What is Quantum Entanglement

Of all the weird concepts in Quantum Mechanics, entanglement is the one that I still can’t get my head around.

Those books / web pages that attempt to explain the concept non-mathematically (since there’s no chance of me understanding the maths versions), seem to always describe the situation in one of two ways:

  1. Two particles are emitted, and they must have opposite spins. When you measure one as ‘up’, you know the other must be ‘down’.
    Well, big deal. If I have a bag containing a red and a green apple, and I take out a green apple, I ‘instantly’ know that the other apple is red. Nothing about this is contrary to Newtonian expectations.

  2. When two particles are emitted, they are in a superposition of states. Measuring one fixes the other into a definite state.
    Right, but how can we know a particle is in a superposition? If we can know then it seems to me that entanglement can be used to transmit information, and all explanations are keen to stress that this is not possible.
    If not, then how does the situation differ, measurably, from the situation as outlined in 1?

In regards to you red-green apple analogy and point 2.

If you could say: “I’ll take the red apple out so the other person can then see the remaining one is green.” then indeed you could transmit information (in this case a bit at a time).

But you have no choice as to which apple to take out. You can make a measurement to determine if there is a red (or green) apple but that is not the same as picking the red apple.

I realise that I was being ambiguous, but I meant in point 1 a random pick.

Anyway, what does this mean as a whole? Are you saying that Entanglement is like the situation I described in point 1? If so, then why has this term been coined; a classical interpretation suffices just fine. What’s strange about it?

No, your apple analogy is wrong.

You don’t have a bag containing a red apple and a green apple. You have a bag containing two identical apples of no color at all. Yet when you pull out an apple and study it, you see that it has a color. And no matter what that color turns out to be, the other apple turns out to be the other one.

The question then becomes, how does the second apple “know” what color it has to turn out to be? It can’t be information transmitted from one apple to the second apple, because you can separate that apple by any arbitrary distance so that it would take a speed faster than the speed of light for information to reach it, yet it still “knows” the answer. This remains true even though the color of the first apple is truly random and totally unpredictable by any known means.

That question is unanswerable at the present, and that is the mystery behind quantum entanglement.

As for 2, superposition of states is an entirely different quantum phenomenon than quantum entanglement. Superposition is the problem behind the famous two-slit experiment in which an interference pattern can be built up even if photons are sent through the slits one at a time. It would seem in the classical world that a single photon could only go through one slit, but the quantum world ignores “common sense” and demands its own interpretation of reality.

What is strange about quantum entanglement is that the phenomenon is nonlocal–that is, it doesn’t work by any of the normal causal mechanisms (i.e. exchanging real or virtual particles) but rather by some other link which does no obey normal local causality. The net result of this is that a pair of entangled particles are always in complementary states, regardless of how far apart they are. This is the “spooky action at a distance” that Einstein notably derided, and the EPR Paradox was indented to demonstrate that there is, in fact, a hidden mechanic which allows this phenomenon to occur without requiring an actual link; instead, the particles would share a set of “hidden variables” which would predetermine the outcome, and then God wouldn’t be playing craps with the universe. Unfortunately for Einstein, Rosen, and Podolsky, some smart-alec Irishman named John Stewart Bell demonstrated that there is a minimum uncertainty for distant objects to be related by these variables, and thus if they exist, they must to be nonlocal (i.e. shared across the entangled link), thus dispensing with local realism (the requirement that things are causally connected). Thus, Bells’s Inequality turned the EPR paradox (which was intended by its authors to be a patent absurdity) to be true, and you either have to dispense with causality on the quantum level (leaving you with an interpretatin like Bohmian mechanicsw) or you have to go with some other interpretation where variables are stored behind some hidden, unpassable veil (giving you something like a Many Worlds or Convergent Histories interpretation). Or, you can just shut up and calculate, which is what most QM theorists do, since the interpretations all give you the same practical result, anyway.

Entanglement isn’t useful for transmitting information for the same reason that “looking” at a particle interferes with the double slit experiment; because by examining it, you interact with it, and interacting with it destroys the “purity” of information about its prior isolated state. There are no classical measurements in quantum systems, and by interacting with Particle A you destroy the unique information about its previous quantum state and thus what state Particle B is in. You can interpret its new state if you have information about that whole system, and then you can send it to the other side of the link where Particle B resides, allowing the person at the other end to receive a message via the quantum entanglement link, but because the information about the system Particle A is now in has to be transmitted via a classical channel before you can figure out what the state of Particle B means, it’s no faster than just sending a message before. There are some very bright people trying to find a workaround for this involving systems of multiple particles that are still sufficiently decoherent that statistically pull real information out but nobody at this point has a lot of hope that this will ever work, even in theory.

