July 2013 - mathfun@mailman.xmission.com

[math-fun] quantum theory foundational issues, my theory of how they should be resolved
by Warren D Smith 05 Aug '13

05 Aug '13

> 1. Re: NYTimes: quantum theory w/o observers (meekerdb) > There's a good paper by Schlosshauer and Camilleri that discusses the > historical debate > over the Heisenberg cut and how the question has mostly been answered by the > idea of > decoherence. > > http://arxiv.org/pdf/0804.1609v1.pdf > > I say 'mostly' because pushing the Heisenberg cut all the way to include > conscious > observers, as in Everett's interpretation of QM, is still a little > controversial because > we lack a good theory of consciousness. > You won't learn anything useful from the NYT discussion (Callendar's essay > is good, but > it's short and assumes a lot of background). The best current ideas are > decoherence and > Everett's many worlds. Read Schlosshauer's review papers: > > http://arxiv.org/pdf/0804.1609v1.pdf > > or for more depth > > http://arxiv.org/pdf/quant-ph/0312059.pdf > > Brent Meeker --ok. First of all, the "decoherence program" seemed to me inadequate. This is that every physical system is contained in an "environment" and since it interacts with environment it effectively is being "measured" (no real measurement is needed though, that concept is claimed really not to exist). So for example, why do you not experience being in a superposition of living in Paris and Tokyo? Because some cosmic ray, or air molecule, or whatever (environment) interacts with you in Tokyo only, thus "measuring" the fact you are in Tokyo or not. Sounds great... except why wasn't the cosmic ray in a superposition of being in Paris & Tokyo? This doesn't solve the problem of why the world is not weird; it merely pretends to solve the problem by already assuming the answer. ("It's turtles all the way down.") I once wrote a short paper on "why quantum computers won't work" whose argument rested on 4 axioms about the nature of decoherence, which may or may not be true. Read it: "Argument against quantum computers (or against certain decoherence models)" http://rangevoting.org/WarrenSmithPages/homepage/whywontwork2.ps Recently Scott Aaronson read this paper and pointed out things are not as simple as my paper made it appear... for example, some of the axioms are not really well defined. (What is the "location" of a "qubit"?) Second. What if the physical system is "the whole universe"? I have an idea about that, but it is only very slightly mentioned in the papers Meeker cited. It is this. There is a part of the universe we can perceive, and there is a part we cannot. For example, we have a hard time perceiving dark matter and gravitons. Nevertheless, there are interactions between parts A and B. So my proposal is, since we can only see part A, part B acts as the external environment from our point of view. Now what is needed to make this work, is that almost always (or at least, "often"), when parts A and B interact, they never do so again. Similarly to, if you interact with that cosmic ray, it flies off into outer space, never to interact with you again. This causes it to carry away "measured information" permanently. If you could keep interacting over & over again with that cosmic ray, it'd get entangled with your position, and hence would no longer be "measuring" your position in the sense of Von Neumann measurement. (There is an interpretation of Von Neumann measurement involving randomization of the phase angles of off-diagonal terms in density matrix; this randoms need to be independent.) So with the cosmic ray, the problem is, the whole universe might get entangled with your position, so the whole damn universe would not be capable of "measuring" it, so the whole argument would become doubtful. That's why the cosmic ray explanation is inadequate. Now, to return to my "parts A & B" explanation, I have proven, that gravitons after they are created almost never interact with anything. Ever. For the rest of time. See this paper by me: "From time-irreversibility in gravity to measurement in quantum mechanics" http://rangevoting.org/WarrenSmithPages/homepage/absorber.pdf http://rangevoting.org/WarrenSmithPages/homepage/absorber.ps "Almost never" means the interactions occur for less than any fixed positive constant fraction of gravitons. "Anything" means matter. My point is this. The gravitons form a second, shadow universe, or external environment, for the parts of the universe we can see. There is no issue that this external environment might get entangled with our part and hence unable to "measure" our part, because of my "almost never interacts again" theorem -- the first time our part interacts with a graviton, it is a virgin, and that graviton (now entangled), never comes back to haunt us (re-interact, non-independent randomness). So effectively via gravitons, there is an inexhaustible resource of new, non-entangled, random qubits in part B of the universe, which is able to keep decohering our part A. If you examine the numbers, this effect alone is large enough (even though gravity is an extremely weak interaction) to explain why the world appears classical to a human observer. So that is my theory.

