July 2014 - mathfun@mailman.xmission.com

[math-fun] Backwards Bekenstein argument?
by Henry Baker 29 Jul '14

29 Jul '14

Bekenstein found that the entropy of a black hole was proportional to its surface area, which is also related to its mass. Since Newton, we've always assumed that mass is the "source" of gravity, but perhaps we (and Newton) were misled in the pre-digital world. Perhaps gravity (and particularly the space-time curvature) is really "caused" by the information stored on the Bekenstein surface, and the numerical value of the mass (& hence energy) is merely some statistic associated with this information. Verlinde's ideas of a few years ago are in this direction; I'm not sure where his thinking has led him recently.

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Re: [math-fun] sesqui-imponderables
by Bill Gosper 28 Jul '14

28 Jul '14

On Sun, Jul 20, 2014 at 1:18 AM, Andy Latto <andy.latto(a)pobox.com> wrote: On Sat, Jul 19, 2014 at 12:49 PM, Adam P. Goucher <apgoucher(a)gmx.com> wrote: 1. ((a (chicken)) and (a (half))), not (a ((chicken) and (a (half)))). That doesn't explain why it isn't plural; compound subjects of the form "A and B" are normally plural. Frog and Toad are Friends. Andy So >1 isn't essential for plural, else "Two half-wits writes a grammar book, ..." --rwg

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[math-fun] Asimov's rolling ball
by Warren D Smith 28 Jul '14

28 Jul '14

>From Dan Asimov: Suppose we roll a unit-radius ball without slipping along a closed curve C on the xy-plane in 3-space. This will have the net effect of applying some rotation to the ball. For instance, if C is an equilateral triangle of side-length = ?, the net rotation will switch the N and S poles of the ball. --WDS: I presume by "?" you meant "pi." You should write "pi" not use some unsupported non-ASCII character. QUESTION: What is the shortest closed curve C that also switches the ball's poles? (Or at least, what is the inf of the lengths of all closed curves C that switch the poles?) --WDS: Line segment of length pi/2, same line segment backwards, total length is pi and curve is "closed." "But that doesn't work!" you cry. "It'll just roll sphere back to its start configuration!" Well, make teeny tiny little adjustments in the neighborhood of the two corners of this degenerate polygon. Each corner is replaced by a "foobar," which is an arbitrarily short curve whose effect is to rotate the sphere by 180 degrees round a vertical (normal to the tabletop) axis. Then it'll work. Meaning of "closed" curve here is its end & start points are same. And obviously pi is minimum possible so this is tight up to the foobar.

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Re: [math-fun] Backwards Bekenstein argument?
by Henry Baker 25 Jul '14

25 Jul '14

Not all mass resides in black holes; neither does all information. But in detail, where does the curvature arise for smaller-than-black-hole objects, I don't know. But it seems more likely that this curvature can somehow be correlated with information than some abstract notion of "mass" or "energy". This backward Bekenstein (BB) argument starts making vacuum energy more interesting. So-called "flat space" would be necessarily uninteresting, because if there were something interesting going on, that information would already start curving the space. At 10:45 AM 7/25/2014, Eugene Salamin via math-fun wrote: >But then what is the source of Earth's gravity? > > -- Gene >>________________________________ >> From: Henry Baker <hbaker1(a)pipeline.com> >>To: math-fun(a)mailman.xmission.com >>Sent: Friday, July 25, 2014 10:31 AM >>Subject: [math-fun] Backwards Bekenstein argument? >> >>Bekenstein found that the entropy of a black hole was >>proportional to its surface area, which is also related >>to its mass. >> >>Since Newton, we've always assumed that mass is the >>"source" of gravity, but perhaps we (and Newton) >>were misled in the pre-digital world. >> >>Perhaps gravity (and particularly the space-time >>curvature) is really "caused" by the information >>stored on the Bekenstein surface, and the numerical >>value of the mass (& hence energy) is merely some >>statistic associated with this information. >> >>Verlinde's ideas of a few years ago are in this >>direction; I'm not sure where his thinking has >>led him recently.