Side note: Bell, being a vegetarian and compassionate animal lover, altered the Schrödinger’s cat in his own lectures such that the decay of the isotope in the box opened a can of cat food; hence, rather than being dead or alive, the cat was hungry or not hungry. Og bless the Irish.

Jim Al-Khalili’s Quantum: A Guide for the Perplexed is about the best book I’ve found for explaining this to a non-technical audience and has some beautiful illustrations besides. Give that a shot.

Stranger

OK, so what about this situation requires a Quantum explanation as opposed to a classical one? Why do we say the other apple changes state at the same instant that I view the current apple, instead of just saying that both apples became coloured when they were separated?

Why does it need to?

(To clarify, I’m not some kind of “critic” of QM, I’m simply trying to understand).

Surely it’s some kind of superposition. If we’re saying that a particle that’s separated from us “acquires” the state up, when we measure its entangled partner as down, then surely we’re saying it was neither up nor down prior to our measurement. A superposition of states, no?
What I’m confused about is how we know its state wasn’t set, how we know that both particles don’t have a concrete state at the instant they’re separated.

Or if you have Garfield in the box, he’s either hungry or hungry.

This is what Stranger (and Bell) meant when they referred to “hidden variables.” You’re proposing that when you create an “entangled state” of two apples, the apples collude to decide on their color: “I’m red, you’re green.” That is, each apple has a hidden variable describing its determined, but unknown, color.

And this idea is a perfect description of what is really happening in the classical case. If I have two bags, one containing a red apple and one a green apple, and I give one to you, and when you are far away I open my bag to discover a green apple, then I immediately know that your bag contains a red apple. But I do not have to invent “entanglement” to describe what happened. I just say that each bag contains a “hidden variable”–the color of the apple–which I can reveal by opening the bag.

But Bell proved that this sort of “local” hidden-variable theory (local, in the sense that each hidden variable describes some local property) is incompatible with the other probabilistic rules that describe quantum mechanics. The problem is that the quantum apples don’t just have to decide on one color. For the sort of particles that Bell was considering, you can choose to measure “color” (the example given in quantum mechanics is usually a property called “spin”) along any direction you choose. If you have an apple that is definitely red when you look at it from one direction, and you look at it from a different direction, it will have some probability of looking red and some probability of looking green. Quantum mechanics gives rules for figuring out these probabilities. A pair of entangled quantum apples can be set up so that when you measure both apples along any given direction, they always give different colors. It turns out that these entangled particles violate the probability rules that quantum mechanics gives, meaning that in fact they can’t have a definite color (either that, or one of the other quantum axioms was wrong).

To answer in a little more detail, hopefully without too much math:

One quantum property often discussed in connection with entanglement is something called “spin”. Never mind exactly what spin is: Suffice to say that it’s basically a vector, and can in principle point in any direction you want. But when you measure it, you have to pick some direction to measure it along, and the result of that measurement will always be either positive or negative. I can have an electron which absolutely, without a doubt, has its spin pointing straight up. If I hold my measurement device so it’s pointing up, then it will always measure the spin of that electron as positive. If, instead, I had held my measurement device upside-down, it would have instead always absolutely measured the spin as negative. So far so good?

Well, now suppose that I held my measurement device horizontal, and measured that same electron. What would I get? Well, the only answers I can get are positive or negative: An electron can’t have a spin of zero. But positive and negative are both equally good answers here. So my measurement device will randomly give me either answer, with a 50-50 chance of each.

Now what if, instead, I held my measurement device at some angle, neither vertical nor horizontal? I would get a mixture of positive and negative answers, with one more common than the other. The laws of quantum mechanics allow us to calculate just what the mix will be, for any given angle, and those results are confirmed by experiment.

