July 2013 - mathfun@mailman.xmission.com

Re: [math-fun] math-fun Digest, Vol 125, Issue 41
by Adam P. Goucher 29 Jul '13

29 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? > 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 Poincaré 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. > 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

1 0

Re: [math-fun] math-fun Digest, Vol 125, Issue 41
by Warren D Smith 29 Jul '13

29 Jul '13

>> Warren Smith wrote: >> >> And it does not just increase "on average," > > You're wrong, by the Poincar? Recurrence Theorem. > > > Sincerely, > > > Adam P. Goucher --correct comment... for classical Hamiltonian mechanics (which is what Poincare Recurrence thm is about). But for Von Neumann formulation of quantum mechanics, 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." 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 i.e. infinity degrees of freedom involved. In contrast in classical mech we have fixed finite dimensionality. This distinction seems essential for explaining why it is that my picture can work and "entropy (of the part of the universe we perceive) can keep increasing forever." --- You all really ought to read my paper, I hope this little back & forth has acted as a successful advertisement to inspire that. :)

1 0

[math-fun] stupid expanding universe question
by Henry Baker 29 Jul '13

29 Jul '13

OK, if the universe is expanding, exactly _where_ is it expanding? The usual 'blowing up a balloon' explanation says that it is expanding _everywhere_, so that everything is moving away from everything else at the same rate. OK, so does this mean that the Planck length gets bigger? That's the only way I can think of that allows 'everything' to move away from 'everything else' uniformly. Does this mean that a black hole gets bigger, merely by virtue of its being part of the expanding universe? Otherwise, the expansion of the universe would try to pull atoms & molecules apart, which would either _do work_, and provide for a source of power. This power might be tiny in any particular part of the universe, but as a whole, it's pretty big.

1 0

Re: [math-fun] quantum theory foundational issues, my theory of how they should be resolved
by Adam P. Goucher 29 Jul '13

29 Jul '13

> Warren Smith wrote: > > And it does not just increase "on average," You're wrong, by the Poincaré Recurrence Theorem. Sincerely, Adam P. Goucher

1 0

Re: [math-fun] Yet another weighing problem
by Michael Kleber 29 Jul '13

29 Jul '13

And indeed Erich just independently said the same as in my last message. On Mon, Jul 29, 2013 at 10:29 AM, Erich Friedman <efriedma(a)stetson.edu>wrote: > the weighing of 2 coins versus 2 coins is a very powerful tool. > > whenever we weigh AB<CD and lose D, either A=B (and are therefore light) > or C is heavy. > > so we can use this trick repeatedly to reduce the (H,L) problem to the > (H-1,L-2) problem. > > i can't for the life of me see how to use weighings of more than 3 coins > effectively. > > so i'm guessing this is optimal. that is, (H,L) is feasible for L <= 2H-2. > > but i'd be glad to be proved wrong. > > erich > > > > On Jul 29, 2013, at 9:35 AM, Veit Elser wrote: > > > > > On Jul 28, 2013, at 6:56 AM, Erich Friedman <efriedma(a)stetson.edu> > > wrote: > > > >>> More natural questions: What's the first feasible (H,L) with L > H? > How > >>> about with L >= H + k for k=1, 2, 3, ...? Must some (H,L) work for > any k? > >> > >> > >> i'm in the weird position of receiving math-fun posts, but am unable to > post to the list. > >> > > > >> but (3,4) is feasible. > > Nice solution! Just two quibbles: > >> > >> randomly weigh AB against CD until AB<CD and D is removed. > > If EFG are the heavy ones then this will never happen, so you have to > try out > > all three weighings to be able to detect that case. > > > >> then weigh A against B. if they don't balance, C is heavy. > > And if they do balance I would then say the problem has been reduced to > (2,2) > > (because we've eliminated two light coins) which is already known to be > feasible. > > > >> then randomly weigh CE against FG until they don't balance. > >> the remaining coin from the heavy side is guaranteed to be heavy. > >> > >> erich > > > > > > > > > > -- Forewarned is worth an octopus in the bush.

