Quantum entanglement

A non-physicist friend expressed deep puzzlement about measurements at opposite ends of the Universe being somehow linked. Here I describe what I take to be the current state of theoretical and experimental knowledge about the “spooky action at a distance” that bothered Einstein and many other people.

The aspect of quantum mechanics that is pretty widely known and accepted is that small objects (atoms, electrons, nuclei, molecules) have “quantized” properties and that when you go to measure one of these quantized properties you can get various results with various probabilities. For example, an electron can have spin “up” or “down” (counterclockwise or clockwise rotation as seen from above; the Earth as seen from above the North Pole rotates counterclockwise, and we say its spin is up if we take North as “up”). The Earth, being a large classical object, can have any amount of spin (the rate of rotation, currently one rotation per 24 hours). The electron on the other hand always has the same amount of spin, which can be either up or down.

Pass an electron into an apparatus that can measure its spin, and you always always find the same amount of spin, and for electrons not specially prepared you find the spin to be “up” 50% of the time and “down” 50% of the time. (It is possible to build a source of “polarized” electrons which, when passed into the apparatus, always measure “up”, but the typical situation is that you have unpolarized electrons, with 50/50 up/down measures.) It is a fundamental discovery that with a beam of unpolarized electrons it is literally impossible – not just hard, but impossible – to predict whether the spin of any particular electron when measured will be up or down. All you can say is that there is a 50% probability of its spin being up. It’s also possible to prepare a beam of partially polarized electrons, where for example you know that there is a 70% probability of measuring an electron’s spin to be up, but that’s all you know and all you can know.

So much for a review of the probabilistic nature of measuring a quantized property such as spin for a single tiny object. Next for the aspect of quantum mechanics that is less widely appreciated, which has to do with measures on one of a group of tiny objects. A simple case is two electrons that are in a “two-particle state”, where one can speak of a quantized property of the combined two-particle system. For example, in principle it would be possible to prepare a two-electron state with total spin (“angular momentum”) zero, meaning that electron #1 could be up, and electron #2 would be down, or vice versa. As a matter of fact, it was only in the last few decades that experimental physicists learned how to prepare such multiparticle states and make measurements on them, and it is these experiments, together with superb theoretical analyses, that have clarified the issues that worried Einstein. (Actually, most experiments have involved photons rather than electrons, but I’ve chosen the two-electron system as being more concrete in being able to make analogies to the spinning Earth.)

Suppose Carl prepares a zero-spin electron pair and gives one electron to Alice and the other to Bob (Alice and Bob are in fact names used in the scientific literature to help the reader keep straight the two observers.) Alice and Bob keep their electrons in special carrying cases carefully designed not to alter the state of their electron. They get in two warp-speed spaceships and travel to opposite ends of our galaxy or, if one prefers, to opposite ends of the Universe (if the Universe has ends). Many years later, Alice measures the state of her electron and finds that its spin is up (there’s an arrow pointing up on her carrying case indicating what will be called “up”, and a similar arrow pointing up on Bob’s carrying case). If Bob measures his electron, he will definitely find its spin to be down.

One might reasonably interpret these observations something like this: Carl happened to give Alice an “up” electron and (necessarily) gave Bob a “down” electron. There was a 50/50 chance of giving Alice an up electron, and this time Carl happened to give her an up electron. Then of course no matter how long Alice waits before measuring her electron, she’s going to find that it is “up”, and no matter how long he waits Bob is going to find that his electron is “down”. Yes, there are probabilities involved, because neither Carl nor Alice knows the spin of the electron until Alice makes her measurement, but the electron obviously “had” an up spin all the time.

The amazing truth about the Universe is that this reasonable, common-sense view has been shown to be false! The world doesn’t actually work this way!

