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Quantum Cheshire Cat: Even Weirder Than Schrödinger’s


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Just when you thought you’d heard every quantum mystery that was possible, out pops another one. Jeff Tollaksen mentioned it in passing during his talk at the recent Foundation Questions Institute conference. Probably Tollaksen assumed we’d all heard it before. After all, his graduate advisor, Yakir Aharonov—who has made an illustrious career of poking the Schrödinger equation to see what wild beasts come scurrying out—first discovered it in the 1990s and discussed it in chapter 17 of his 2005 book, Quantum Paradoxes. But it was new to me.

The situation is an elaboration of Schrödinger’s thought experiment. You have a cat. It is either purring or meowing. It is curled up in one of two boxes. As in Schrödinger’s scenario, you couple the cat to some quantum system, like a radioactive atom, to make its condition ambiguous—a superposition of all possibilities—until you examine one of the boxes. If you reach into box 2, you feel the cat. If you listen to the boxes, you hear purring. But when you listen more closely, you notice that the purring is coming from box 1. The cat is in one box, the purring in the other. Like a Cheshire Cat, the animal has become separated from the properties that constitute a cat. What a cat does and what a cat is no longer coincide.

In practice, you’d pull this stunt on an electron rather than a cat. You’d find the electron in one box, its spin in the other. Even by the standards of quantum mechanics, this is surprising. It requires what quantum physicists call “weak measurement,” whereby you interact with a system so gently that you avoid collapsing it from a quantum state to a classical one. On the face of it, such an interaction scarcely qualifies as a measurement; any results get lost in the noise of Heisenberg’s Uncertainty Principle. What Aharonov realized is that, if you sift through the results, you can find patterns buried within them.

In practice, this means repeating the experiment on a large number of electrons (or cats) and then applying a filter or “postselection.” Only a few particles will pass through this filter, and among them, the result of the softly softly measurement will stand out.

Because you avoid collapsing the quantum state, quintessentially quantum phenomena such as wave interference still occur. So, for a Cheshire Cat, you apply the following filter: you change the sign of one term in the superposition, causing the location and spin of the electron to interfere constructively in one box and destructively in the other, zeroing out the probability of finding the electron in box 1 and zeroing out the net spin of the electron in box 2. Voilà, the electron is in box 2 and its spin in box 1.

If this leaves your head spinning, it should. The word “weak” describes not only the measurement but also my intuitive grasp for what’s really going on. The best I can do is recommend the article on weak measurement by Aharonov, Tollaksen, and Sandu Popescu in last November’s Physics Today, but be prepared to read it several times before you have the slightest idea of what they’re saying. I’ve commissioned an article about Aharonov’s work for an upcoming issue of Scientific American to collapse some of the uncertainty. In the meantime, try sitting in a different room from where your confusion is.

George Musser About the Author: is a contributing editor at Scientific American. He focuses on space science and fundamental physics, ranging from particles to planets to parallel universes. He is the author of The Complete Idiot's Guide to String Theory. Musser has won numerous awards in his career, including the 2011 American Institute of Physics's Science Writing Award. Follow on Twitter @gmusser.

The views expressed are those of the author and are not necessarily those of Scientific American.





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  1. 1. terrybollinger 12:58 am 09/22/2011

    This is a delightful thought problem!

    If I am rightly following your next-to-last paragraph in particular, what Aharonov noted is that independently conserved quantities need not necessarily share exactly the same regions of high probability in ordinary space.

    That actually makes frighteningly good sense. If QM allows a single particle to be in two places, why should it not also two separately conserved properties, in this case mass and spin, to be reduced right after such a separation into the conceptually simpler case of each independent property having only one main location ordinary space? While odd sounding, this is actually closer to their original state of having more ordinary singular locations. The two regions just happen to be a bit dislocated from each other!

    Both are of course necessarily quantum probability distributions, so in one sense you can’t really “find” just a spin or just a mass in one or other locations. I presume this is what is meant by “weak” or gentle measurements, that is, measurements that poke just hard enough in the right way to say “spin is here” without at the same time inquiring “where is mass?”, or conversely “where is mass?” without inquiring too carefully as to “where is spin?” A weak measurement process thus must necessarily must leave the exact pairing ambiguous at all times, else it would instead find what one would have expected all along: A single, unified particle.

    I would point out that at least two other properties should be accessible to such experiments: charge and linear momentum, since both are absolutely conserved and so potentially capable of independent entanglement relationships across space.

    I have no idea if Aharonov or anyone else addresses these other two cases for this scenario. Entanglement of charge would be tricky because charges interact so easily. However, if doable, it would exhibit itself as (weakly measured!) fractional charges such as those discussed for certain solid state systems.

    In terms of spatial separation, this translates into an intriguing three-way possibility: mass, charge, and spin each in separate space locations! What a delightful thought (and potentially real) experiment that might present!

