Re: Schmidhuber II implies FTL communications
On Thu, Sep 05, 2002 at 07:32:49PM -0700, Hal Finney wrote: > This was an interesting paper but unfortunately the key point seemed > to pass by without proof. On page 5, the proposal is to use entangled > particles to try to send a signal by measuring at one end in a sequence > of different bases which are chosen by an algorithmically incompressible > mechanism. The assumption is that this will result in an algorithmically > incompressible set of results at both ends, in contrast to the state > where stable measurements are done, which we assume for the purpose of > the paper produces algorithmically compressible results. > > The author writes: "This process of scrambling with the random template T > guarantees that Bob's modified N-bit long string of quantum measurements > is almost surely p-incompressible..., and that Alice's corresponding > string (which is now different from Bob's) is also (almost surely) > p-incompressible" > > It's not clear to me that this follows. Why couldn't Bob's measurement > results, when using a randomly chosen set of bases, still have a > compressible structure? And why couldn't Alice's? I think you're right, the author skipped some steps in his reasoning here. I'll try to fill in with my guesses. When Bob randomizes his measurement directions, it could have one of three effects. It could predictably change Alice's measurement outcomes, it could unpredictably randomize Alice's measurement outcomes, or it could not affect Alice's measurement outcomes at all. The first two can both be used for FTL communications. The last one is ruled out by experiments relating to Bell's inequality. To see why, let Alice and Bob agree on 3 coplanar directions each seperated by 120 degrees, and label them a, b, and c. They're going to independently randomly choose one of these directions and measure the spin of their particles along it. They do this a bunch of times and then compare notes. Suppose Alice can predict her outcomes as a function of her choice of direction independent of Bob's choice of direction. She can say something like if I choose a, outcome will be 0, if I choose b, outcome will be 1, and if I choose c, outcome will be 1. These predictions must apply to Bob just as well. So it's like there is a local hidden variable in the particle that determines what the outcome is in all three cases. Bell's inequality says if you look at the times when Alice and Bob choose different directions, their measurements should agree at least 1/3 of the time. Take the <0,1,1> case above. There are 6 ways that Alice and Bob can choose different directions, and at least 2 of them (b,c and c,b) result in agreement. This applies to every possible prediction, hence the 1/3 figure. However, QM predicts and actual experiment shows they agree only 1/4 of the time, therefore Alice must not be able to predict her outcomes without knowing Bob's choice of direction.
Re: Schmidhuber II implies FTL communications
From: Osher Doctorow [EMAIL PROTECTED], Thurs. Sept. 5, 2002 10:25PM I don't know whether Hal Finney is right or wrong after reading pages 5-8 of Yurtsever, since Yurtsever writes like David Deutsch and Julian Brown and so many other members of the quantum entanglement school - no matter how many words they put in, they always leave out interconnecting logic and physics. Most mathematical psychology models have in the past been of this type, believe it or not, which is probably why mathematical psychology is today one of the most backward fields. I think that, despite NASA's alleged use of chaos avoidance in some satellite or missile, chaos theory is more or less in the same boat. I spent some time on an internet forum discussing David Deutsch's work some time ago, and neither Deutsch nor his friends had the faintest idea what I was talking about, and the feeling is mutual. I used to think that misunderstandings between scientists (including mathematicians) are not usually deliberate, but I am beginning to even question that in reference to quantum entanglement because such dogmatism and intolerance and lack of spelling out steps characterizes the field. And it's OK with some people, because they've been doing that as a way of life with less complicated stuff and getting away with it! If nothing else, entanglement as a continuous or connected process/event can't be as easily faked or double-talked as entanglement as a bunch of discrete steps. Unless somebody has some comments to make about my work, much of which is at http://www.superstringtheory.com/forum, I'll go back to the forum where I can continue my continuous are piecewise continuous approach. Actually, they can reach me at [EMAIL