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Re: [math-fun] Black Holes Aren't Black After All?
by Warren D Smith 25 Jul '14

25 Jul '14

I tried reading Vaz's paper http://arxiv.org/abs/1407.3823 and failed to understand it. He goes fast, uses variables without defining them, assumes a lot of reader familiarity with Wheeler deWitt equation and blows off all kinds of minor details which don't seem so minor -- at least not to those of us not already experts about Wheeler deWitt (which is to say, 99%+ of physicists & mathematicians). So... I can't say if it is brilliant, nutty, or what. To understand it, perhaps somebody could rewrite he paper about 4X times the length now actually explaining stuff, or a more dedicated reader than I could also read lots of other things in parallel.

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Black Holes Arent Black After All?
by Henry Baker 25 Jul '14

25 Jul '14

FYI -- It sounds like physicists are starting to utilize the Sherlock Holmes principle: "When you have eliminated the impossible, whatever remains, however improbable, must be the truth". Apparently, quantum destruction of information is even more unpalatable than the non-existence of black holes, so perhaps black holes don't exist after all. https://medium.com/the-physics-arxiv-blog/d0758c7c88b5 Black Holes ArenÂt Black After All, Say Theoretical Physicists Collapsed stars are just too big to trap light forever Black holes are a crucial part of the great cultural legacy of EinsteinÂs theory of general relativity. They have fascinated scientists and laypeople alike since they entered the public consciousness in the latter half of the 20th century. But it may be time to say goodbye to the notion of regions of space so dense that even light becomes trapped within them. In the last year or so, an intense debate about the paradoxical properties of black holes has left a number of theoretical physicists, including Stephen Hawking, suggesting that black holes might not exist at all, at least not in the form that anyone had imagined. If theyÂre right, it may finally be time to say goodbye to one of the most exotic objects in the theoretical universe. The black hole may finally be dead. First some background. Stars form when matter becomes dense enough to generate a gravitational field that compresses matter to the point where atoms fuse and release energy. This energy release prevents further collapseÂthroughout a starÂs lifetime, its gravitational collapse is balanced by its thermal expansion. Theoretical physicists have long predicted that black holes form when massive stars stop producing energy at the end of their lives. When that happens, thermal forces cease and the gravitational collapse takes over. If the star is relatively small, like the sun, the gravitational forces are not strong enough to overcome the force between neutrons and this stops the collapse forming a neutron star. But when much larger stars end their lives, there is no known force that can stop the collapse. Consequently, theoretical physicists have always assumed that the collapse must continue until the star becomes infinitely dense and forms a singularity in the fabric of space-time. The gravitational field around such a star would be so intense that not even light can escape. Hence the name Âblack holeÂ. ThatÂs never been an entirely satisfactory approach. Many physicists scratch their feet and stare at the ground when confronted with the idea of an infinitely dense object. WhatÂs more, the mechanism of collapse does not take into account quantum gravity, a theory that that is not yet fully understood in such extreme conditions. ItÂs quite possible that a better understanding of quantum gravity could point to an entirely different result. Indeed, thatÂs exactly what appears to be happening. In the last few years, theoretical physicists have begun to think about what happens to information when it falls into a black hole. The general feeling is that information cannot be destroyed in this process and yet thatÂs exactly what seems to happen. Information is ultimately carried by quantum particles such as photons. So at issue here is the nature of quantum mechanics. A fundamental postulate of quantum theory is that all the information about a system is encoded in its wave function and this always evolves in a way that conserves quantum information. But the quantum information associated with matter that enters a black hole seems to devolve into a single state. When that happens, the information must be lost. This information paradox has triggered some intense soul-searching. And as a result of this, Stephen Hawking proposed a potential solution earlier this year. His idea is that gravitational collapse can never continue beyond the so-called event horizon of a black hole beyond which information is lost. Gravitational collapse would approach the boundary but never go beyond it. Today, Cenalo Vaz at the University of Cincinnati takes this idea and runs with it. The question he tackles is this: if a dead star does not collapse beyond the event horizon and so does not produce a black hole, what does it end up like? To find out, he models the quantum behaviour of dust as it collapses towards the event horizon. ÂIn this simple model, the picture that emerges is very different from the traditional view of a black hole,Â says Vaz. In this new model, there are two important parameters. The first is the so-called Schwarzschild radius, which is the size of the black hole that would form in a conventional model. The second is the radius of the dust ball as measured by distant observer. The difference between these radii is a region in which the universe is unlike anything physicists have imagined. The total energy here is negative and quantum fluctuations are likely to dominate. But exactly what goes on will depend on the exact model of quantum gravity that turns out to be correct, something that physicists are some way from determining. By contrast, the behaviour outside this region is strangely conventional, says Vaz. The collapsed star should swelled to about twice the radius of a conventional black hole. There is no event horizon and the space-time geometry is regular. ÂObservationally, what is being encountered has more in common with a neutron star, except that what holds the system up is not matter degeneracy pressure but vacuum energy,Â says Vaz. ThatÂs a fascinating conclusion. WhatÂs interesting here is that there is plenty of observational evidence that highly dense objects exist in the universe, some of them on a supermassive scale. For example, the supermassive black hole, or something like it, that sits at the very centre of the Milky Way galaxy. Vaz isnÂt disputing the existence of these superdense objects, just what they look like. What he and others are saying is that these objects are not black at all. Indeed, it should be possible to observe them, just like ordinary neutron stars. The difficulty, of course, will be to distinguish them from traditional neutron stars. If Vaz and co are right, astronomers are set to have some fun hunting for these exotic objects. Time to get looking. Ref: arxiv.org/abs/1407.3823 : ThereÂs Nothing ÂBlackÂ about a Black Hole http://arxiv.org/abs/1407.3823

