Via Science after Sunclipse, I find a comment by Greg Egan on The n-category Cafe where I was led to this letter to New Scientist:
Superluminal siblings
22 September 2007
From New Scientist Print Edition.
Nick Webb, London, UK
Robbie and Fred are twins who live together. Wearing identical suits, they leave their house at the same time heading in opposite directions. One twin carries a hidden green wallet; the other has a red one. The wallets are not visible.
Unfortunately, Robbie is mugged and the redness of his wallet is revealed. In quantum terms he is measured and forced to take a value.
An observer can now deduce that Fred’s wallet is green, and if put to the test this will prove to be the case no matter where or when Fred is interrogated.
There is no need for faster-than-light communication or spooky interaction at distance – just knowledge of the initial conditions. I can’t see anything wrong with this analogy. Am I missing something?
The editor writes:
No, it’s exactly right.
At which point my brain just exploded.
Um, isn’t that just Bertlmann’s socks all over again?
Maybe the original was horribly wrong, so just wrong is an improvement?
Yeah and I think John Bell is spinning in his grave.
Did you see the New Scientist fellow’s reaction? “The editor’s comment was cut back so heavily from the original that it ended up being wrong.”
I’m not sure how that works.
Firstly, with the wallets you can only ask of each one “What is its colour?”, or in this case, specifically, “Is the colour red or green?” For quantum particles, you can ask many different questions. For example, if you are looking at spin-1/2 particles, you can pick any direction in space and ask “Is the particle spinning parallel or antiparallel to this direction?”
If you create a pair of spin-1/2 particles with their spins perfectly “anticorrelated” (for example, this can happen if a spin-0 particle decays into two spin-1/2 particles), then if you measure both spins along exactly the same direction — call it direction A — it will turn out that if particle Fred has its spin parallel to direction A, then particle Robbie will be antiparallel to direction A, and vice versa. So to that extent, the coloured wallet analogy holds.
But that’s ignoring everything that’s interesting about quantum entanglement! Suppose you pick another two directions for spin measurements, and call them B and C. To make this concrete, suppose the angle between A and B is 120 degrees, the angle between A and C is also 120 degrees, and the angle between B and C is 60 degrees.
Now, imagine measuring the spin of particle Fred along any direction chosen from {A,B,C}, and measuring the spin of particle Robbie along any direction chosen from the same set. If we get a parallel spin, call the result 1; if we get an antiparallel spin, call the result -1. (I know I said the particles had spin 1/2, but let’s keep life simple by scaling our units this way.) For each pair of particles, multiply the two individual results, so we’ll get a result of 1 if Fred and Robbie are both parallel or both antiparallel to the directions of measurement we chose for them, and a result of -1 if one of them is parallel and the other is antiparallel.
If we repeat the experiment many times, quantum mechanics lets us calculate an expectation value for this product of the spins. From what we’ve said previously, it should be clear that if we choose (A,A), (B,B) or (C,C) as our measurement directions, the expectation value will be -1: when the measurement directions are identical, the two particles are always found to have opposite spins.
But if we choose (A,B) or (A,C) as the measurement directions — directions that are 120 degrees apart — the expectation value for the product of the spin measurements will be 1/2 (because sometimes the result will be -1, but more often the result will be 1). And if we choose (B,C) as the measurement directions — directions that are 60 degrees apart — the expectation value of the product will be -1/2 (because sometimes the result will be 1, but more often the result will be -1).
OK, these are nice simple figures and there’s a certain symmetry here … but what’s the big deal? What’s going on with these particles that can’t be achieved with wallets or socks?
Well, suppose we had actual twins called Fred and Robbie, and each time they left home they were carrying some classical machinery that would determine their answers to the measurements A, B or C as being 1 or -1. To make life simple, suppose we always measure either A or C for Fred, and either B or C for Robbie. Then each time they leave home, there will be three numbers, a, b and c, defined as follows:
a is Fred’s answer if A is measured
c is Fred’s answer if C is measured
b is Robbie’s answer if B is measured
and we must have, also:
-c is Robbie’s answer if C is measured
if we want to get the guaranteed result of -1 when the measurements for both twins are in the same direction.
