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EPR (Einstein Podolsky Rosen) paradox Answered

. Following a link in one of kelseymh's posts, I started reading the Wikipedia page on Bell's Theorem. Before I got through the first sentence of the Overview, I got sidetracked on the EPR paradox (read about it before, but found I had forgotten or misunderstood a lot of it). A lot of it still doesn't make sense. They didn't teach us a lot a quantum physics back in the '70s. heehee
. Looks to me like I need to understand EPR before I try to go any further. Any volunteers to try to explain it so that Joe Plumber can understand?


. Whew! I been reading Bell's Theorem. Meas in QM, Copenhagen interpretation, and misc others at Wikipedia.
. I'm having trouble getting my brain wrapped around wavefunction and collapse. Is wavefunction only a convenient way to say it's located somewhere close to here, but we're not sure exactly where until we measure it? Observer may not know if S's cat is dead or not, but the cat is definitely one or the other (and the cat knows)?
. At any particular point in time/space the object is in a definite spot with a definite set of properties, but we can only make a reasonable guess?
. Time for more aspirin.

Hey, NM, sorry I missed this post of yours. I'm going to try to write a reply here, but it ought to be a separate Physics topic (sigh...). ... Yup, it got way too long. See my Physics topic instead.

You're welcome! I tried to include both arm-waving conceptual stuff, and some concrete mathematics.

If you've played with diffraction gratings, interference fringes, or even standing waves in water, I think that's enough to give you a vague mental picture of wavefunctions.

For some mental imagery on how they can "also behave like particles," I recommend reading up on solitons.

This may be the stupidest idea ever, but what if "spooky action at at distance" is a reflection somehow? Not in the sense of one particle being an illusion, but almost like your reflection in a mirror, except that unlike the reflection of yourself in the morning, it has mass and can move and affect its "sister" particle. Or is that totally crackpot and nonsensical?

That is actually not a bad "classical metaphor" for what's going on. The two "parts" of an entangled system are as tightly and inextricably bound as you and your reflection.

The "weird" quantum mechanics part is that the binding is (apparently) instantaneous. For a real reflection in a mirror, there is a delay between your motion and your perception of the reflection's motion, dictated by the round-trip time for the light from you to the mirror and back again.

The Nature article I had cited elsewhere was explcitly testing that instantaneity for a system of two entangled photons, separated by some 20 km.

Oh cool, I just stumbled on ths why didn't anyone tell me ? :-) I have got to take some time and read through this more carefully....I have done a cursory reading of all the posts, but not the links. I love this stuff, or at least, what amount of it I can grasp ( sadly my math skills are VERY lacking in this area).

You wrote, "I love this stuff ... (my math skills are ... lacking in this area)." I would highly recommend Feynman's ''QED: The Strange Theory of Light and Matter. He was able to describe wavefunctions, interference, etc., without any mathematical equations.

Thanks, I will look into that.

It isn't just this stuff as it were, that I love though....I like to stretch my thinking in lots of ways, including the imagination thing I mentioned in another forum (Hawking? ;-)

I was once asked if I could "see" in my mind's eye, a mobius strip, then I was asked to cut it length wise, and then again. The second (or was it the third?) cut, caught me by surprise.
Then I was asked to imagine a "2 dimensional" mobius strip. That took awhile and I am not sure I had it quite right when he showed me his rendition (drawn). I would love to be able to see a 3-d version of a mobius strip (that is, a structure that is twisted in each of the 3 dimensions).

You wrote, "I would love to be able to see a 3-d version of a mobius strip (that is, a structure that is twisted in each of the 3 dimensions)." Try a Klein bottle.

There's a "puncture" needed when building one only because what you're building is a "projection" onto 3D space. If you could build (or visualize) the object in four spatial dimensions (not "spacetime"), there's wouldn't be the self-intersection.

This is the same effect as if you try to sketch a Möbius band on a sheet of paper. The line you draw for the edge has to cross itself because the twist is getting "flattened out."

Yeah, I have seen the Klein bottle before....there is something about it that bothers me, but I don't yet have the vocabulary to describe what I am thinking.