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Re: [math-fun] Black Holes Aren't Black After All?
by Henry Baker 25 Jul '14

25 Jul '14

Bekenstein quantified "crapload", at least if you still believe in "classical" (Shannon-style) information theory. It is still possible that Shannon's information theory didn't get at the real essence of information in a quantum world, which should presumably do a better job of explaining EPR/Bell's Theorem/Aspect, etc. At 08:17 AM 7/25/2014, Warren D Smith wrote: >My conclusion: we must accept that black holes have interiors. >Or store a crapload of information on their surfaces.

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[math-fun] Revolutionary new (?) idea about black holes -- they are weird inside
by Warren D Smith 25 Jul '14

25 Jul '14

Henry Baker's post about "Nothing black about black holes" (by Cenalo Vaz, http://arxiv.org/abs/1407.3823 ) stimulated me to think on this again (I've thought about it a lot) now generating what seems like a new hot idea. (I don't think it has anything at all to do with Vaz's ideas, but this did stimulate me.) Here it is. In a previous (2003) work, I had pointed out that gravitons, i.e. the analogue of photons but for gravitational not electromagnetic waves, were sort of "one way." That is, a typical graviton interacts at most ONCE with matter, and never again. I proved a theorem of this kind, stating that "plane gravitational waves" in a flat space background could not be absorbed by (or redirected by) any absorber (or reflector, refractor, polarizer) with any efficiency greater than zero. This is one example of the fact that GR (general relativity - Einstein gravity) is IRREVERSIBLE unlike the rest of accepted physics which obeys CPT invariance and is a unitary transformation and in those senses is time-reversible. And there are other ways GR exhibits an "arrow of time" such as the theorem that black holes can merge but never bifurcate. These GR arrows of time are somewhat mysterious in the sense that they come from global and/or topological effects; the local laws of GR are time-reversible. Anyhow, I had in that previous work then pointed out that Von Neumann "measurement" in quantum mechanics was also "irreversible" and hence proclaimed the manifesto that decoherence/measurement effects in quantum mechanics all should be traceable to, and ultimately entirely caused by, time-irreversibility effects in quantum gravity. Furthermore, gravitons cannot be shielded out, and they interact with everything, and they do so usually only once, causing a "measurement by external environment" effect, causing everything to become non-weird. Why do you not experience being in a superposition of being in Tokyo and Paris? Because of such effects. Even though gravity is extremely weak I calculated numerically this effect alone could go a long way toward (probably the whole way toward) eliminating quantum weirdness from human experience. You can read said "previous work" here as paper #70 here: http://rangevoting.org/WarrenSmithPages/homepage/works.html That all was prologue for my new idea. Suppose you fall in thru the event horizon of a black hole. The usual old thinking based on exact solutions of GR had been: if it is a large enough hole, then you'll experience nothing out of the ordinary, will not notice anything, during the horizon crossing -- albeit eventually you are going to get crushed, tidally drawn & quartered, and die. But now here is my radically new (?) thinking. Nothing inside the event horizon can escape. Including gravitons. Further, if you emit a graviton, it is going to come back and hit you, since (at least for a Schwarzschild hole, the simplest exact solution) everything falls into the point singularity, including that graviton. Hence, the whole postulated mechanism underlying quantum decoherence, will simply stop operating inside event horizon. Hence HYPOTHESIS: INSIDE EVENT HORIZONS, QUANTUM "WEIRDNESS" REIGNS. MACROSCOPIC PHYSICS IS NO LONGER "CLASSICAL." In other words, if the Earth were inside some event horizon of some huge hole, with old-think, we would not necessarily know it, or anyhow it'd be hard to detect. With