Now, each time the twins leave home, it must be the case that either:
a(b+c) = 1+bc
or
a(b+c) = -(1+bc)
since if b=-c then everything is zero, while if b=c then all three expressions have magnitude 2, so they can’t all be different.
We can express this result as a pair of inequalities:
-(1+bc) ≤ ab + ac ≤ 1+bc
Then if we take expectation values, i.e. averages over Fred and Robbie leaving home many times, we get:
-1-E(bc) ≤ E(ab) + E(ac) ≤ 1+E(bc)
or |E(ab) + E(ac)| ≤ 1+E(bc)
This is known as Bell’s inequality. If the numbers a, b and c are pre-existing quantities each time Fred and Robbie leave home, this inequality follows from simple algebra, so it must be true.
But if we look at the expectation values for our spin-1/2 quantum particles, they are:
E(ab) = 1/2
E(ac) = 1/2
E(bc) = -1/2
Substituting these values into Bell’s inequality we get:
|1/2+1/2| = 1 ≤ 1+(-1/2) = 1/2 !
So the results we get from entangled quantum particles can’t be reproduced by any kind of “local hidden variables”: non-communicating systems carried by the twins that predetermine the outcomes of whatever measurements might be performed.
So, I’m not too proud to ask. What is wrong with that analogy?
I got one detail a bit mangled in my comment above. Because Robbie’s answer when direction C is chosen for him is -c, not c, the expectation value for the product of the twins’ spins when direction A is chosen for Fred and direction C is chosen for Robbie is -E(ac), not E(ac).
So to get a violation of Bell’s inequality, we need an angle between A and C of 60 degrees, not 120 degrees. Then -E(ac)=-1/2, E(ac)=1/2, and everything works out.
The reasons as to why the analogy is no good are pretty subtle. — well, at least one has to know a little bit about QM to see why the analogy isn’t good.
Looking at Greg’s and Joe’s explanations, I think it is pretty easy to imagine that the original response (“No, it’s exactly right.”) could well have been taken from a heavily cut down response. eg. “It’s exactly right for the case where colour is the only thing that can be measured… (etc)”
But I must say, the more I learn about science the less I find appealing in New Scientist.
Besides Greg’s comments about the analogy with wallets being flawed because you can’t do the wallet color measurement in bases other than {|red>, |green>}, and his demonstration that you can’t violate Bell’s Inequality classically, I have another criticism of the analogy:
Even though we may not know the color of the wallet that a particular twin has, we do know before measurement that the wallet has a definite, particular color. Obviously there’s no “spooky action at a distance” because when you measure the color of one twin’s wallet, nothing happens (or even appears to happen) to the other twin’s wallet. You simply learn which color it was all along.
However, if you have two entangled particles (say, polarized photons with horizontal and vertical polarizations, so basis {|H>,|V>}) in the state |psi>=1/sqrt(2) ( |HV> + |VH> ), the first photon doesn’t have a definite polarization until you measure it, and neither does the second photon. The act of measurement on one photon appears to change the state of the second photon as well as that of the first photon.
I think the notion that photons that are in a superposition of horizontal and vertical polarizations aren’t actually in one or the other state until you measure (in the {|H>,|V>} basis, say) is very important to understanding how entanglement is so strange compared to anything you can imagine classically.
Pete, here’s my take on a way you could extend the colour analogy. Suppose the twins leave home, each carrying a marble and a book of colour swatches (you know, the kind of thing that’s used for matching house paints).
The marbles look kind of muddy unless you hold them beside a colour swatch, and then they have the peculiar property that either they look exactly like the swatch, or exactly like its complementary colour. For example, holding a marble next to a yellow swatch, it will either look yellow or blue, with a 50% chance of either.
If Fred and Robbie happen to check the marbles against swatches that are either identical or complementary in colour, the two colours they see will be guaranteed to be complementary to each other. However, if the swatches the twins use are different (without being complementary), then the correlations between each twin seeing either their chosen swatch colour or its complement will become probabilistic, departing from the “same-swatch” situation in a well-defined, quantifiable way that depends on how different the swatches are.