Oh good, it is by Richard P. Feynman, I have a few of his books already (including: Surely You're Joking, Mr. Feynman? ) :-)

Oh sorry Goodhart, I should've remembered you are interested in this kind of thing... Yeah, what's cool is we have our very own particle physicist talking about it on here!

No need to apologize, I was joking about the tell me part. I need to dig out my books and add to the forray a bit

Haha, you're telling me no need to apologize? That's quite a switch. :D

Hmmm, well looks left......looks right lately it seems I have either rubbed off on a few others, or they have caught my disease since I have been having to do that a bit more lately also (tell others they needn't apologize :-)

Okay, the EPR "paradox." I want to try to give an example of an EPR system and what it's good for, rather than confusing readers with "mystical quantum uncertainty" bulls**t. The BaBar experiment, which I've been working on for the past 12 years, took advantage of an EPR system to make the precision measurement for which it was built. The US and several European countries wouldn't spend $300 million on some mystical quantum BS. Really, they wouldn't.

So...at BaBar we collide electrons and positrons to make pairs of B0 and anti-B0 mesons. They come in pairs just because of conservation laws -- since the e- and e+ don't have any net b-quarks, the system you produce must have a net b-quark content of zero (i.e, one B and one anti-B).

B0 mesons can decay in many (hundreds) different ways. One (of several) is interesting, namely B0 -> J/psi K0S. This is interesting because the anti-B0 can decay to precisely the same final state; in most cases, for example B0 -> D- µ+ anti-nuµ, the corresponding anti-B0 decay has all the signs reversed (anti-B0 -> D+ µ- nuµ.

BaBar's main goal was to measure CP symmetry violation. That jargon means measuring a difference in the decay rates (probabilities) for B0 to a particular final state, compared to the rate for anti-B0 to the same final state.
In order to do that, you have to know, when you reconstruct what happened in the decay, whether it was a B or an anti-B that decayed in the first place. This is where EPR comes to our rescue.

B decays where a lepton (e or µ) and neutrino are produces, directly identify (tag) which flavor of B decayed: a positively charged lepton means a B0, while a negatively charged lepton means an anti-B0.

As I mentioned earlier, at BaBar we produce B and anti-B mesons in pairs. A priori you don't know which is which when you reconstruct an event (one collision with the particles produced in the two B-meson decays) However, what we can do is fully reconstruct both B decays. That means that the various detector components successfully find all of the charged and netrual particles produce, and group them together correctly.

We (actually our thousands-of-CPUs computer farms) then filter through all the data, and pick out events where one B decays to a set of particles including a lepton ("semileptonically"), and the other decays to J/psi K0S. The charge of the lepton tells us whether the "tagging" B was a B0 (l+) or an anti-B0 (l-) at the instant it decayed. Because the B-anti-B system was produced in a correlated way (as an EPR system) we know that the other ("signal") B must have been an anti-B0 (l+ tag) or B0 (l- tag) at that time.

We can then count the rate (branching fraction) at which tagged B0's decay to J/psi K0S, compared to the rate for anti-B0's. We see that the rates are not identical, in fact the asymmetry (difference divided by sum) is around 72%!

We could not do this kind of measurement without the correlation that the EPR "paradox" provides us, between the produciton of the B--anti-B system and the decays of the two mesons.

We (actually our thousands-of-CPUs computer farms)

The creation of a quantum computer would definitely help your cause here :-)

That would be ironic, wouldn't it ;->

I've gone back over my two excessively long postings from yesterday evening. I think I can describe an EPR measurement much more simply than that. Here goes.

Set up an experiment where you produce a pair of identical particles (electrons, photons, whatever), in such a way that the sum of one of their properties (lets say total spin of the two electrons) is constrained to a specific value (like zero).