Thanks to major theoretical and experimental work over the last few decades, we know for certain that until Alice makes her measurement, her electron remains in a special quantum-mechanical state which is referred to as a “superposition of states” – that her electron is simultaneously in a state of spin up AND a state of spin down. This idea is very hard to accept. Einstein never did accept it. In a famous paper in the 1930s, he and a couple of colleagues proposed experiments of this kind and, because quantum mechanics predicts that the state of Alice’s electron will remain in a suspended animation of superposed states, concluded that quantum mechanics must be wrong or at least incomplete. It took several decades of hard work before experimental physicists were able to carry out ingenious experiments of this kind and were able to prove conclusively that, despite the implausibility of the predictions of quantum mechanics, quantum mechanics correctly describes the way the world works.

I find it both ironic and funny that Einstein’s qualms led him to propose experiments for which he quite reasonably expected quantum mechanics to be shown to be wrong or incomplete, only for it to turn out that these experiments show that the “unreasonable” description of nature provided by quantum mechanics is in fact correct. These aspects of quantum entanglement aren’t mere scientific curiosities. They lie at the heart of work being done to implement quantum computing and quantum encryption.

What about relativity, and that nothing can travel faster than light? Not a problem, actually. The key point is that Alice cannot send any useful information to Bob. She cannot control whether her measurement of her electron will be up or down. Once she makes her “up” measurement, she knows that Bob will get a “down” measurement, but so what? And all Bob knows when he makes his down measurement is that Alice will make an up measurement. To send a message, Alice would have to choose to make her electron be up or down, as a signal to Bob, but the act of forcing her electron into an up or down state destroys the two-electron “entangled” state.

I recommend a delightful popular science book on this, from which I learned a lot, “The Dance of the Photons” by Anton Zeilinger. Zeilinger heads a powerful experimental quantum mechanics group in Vienna that has made stunning advances in our understanding of the nature of reality in the context of quantum mechanics. In this book he makes the ideas come alive. The book includes detailed discussions of Bell’s inequalities and much else (Bell was a theoretical physicist whose analyses stimulated experimentalists to design and carry out the key experiments in recent decades).

It seems highly likely that Zeilinger will get the Nobel Prize for the work he and his group have done. A charming feature of the book is that Zeilinger is very generous in giving credit to many others working in this fascinating field. Incidentally, there is some movement in the physics community to bring contemporary quantum mechanics into the physics major’s curriculum, which in the past has been dominated by stuff from the 1920s.

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15 Responses to Quantum entanglement

  1. sherwingooch says:

    Dr. Sherwood,

    I would be interested in hearing: What are your thoughts regarding the independence of the order of observation? More specifically:

    Let us examine the case where two observers, let’s call them Charlene and Darlene, are independent observers located respectively in different inertial reference frames ‘C’ and ‘D’. Their velocities relative to Alice and Bob are such that Charlene sees that Alice observes the spin of her entangled electron before Bob observes the spin of his electron, while Darlene observes that Bob determines the spin of his electron prior to Alice. As “elucidated” by Bram Gaasbeek in “Demystifying the Delayed Choice Experiments”

    ( http://arxiv.org/abs/1007.3977v1 ),

    quantum mechanics dictates that the entanglement is independent of both ‘space’ and ‘time’.

    Because the two electrons seem to “know” their spins independent of which is measured first, it would seem to imply either a hidden rule or a deterministic Universe. How does quantum physics resolve this conundrum?

    Thank you,

    Sherwin Gooch

  2. I’ll emphasize again that the key aspect of entangled states, confirmed in detail by many recent experiments, is that the electrons DO NOT “know” their spins from the beginning. As I said, a “reasonable” notion is that at the time of the creation of the entangled state, Alice’s electron is in a specific state (“up”, say), and Bob’s electron is in a specific state (necessarily “down”). This interpretation has been definitively ruled out. Alice’s electron is simultaneously in both the up and down states, as is Bob’s. There is no hidden rule, and the interpretation involving “hidden variables” has been ruled out. Quantum physics doesn’t “resolve” this “conundrum”. Rather, quantum physics correctly predicts the outcomes of experiments, and it doesn’t care whether this description doesn’t “make sense” to us, or seems to be a “conundrum”. Nature is what it is and has no responsibility to satisfy our notions of what is proper or sensible.