If this behaviour seems frustratingly arbitrary, I guess the point is that it demonstrate how far it is from the behaviour of any real classical objects. By the time you add the footnote that even marbles with microprocessors, light sensors and a secret radio link to each other couldn’t mimic this behaviour perfectly, hopefully the reader will grow so sick of the ineffectual nature of analogies here that they’ll want to go learn some linear algebra and understand the real quantum system.
Anonime, sure, you can have perfect correlations instead of perfect anticorrelations, and all kinds of other imperfect things in between. At which point, we can only hope that everyone will throw away their colour analysers and run screaming into the welcoming arms of mathematics.
In quantum world you get with probability one or another answer. And there is proven, that particles gets information one about another with speed faster than light, BUT you can’t this effect use for faster than light USEFUL communication/information transmission. For example, you can’t build internet, which using this effect will changes information with infinity speed, like in this experiment one particle know information about another particle with infinity speed.
Just need new teory, that at some physical Nature level, information can be transmited faster than light, but this information is unpredicted and is finded with some probability: information 00 or inforamtion 11. So looks like Nature from one unstable (unpredicted, probable) information form goes/transforms into another stable (unchanged) form, but with finity speed and position…
You just think, that to be in many parts simultaneously is goal (for quantum computation it is…), but maybe it is defect (becouse only with some probability you can get some state, but never HAVE this state always)?
Because it is so important, and some of us need to think in pictures, here’s my attempt at the correct analogy:
Robbie and Fred’s wallet are initially yellow, and remain yellow while left in the dark. But when a wallet is exposed to the light it briefly changes color, either to red or green. It’s random whether a wallet will turn red or green. But once one wallet turns red (or green), you know the other MUST flash green (or red) when it’s exposed to the light.
And there are other ways of getting the wallet to change color – like exposing it to heat. But once exposed to heat, everything you knew about the color has to be forgotten.
And some measurements might produce colors other than red or green.
(And if I’d screwed that up, somebody correct me so I can learn.)
In dark two wallets are grey and you don’t know, which wallet is red and which wallet is green. But if you choose one and look at it in light, then you know what is colour of another wallet.
But you can qubits setup, that if you look in light one wallet and if it red, then another wallet also is red, and if one wallet is green, then another wallet is also green. And if you setup qubits in such way, then how two wallets can be either both red either both green?
In dark two wallets is grey. You take one wallet and expose it to light and you now know that this wallet is say red, then you know, that another wallet is also red (if you expose it to loght). Now you turn of light and two wallets are now again grey and you pick up one wallet to light and now you see that this wallet is green, you look to another wallet at light and it is also green. How this classicaly can be explained that you prepare (set up) many times entanged state of two qubits (wallets) always in same way, but always get answer two red or two green wallets (when one wallet is exposed to the light and then after that another wallet exposed to the light ALWAYS is the same colour like first)?
Or another example. You get either 99% FIRST (first qubit) wallet red and then 99% SECOND wallet (second qubit) is always green (only if first wallet is red), either 1% FIRST wallet is green and then 1% SECOND wallet is always red (only if first wallet is green).
I think I understood, about what this is…
Supose there is two entangled photons, they fly each from another 500km and then if first photon is 0 then another photon is 1 and if first photon is 1, then second photon is 0 (don’t matter how many times you reaped experiment). Photons initialy, when distance between them was 0 (zero) km choose state either FIRST 1 ant SECOND 0, either first 0 and second photon 1. Then they flying long distance in opposite directions and some scientcists waiting for them and say NORTH scientist measure 1, then scientist in SOUTH measure 0 (after when NORTH scientist measure 1). And SOUTH scientist, think, that it was spooky interaction at distance (faster than light communication). But in real entangled photons was changed information before they flew far away each from another in opposit directions. Photons exange inforamtion then they was near each over (when wasn’t distance between photons).
But if you can explain entanglement without faster than light communication, then you still can’t explain superposition, when photon split in two parts, but is always finded in one (of two) direction. If photon split into two parts like wave, then if you measure one part you get photon with 50% probability. But then energy or information from another part must to go back to this one part, which you measure like photon… http://www.upscale.utoronto.ca/GeneralInterest/Harrison/MachZehnder/MachZehnder.html
Nick Webb writes to New Scientist about Bell’s theorem and the conclusion that information has been transmitted faster than light (indeed, backward in time). He describes identical twins Robbie and Fred carrying different colored wallets as they travel in opposite directions.