1 0

[math-fun] Exact Cover Solver
by quad 29 Jul '13

29 Jul '13

Hello: I just wanted to announce that I wrote a program to find the exact cover of a set S = {0, ..., n-1}. It uses Knuth's Algorithm X with his Dancing Links strategy. The code is here in Lisp: https://bitbucket.org/tarballs_are_good/dancing-links Example: Given the sets A = {0, 3, 6} B = {0, 3} C = {3, 4, 6} D = {2, 4, 5} E = {1, 2, 5, 6} F = {1, 6}, find all disjoint unions of the above that equals S. This is an exact cover problem for n = 7. Input into the program is easy: > (exact-cover 7 '((0 3 6) ; A (0 3) ; B (3 4 6) ; C (2 4 5) ; D (1 2 5 6) ; E (1 6))) ; F It will think, and spit out Solution #1 at depth 3: 6 1 5 2 4 3 0 and then return the total number of solutions found (1) and the total number of "positions" checked (5). Note that the solution above corresponds to F, D, and B respectively, just the elements were permuted. Note that they are indeed disjoint and their union is S. The program still needs a little polishing, but may be useful to some people who want to solve pentomino or n-omino packing, sudokus, or whatever. If anyone is interested in having it as a stand-alone binary that takes a file as input, let me know, and I can probably accommodate. :) Cheers, Robert Smith

1 0

[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: Gareth McCaughan <gareth.mccaughan(a)pobox.com> >On 27/07/2013 11:18, Warren D Smith wrote: > So for example, why do you not experience being in a superposition of > living in Paris and Tokyo? Because [...] Why would you expect a superposition of experiencing being in Paris and experiencing being in Tokyo to resemble, in any way, experiencing being in a superposition of Paris and Tokyo? In default of some reason to expect that, I don't see why the question arises at all. And I know of no such reason, though I'm not a QM expert and maybe there is one that I've never encountered. --this is an excellent point, and there's plenty of arguments of that vague ilk which may sound good..., but the problem is, these questions don't seem addressable by mathematics or precise reasoning. So when various philoso-physicists (at least those in the Everett camp) are going around saying "the foundational problems of QM are solved" it's all hogwash. It's basically religion, and hopes+dreams, not science. That debate probably would never end and it'd never be clear if it really solves the problem. However, with my approach to the foundations of QM, the gordian knot is cut. It could really be science. And not only that, I can kick their asses with more paradoxical issues. For example, why is the "position basis" favored over others? Decoherence tends to localize things. Give them precise positions. Why? With pure QM unitary symmetry, no basis favored over any other. Well, my view explains that. And if (say) in the early universe, everything were in a momentum eigenstate, with pure QM, no localization of anything would ever be possible, translation symmetry could never be broken. This (in flat spacetime) is a theorem of mathematics. So the physicists who somehow convince themselves that positions being the "pointer basis" is somehow caused by QM, thru mysterious measurement-simulating environmental effects, are full of crap. The true explanation is quantum gravity, I claim via my reasoning. What about the "direction of time"? QM with measurement features a time direction. QM without features CPT symmetry. Again, the hogwash camp somehow deduces this is not a paradox, using religious reasoning. My way, gordian knot cut.

6 9

[math-fun] arrow of time, myth vs reality ("reality" meaning my views:)
by Warren D Smith 29 Jul '13

29 Jul '13

> Asimov: > I don't really believe in the 2nd Law of Thermodynamics anyway for large or > high-entropy initial conditions. (E.g., although the universe near us is > expanding, galaxies and stars are being formed at the same time.) > ------------------------------------------------------------------------- > > So let me bring up a related subject, as long as we're discussing physics. > There are two striking aspects of the universe that are so difficult to > address that physics can't touch them (so far): a) the flow of time, and b) > conscious awareness. These two things must be very closely related. But > very mysterious. --jeez.. A.S.Eddington once stated (1927), QUOTE If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations—then so much the worse for Maxwell's equations. If it is found to be contradicted by observation—well these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation. END QUOTE 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). Now if the universe were to turn round and start contracting, I assure you entropy would continue to not decrease (and to increase). 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. Efficient gravity wave emitters can exist but not absorbers. Small perturbations of the Schwarzschild metric die out with time, not grow. Previous authors have claimed GR also says nothing about time direction... the resolution of that paradox is subtle and discussed in my paper. I therefore claimed that since this is the ONLY place in accepted physics that says something about time direction, the arrow of time (and hence measurement, entropy, etc etc) must derive from it. There are a lot of philoso-physicists who seem to think via religious/hope "reasoning" that the arrows of time, phenomena of quantum "measurement," etc, somehow arise from nongravitational physics. They have nothing solid and never will. They need to come round to my picture.