Treating the pair of electrons "classically", put them on trajectories such that they become separated in space (do this with some charged metal plates, for example). Use a device to measure the spin of one of the electrons (is it pointing up or down). Now you immediately know the spin of the other electron must be down (since the total spin of the system is constrained to be zero). If your partner far away sets up their detector, they will definitely measure their electron to have spin down. So far, there's nothing weird or magical going on, just algebra: Stot = S1 + S2 = 0; you measure S1 = +1, so obviously S2 = -1.

If you always measure spin up, your partner will always measure spin down, and vice versa. This is true even if you and your partner do your two measurements simultaneously (we're all sitting on the surface of the Earth in buildings, so issues of "relativistic simultaneity" don't matter).

Suppose that you and your partner far away have agreed to keep doing these spin-up vs. spin-down measurements and you both keep getting +1/-1 measurements. But you decide to adjust your detector, and measure spin-left vs. spin-right instead. Now, your partner is going to start getting results where he measures (there are some subtleties here which I will ignore for now) spin-right when you measured spin-left, and vice versa. Even if your partner doesn't know you switched your detector, and even if they don't switch their detector themselves, the correlated measurements will still be there.

But wait! I thought the electrons were coming out spin up-or-down. No; they're in a coupled (entangled) state where their total spin has to add up to zero, but the individual spins of each electron are indeterminate -- the value you get on any measurement is "random", with some probability distribution.

No matter what spin value you measure, the other electron is "forced" (projected) into the corresponding opposite spin, instantaneously. That is what Einstein called "spooky action at a distance," and this is what the EPR "paradox" is about.

So, the paradox in a nutshell is that "measurements performed on spatially separated parts of a quantum system" affect each other?

Yes, and more. A measurement performed on one "component" (we really do not have any good words to describe quanta or their properties) of a correlated ("entangled" in the jargon) quantum system instantaneously puts the other component(s) of that system into precisely defined states correlated with the measurement that was made.

The "paradox" has two parts. First is the problem of projection -- both components of the system are quantum mechanical. That means that you could choose to measure either one, and the result of your measurement would not be knowable (or even defined) until after you make the measurement and the wavefunction's probabilities get "evaluated" (I am avoiding using the word "collapse", becuase I don't like it). If the probabilities happen whichever side you choose to measure, then how can measuring one project out the other?

The second paradoxical issue is simultaneity. The projection happens, in the orthodox view of QM at the same time the measurement is made. That trivially violates special relativity in lots of ways. Nevertheless, it appears to be true, and was recently tested with a beatifully macroscopic experiment.

. So it boils down to: there is a "force" (apparently FTL) that links "quantum objects" and we don't know what it is? The paradox is not really a paradox, it just points out that there's something going on (entanglement) that we don't understand?

Not exactly. We (physicists) do not actually believe there is a force, or a communication, going on. The Geneva experiment, and in particular the quantitative limits they put on possible communication to "explain" the correlations, is more or less a reductio ad absurdum.

FTL communication, and even more the necessary of a special, preferred reference frame, is such a blatant violation of special relativity that we don't consider it a sensible or realistic model for what's going on.

The quantum world is just different than our classical expectations. Which is just what you said: The paradox is not really a paradox, it just points out that there's something going on (entanglement) that we don't understand.

. What is the Geneva experiment? All I can find is the "little bang" scheduled at LHC and that doesn't seem to fit. . . Then entanglement exists? The state of two (spatially separated) objects collapse/decohere instantaneously? . OK. If FTL communication is out, what is the best guess as to how entanglement works? Does decoherence (not sure that's the right word) have universal range? . . Owww! This makes my head hurt. :)

I didn't reply to all of your questions in my previous post. You wrote, "If FTL communication is out, what is the best guess as to how entanglement works? Does decoherence (not sure that's the right word) have universal range?"

If you're asking for a nice, Enlightenment Era, reductionist/mechanist explanation, you're out of luck SOL. We (physicists) just don't know. If you believe in Everett's model then decoherence is chimera. If you believe in Mach's principle, then yes, decoherence certainly has infinite range.

My personal perspective is very pragmatic: if you can't measure the time evolution, then QM can do whatever it needs to do. If you can measure the time evolutiion, then intreraction with the environment means you're going to see classical-looking behaviour.