Concerning what is at stake, Mr Webb has understood it clearly, and he has it exactly right. But concerning the strange nature of our world, Mr Webb has it exactly wrong. In fact, what the theorem of J.S. Bell (1968) demonstrates is simply that the world Mr Webb describes is not the world in which we live. The most comprehensible and straightforward version of Bell’s theorem was created by Nick Herbert and published by New Scientist (1986). (Herbert’s proof can be read at http://quantumtantra.com/bell2.html.)
In Mr Webb’s reasoning about red and green wallets, the wallet color represents the spin of an electron – whether that spin points up or down. But we live in a three-dimensional world, and the spin of the electron must have three components corresponding to the x, y and z directions in space. Dr Herbert makes a straightforward argument about what would happen if each ‘twin’ (electron) started life with three separate ‘wallet colors’ (spins) corresponding to the x, y and z directions. He follows the reasoning for a hypothetical Ms A who has turned two spin directors along the directions x and y. Herbert goes on to describe the way the world looks to Mr B, who happens to use spin detectors that are 30o rotated from Ms A’s detectors in the xy plane. From this simple scenario, Herbert proves that Ms A and Mr B cannot both experience a world in which ‘wallet colors’ were fixed at the moment the twins separated.
The scenario as described by Mr Webb is called by physicists ‘local realism’. What Bell’s Theorem demonstrates is precisely that local realism is inconsistent with quantum mechanics. Experiments (Aspect 1981) have shown that the world we live in is the quantum world, and not a world that is ‘locally real’.
Our intuition runs deep: objects have separate, independent existence, and the past causes the future but not vice versa. It seems to us that this is logic, not physics, and that the world cannot possibly be any other way. But indeed the laws that govern our world are neither causal nor separable. It is exactly this insight that prompted Richard Feynman’s remark, “Anyone who is not shocked by quantum theory has not understood it.â€
J. S. Bell, 1965, Physics 1, 195
N. Herbert, 1986, New Sci 111, 41
A. Aspect, P. Grangier, and R. Gerard, 1981, Phys Rev Let 47(7):460-463
Quantum mechanic is 1% true and 99% bullshit. Nobody know what is behind quantum mechanic. I think behind quantum mechanic is analog world. In analog world one particle can have infinity small degree of freedom. For example, 2^n states, I can explain with analog world, for example then n=2, then say one particle can be rotated about another particle 90|00>+180|01>+270|10>+360|11>. If are more states, then more posible rotations can be, and you say 2^1000 states can split into tiny positions… And all posible interference in superposition can be expalined just like analgo rotation one particle about another particle with infinity or 2^1000 precision. So quantum mechanics is just projection of analog nature, which has infinity precision… And with infinity precision is possible describe infinity many states and all quantum mechanical interactions in superposition. To understand how work our Universe is NP-complete problem. Nobody undesrtand quantum mechanics, becouse behind quantum mechanics is calculation, which is NP-complete with infinity precision. If I don’t understand quantum how computer work and if I nothing know about computers I can think, that it is a miracle. If you don’t understand how quantum mechanics work, then you can think, that this is God or miracle. But maybe quantum mechanic is based on classical rules? To simulate on computer quantum mechainc need exponentional power, but to simulate classical phisics with infinity precision, also need exponentional power. So what magical has quantum mechanic?
Qubit? Is that you?
Just because you don’t understand it doesn’t mean its bullshit.
And, damnit, quantum mechanics aint’ analog:
http://dabacon.org/pontiff/?p=882
Pete, I take your point. Still, when you tell someone “Your mistake is assuming the wallets’ colours are initially determined”, they’re quite likely to respond “Oh yeah? Prove it!” Then there’s really no avoiding beating them over the head with Bell’s theorem.
Looking for the simplest possible explanation is great, and if someone’s willing to take it on faith that the proper description is |red green> + |green red>, that’s something, but I suspect the correspondent here had already heard of superpositions and was nonetheless angling for some local hidden variables.
