particles. Does the simulated chunk of universe end up looking like the part of the universe where we live?

The answer is yes (and there is some nice eye candy to enjoy as well).

How extraordinary ... the local universe looks just like a realistic simulation that includes the assumption that CDM is real!

But wait ... (boring; I'll turn it off)

Most readers of this post will surely have read about the CMB, the Cosmic Microwave Background, and perhaps how it was discovered (did you like the bit about pigeon droppings?), who got Nobel Prizes, a little satellite called COBE, and so on.

Many will also have read about how WMAP, another small satellite, observed the CMB for more than five years and a how bunch of über-geeks crunched the bazillions of individual data points to conclude that the universe is comprised of "4.6% Atoms and 23% Dark Matter" (one of the technical papers is here).

How extraordinary!

Fancy staring intently at the whole microwave sky, for five years, and coming up with a number that's the same as what you get if you measure the line of sight motion of a bunch of galaxies in the Coma cluster!

Here's another extraordinary thing: you absolutely need that 4.6% atoms to 23% CDM ratio in order to make sense of the abundance of deuterium, helium (both stable isotopes) and lithium (just one stable isotope), relative to ordinary hydrogen in the parts of the universe that haven't been through the guts of stars yet.

How extraordinary!

Who'd a thunk that one little innocent assumption (CDM) could make sense of so many bazillion observations of so many different kinds.

It must be magic.

 

[Belz...]

I think there was also some discussion about the "real" shape of the Universe. Which led to this incredibly convoluted conversation which boils down to the claim that a mathematical model is more real than a strip of paper.

Or something like that.

"Skepticism" can be hazardous to your mental health when applied improperly, robinson.

 

[Dancing David]

There is a convergence of data that something like darm mattere exists... some people say it is boojum but they haven't presented a good alternative yet.

There has been a lot of handwaving and arm twirling, which perhaps is what accounts for the expansion of the universe.

I am personaly thrilled to think that there are things we don't understand and some we can't understand.

 

[robinson]

Suppose you simulate the evolution of a chunk of the universe, from a time astronomers call 'z = 127', to now, using textbook physics and cold dark matter (CDM) particles.

Neither link seems to supply the physics of DM particles. Could you explain what they are? Or is this a case where the simulation uses observed reality to reverse engineer what the properties are?

"Skepticism" can be hazardous to your mental health when applied improperly, robinson.

I doubt that. Why do you think that is true?

There is a convergence of data that something like darm mattere[sic] exists...

Well, darm mattere is another story. I don't think anybody doubts that exist.

I am personaly[sic] thrilled to think that there are things we don't understand and some we can't understand.

Hush yore mouth. If we don't understand it, we just need better maths.

 

[Reality Check]

Neither link seems to supply the physics of DM particles. Could you explain what they are? Or is this a case where the simulation uses observed reality to reverse engineer what the properties are?

The physics of dark matter is that it does not omit radiation (is dark) and has mass (is matter). The model is looking at cold dark matter (slow moving) as opposed to hot dark matter (fast moving).

 

[DeiRenDopa]

Suppose you simulate the evolution of a chunk of the universe, from a time astronomers call 'z = 127', to now, using textbook physics and cold dark matter (CDM) particles.

Neither link seems to supply the physics of DM particles. Could you explain what they are? Or is this a case where the simulation uses observed reality to reverse engineer what the properties are?

(rest of post omitted)

.
Actually, the first link does ("supply the physics of DM particles") ... though I'd be the first to admit that it's not immediately obvious where!

Perhaps the best place to start would be the Supplement, which begins on p27 (you have to open the full paper, not the abstract; you can do this by clicking on PDF in the top right hand box, for example).

There's a fair bit about how they set about establishing the initial conditions, then on p30 you read the following:

Dynamical evolution. The evolution of the simulation particles under gravity in an expanding background
is governed by the Hamiltonian

(equation omitted)

where H = H(p₁, . . . , p_N, x₁, . . . , x_N, t). The x_i are comoving coordinate vectors, and the corresponding canonical momenta are given by p_i = a²m_ix_i. The explicit time dependence of the Hamiltonian arises from the evolution a(t) of the scale factor, which is given by the Friedman-Lemaitre model that describes the background cosmology.

(part skipped)

The density distribution function δ_ε (x) of a single particle is spread over a finite scale ε, the gravitational softening length. The softening is necessary to make it impossible for hard binaries to form and to allow the integration of close particle encounters with low-order integrators. We use a spline kernel to soften the point mass, given by δ_ε (x) = W(|x|/2.8ε ), where
W(r) = 8(1−6r² +6r³)/π for 0 ≤ r < 1/2, W(r) = 16(1−r)³/π for 1/2 ≤ r < 1, and W(r) = 0 otherwise. For this choice, the Newtonian potential of a point mass at zero lag in non-periodic space is −Gm/ε, the same as for a ‘Plummer-sphere’ of size ε, and the force becomes fully Newtonian for separations larger than 2.8ε. We took ε = 5h⁻¹kpc, about 46.3 times smaller than the mean particle separation.

(there's more)

.

That's (part of) the physics (actually one symbol doesn't show properly; there's a dot over the x_i in p_i = a²m_ix_i).

Would you like someone to have a go at explaining this physics without symbols and equations?