So...for some reason the measurements affect each other, but nobody knows why or how? Wow...

Yes, but I think that depends on what you really mean by "why". An EPR entangled system is one system, not two separate particles. Quantum mechanics requires that you treat a single system in a unified way. Indeed, we use the word "entangled" to specifically mean that you can't break it apart into separate entities.

When you make a measurement on a single QM system, the whole system is affected. That's the nature of QM. Asking the philosophical (ontological) question "why is it that way" doesn't seem very useful to me --- it's kind of like asking "why is the absence of light darkness?"

You could try to ask a related question, "why does the Universe behave quantum mechanically." That question, and corollaries about whether non-QM Universes could exist, will eventually lead you either to the anthropic principle or to a good pitcher of beer.

Well, what I mean by "why" is more "by what mechanism" or "by what cause". But if I am understanding right, the whole thing is that we just don't know at this point.

Quantum mechanics is weird. o_0

Yes. QM is weird; so is relativity. Unfortunately, they also seem to be right -- every proper experimental test we've done has confirmed their predictions At some point it becomes hard to ask why things are as they are -- why does oxygen have eight protons and eight neutrions? As a real working physicist, I use both every day in my work, and I couldn't get any results without them.

Sorry, I thought I provided a link to the abstract. The Nature article is titled "Testing the speed of 'spooky action at a distance'"; but there was substantial press coverage elsewhere in the science community.

You asked, "Then entanglement exists? The state of two (spatially separated) objects collapse/decohere instantaneously?" Yup. It's passing strange, but for sure it's real.

We do not have any sort of consenus model for what is "really" happening. This is one of the cutting-edge research topics. It has applications both in fundamental physics (understanding the Universe), as well as in quantum computing, encryption, blah-blah-blah applications. There are lots of theories/models, but really, we don't know much more than you do.

. Ah! You gave the link earlier, but I didn't make the Geneva connection. (That sounds like the title of a spy movie. heehee) . . From that link: "exceed that of light by at least four orders of magnitude" . So decoherence is FTL, but not instantaneous? Interesting. . . OK. I think I understand EPR (at least as well as I'm going to). Guess it's time to go back to Bell's Theorem. . This is getting curiouser and curiouser. Has anyone predicted a "bottom" to all this? Or is The Universe infinitely small and large? My head is hurting again.

Beer. Beer stops your head hurting and lets you think about QM issues. Mmmm.....beer.

Give another shot at Bell's theorem. The basic (qualitative) idea is that there are three possibilities for how the Universe works:

1) Quantum mechanics is exactly right.
2) QM is wrong, but the Universe fakes its predictions via non-local classical interactions.
3) QM is wrong, but the Universe fakes it's results via local hidden variables

Bell's Theorem (called a "theorem" rather than a "theory" because it has been proven in the rigorous mathematical sense) tells us that exactly one of those three possibilities must be true. You can distinguish between the three by making measurements of "quantum" systems, and looking at the correlations between different measurements in your experiment.

The "Bell inequalities" are limits that Bell proved -- if you measure correlations higher than a certain fraction, then possibility (3) or (2) above must be wrong. That is what has actually been observed, in many experiments over the past several decades: QM is, as near as well can tell, always correct.

. Ethanol + Nacho = Trouble ( With a capital T... )
. That makes sense. Or at least I think it does. I think I'll ruminate on that for I while and then re-read the Wikipedia page.
. WP needs to add a "... For Dummies" section. heehee

Mmmmm....Kelsey-sleep = equal trouble, or at least many more typos.

Thanks for not pointing all of them out. (1) I didn't mean for that whole second-to-last paragraph to be bold italics (not quite ALL CAPS!!!1!!!, but close enough); and (2) "as near as well can" should obviously have ben "as near as we can". Sigh...

QM often "seems" to make sense, especially when you're a grad student taking notes in class. Everything seems crystal clear and simple, then you try to work through the week's homework, and the whole house of cards comes tumbling down around you.