I think there was a nice paper by Peres a few years ago that put various measurement combinations in bins in a table, and gave a fairly painless argument that showed why they couldn’t arise if the results of all measurements were pre-existing quantities. But we’re stuck with the fact that you can’t rule out hidden variables without invoking more than one observable, so any explanation of how the “definite colours before leaving home” scenario can be experimentally falsified has to invoke something more complex than wallets that are always either red or green.
I have three proposals:
Either quantum mechanic is result of analog classical mechanics, or quantum mechanic is GOD, either quantum mechanic is result of many universe interaction and then quantum mechanic is many GODs (multiGod).
http://quantumtantra.com/bell2.html 99% of proofs and text is bullshit… There don’t need rotate 0, 30, 60, 90 degrees, to understand, that entanglement is faster than light (enough choose arbitrary rotation of both spot-detectors, becouse you always get 0 or 1 (classicaly you must get arbitrary polarizastion)). What is diferent or rotate 60 degrees or rotate, one spot 30 degrees and another -30 degrees? This is the same.
I adored your peculiar marbles Greg. 🙂 And the thought of MPUs pre-programmed with a pseudorandom number generator made me LoL and gave me new insight into hidden variables issues.
But whenever I’m struggling, I find a well-meaning switch of metaphor doesn’t help – I really need the explainer to bring their armies to my “battlefield” and populate my space, and beat me there. And I didn’t read Nick’s letter as an EPR-style challenge to QM that needed steam-rollering with Bell’s inequality, just an honest misunderstanding about the wallets’ initial state being |red green> + |green red>. On reflection, my wallets ought to have disintegrated as soon as exposed to the light – corresponding with the photon case Joe outlined, and that was where I should have been upbraided. But anyway, I wanted to say to Nick, ‘Look, your mistake is assuming the wallets’ colors are initially determined. They’re not. The color isn’t chosen until you observe it. So yes, if Fred and Robbie are sufficiently far apart, then you do need “faster-than-light communication or spooky interaction at distance” (unless I can persuade you to give up a little causality and buy into the Transactional Interpretation ;))’.
I’m not shy of the math BTW. (Although its not my mind’s natural language.) But I recently tutored a mature student in elementary math, and so am mindful of how assiduous you must be to grapple with quadratic equations and some right-angled trig, let alone the kinda math that my physics degree didn’t cover. And I want to be able to explain this stuff to people on the street, and inspire kids to learn the math so they can understand it. Plus, there’s still plenty of stuff (much of GR, M-theory) where I definitely need the math-lite version…
http://quantumtantra.com/bell2.html there is faster than light comunication during entanglement. I explain.
Each photon is 2D wave rotated at arbitrary angle (for example 20, 30, 40, 64, 83 degrees). Polarized photon is 2D wave rotated either 0 degrees, either 90 degrees. Single blue unpolarised photon is pumped with laser in some cristal and then become two entagled unpolarized red photons flying in oppsit directions. If you put polarized glass (detector) then unpolirized photon has 50% probability pass trough this polirized glass (becouse either photon pass, either photon is reflected). If now here flying polirized photon then it 100% pass if polirized glass (detector) is 0 degrees polarized and photon is also 0 degree polarized and reflect if photon is 90 degrees polarized, when glass is 0 degree polarized. And if glass is 90 degree polarized then trough this glass can pass only 90 degree polarized photons.
What is probability to pass photon through 0 degrees polarized glass if photon is polarized say 30 degrees? Answer: (cos(30))^2=(cos(pi/3))^2=0.75. So probability, that photon pass through the polarized glass is (cos(x))^2, where x is polarization angle.
So If we put detector A to measure one red unpolarized entangled photon, then we measure 50%, that photon pass trough polarized glass, don’t matter, what angle you rotate this glass. The same for B detector – don’t matter how you rotate polarized glass, you always with 50% probability will measure second red entagled photon.
Now detector A and detector B you rotate by angle 0 degrees. And you see, that if through detector A photon pass, then photon pass also through detecor B. If photon don’t pass through detecor A, then photon don’t pass trough detecor B. In classical way, this must be unrealted – photon must pass with random probability detector A and detector B. So this is evidence that probability always is related on two measurements in both detecors A and B.