  3. sherwingooch says:

    Bruce,

    Please allow me to restate my question more succinctly:

    Let’s assume ideal conditions, so the probability of observing spin-up and spin-down are both 50%, etc. Charlene in inertial reference frame ‘C’, zooming by, but located near Alice, sees that Alice observes spin-up, and immediately transmits a message to Darlene to that effect. Due to the time required for the message to travel from Charlene to Darlene, Darlene will not receive this message until later.

    Now we shift our attention to Darlene, in inertial reference frame, ‘D’, near Bob, at an instant just prior to Bob making his measurement. In Darlene’s reference frame, Alice has not yet made her measurement. Neither has Bob, although he will in the next instant. At this moment in Darlene’s reference frame, there is a 50% probability that Bob will measure spin-up. As it happens, Bob makes his measurement, and Darlene sees that Bob, indeed, measures spin-up. She records this result.

    Sometime later, Darlene receives the message from Charlene.

    Both electrons being observed to have spin-up would contradict the requirement that each of the entangled electrons, when observed, acquire an opposing spin. To maintain this requirement, either Charlene’s message to Darlene must be garbled, or never arrive. Or Darlene must have recorded Bob’s result incorrectly. Or either Alice or Bob must realize after-the-fact that they have made an erroneous measurement.

    Or perhaps the spin-state of one or the other electrons, along with all ensuing causally-based effects, changes after-the-fact to obtain an internally-consistent universe. But, once it has reached consistency and can be observed, this mechanism would have the same appearance to experimental physicists as the spin-state being maintained — throughout — in a hidden variable.

    What does physics say will happen?

    Thank you for your patience. I would really like to know the answer to this question.

    Sherwin

    • Jeff says:

      I think the answer (based on the premises we are apparently given) has to be that Bob has a 50/50 chance of detecting spin-up, and the result of his measurement must be spin-down. When Alice’s message arrives, it reports that Alice had spin-up. (Or vice versa.) From this we would be hard-pressed not to understand that Bob actually always had a spin-down electron. For this not to be so, we’d have to say that the detection events have some super-luminal relationship, which I gather would constitute a hidden variable. I’ve heard of local hidden variables and global ones. Have both been ruled out?

      • I guess I’ve failed in my attempt to report what is now known from lots of experiments of many kinds. You simply must suspend your natural desire to make common-sense, reasonable interpretations of what “should” happen. Hidden-variable theories are ruled out by the many experiments. Unless Alice or Bob makes a measurement, each of their electrons remains forever in a superposition of up and down states, neither electron is up or down. All attempts at interpreting what happens in terms of Alice’s electron having been born in the up or down condition have run aground, through experiments that show conclusively that her electron CAN NOT have been in the up or the down state at the start of the experiment. I again recommend Zeilinger’s book for details.

        It’s admittedly strange, but it’s the way the world actually works. Nature has no obligation to work in a way that seems reasonable to us. Nature just is, and the task of physicists is to discover how Nature actually behaves. As for superluminal issues, I tried to deal with that: Alice cannot use entanglement to send a message to Bob.

      • Jeff says:

        Thanks for the response. I was just trying to capture the challenge for conceptualization, according to what I understood from your explanation, which did lead to a question.

  4. Sorry, but I don’t know enough about the subject to answer your question, but a quick glance at the physics article you cited suggests that that article does address questions very similar to yours.

  5. sherwingooch says:

    Yes, but like so many things in QM, it also seems to make no sense at all. The fact that both ‘time’ and ‘location’ cancel out of the mathematical description of entanglement seems to indicate that an entangled pair is entangled for all time — including the time before the entangled pair was even created. This begs the question, “what is time?” which, of course, no one knows!

    Thank you for your attention.

    • Bob Rader says:

      Hi Sherwin (and Bruce). The choice of which experimenter measures “first” is an artifact of human language storytelling: it doesn’t matter. Neither can tell that the other electron has (or has not) been measured. After the fact, when we (or they) get all the results to one location and analyze them, those doing that analysis will see the perfect correlation. The perfect correlation is required by our having specified a correlated (spin 0, in this case) state.