. From what I can tell, that's part of it, but not all of it. I'm still reading (and re-reading), but, so far, no epiphany.

Very... interesting...

Okay, the EPR "paradox." First off, it's called a "paradox" because it patently contradicts all sorts of assumptions we make about the behaviour of objects in the classical world (see my follow up to Adrian). It is a natural feature of the quantum world, and there is (by definition) no paradox there, just stuff we classical humans can't wrap our brains around. With that out of the way ...

Before I can explain the EPR paradox, you need to understand basis states and superposition. I'm going to do that with a very cool experiment that some people will probably recognize. [I probably ought to write this as an I'ble, but I don't have the time or energy right now...]

First, a very quick introduction to quantum states and (alternative) basis states. We describe quantum mechanical states mathematically, using the notions and notations of coordinate systems. You can identify any point on the plane with (x,y) coordinates, writing r-vector = x*x-hat + y*y-hat, where "x-hat" and "y-hat" are orthogonal (perpendicular) unit (basis) vectors in each direction.

While the location of a point in space is fixed and absolute, the values of its coordinates is not. Consider navigating south of Market in San Francicso. If you have a GPS system, you can use longitude (North) and latitude (East) to identify your position. If you're old school, you can use street locations (northeast and northwest). Your actual location is unique, but the values of the coordinate numbers depend on which coordinate system (basis) you choose.

Similarly we can write (decompose) a quantum mechanical state into a sum of mutually orthogonal basis states, each with a coefficient which is a complex number (amplitude and phase). I will describe a very simple quantum system with just two basis vectors, namely linearly polarized light (for the cognoscenti, you can do exactly the same analysis using a circular polarization basis, but it would be much less accessible to the reader, so don't give me a hard time).

Light can be polarized in any direction -- up and down, side-to-side, or at any angle perpendicuar to the direction of the light beam. If you have a (cheap) pair of polarized sunglasses, take some Liquid Paper and paint a stripe on each lens, then pop them out of the frame. That stripe will define, for this experiment, the polarization direction of the lens. Actually, you're going to need two pairs of sunglasses, hacked the same way.

Take a non-coherent light source, like a nicely focused incandescent Maglite, and put one of your polarizers (lenses) in front of it with the stripe vertical. You now have a light beam which is 100% "vertically polarized." Keep it and cherish it, because shortly you're going to make it very confused.

Take a second polarizer, and put it in front of the first with the stripe horizontal. No light will come through. Since your beam is 100% vertically polarized, obviously it is 0% horizontally polarized, right? Right.

Now turn that second polarizer 45 degrees left (let's call it NW, by analogy with the streets I mentioned above). You'll see that some light (in fact, half the light) comes through. the 100% vertical polarization can be equally described as a sum of NW plus NE polarization (this is just vector arithmetic; technically V = 1/sqrt(2) NW + 1/sqrt(2) NE). By putting the NW polarizer in front of the beam, you're picking out just the NW component of that sum.

So far, all this is simple and obvious, right? Put a third polarizer in front again, this time oriented 45 degrees right, NE. It's dark, right? Obviously. NE is perpendicular to NW, and by the same argument as before nothing comes trhough.

Now for the fun part. Set up two polarizers, one N and one E (horizontal), in front of each other. This is back to the setup I described earlier. No light gets through, since the two are orthogonal.

Take a third polarizer, and put it in between the two you have set up, oriented
NE. What do you see? There's light getting through! about 25% intensity, but definitely not dark. "What the BLEEP is going on?" (no, Ramtha is not channeling the photons).

Follow the changes of basis in sequence. You start with 100% N polarization, which can be written as "1/sqrt(2)NW + 1/sqrt(2)NE". The NE polarizer picks out just the NE component at (1/sqrt(2))2 = 1/2 intensity. Now, NE can equally well be rewritten in the (N,E) basis as "1/sqrt(2)N + 1/sqrt(2)E". The next, E polarizer picks off the E component of that, again at 1/2 intensity. The net result is 1/4 the original intensity, because you've changed basis twice.

This change of basis will be an important piece of what's going on in EPR systems.