OK, this was all starting with an electron for which we absolutely knew its spin ahead of time, and moving our detector around. What if we don’t know the spin in advance? In particular, let’s suppose that we start with two entangled particles. A typical situation for entangled particles is that they must have opposite spins (for instance, the particles might have been produced by the decay of something that has no net spin, and spin must be conserved). The two particles go their merry ways, and I set up detectors to measure both of them. If I have my two detectors pointed the same way, then they’ll always give opposite answers (one positive and one negative). If I have them pointed in opposite directions, they’ll always give the same answer (either both positive, or both negative). And if I have them pointed at right angles to each other (say, one vertical and one horizontal), then there will be no relation at all between the results: Half the time they’ll agree, and half the time they’ll disagree, and when they agree and disagree is completely random. So far, this can still all be explained by hidden variable theories.

However, suppose I put my two detectors at some other angle relative to each other? I might, for instance, put one vertical, and the other pointing up diagonally at a 45 degree angle. As you might expect, now they’ll sometimes agree and sometimes disagree, but they’ll disagree more often than not. The problem is that the probability that they’ll agree can again be calculated exactly from quantum mechanics, and it can also be calculated based on hidden variable theories, but the two calculations give different answers. The experiment has actually been done, and the results are consistent with quantum mechanics, but not with hidden variable theories.

It is my personal, undereducated (and possibly uneducable) opinion that the non-locality of quantum entanglement is proof that our fundamental construct of what particles and space are is wrong.

When the Theory of Everything shows up, part of its beauty is going to be that common-sense explanations are possible and that paradoxes go away along with notions that entangle two non-local behaviours. My own ignorant gut is that the piece which is most poorly understood is the fabric/matrix/whatever of space itself, and the idea that there is such a thing as a particle. It seems to me that it probably isn’t particles moving through space; it’s space moving–i.e. what we think of as particles is a behaviour of the matrix of space. The nature of that matrix is contiguous in the sense that nothing is isolated from–non-local to–anything else.

I am completely unable to defend that, and don’t expect anyone to waste time trying to educate my three neurons about it…

My larger observation is that when current scientific paradigms begin to produce oddball and self-contradictory scenarios, the underlying paradigm is fundamentally flawed–it’s not just a deficiency of mathematics. In the same way that Special Relativity–however strange and wonderful it is–can be explained to the Special Needs crowd such as I, quantum entanglement will have an equivalent common-sense non-paradoxical explanation some day.

Nitpick: “not consistant with…[local] hidden variable theories.” One can construct a theory or nonlocal hidden variables that is fully consistant with these results, or indeed, any set of results you can come up with. The result isn’t especially meaningful, of course, because you can’t access nonlocal variables and thus, you can’t distinguish between “happened because it was planned” from “happened because of ‘spooky’ connections at a distance” from “happened because that’s just the way it shakes out”.

I only mention it because the Bohmian interpretation lets me sleep at nights, whereas the whole “collapsing probability waveforms” is distrubing in an existential horror way, and “consciousness causes collapse” is just irredeemably silly. I can deal with nonlocality better than the idea that nothing is “really real”; hell, you can’t even parse that in a grammatically acceptable sentence.

Stranger

Yeah, but unlike a sort of non-local story, the Bohmian interpretation is explicitly non-local. I think if I had to go with a pilot wave type interpretation I’d choose Cramer’s Transactional interpretation. I move backward in time a lot.

Nitpick noted and appreciated. You’re quite correct, and I happen to agree with you on the æsthetic aspects, as well.

I stepped away from the computer after writing this post, and Chronos said everything I wanted to say, only better. But I suppose it doesn’t hurt to have the same thing explained in different words, so I’m posting anyways.

There are a couple things that happen in the real quantum experiments that are missing from your apple analogy, Mijin. These extra factors rule out any classical interpretation.

What happens in the particle experiment is this: Two particles, x and y, are emitted in opposite directions. After they have both traveled some distance, x encounters a spin-measurer, which we’ll call A. Then, a short time later, y encounters another spin-measurer called B. We assume that A and B are far enough apart that a light signal could not leave x when it measured by A and reach y before y is measured by B.

Now, there are two more crucial details that are not represented in your apple analogy. First, each spin-measurer can be in one of several different states, and the particles don’t “know” what states their respective spin-measurers will be in before they meet them. Second, experiments show that the spins measured for x and y will agree a certain percentage of the time, but, and this is crucial, the value of that percentage will depend on the respective states of A and B.