7 16

[math-fun] Politics is neither math nor fun?
by Warren D Smith 31 Jul '13

31 Jul '13

--actually politics can be math: http://RangeVoting.org Here is a recent matholitical puzzle I posed, anybody want to solve it? (I presently have solved all but the lattermost parts.) http://groups.yahoo.com/group/RangeVoting/message/16279

1 0

Re: [math-fun] that Swiss Army hook gadget
by Bill Gosper 31 Jul '13

31 Jul '13

Fred>Can it also extract superfluous diacriticals? https://en.wikipedia.org/wiki/Habanero And are they still radioactive? (The capsicums, that is. Not the diacriticals ...) WFL Half a big one steeped in Bundaberg: Fukushima primary coolant. Hyperforeignism, eh? At g4gX I asked Richard Guy, recently back from Copenhagen, whether it was CopenHAYgen or CopenHAHgen. He replied Copen<unrepeatable snarl>en. --rwg

1 0

[math-fun] that Swiss Army hook gadget
by Bill Gosper 31 Jul '13

31 Jul '13

http://www.smartknives.com/Swiss-Army-Knife-Tools/Victorinox-Hook.htm (Off topic, but sufficiently momentous) I finally found its true purpose: Extracting depleted habañeros from your bottle of ginger beer. --rwg

2 1

[math-fun] asteroid lasso plan?
by Warren D Smith 30 Jul '13

30 Jul '13

NY Times science section today says that in a straight party line vote, 100% Republican majority killed a NASA (+100% Democrat) plan to lasso a small asteroid & haul it back to earth orbit. Instead they demand NASA build a manned Moon base and plan for a future manned Mars expedition. I have no clue whatever why Republicans are anti-asteroid & Democrats pro, but I believe manned space exploration, especially of Mars, is asinine. (The only theory I can think of is that the manned Mars plan will consume a huge amount of money and the Republicans like that?) Their latest asteroid capture plan supposedly could have been done for only about $1 billion. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

5 4

[math-fun] Does entropy increase because the universe is expanding?
by Warren D Smith 30 Jul '13

30 Jul '13

> From: Eugene Salamin <gene_salamin(a)yahoo.com> > To: math-fun <math-fun(a)mailman.xmission.com> > Subject: [math-fun] Does entropy increase because the universe is > expanding? > Will someone who holds an affirmative view on this question answer the > following. > > A chemist constructs two vessels separated by a closed stopcock.? One vessel > is filled with gas, the other is evacuated.? The stopcock is opened.? In our > expanding universe, the gas expands into the empty vessel until the > pressures are equalized.? Entropy has increased.? What would be observed in > a contracting universe? > > ? --? Gene --quite. It used to be believed maybe 20 years ago the universe (quite possibly) was expanding but would eventually turn round and we'd get a "big crunch." Presently, though, with the supernova redshift evidence, it is believed that the expansion will accelerate due to EInstein cosmical constant and continue forever. Anyhow, in the turnaround/crunch universe, we'd all be observationally aware the turnaround had happened, same way we now are aware of the expansion... and the stars would keep getting older as usual, dropped balls would lose energy each bounce as usual, and the gas would keep expanding into vacuum when stopcock opened, and life would go on normally for billions of years, etc etc. Eventually, human life would become impossible as the crunch neared, and still later all life presumably would get killed, both due to high temperatures. It is difficult for me to comprehend the idiocy of anybody who asserts the contrary, they presumably have no understanding of the basics of statistical physics... if I could understand what they had in mind I could perhaps construct a genuine argument against them rather than merely branding them idiots. It's kind of like arguing against a flat-earther. In the case of H.Brady wondering about what the universe is "expanding into" etc, well, you have to learn general relativity, then you know. If you don't then it'll just sound like voodoo. I personally taught myself GR initially from Pauli's book, which is available in English from Dover, and I recommend it highly for beginners. But learning GR may be tough for somebody without the right background. Personally I feel I've learned GR pretty well, thank you, but for QFT (quantum field theory) I feel a lot less happy about my depth of understanding. And when it comes to string theory, AdS-CFT correspondence, and all that recent jive, my understanding is not much further along than "is great and strange voodoo, kemo sabe" and I fear I'll never surmount that.

3 2

[math-fun] Does entropy increase because the universe is expanding?
by Warren D Smith 30 Jul '13

