March 2015 - mathfun@mailman.xmission.com

Re: [math-fun] Dark matter exists?
by Warren D Smith 30 Mar '15

30 Mar '15

> From: Eugene Salamin > According to people in the UCSC Physics Department, it is consistent with > current observations that dark matter interacts only gravitationally.? I'll > ask again when I next go to the Physics Colloquium, in case that claim is > now out of date. --the paper that began this thread claims dark matter must interact in some manner that is not just gravitational, to satisfy the 0.1 cm^2/gram cross section lower bound, to meet observations. > The density of dark matter can be calculated from galactic velocity curves.? > For the Milky Way, the velocity of orbiting visible matter is pretty much > constant at 225 km/s, except near the center, where it decreases.? From > m v^2 / r = G M(r) m / r^2, > we get for the enclosed mass within radius r, > > M(r) = (v^2 / G) r. > The mass density is > ?(r) = (dM(r)/dr) / (4?r^2) = (v^2 / 4?G) r^-2 > ???? = (6.0e19 kg/m) r^-2 --note the large number "?" symbols. This is due to you using non-ASCII characters which my emailer barfs on. A common problem by some mathfun posters. > At our location 28000 ly = 2.8e20 m from the galactic center, > ? = 7.7e-22 kg/m^3 = 0.43 (GeV/c^2) / cm^3. > The gravitational acceleration varies as 1/r, so the potential ? varies as > log r, and the Laplacian of ? varies as 1/r^2, just like ?, so that ? and ? > satisfy the Poisson equation.? Also, for a suitable choice of m/T, > ? = exp(-m?/kT), > so that ? and ? satisfy the Boltzmann equation.? Thus the 1/r^2 density > implies that the dark matter has equilibrated. --not so: I also can, and have, derived such densities (in my paper-draft you haven't seen...) without any need for any equilibration ever. And anyhow Boltzmann law might be expected on maxent grounds without needing equilibration. > Now here's a question for which I don't know the answer.? If dark matter > equilibrates with itself, it should presumably also equilibrate with > ordinary matter.? But ordinary matter can dissipate energy and coalesce.? So > why can't dark matter do so too using ordinary matter as an intermediate? --dark and ordinary matter have very small cross section for interaction, which is why dark matter has never been directly detected yet. Any such "equilibration" would take longer than age of universe. The dark-dark interaction is now postulated to be considerably larger than the dark-normal interaction (although still small). Now the whole thought, which Eugene & I explored in posts so far, that I used to generate the conclusion that the dark-dark interaction had to be via a NEW force, not a member of the usual known forces {Higgs,weak,strong,EM,gravity}... I thought that was a new insight... but looking, it seems it, or anyhow something somewhat like it, was already thought of by the Dark Side. Various members of the Dark Side had already came to the conclusion there had to be a new "Dark Force" between dark matter particles to allow this. So we see the Dark Side is now not only postulating most of the universe is made of invisible particles we've never detected, but there also are new forces we've never seen. In fact, why stop there? You can add an entire new Dark Sector to the standard model containing however many new particles and forces it takes -- that gives you more power to fit observational data. Conceivably no matter what you added it still would be unable to match observation, in which case the DM hypothesis would be falsified... but as far as I can tell nobody knows how to prove that, which would mean it is effectively an unfalsifiable hypothesis, i.e "not science." They are constructing castles in the air. If an observation-based criticism comes, they overcome it by fantasizing further extensions to their castle. So, Dark Matter is not in a very healthy state. But, hell, maybe the whole Dark Sector thing is really true anyhow. In some sense it is completely free of new ideas: the Standard Model gives well known recipes for adding new forces and particles (so long as you stay within the allowed patterns) so there is nothing stopping you from adding them and in some sufficiently abstract mathematical sense this is "adding nothing new". -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

1 0

[math-fun] combinatorial puzzle
by Fred Lunnon 30 Mar '15

30 Mar '15

While pootling around the arcane labyrinth of multi-dimensional sodalite, I encountered a combinatorial puzzle which seems of independent interest, and reasonably straightforward --- more than can be said for numerous other heffalump-traps lately encountered over the course of that tortuous expedition! Given n > 0 integer, evaluate the number f(n) of integer vectors P of length n such that 0 < P_(i+1) - P_i < n for all i , and (P_i - P_j) mod n /= 0 for all i /= j , and sum_i P_i = n(n-1)/2 . For example when n = 4 there are f(4) = 6 such vectors: [ 0, 1, 2, 3 ], [ -1, 1, 2, 4 ], [ -2, 1, 3, 4 ], [ -1, 0, 2, 5 ], [ -2, 0, 3, 5 ], [ -3, 0, 3, 6 ]. The explicit function f(n) is surprisingly simple; but the proof is not immediately obvious. Fred Lunnon

