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Quantum Randomness (americanscientist.org)
54 points by Tomte on June 16, 2014 | hide | past | web | favorite | 21 comments

Enjoyed the shout-out to Bohmian mechanics. Nonlocality may be weird, but you know what else is weird? Everything else about quantum mechanics. I'd actually prefer a nonlocal deterministic theory to a local indeterministic one, though I know that's just a philosophical preference. Still, I wish Bohmian mechanics was more popular; I wasn't even aware it existed until recently.

Multiverse is perfectly deterministic without all the issues with Bell's Inequality and needing a superfluous particle in addition to the wavefunction. I think pilot wave is throwing the baby out with the bathwater.

Pure randomness doesn't need physicality. The expansion of Omega, Chaitin's constant, is random. There is no model, program, or equation, that can predict the next bit.

Perhaps its possible the universe could be run on a cellular automata that is unpredictable in the same way. Is say, radioactive decay, truly random, or just can't be predicted by any program shorter than the underlying cellular automata process itself.

The fact that we can model the universe at all and predict parts of it at various scales -- that math works at all for physics -- is either remarkable, or perhaps required in any universe capable of intelligent life. :) Perhaps in a universe that is incomprehensible otherwise, evolution would not select for intelligence.

That's referenced in the article -- Chaitin's constant is 'algorithmically incompressible' according to Kolmogorov complexity -- though note that this definition means it's "assymptotically" random, but the first n bits can be approximated in finite time (there are other numbers with more strict randomness). What the article addresses is that if you're given a long string with that property you can't verify the randomness, by definition. But using the CHSH method outlined you can, assuming only some physical principles -- provided you're given a small 'seed' to start.

Note that the underlying "way" that the universe generates randomness doesn't matter from a scientific standpoint -- as long as we can't predict it, you can think of it as being generated by either an enormous computer or truly random (whatever that means).

About 3/4 of the way down, in response to: "The central idea in all of these protocols is simply to be stingy with the use of randomness. We ask Alice and Bob to play the CHSH game over and over again. However, in almost all of the plays, they simply both receive red cards—leading to a boring but also “cheap” (in terms of randomness) game. Only for a few randomly chosen plays does one of them receive a blue card."

If this is true, then these "clever" protocols are breaking the 50/50 rule of the CHSH game. Right?

Yes. In the normal CHSH game, the questions to the players Alice and Bob are independent random bits (50/50, as you say). That's a problem, though, if you want to create new randomness, because you put into the game two random bits and you get out less than two random bits! If you want to get out more randomness than you put in, you need to be a little more clever and more stingy with using random bits.

(If the players are honest, the first player's output is uniformly random, but the second player's output is ~85% predictable given the first player's output. Measured in terms of entropy, this means you are getting a fraction more than 1 bit out.)

The standard 50/50 CHSH is still useful for generating randomness, though. Even though it uses up more randomness than it creates, the output randomness can be of higher quality than the input randomness. More precisely, if the input bits are independent to the players Alice and Bob, but perhaps are known to an outside adversary, the game's output bits will be unknown to the adversary.

It is interesting to see how outcomes of the CHSH game to generate random bits. However, I am left wondering how Alice, Bob, or an external observer learns about the outcomes of the game?

Or, maybe I am misunderstanding the mechanics itself.

The idea of infinite randomness expansion really fascinates me, it's like watching Münchhausen pulling himself out of the swamp by his own hair.

How exactly do Alice and Bob use entangled electrons to win CHSH game with higher than 75% probability?

This may not answer your question, but you might enjoy seeing how the 85.4% probability is derived in http://arxiv.org/pdf/1209.0448v1.pdf and http://arxiv.org/pdf/1209.0449v1.pdf

A note -- if you're linking to arXiv, it's better to link to the abstract (http://arxiv.org/abs/1209.0448, http://arxiv.org/abs/1209.0449) rather than directly to the PDF. From the abstract, one can easily click through to the PDF; not so the reverse. And the abstract allows one to do things like see different versions of the paper, search for other things by the same authors, etc.


Having perfect knowlege about a system, and still being unable to predict the next state seems pretty random to me.

If "perfect" knowledge doesn't include knowledge of other universes which control our own, us being a simulation, then, I mean, I guess it becmes a philosophical question, since if we can't know, well then, by definition we can't know and we have to work with what we got. If what we got is the current quantum state of everything, and it's still random, then Ill continue to call it random.

Yeah you bring up an excellent point.. that there's not a way to prove perfect knowledge of any given system because you can't rule out the existence of factors that you don't know about and are unable to measure. Your idea of "a universe that controls our own" seems a little far out and quasi-mystical to me, but I do think that the probability seems quite high that there may be forces acting upon any given system which we are not yet capable of measuring (within our universe). After all throughout history science has continually discovered new factors outside of it's previous range of measurement.

I suppose that as long as you're using the word random as a placeholder for a best guess, estimate, or assumption about reality then I think you're on solid ground. I only meant to point out that there's no way of scientifically proving that randomness exists apart from a concept or pointer in the mind of man.

Well, what I meant to mean was that given perfect information about _our_ universe, which would exclude something like the run-time that we're being simulated in for instance, we still can't know the outcome of certain quantum processes with 100% certainty.

Given knowledge of _all input to a system_ and still not being able to know the outcome seems like a good definition for random. You're right, though, it could just have an extremely long period.

You start by asking me to make an enormous leap of faith (free miracle) which is to assume that it's possible to know for sure whether or not you have perfect information about any given system. I simply can't fathom how such an assumption could ever be reasonably made so therefor I really have no way to follow along with the rest of your reasoning. I appreciate hearing you perspective though.