30 Jul '13

>Read L.S. Schulman's book --ok. I have not read Schulman's "Time's Arrows and Quantum Measurement" but I will try later. I had read some edition of "The Physical Basis of the Direction of Time" by HD and/or DH Zeh. There are many many books on those subjects, most of which I have not even seen, some of which are quite good, such as Roland Omnes: "The interpretation of Quantum Mechanics," and some of which are appallingly bad, such as Roger Penrose: "Emperor's new mind." There also was a good article on decoherence by W.Zurek in Physics Today 44,10 (Oct 1991). But in all the papers & books I saw, I never saw anything that convincingly resolved the issues associated with the quantum-classical transition, entropy, time-direction, etc using only the "standard model." If they tried, at some point they all had to rely on intuitive hopes/dreams "reasoning" which may or may not be valid, it became basically religion. Right now I'm not sure why, but the Everett school seems to be the most fashionable. Here's a random article about that from the web: http://plato.stanford.edu/entries/qm-manyworlds/ and if you think this solves everything rigorously and isn't religious hogwash, good luck to you. Now re > In general relativity the direction of time is not arbitrary.? The future is > the direction in which black holes form.? --I agree. > To continue the saga of this > chemist in the contracting universe who observes the gas filling both > vessels and the universe expanding, does he observe black holes or white > holes? --black. > In that contracting model, t is just a coordinate parameter. I collapses to a big crunch > which is just a time-reversed big bang. Physical time has to correspond, at least > locally, to increasing entropy so that one can form memories, etc. I think that for > life to have evolved it has to have been in an expanding universe for a long time. --the big crunch is a time-reverse big bang if all the microscopic details are ignored and we have a maximally symmetric universe filled with mythical uniform-density continuum-fluid matter & radiation, and in that model there is no such thing as entropy and indeed there is no statistical mechanics since no particles. --However in the real universe with things like stars, galaxies, etc, entropy exists and continues to increase with time including during & after turnaround and shrinkage toward a crunch. There is indeed a theorem (or pretty close to a theorem) in GR called "generalized second law" which includes both normal and black-hole entropy and says the sum cannot decrease. I think this stuff was treated in the excellent book by Hawking & Ellis "large scale structure" (but you have to know GR to read said book). --life certainly had to have been in expanding universe for long time, otherwise we'd be in unexpanded universe, which would not be friendly to life. However, if turnaround occurred, life presumably would continue until things got too hot, and life could certainly evolve on some planet where the first life there happened after the turnaround.

1 0

[math-fun] quantum theory foundational issues, my theory of how they should be resolved
by Warren D Smith 30 Jul '13

30 Jul '13

>> Warren Smith wrote: >> >> --correct comment... for classical Hamiltonian mechanics (which is >> what Poincare Recurrence thm is about). But for Von Neumann >> formulation >> of quantum mechanics, > > Okay, I accept that there exists a quantity that is invariant under the > deterministic QM laws and strictly increases during probabilistic > wavefunction collapse (for a rather crude example, you can simply define an > integer N, which is the number of wavefunction collapses since the beginning > of time). > > But is the von Neumann entropy compatible with the standard concept of > entropy? --pretty well. It obeys a set of axioms like Shannon entropy... it basically IS Shannon entropy if interpreted right... >> entropy stays same - except that during >> measurements it increases. Since quantum is more true theory of >> nature than classical... it >> would be you who "are wrong." > > There are quantum-mechanical analogues of the Poincar? Recurrence Theorem, > such as this one: http://elcent.shinshu-u.ac.jp/wakate/abstracts/sasaki.pdf > Hence, I am not ready to accept defeat just yet. --hmm. Well, that pdf just makes an undefined claim without a proof. I think with appropriate words it is true though. There is an entropy bound in a bounded region with bounded energy. But in my picture we are NOT in a "bounded region" we are infinite spatial extent (my proof of the no-gravity-wave-absorber theorem requires plane gravity waves to exist to even be able to talk about it, which requires infinite space which is asymptotically flat... the "positive energy theorem" about positive mass in GR, proven by Witten et al, also requires asymptotic flatness as an assumption). >> In my picture of quantum mechanics & decoherence, the graviton sea serves >> as >> an infinite "entropy sink" (as Meeker was calling it). It actually is >> infinite dimensional > > That comes as no surprise. Most phase-spaces in quantum mechanics are > infinite-dimensional Hilbert spaces. > Sincerely, > Adam P. Goucher --Well, imagine you are a hot body. (Actually a true fact.) Your atoms bounce around hence accelerate. Hence they emit gravity waves. (At a very low rate.) If you lived inside a perfect reflecting wall mirror box, your emissions of photons, even neutrinos in principle, would not act as "measurements" of you so you'd be able maybe to be quantumly weird. Also, the space of modes inside the box with bounded total energy, would actually be finite-dimensional, hence recurrence would apply. BUT gravitons cannot be shielded even in principle. When you emit them, they fly away right thru the box walls. Bingo -- you've been measured by an "external environment." You now cannot be too weird. Note this happens no matter how good your shielding, refrigeration etc are. Also note, you lost info to that external environment, it "measured" something about you, and hence you gain Von Neumann entropy (at least to the degree the approximation of this emission as a "measurement" is correct). This happens forever. It cannot be avoided. Not even in principle.