2 2

Re: [math-fun] Dark matter exists?
by Warren D Smith 30 Mar '15

30 Mar '15

To Meeker: dark matter could not be gravity-only because then it would be too-little-interacting to achieve that paper's claimed 0.1 cm^2/gram cross section lower bound. (If believed.) But yes, it definitely gravitates, that's only reason why it is claimed we know it is there. To Diffie: GOM (gravity-only-matter) could not clump, far as I can see. E.g. two particles would head toward each other, fly off, hyperbolic orbit, no energy lost, no capture possible. However... if the matter ALSO interacts via EM forces, then capture is possible, for example 2 planets collide, lots of heat photons emitted, result is a bigger planet, or in the Earth's case planet+moon, plus lost energy. GOM actually could lose energy via gravity waves (gravitational bremstrahlung) but that'd be an incredibly weak loss mechanism, way insufficient to achieve clumping given the present young age of the universe. The only reason normal matter has clumped into nuclei, atoms, molecules, planets, stars is, EM forces allow energy loss to far away via photons. Dark matter by definition fails to couple to photons, ergo no clumping. Furthermore, blow off that theoretical jive and just look at the facts ma'am: the distribution of dark matter is tolerably well known in various galaxies, etc, and it evidently did not clump, did not lose energy to form disk not blob, etc. Somebody else: Is dark matter fermions or bosons? Well, I would presume fermions since they are less easily created & destroyed than bosons, and DM seems to be pretty permanent stuff. But given how little is known about DM, it's hard to be sure. In fact, I am unsure DM even exists at all, I think it might be there is no DM and it is just that we have a wrong theoretical picture of the laws of gravity. (There is a small but fairly determined minority who hold that view.) In fact I have a perpetually incomplete paper I am writing about such a possible improved(?) theory of gravity which I've invented as a counterweight to DM-mania. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

3 2

Re: [math-fun] Dark matter exists?
by Warren D Smith 29 Mar '15

29 Mar '15

Also, my same analysis based in Salamin's simple calculation, also would indicate (if you believe that paper's 0.1 cm^2 / gram claim) that Dark Matter cannot interact via EM force (would then not be "dark") or gravity, weak force, or strong force, or Higgs force (too small cross section since the latter 3 forces too short ranged, and gravity too weak). In short, dark matter cannot be a particle at all subject to any of the forces were are aware of, it must be subject to some new force we have never yet found. Specifically, the length scales for the forces are: weak: r=10^(-17) meter, arising from masses of W and Z bosons m=80-92 GeV/c^2 hence r=hbar/(m*c)=2.47*10^(-18) meter is the factor-e-falloff length for Yukawa potential. higgs: similar but a little shorter range, using mass of Higgs boson 126 GeV/c^2. strong: the "residual strong force" using pions as a force carrier has range 1-3 fm (but using gluons is shorter ranged). Anyhow, strong is the crux. If the dark matter particles have mass=300*ProtonMass, which seems the smallest one could possibly hope for, then with a cross section of pi*(3fm)^2 = 2.8*10^(-29) meter^2 = 2.8*10^(-25) cm^2 per particle, that is for a gram of particles a cross section of 5.7*10^(-4) cm^2. This is way smaller than the minimum the paper claims is allowed by observation, namely 0.1 cm^2. So we conclude either the paper's 0.1 claim is garbage, or dark matter cannot exist as particles, or a new force is involved. That awesome News Source, the "Daily Mail" appears to have somewhat figured this out(!): http://www.dailymail.co.uk/sciencetech/article-3013284/Is-dark-matter-FLUID…

2 1

Re: [math-fun] Dark matter sci-fi mirror world?
by Warren D Smith 29 Mar '15

29 Mar '15

KF Lynch: Is it possible that dark matter particles interact among each other in exactly the same way that matter particles interact among each other? In other words, they have their own exact analogs of protons, electrons, photons, etc., which interact with each other but which only interact with ordinary matter via gravitation? I ask because one of my favorite science fiction novels, _Twistor_ by John G. Cramer, takes this as its premise. It depicts a present-day physicist at the University of Washington (the same university at which he is a professor of physics) discovering a way to convert matter from our form to this other form. Actually, there are several forms. He converts a camera into one of the other forms and back, and captures star field images from his basement lab, similar but not identical to the constellations we know. In one of the forms, there's a planet co-extant with ours. It's been cross-fertilized with small Earth life (or vice versa) --nope, that sci-fi stuff is garbage. Dark matter, whatever it is, clearly is far less interacting than normal matter, and cannot form "molecules" and "atoms" and "planets" and "life". We know this because the dark matter does not clump, does not lose energy via self-scattering, hence does not form disk-like galaxies, etc.