2 1

Re: [math-fun] Yet another weighing problem
by Michael Kleber 29 Jul '13

29 Jul '13

Forwarded for Erich Friedman, whose messages are being rejected by the list server: On Sun, Jul 28, 2013 at 9:56 AM, Erich Friedman <efriedma(a)stetson.edu>wrote: > > More natural questions: What's the first feasible (H,L) with L > H? How > > about with L >= H + k for k=1, 2, 3, ...? Must some (H,L) work for any > k? > > > i'm in the weird position of receiving math-fun posts, but am unable to > post to the list. > > but (3,4) is feasible. > > randomly weigh AB against CD until AB<CD and D is removed. > then weigh A against B. if they don't balance, C is heavy. > then randomly weigh CE against FG until they don't balance. > the remaining coin from the heavy side is guaranteed to be heavy. > > erich

1 0

[math-fun] Fw: quantum theory foundational issues, my theory of how they should be resolved
by Eugene Salamin 29 Jul '13

29 Jul '13

I'm forwarding this, my email, to math-fun because I somehow originally sent it only to the poster. ----- Forwarded Message ----- >From: Eugene Salamin <gene_salamin(a)yahoo.com> >To: meekerdb <meekerdb(a)verizon.net> >Sent: Sunday, July 28, 2013 4:05 PM >Subject: Re: [math-fun] quantum theory foundational issues, my theory of how they should be resolved > > > > > >>________________________________ >> From: meekerdb <meekerdb(a)verizon.net> >>To: Eugene Salamin <gene_salamin(a)yahoo.com>; math-fun <math-fun(a)mailman.xmission.com> >>Sent: Sunday, July 28, 2013 3:16 PM >>Subject: Re: [math-fun] quantum theory foundational issues, my theory of how they should be resolved >> >> >>On 7/28/2013 3:06 PM, Eugene Salamin wrote: >>> >>> >>> >>> >>>> ________________________________ >>>> From: meekerdb <meekerdb(a)verizon.net> >>>> To: Eugene Salamin <gene_salamin(a)yahoo.com>; math-fun <math-fun(a)mailman.xmission.com> >>>> Sent: Sunday, July 28, 2013 2:49 PM >>>> Subject: Re: [math-fun] quantum theory foundational issues, my theory of how they should be resolved >>>> >>>> >>>> On 7/28/2013 2:05 PM, Eugene Salamin wrote: >>>>>> From: meekerdb <meekerdb(a)verizon.net> >>>>>> To: math-fun <math-fun(a)mailman.xmission.com> >>>>>> Sent: Sunday, July 28, 2013 11:53 AM >>>>>> Subject: Re: [math-fun] quantum theory foundational issues, my theory of how they should be resolved >>>>>> >>>>>> The direction of physical time is determined by expansion of the universe (which allows >>>>>> entropy to increase) - which in a sense is a gravitational effect. >>>>>> >>>>>> Brent >>>>> What would be observationally different in a contracting or steady state universe? >>>> Depends. If it contracted enough it would reach the maximum possible entropy density and >>>> everything would be in thermal equilibrium (and very hot). We're possible because the >>>> rapid expansion of the universe provides an entropy sink, so we can live off the >>>> far-from-equilibrium radiation from the Sun. >>>> >>>>> Can >>>>> the Hubble constant or the cosmological constant be deduced from a >>>>> thermodynamic measurement, perhaps some chemistry experiment? >>>> No by any theory I know of. >>>> >>>> Brent >>>> >>>>> -- Gene >>>>> _______________________________________________ >>>> Suppose the universe were contracting at the same rate it is expanding. What would be observationally different concerning the increase of entropy in ordinary laboratory measurements. >> >>Contracting at the same rate it's expanding AND is the same size? Nothing >> >>>> If nothing different, then in what sense is the statement "The direction of physical time is determined by expansion of the universe (which allows entropy to increase)" anything other than a collection words strung together into a grammaticaly correct English sentence? >> >>It's a sentence that expresses a relationship between a past event and a direction (not a >>rate), as in you are the size your are because you grew from a zygote. You'd be the same >>size if you had shrunk from a giant, but in fact the former occurred and not the latter >>and hence it's correct to say you grew with time. >> >>Brent >> > > > >Then we seem to agree that the second law of thermodynamics, discovered by Clausius in the mid 19th century, has little relation to the expansion of the universe, discovered by Hubble in the early 20th century. A contracting universe would "allow" entropy to increase just as much as does the expanding universe. > >As for the other part of that statement, "The direction of physical time is determined by expansion of the universe", what does that mean? Would the direction of time be reversed in a contracting universe, so that maybe observerers always see the universe to be expanding? What happens at the boundary between a contracting region and an expanding region? What sort of experiment might one perform to either confirm or refute this idea? > > -- Gene > > > >

1 0