      • Bob Rader says:

        (Continuing…)
        The experiment doesn’t make much progress in addressing “What is time?” because it
        implies the universe-wide common “time” of quantum mechanics: the problem is not
        set up with a relativistic notion of time, for example. At which point one should point out that the order of the two experimenters actions can be anything, from the point of view of different observers.

        We set up a problem with a time-independent global state. The interesting thing is that this way of describing the world really does seem to work. The experiments being done to check this out are amazing.

      • sherwingooch says:

        I notice that I neglected, above, to include in my description the detail that, for this experiment to be performed, Alice and Bob are required to be in different inertial reference frames. Mea culpa! (Considering fringe-effects due to Doppler-derived distortion off-axis from the direction of propagation, I don’t think this is strictly true, but let’s avoid that red herring.)

        – — — — — — — — — — — — — — —

        Thank you, Bob. I’m sure you’re right.

        In fact, in the course of writing what was quickly becoming a long-winded response, I hit upon this resolution to what I perceived as a paradox:

        A way to resolve this conundrum would be to declare that two measurements of a single quantum state (entangled state), by definition, make sense only if each measurement is regarded as taking place in an inertial reference frame in which both measurements occur simultaneously. I.e. it makes sense only to compute details related to such measurements if the decoherence is regarded as occurring in space-time continua in which both events occupy a time-like point on a space-like line.

        A more general statement can be obtained by increasing the number of entangled states while maintaining the requirement that all measurements of the state, if made, must be regarded as being made from corresponding reference frames which provide simultaneity.

        This resolves the conflict, but it makes it more difficult to describe related events taking place in the environment of either entangled electron, as they must be considered in reference to this time-like point. (So be it.)

        What does this say about other quantum measurements taking place in the same, or distant, neighborhoods of space-time? Can they all also be connected in this way without leading to a contradiction? (Yes, I think they can.)

        Sorry about being too ignorant to have perceived this before. I thank you both very much for your patience in aiding me to resolve this misunderstanding. I hope I didn’t consume too much of your time.

        Thanks, again,

        Sherwin

  6. To sherwingooch; Your question isn’t clear. Could you please draw a space-time diagram of events as you describe them. In particular, please pay attention to signals you send and light cones they travel along.
    Just saying that something is before or later does not necessarily make it so. Relativity is still a causal theory and I suspect that in fact there is no issue at all. Your drawing events as you describe them may clarify your question.

    • sherwingooch says:

      Dear Zvonko Hlousek,

      Thank you for your suggestion.

      A vanishingly small magnitude of Lorentz-affected variation in relative time is required to toggle the precedence of two quasi-simultaneous events, so I think we can set aside consideration of light-cones.

      But your suggestion to draw a space-time diagram was spot-on.

      Thank you,

      Sherwin Gooch

  7. David Trowbridge says:

    Hello Bruce,
    First let me thank you for suggesting Anton Zeilinger’s book, which I’ve now renewed four times already from the local library. I’ve read it twice and filled the book with colored sticky tags reminding me of the most striking results.

    I was particularly struck by his discussion of delayed-choice teleportation in the section, “A Ghostly Idea,” pp 227-232. He concludes, “The message to be learned is that individual events in quantum physics are primary: the are more fundamental than the explanations that we later construct based on our physical pictures.” My main takeaway is that we probably need to take a much closer look at what our minds are doing when we try to interpret the world. For example, we like to think that objects have properties– that somehow there are attributes connected to things that are completely independent of our internal mental operations. But is that true? The universe does what it does, and presumably has been doing so long before humans emerged from the muck. Now a species has evolved that thrives by telling itself stories. It likes to believe that certain worldviews do in fact reflect reality, but often neglects to examine where those thought processes come from. Perhaps the time has come to look more closely into just what our minds are doing when we apprehend the world.

    These certainly are exciting times we live in!

    David

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