2 1

Re: [math-fun] Dark matter exists?
by Keith F. Lynch 29 Mar '15

29 Mar '15

Warren D Smith <warren.wds(a)gmail.com> wrote: > In short, dark matter cannot be a particle at all subject to any of > the forces were are aware of, it must be subject to some new force > we have never yet found. Is it possible that dark matter particles interact among each other in exactly the same way that matter particles interact among each other? In other words, they have their own exact analogs of protons, electrons, photons, etc., which interact with each other but which only interact with ordinary matter via gravitation? I ask because one of my favorite science fiction novels, _Twistor_ by John G. Cramer, takes this as its premise. It depicts a present-day physicist at the University of Washington (the same university at which he is a professor of physics) discovering a way to convert matter from our form to this other form. Actually, there are several forms. He converts a camera into one of the other forms and back, and captures star field images from his basement lab, similar but not identical to the constellations we know. In one of the forms, there's a planet co-extant with ours. It's been cross-fertilized with small Earth life (or vice versa) since this conversion sometimes happens spontaneously near lightning bolts. He and two children visiting the lab discover this the hard way when an accident causes the whole lab to be transported to this other form, with him and the children in it. Can they survive in this parallel world? With the equipment in the lab, can they return home, or at least send a signal? Even though nobody else knows about this discovery? I like it because it makes me think. The physics is radical, but not totally implausible. It implies that Earth's true density is only about half what it's said to be, since half of the gravity comes from the other Earth. Is that possible? How can the rotation rates just happen to be the same? (I came up with an explanation, can you?) How much can the terrain differ between the worlds without someone having already noticed? (If there were a mountain range in parallel- Florida, would anyone have noticed its gravity? Or if they had, would they have come up with another explanation, such as mass concentrations close underground?) If you converted a rocket to "vacuum Earth" and let it fall to the center of the world before you lit its engines, how much extra boost would you get? And how many times could you do this before an accumulation of spent rocket exhaust at the center made this unworkable? And how can property be protected if burglars can walk through walls and snatch it from a parallel world?

1 0

Re: [math-fun] Dark matter exists?
by Warren D Smith 28 Mar '15

28 Mar '15

> From: Allan Wechsler <acwacw(a)gmail.com> > Is the dark matter phenomenon consistent with there being a stack of > parallel universes which can gravitationally "feel" each other, but > otherwise don't interact? > > Note that the universes couldn't be electromagnetically coupled, or we > would see the light of parallel stars. Also, electrons would occasionally > carom off parallel atoms, and so forth. --in your scenario, there ought to exist "gravitational lenses" even though there is no visible mass anywhere neat that causes the lensing. Far as I know no such lens has been observed yet. Be way-impressive if you find one! Bring out your computer software, O hackers, and run it on publicly available telescope image databases, to win your nobel prize for discovering parallel universes. Also, dark matter basically is a halo round and about each galaxy of invisible matter, which causes extra gravity which causes the galaxy to rotate faster than it would have if the only stuff gravitating were the visible stuff. And it isn't just a scale factor because the dark matter is distributed in a spherical blob even though the visible matter in that galaxy is distributed like a bar or flat disc or spiral. > From: Eugene Salamin <gene_salamin(a)yahoo.com> > A gram of nucleons is Avagadro's number, 6e23, of particles.? A nucleon has > a collision cross section of about 1e-26 cm^2.? --I find 2*10^(-30) meter^2... ok, about same as you find up to factor 2 > So a gram of nucleons has a > cross section of 0.006 cm^2.? If dark matter is to be at best weakly > interacting, it had better have a cross section way less. --well, the relevant "cross section" is not for "collision" (whatever that would even mean) it is for "scattering." Two protons interact via EM long range force and will scatter with a cross section far larger than you said if they have low energies compared to their masses. Also, most gas in the universe is "gas" i.e. H atoms, not "plasma" i.e. bare proton and electrons. For an H-atom the radius is the Bohr radius, not the "proton radius" you mentioned. Bohr is about factor 6*10^4 larger, i.e. cross section about 4*10^9 factor larger. But anyhow, I like the calculation you did, if you correct its misleading aspects. The reason they claim dark matter "must" self interact is that there seem to be astronomical observations (they cite) incompatible with the dark matter hypothesis, unless you assume the dark matter particles can scatter off each other with cross section between 0.1 and 1 cm^2 per gram.. This has nothing to do with assumptions about the "weak force" nature of the alleged interaction, it is purely an attempt to agree with observation. (Whether you believe in those attempts and conclusions, is another question... I've got a good deal of skepticism they can compute what they think they can compute, and certainly their so-called deductions far way short of rigorous math standards.) -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

1 1

[math-fun] Dark matter exists?
by Warren D Smith 27 Mar '15

27 Mar '15

http://arxiv.org/abs/1503.07675 claims they tested some colliding galaxy clusters and found the gas got moved, but the mass got moved by a different amount than the gas. Their techniques for measuring this seem remarkably sensitive (if we believe them). This "proves" dark matter exists [claimed p-level 10^(-14) or so]. This contrasts with earlier "proofs" which involved the rotation curves of galaxies. Two proofs are more convincing than one, and alternate "new physics" explanations (different from assuming dark matter exists, that is) now may have more trouble surviving. They then go further and estimate the interaction cross-section of dark matter particles with other dark (or non-dark) matter particles. They claim it is too small for them to detect, less than 0.47 square-cm per gram. If this can be brought below 0.1 this may actually disprove the existence of DM (!?) they say, because they say other observations of DM suggest it must self-interact. So this whole line looks very promising, at least on its face.