By the way, this experiment can be explained with analog nature and then don’t need faster than light communication. When two red photons is entangled, then they have analog information with infinity precision about how they do this time…
Entanglement can be explained with double probability. One kind probability for unentagled photon and another kind of probability for entagled photon. If photon unentagled, then this is fine, he is described with first kind probability like usualy everybody do: (cos(x))^2, where x is photon polarization angle for 0 degrees (horizontal) polarized glass (for vertical polarized glass: (sin(x))^2).
Now what if two photons is entangled? Then they has initial information about how they must behave (and then no need faster than light communication).
So supose, that two entangled photons is both polarized at 67 degrees and we measure one photon with detector A and another photon with detector B. Both detectors A and B we rotate 0 degrees. Then two photons before they fly far away each from over decide, that if will be detectors polarized at same angle, then they do the same thing (pass or not pass trough polarized glass). So there is (cos(67))^2=~0.15267 (~15%) probabilty, that both photons will pass through polarized glass and roughly 85% probability that both photons will be reflected from polarized glass. So here is only two passible accidents: either both photons with ~15% probability pass trough detectors A and B (one photon through detector A and another through detector B), either both photons will be reflected with ~85% probability from horizontaly polarized glass.
Now suppose, that again flying two polarized photons a and b. Photon a polarized 67 degrees and photon b is polarized 67 degrees. Now detector A is rotated 0 degrees and detector B is rotated 30 degrees. Probability, that photon a will fly trough detector A is (cos(67))^2=~0.1525670814 or about 15%. Probability, that photon b will pass trough detector B (through polarized glass) is: (cos(67-30))^2=(cos(37))^2=~0.637818677 or roughly 64%. Match probability of two photons (two photon pass or two photon was reflected) is (cos(30-0))^2=(cos(30))^2=0.75. So suppose we made experiment 100 times. And in this experiment imagine both photons was polarized at 67 degrees. And need, that 75 times both photons either will be pass, either both will be reflected. So photon a 15 times pass detector A and 85 times was reflected. And photon b 64 times pass detector B and 36 times was reflected. So what we need to do? This: 36+15=51, becouse photon a can be 15 times pass, when photon b also pass trough detector. And photon b can 36 times be reflected. So 51
So 51 less than 75. How this can be, that photons 75 times of 100 match?
Maybe photons work with amplitudes, but not with probabilites?
But photons don’t fly always with 67 degrees polarization. They fly with arbitrary (random) polarization but in such way, that photon a polarized by angle x and photon b polarized by angle x. And so there is double probability: probability to pass trough polarized glass and probability to do the same as make another polarized photon. If polarized detectors A and B are rotated by same angle y, then photon a and b will pass trough detectors A and B or both don’t pass. And match probability (both pass or both don’t pass trough polarized glass) is 100%. If A detector is rotate 0 degrees and b detector is rotated y degrees, then match probability is (cos(y))^2.
So double probability explain without faster than light communication, that both entangled photons have initial information (decition) how they behave when will pass trough polarized glasses (detectors). You can disagree. And you can’t proof the true. Maybe there is faster than light communication and maybe not, you can’t know this.
You can explain how photon behave in Mach-Zehnder-Interferometer or double slit experiment (becouse in this both case also need faster than light communication) and you trying explain or proof, that entanglement is or isn’t faster than light. You can’t proof this and you don’t know this…
P.S. What distance is from crystal (from which fly two entangled photons) to detector A and detector B? If we measure first of all photon in detector A and then after say 3 hours photon in detector B, then what will be? One photon is 3 hours absorbed and another photon after 3 hours is measured with detector B. And how then first photon can be entangled with second photon if first photon no exist 3 hours? Or measurment need do to two photons in same time? Interesting then, how scientciest make measurement of both photons in same time, if photons was 500km from each over? If don’t need measure photons at same time, then about faster then light communication you can forget forever.
Crap must fight resistance to feed quantum trolls. Darnit, in one universe I think I just did.
Damn, New Scientist is so crap, they will literally publish any old story by any old crank and sell it as a `renegade view’ held by `some scientists’. I want to start my own magazine called REAL scientist.