PROTECTED],. if they have any useful comments. Osher Doctorow Osher Doctorow - Original Message - From: "Hal Finney" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Thursday, September 05, 2002 7:32 PM Subject: Re: Schmidhuber II implies FTL communications > Wei writes: > > I just found a paper which shows that if apparent quantum randomness has > > low algorithmic complexity (as Schmidhuber II predicts), then FTL > > communications is possible. > > > > http://arxiv.org/abs/quant-ph/9806059 > > This was an interesting paper but unfortunately the key point seemed > to pass by without proof. On page 5, the proposal is to use entangled > particles to try to send a signal by measuring at one end in a sequence > of different bases which are chosen by an algorithmically incompressible > mechanism. The assumption is that this will result in an algorithmically > incompressible set of results at both ends, in contrast to the state > where stable measurements are done, which we assume for the purpose of > the paper produces algorithmically compressible results. > > The author writes: "This process of scrambling with the random template T > guarantees that Bob's modified N-bit long string of quantum measurements > is almost surely p-incompressible..., and that Alice's corresponding > string (which is now different from Bob's) is also (almost surely) > p-incompressible" > > It's not clear to me that this follows. Why couldn't Bob's measurement > results, when using a randomly chosen set of bases, still have a > compressible structure? And why couldn't Alice's? > > Also, does this result depend on the choice of an unbalanced system > with alpha and beta different from 1/2? This short description of > the signalling process doesn't seem to refer explicitly to special > alpha/beta values. > > If not, could the procedure be as simple as choosing to measure in > the X vs + bases, as is often done in quantum crypto protocols? If we > choose between X and + using an algorithmically incompressible method, > will that guarantee that the measured values are also incompressible? > > Hal Finney >
Re: Schmidhuber II implies FTL communications
Wei writes: > I just found a paper which shows that if apparent quantum randomness has > low algorithmic complexity (as Schmidhuber II predicts), then FTL > communications is possible. > > http://arxiv.org/abs/quant-ph/9806059 This was an interesting paper but unfortunately the key point seemed to pass by without proof. On page 5, the proposal is to use entangled particles to try to send a signal by measuring at one end in a sequence of different bases which are chosen by an algorithmically incompressible mechanism. The assumption is that this will result in an algorithmically incompressible set of results at both ends, in contrast to the state where stable measurements are done, which we assume for the purpose of the paper produces algorithmically compressible results. The author writes: "This process of scrambling with the random template T guarantees that Bob's modified N-bit long string of quantum measurements is almost surely p-incompressible..., and that Alice's corresponding string (which is now different from Bob's) is also (almost surely) p-incompressible" It's not clear to me that this follows. Why couldn't Bob's measurement results, when using a randomly chosen set of bases, still have a compressible structure? And why couldn't Alice's? Also, does this result depend on the choice of an unbalanced system with alpha and beta different from 1/2? This short description of the signalling process doesn't seem to refer explicitly to special alpha/beta values. If not, could the procedure be as simple as choosing to measure in the X vs + bases, as is often done in quantum crypto protocols? If we choose between X and + using an algorithmically incompressible method, will that guarantee that the measured values are also incompressible? Hal Finney
Re: Schmidhuber II implies FTL communications
From: Osher Doctorow [EMAIL PROTECTED], Thurs. Sept. 5, 2002 5:43PM I have accessed the paper by Yurstever, and I want to mention that I have been pursuing the algorithmic incompressibility thread on [EMAIL PROTECTED] in connection with supersymmetric theories of memory. The reception there was partly one of interest from a member of the Royal Statistical Society, but lately two members have complained about (a) off-topic, and (b) too lengthy emails of mine. This is definitely progress toward the Socratic position, and I am encouraged. : > ) I am very impressed by the algorithmic incompressibility viewpoint of randomness, although I should point out that it is only one (but a very good) viewpoint. Now I will continue reading the Yurtsever paper. Osher Doctorow