“The hard swallow built into science is this business about the big bang… This is the notion that the universe, for no reason, sprang from nothing in a single instant… notice that this is the limit test for credulity. Whether you believe this or not, notice that it is not possible to conceive of something more unlikely, or less likely to be believed. I defy anyone. It’s just the limit case for unlikelihood: that the universe would spring from nothing in a single instant for no reason… It is in fact no different than saying, “and then God said, ‘Let there be light!’ What the philosophers of science are saying is “give us one free miracle and we will roll from that point forward, from the birth of time to the crack of doom.” -Terence McKenna

Nobody's asking for anything. Its an observation, nothing more - the universe used to exist as a point and expanded from there. Everything we see, everywhere, points to this. No more a miracle than anything else we see - gravity, light, matter.

> the universe used to exist as a point and expanded from there. Everything we see, everywhere, points to this.

Yes but if I understand them correctly most modern scientists think that "everything we see" is only a miniscule fragment of the universe. The vast majority of the universe they assert is invisible and it's characteristics are said to be unknown to man. They use placeholder words to describe the vast majority of the universe such as "dark energy" or "dark matter".

If you hold to such a view then how is it reasonable to assume that science has enough data to draw any conclusions about the mechanics of the universe as a whole ? Isn't it analogous to the proverbial blind man who feels one small part of an elephant and assumes he understands what it is and how it works ?

To be clear I haven't been arguing against the existence of randomness nor against the existence of the big bang, because truly I don't hold any beliefs either for or against their existence. I'm just honest enough to admit that I don't know, whereas it seems most academics at least are convinced that they do know. My larger point is simply that science does not have the means by which to ascertain whether or not these things exist or ever have existed with any kind of reasonable accuracy.

Society just likes to pretend that we know more than we really do for political reasons and because it makes us feel more at ease in general. This psychological phenomena is well documented with vast amounts of supporting evidence dating all the way back through the history of science.

"Perfect knowledge" in this case is probably an assumption as part of a mathematical definition. E.g. "Assume a hypothetical time-varying universe U exists, and the current time state and all previous states of the universe are perfectly known. Iff the following state of U is unpredictable even with this knowledge, U is defined to be truly random."

The idea that randomness has to "come from" somewhere is a different idea, and the question of whether randomness or order is the fundamental state, and the other an emergent property, is an interesting question indeed.

> I'm just honest enough to admit that I don't know, whereas it seems most academics at least are convinced that they do know.

If you don't know, how can you be sure they don't either?

To posit such a thing as "all previous states" implies that a universe is a finite state machine whereas for all we know the universe could be infinite in which case the value "all previous states" becomes a mathematical impossibility.

> If you don't know, how can you be sure they don't either?

I don't mean to assert any claim about individuals and their personal knowledge I'm merely suggesting that in my opinion the global community of scientists as represented in academia, scientific journals, and in popular literature hasn't made a compelling case for having met it's own scientific burden of evidence (scientific method) to be able to say that "science knows".

In the past that burden of evidence was lower because we had reason to believe that the universe was a much smaller place and that we could measure a much larger percentage of it, but given what we know today that burden of evidence has grown tremendously to the point where any serious scientist should admit to himself that science doesn't know.

Regarding infinite states, let's assume infinite storage capacity and a time step approaching 0 (in the limit sense:. It's not science, it's math.

Regarding science, the point is not knowing. Science isn't just answers, it's a process for finding new questions to answer. Something could always come along that radically changes our understanding of some aspect of the universe, but that doesn't necessarily mean what we knew before was wrong, just incomplete. If an old theory explains everything measured up to a point, the old theory is still "right" within the context of those measurements. A new measurement that invalidates the theory doesn't invalidate the previous measurements in almost every case.

It's also important to distinguish between math and science. Mathematicians can make definite claims to correctness because they study "universes" of their own creation. Science only claims correctness in light of current knowledge, within certain error bars. Ignore sociology.

> Science only claims correctness in light of current knowledge, within certain error bars.

I concur, but my point is that with regard to the mechanics and composition of the universe in which we live it would seem that the more we measure the larger those error bars appear to be. Every once in a while measurements come along which multiply the size of those error bars exponentially and once that happens scientists should take note to adjust the English language they use in characterizing the limitations of their own knowledge. Modern scientists seem to be notoriously slow at this and my suspicion is that this is because it would give the impression that certain fields of science are becoming less knowledgeable as time goes on, and that's not good PR. In other words my only complaint here is related to sociology, the use of language.

Thank you for prompting me to refresh my memory on the differences between mathematics and scientific inquery because in so doing I ran across a quote having to do with the role of the theorist (my favorite) who is caught between the two worlds:

"Before an experiment can be performed, it must be planned — the question to nature must be formulated before being posed. Before the result of a measurement can be used, it must be interpreted - nature's answer must be understood properly. These two tasks are those of the theorist, who finds himself always more and more dependent on the tools of abstract mathematics. Of course, this does not mean that the experimenter does not also engage in theoretical deliberations. The foremost classical example of a major achievement produced by such a division of labor is the creation of spectrum analysis by the joint efforts of Robert Bunsen, the experimenter, and Gustav Kirchoff, the theorist. Since then, spectrum analysis has been continually developing and bearing ever richer fruit." — Max Planck

'The Meaning and Limits of Exact Science', Science (30 Sep 1949), 110, No. 2857, 325. Advance reprinting of chapter from book Max Planck, Scientific Autobiography (1949), 110.

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