Here is where the problem arises. When x meets A, A is in one of its several possible states, and A measures the spin of x. Meanwhile, far away, y is about to meet B. Now, y has to somehow arrange that its spin, measured over many experiments, agrees with x’s measured spin a certain percentage p of the time. But the problem is that p depends on the state that A was in, and y has no way of knowing what that state was, so how can y contrive to have the right spin the right percentage of the time?

In fact, using Bell’s inequality, it’s possible to show that the only way that y could arrange to have the right spin the right percentage of the time would be for it to receive a signal somehow from x saying “Hey, I just reached A, and it was in state 1” (say). What makes things weird is that x was so far away from y that such a signal would have to travel faster than the speed of light. This strange bond between x and y, which allows each to know the state of the other more quickly than a light ray could travel between them, is what is called entanglement.

I love these clear explanations, folks; much appreciated that you take the time to post them. I realize translating mathematical and experimental concepts to plain language unavoidably anthropomorphizes them, but it seems to me it’s not so much that each particle must “know” what the other’s state is. Rather, both “particles” must be components of the same underlying perturbation of space. They cannot be two non-local particles. They are the same event. We simply do not know what that event is because we do not know what space is.

That’s certainly no less valid than any other interpretation, and it may even be correct. If it helps keep your head from exploding, roll with it.

Good point, and nothing particularly wrong with it either. I happen to subscribe to a different viewpoint, which is that all of constructs/paradigms/whatevers about particles, space, waves, and “reality” are fundamentally no more than mathematical models that serve us well.

That is, many true quantum physicists (and I don’t include Einstein among them) from the very beginning were uncomfortable with any notion that their theories described some sort of “physical reality”.

It’s more a matter of making models that are internally consistent (ie a result in one place doesn’t contradict other results), do reasonably well at predicting phenomena we can observe and measure, and fit in with other existing models. The models are not the same as reality.

One of my favorite examples is Planck’s equation for black-body radiation. He came up with the idea of “quantizing” the equation not because he thought that was what was going on, but because he perceived that it resulted in an elegant mathematical solution that fit other observations and theories. Only afterwards did anyone ascribe some sort of meaning to the “quanta”.

That, really, defines physics. As much as we’d like to think that we can relate our macroscopic, classical world to the “master” reality, I’m not sure we can. Atoms are not little billiard balls or solar systems, electrons are not little ping-pong balls, and so forth.

What they “are” comes back around to a question of philosophy rather than physics. I argue that to us, as humans, they either have to be solar systems and ping pong balls, or they have to be completely beyond our understanding. At some point, even the most extraordinary genius possible will be unable to go beyond the built-in limitations of our perception of the world, and thus be unable to experience anything more profound than what you and I see.

In that sense, Plato’s idea of forms and essences may be more right than we thought. A fundamentally different reality may be out there, but we do not have any hope of seeing it.

Perhaps a better analogy of it is Neo’s perception of the Matrix in one of the last scenes from “The Matrix” part I, where he sees the agents and the hallway in the green running numbers. He, at least, gets a glimpse of what reality is really like. As humans, we’re eternally stuck within the artificial reality of the Matrix, and our consciousness and perceptions define a state in which we can never see anything else. Or contrariwise, if we could see something else, then we would no longer be human.

For this reason, Niels Bohr was careful to avoid saying that his work “described reality”. He also said, "the universe may not only be stranger than we imagine, it may be stranger than we can imagine.

Thanks everyone, some nice explanations. I understand entanglement now…and by “understand” I of course mean “I understand what the mystery is”.

Once again the straight dope beats wikipedia :slight_smile:

That was biologist J.B.S. Haldane, and the correct quote is “my suspicion is that the universe is not only queerer than we suppose, but queerer than we *can * suppose.”

Emphasis Added
Let’s say there were a way for a ‘signal’ to get from x to y in a way that was either consistent with current understanding (assume we have just been forgetting to carry the one or something) or explained by some new model that corrected for the speed the signal would need to travel.

I know I’m overstraining the physical limits of the analogy here, but what information could possibly be transmitted that would account for the behavior of the particles? Is the idea that there is some unknown particle, particle — similar to a graviton? — that would keep the particles in alignment? Possibly some undiscovered force that keeps the particles arranged ‘correctly’?

Or is the idea that, even if there were such a force or signal, it would still be beyond the laws of physics for that signal to travel the given distance or for a force to have an effect?