1 0

[math-fun] Does entropy increase because the universe is expanding?
by Eugene Salamin 29 Jul '13

29 Jul '13

Will someone who holds an affirmative view on this question answer the following. A chemist constructs two vessels separated by a closed stopcock. One vessel is filled with gas, the other is evacuated. The stopcock is opened. In our expanding universe, the gas expands into the empty vessel until the pressures are equalized. Entropy has increased. What would be observed in a contracting universe? -- Gene

3 5

[math-fun] quantum theory foundational issues, my theory of how they should be resolved
by Warren D Smith 29 Jul '13

29 Jul '13

> From: meekerdb <meekerdb(a)verizon.net> >> and, quite so. >> The 2nd law is true. It actually is a theorem of mathematics in Von >> Neumann's formulation of quantum mech with his defn of "entropy" >> (entropy increases during "measurements", stays same rest of time). > > Being "a theorem of mathematics" just means it follows from some assumed > axioms. Von > Neumann's formulation is like decoherence theory without mentioning the > environment. So > it has the same weakness plus one more. --well, I suppose I'd agree with that, but... the point is, this picture by Von Neumann of quantum mechanics, although clearly "wrong" in the sense essentially everybody agrees there must be no such thing as "measurement" really... also is clearly "right" in the sense everybody agrees that Von Neumann quantum mech agrees with every experiment. If you deny there is measurement, then this theorem shows entropy always stays the same. Which proves something is screwed up. The truth (i.e. my picture) is that entropy associated with the part of the universe we can perceive, increases. Random information swap effects occur with the other part, this causes us to perceive measurement-like effects and entropy increase. (Any observer "in the other part" who could not perceive our part would also perceive entropy increase.) The fact that I show theorem that the info once swapped "cannot come back to haunt us" means this can keep happening forever, and will keep seeming like measurement and hence entropy increase forever. >> Now if the universe were to turn round and start contracting, I assure >> you entropy would continue to not decrease (and to increase). > > If you just did a CPT transformation on the state of the universe you'd have --no. CPT is a symmetry of flat space quantum field theories (e.g. the standard model). But, it is NOT really a symmetry of general relativity. General relativity CANNOT be solved going backward in time, it can be solved going forward in time. Situation is like the 1D heat equation, which has solutions going forward in time, but not going backward in time. (Another theorem of mathematics.) My paper explains this. I think this observation, although easy, was new. > universe that > was obeying all the same laws of physics, except it was contracting - and > hence the > entropy would be decreasing. --your reasoning here bogus, see above. > Of course no one living in this universe would > notice this > because the physical arrow of time would still point in the direction of > expansion. So > yes entropy increasing (on average) is a kind of tautology. --no, it is not. And it does not just increase "on average," in Von Neumann's theorem. >> If the >> universe started out high entropy, it >> would not matter either. This is a statement about enormous >> probabilistic "forces." It holds regardless of the shrinking or >> expanding of the universe >> which is an irrelevancy. This whole ludicrous myth was started by >> S.Hawking in his popular book "history of time" and even though >> Hawking later publicly stated that him saying this was the greatest >> and most humiliating error he ever made in his life, this absurd myth >> then attained a life of its own. >> >> Now in my paper I cited I pointed out that general relativity DOES say >> something about the direction of time (unlike every other physical >> theory in the standard model if >> "measurement" is regarded as not existing). Namely, there are theorems in >> GR >> like black holes can merge but not bifurcate. > But can white holes bifurcate? I think so; it is only statistically > improbable because of > the retarded radiation boundary condition. --there are no white holes. Anyhow, my paper discussed this, if there were a solution describing white holes bifurcating then an observer would perceive it as black holes merging. >> Efficient gravity wave >> emitters can exist but not absorbers. Small perturbations of the >> Schwarzschild metric die out with time, not grow. > > That's because they radiate away energy. --no, it is because the perturbations get absorbed into the black hole (or anyhow this seems more true description). It is actually again rather like 1D heat equation, where small ripples just die out. Not because they are "radiated away" (1D heat equation has no "radiation"). A Schwarzschild black hole is like a bell. It can "ring" with characteristic frequencies. But these frequencies are actually complex numbers, i.e. both oscillation and exponential die-out occurs. (These are called in the literature "quasimodes" of the black hole.) Every quasimode always has the imaginary part of the frequency of the right sign for die-out, not exponential growth. Similarly to the 1D heat equation where any fourier mode will die out exponentially with time, not grow. GR features a unique time-sign-direction just like the 1D heat equation. Physicists had not previously seen this, or at least the usual GR books never say so. And it is not a tautology. Now if these bell-ringing eigenmodes "radiated" energy away, then their amplitudes could not fall exponentially (which they do, everywhere, with the same e-folding time everywhere), they instead would fall like a power law. That is why I say it is a better description that the modes get absorbed into the hole. The direction of time in GR is "into" not "out of" a black hole. It thus is uniquely signed. It is highly related to the positivity of mass (and quantum field theories also agree mass is positive only, so presumably quantum gravity -- whatever that is -- which somehow merges the standard model with GR, also agrees mass positive). This discussed in my paper.

2 1