Re: Schmidhuber II implies FTL communications
From: Osher Doctorow [EMAIL PROTECTED], Thurs. Sept. 5, 2002 5:07PM Wei Dai, Good! I will try to access the paper almost immediately. I have long been partial to FTL as a conjecture. When Professor Nimtz of U. Koln/Cologne came up with his results, or shortly thereafter, and interpreted them favorably toward FTL, I emailed him, and he was kind enough to send me copies of some of his papers by regular (*snail*) mail/post. Some of the non-Analysis school have indicated here and on other forums that the pendulum has swung too far away from algebra/arithmetic/number theory, but the loop theorists like Smolin and Ashtekar and a number of people in string/brane/duality theories who follow their leads, not to neglect the MacLane/Lawvere Category theorists in mathematics and physics, actually constitute an extremely large Mainstream today rather than a downtrodden minority (although the Gauge Field Theorists still claim the *largest Mainstream* title). My tendency is to follow the least popular path in science and in several other fields. That was the way of life of Socrates, and also of many of the greatest Creative Geniuses in history - including Kurt Godel, who is still being berated by conformists shuddering at the thought that there might be limitations as to what assumptions can lead to. Osher Doctorow - Original Message - From: "Wei Dai" <[EMAIL PROTECTED]> To: "Russell Standish" <[EMAIL PROTECTED]> Cc: "Hal Finney" <[EMAIL PROTECTED]>; <[EMAIL PROTECTED]> Sent: Thursday, September 05, 2002 4:50 PM Subject: Schmidhuber II implies FTL communications > On Mon, Sep 02, 2002 at 12:51:09PM +1000, Russell Standish wrote: > > This set of all descriptions is the Schmidhuber approach, although he > > later muddies the water a bit by postulating that this set is generated > > by a machine with resource constraints (we could call this Schmidhuber > > II :). This latter postulate has implications for the prior measure > > over descriptions, that are potentially measurable, however I'm not > > sure how one can separate these effects from the observer selection > > efects due to resource constraints of the observer. > > I just found a paper which shows that if apparent quantum randomness has > low algorithmic complexity (as Schmidhuber II predicts), then FTL > communications is possible. > > http://arxiv.org/abs/quant-ph/9806059 > > Quantum Mechanics and Algorithmic Randomness > Authors: Ulvi Yurtsever > Comments: plain LaTeX, 11 pages > Report-no: MSTR-9801 > > A long sequence of tosses of a classical coin produces an apparently > random bit string, but classical randomness is an illusion: the > algorithmic information content of a classically-generated bit string lies > almost entirely in the description of initial conditions. This letter > presents a simple argument that, by contrast, a sequence of bits produced > by tossing a quantum coin is, almost certainly, genuinely > (algorithmically) random. This result can be interpreted as a > strengthening of Bell's no-hidden-variables theorem, and relies on > causality and quantum entanglement in a manner similar to Bell's original > argument. >
Schmidhuber II implies FTL communications
On Mon, Sep 02, 2002 at 12:51:09PM +1000, Russell Standish wrote: > This set of all descriptions is the Schmidhuber approach, although he > later muddies the water a bit by postulating that this set is generated > by a machine with resource constraints (we could call this Schmidhuber > II :). This latter postulate has implications for the prior measure > over descriptions, that are potentially measurable, however I'm not > sure how one can separate these effects from the observer selection > efects due to resource constraints of the observer. I just found a paper which shows that if apparent quantum randomness has low algorithmic complexity (as Schmidhuber II predicts), then FTL communications is possible. http://arxiv.org/abs/quant-ph/9806059 Quantum Mechanics and Algorithmic Randomness Authors: Ulvi Yurtsever Comments: plain LaTeX, 11 pages Report-no: MSTR-9801 A long sequence of tosses of a classical coin produces an apparently random bit string, but classical randomness is an illusion: the algorithmic information content of a classically-generated bit string lies almost entirely in the description of initial conditions. This letter presents a simple argument that, by contrast, a sequence of bits produced by tossing a quantum coin is, almost certainly, genuinely (algorithmically) random. This result can be interpreted as a strengthening of Bell's no-hidden-variables theorem, and relies on causality and quantum entanglement in a manner similar to Bell's original argument.