3 2

[math-fun] Polynesian (Pacific Ocean) navigation pre-clocks, pre-GPS
by Henry Baker 27 Mar '15

27 Mar '15

I heard a recent program on the ability of ancient Polynesians to navigate the Pacific Ocean w/o clocks/longitude or GPS. Supposedly, the Polynesian navigators use information about waves/swells/etc. to detect the presence & direction of islands over the horizon. I'm a bit skeptical about this, because unless these skills are relatively easily acquired, anyone with less than a certain critical mass of skills will die, and even partial skills won't be transferred to the next generation. (This is semi-analogous to the spread of a communicable disease, only in this case we _want_ the navigational information/techniques to propagate.) On the other hand, if this information is available in the wave/swell patterns, then presumably an "AI" computer program could learn these techniques by sending out lots of little buoys with GPS, sky-facing camera (for sun & star info) & wave-sensing capabilities, and eventually learn how to correlate these wave/swell patterns with positions relative to known islands. http://web.archive.org/web/20090917235953/http://pvs.kcc.hawaii.edu/navigat…

12 14

Re: [math-fun] Polynesian (Pacific Ocean) navigation pre-clocks, pre-GPS
by Landon Curt Noll 27 Mar '15

27 Mar '15

Hello, > I heard a recent program on the ability of ancient Polynesians to navigate the Pacific Ocean w/o clocks/longitude or GPS. > > Supposedly, the Polynesian navigators use information about waves/swells/etc. to detect the presence & direction of islands over the horizon. > > I'm a bit skeptical about this, because unless these skills are relatively easily acquired, anyone with less than a certain critical mass of skills will die, and even partial skills won't be transferred to the next generation. (This is semi-analogous to the spread of a communicable disease, only in this case we _want_ the navigational information/techniques to propagate.) During our 2009 Total Solar Eclipse expedition to search for Vulcanoid asteroids we flew into the Enewetak atoll in the Marshall Islands. During our stay I met a native who had used his canoe to visit Enewetak from Bikini: almost 200 nautical miles away. Through a translator, I was curious how he made the journey. He showed me his craft .. a sort of dugout canoe with an outrigger. He had no GPS, no compass, no radio, no electronics of any kind. Only some dried food, coconuts, some water and stuff that looked like it could be used for fishing. He said he does this run several times a year to visit friends and relatives and to carry news. I was curious how he made the journey in such a craft without any apparent navigational aide. So I asked him how he knew where to go. The look he gave me was one of "are you that stupid" saying that the direction should be obvious to anyone. :-) When I expressed a child-like ignorance of how to go such a long distance he explained a process of birds, the sun, the stars, waves and listening to surf when he was close, etc.. He explained how to tell if a bird was going a direct route between islands or wondering .. plus a bunch of other stuff I didn't understand in context. He really knew his star fields! I showed him a star chart of stars down to 6th magnitude. Although our names were different, he definitely knew his was around the sky and seemed to recognize stars on the charts with ease giving me names in his language of a fair number of the brighter stars. I asked him for directions to places like Ujae (where he was going next, some 240 nautical miles away), Amo, Bikini, Kili, Wotho, etc. He pointed with dead certainty to any atoll/island I could name. I got out my GPS compass and asked him to turn my hand in the direction of an island/atoll. He could repeatedly orient me within about 2 degrees of any atoll/island I could name .. and I suspected some of that error was my not keeping the GPS/arm steady. He seemed very puzzled that an adult such as myself could grow up not knowing how to navigate on the ocean. He talked about the currents, what the islands were like, where to find water or coconuts when the rain did not fall, etc. I'm still not entirely sure how he did it but he claimed to do all with ease. I showed him a physical compass. He had seen such things before but dismissed them as "they would only get wet .. they were useless". BTW: He was impressed with the 2009 eclipse. He said he was going to carry that tale with him through the islands. No doubt he was going to tell jokes about meeting adults who can't find their was around the pacific islands. ;-) Our translators said this navigators such as this man made a living carrying news and messages between islands. chongo (Landon Curt Noll -- just back from the 2015 Polar eclipse warming up in Switzerland) /\oo/\

6 6