new-think, you'd experience superpositions of being in Paris & Tokyo, and actually, you'd probably not even be "alive" at all because everything would be too weird. Passing thru an event horizon would with new-think would probably instantly kill you, or anyhow radically change the nature of everything you experience, and basically eliminate "classical physics" as a good approximation of "physics." Although this seems a radical change in thinking about black holes and event horizons, it is one that does not require any radical clobbering of accepted physics ideas. It does, however, make one's head hurt and make one worry in new ways about "interpretation of quantum mechanics." Now obvious follow-up questions would be: 1. how does this impact the Hawking "information loss" paradox related to black hole evaporation? 2. ditto re the "firewall paradox." And it may be pretty hard to answer those without knowing (and we do not know) what "quantum gravity" is. GR is a classical gravity theory. If all classical physics including GR breaks down inside event horizons, then the whole description of spacetime as a "metric" and everything just may get blown away, and the replacement will be, whatever the true theory of quantum gravity is. Which we do not know. Now if we are outside the black hole but very close to its horizon, then things ought to be weirder the closer we get. (Only photons or gravitons headed in a very small angular cone of directions will be able to escape.) I.e. it will not be a sudden discontinuous transition to quantum weirdness. This means in principle experiments might be possible, and that some Hawking radiation analyses might change. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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Re: [math-fun] Black Holes Aren't Black After All?
by Warren D Smith 25 Jul '14

25 Jul '14

Jeff Caldwell's recounting of the "interior doesn't exist" interpretation of black holes was fascinating, but I perceive the following problems: 1. There also are horizons in an expanding de Sitter universe (anything on the other side of the horizon can never come back to us, since universe "expanding faster than light"). Also, for a uniformly accelerating observer, there is a horizon (stuff on other side "can never catch up" to us, if we keep accelerating at same rate forever). But unlike for a black hole, these two kinds of horizons are observer-dependent, and the lattermost kind stops existing if you stop accelerating. But like for a black hole these horizons also emit Hawking radiation and feature "uniform surface gravity" and "infinite red shift." So, trying to say the stuff on other side of these horizons "doesn't exist" does not work. So then you'd have a funny situation of treating black hole horizons and these horizons differently, despite their similarities. 2. Caldwell's whole recounting seems in deep trouble if employ quantum gravity instead of GR. Jump into a black hole? Caldwell's way, your mass & charge & momentum & angular momentum merge with the boundary surface, but other than that, you stop existing. But that is a NON-UNITARY, and NON-INVERTIBLE many-to-one transformation, which is totally incompatible with the foundations of quantum mechanics. So, to accept this black hole interpretation, you've got to totally redo QM somehow. My conclusion: we must accept that black holes have interiors. Or store a crapload of information on their surfaces.

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[math-fun] Black torus?
by Henry Baker 24 Jul '14

24 Jul '14

Can a fast rotating "black hole" rotate fast enough to be a "black torus" ? I'll accept an unstable equilibrium black torus for the moment; what I'm asking is whether the event horizon can be toroidal for some finite amount of time. The real issue is whether physicist Eve could theoretically go through the center of such a torus without getting gobbled up by the black object. >From an infinitesimal point of view it seems possible; after all, sufficiently small neighborhoods on the toroidal surface look like small neighborhoods on the surface of a black hole.

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