    Entanglement of linear momentum is the odd one, since wave packets are typically expressed as sums of pure momentum waves. Nonetheless, this form of entanglement is in many ways the most fascinating one due to its behavior as a sort of “bridge” between classical and quantum. The reason is that uncertainty in the measured momentum of a particle cannot be used to create a real violation in momentum conservation for the universe at large. So, if the momentum of a moving particle can be identified with great precision, e.g. via a diffraction grating and detector combination of some sort, entanglement guarantees that an exactly equal and opposite momentum must be imparted to the classical systems that first gave rise to that particle, possibly in the long distant past. You never notice such things because the momenta imparted to the entangled classical systems are incredibly minute, especially when compared to the huge whacks the tiny particles receive from the matching opposite momentum.

    (I’d have to look at it more closely, but I’m pretty sure that momentum entanglement using photons is mathematically equivalent to the Maxwell backwards-in-time (“advanced”) photon “kicker” solutions that Wheeler and Feynman proposed in Feynman’s thesis and in a series of papers. Feynman emphatically did not express the problem in terms of entanglement, however, nor did such terminology even exist then.

    Adding momentum is still more delightful: One can then postulate a thought experiment (and potentially a real one) in which four entities attain separate regions of compact maximum amplitude. Momentum would of course be in motion, so this does not sound like a terribly stable four-part package!

    A final note: Entanglement is almost always described in terms of spin conservation, but that is of course overly restrictive. What causes entanglement, always, is when a universally and absolutely conserved quantity gets dispersed over space by a quantum wave function — nothing more. When that quantity is spin, finding one spin orientation at one location “instantly” says that an equal and opposite spin must become specific to cancel the one found, no matter how far apart the two now are. That one is nicely visual because it has an orientation concept to it.

    But the same fundamental idea also applies for mass. What is usually described in somewhat vague terms of “wave collapse” is simply another form of entanglement, specifically of mass. One way to think of it as mass being entangled with its own absence, so that the total mass within a region of space after the mass is found remains invariant — the particle cannot “show up” in two places at once. Like spin entanglement, this pulling in of the wave function takes place in a very “spooky,” non-local fashion. Einstein in fact used this example of wave function “collapse” in his first highly public argument with Bohr and others about quantum locality, long before his spin-based example that is better known.

    And a final note on Schrodinger’s Cat: Just to be clear about this much-used example, the cat in all such thought problems is never, ever in any danger of entering a true quantum superimposed state. The rule for creating superimposed state is that _no_ giveaway information of any type can ever leak out into the universe at large, since if it does an observer could later detect them. Since a simple room-temperature box is an absolute Niagara falls of information flowing out, e.g. infrared light indicating temperature, sound indicating breathing and heartbeat, the cat is never in the least bit of danger of becoming truly quantum. If it dies, it dies… and I for one would call the SPCA on you if it did.

    Cheers,
    Terry Bollinger

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  2. 2. Postulator 5:37 am 09/22/2011

    But… the act of observing changes the quantum object being observed.

    Oh, and wake me up when he’s done the experiment.

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  3. 3. oldvic 5:39 am 09/22/2011

    There’s no end to the fun we can have with quantum physics even with a very limited grasp of its inner workings (my case).

    It is then possible to have the cat in one box and its scratching abilities in another. This may well bring a revolution in the pet industry: certified non-scratching cats. “Get your cat here and be sure it will never scratch you, as we’ve separated its scratchiness, enclosed it in a box and sent it into a black hole (AKA our archive)!”

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  4. 4. laprankster 8:35 am 09/22/2011

    Does this mean my body can be in one room and my mind in another? Oh, that explains politicians.

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  5. 5. MadScientist72 8:47 am 09/22/2011

    What Tollaksen, Aharonov and Schroedinger all seem to have forgotten is that the CAT is capable of observing, too.

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  6. 6. gmusser 12:54 pm 09/22/2011

    @Postulator: The beautiful thing about weak measurement is that the disturbance can be arbitrarily small. It goes against our standard Heisenberg intuition.

    @oldvic: Ah, introducing a black hole would make this even more fun.

    @laprankster: I would lol if it weren’t so true.

    @MadScientist72: Sure, the cat observes, but it’s still a quantum system. There is a whole literature on the question of observing an observer; see our June issue.

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  7. 7. mmfiore 3:11 pm 09/22/2011

    As an alternative to Quantum Theory there is a new theory that describes and explains the mysteries of physical reality. While not disrespecting the value of Quantum Mechanics as a tool to explain the role of quanta in our universe. This theory states that there is also a classical explanation for the paradoxes such as EPR and the Wave-Particle Duality. The Theory is called the Theory of Super Relativity and is located at: Super Relativity http://www.superrelativity.org
    This theory is a philosophical attempt to reconnect the physical universe to realism and deterministic concepts. It explains the mysterious.

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  8. 8. Percival 10:06 pm 12/31/2011

    I hope somebody still reads the comments on this blog.

    In what sense is “an electron” in one place while its spin is elsewhere? What properties of the electron other than its spin can be expected to be observed where the electron allegedly is in order to call what’s detected there “an electron”?

    Its rest mass makes sense.

    Charge, fine, but then where did its magnetic field go?

    Does the charge stay with the mass and the magnetic field go with the spin?

    Can all four properties be separated into different locations “at the same time”?

    Can we interact with one property without disturbing the others?

    Can this separation be made to persist over time?

    Suppose we have two electrons. We arrange for both their spins to occupy one box, both their masses to occupy another box.

    Are the separated properties of electrons still fermions? Can the spins coincide and if so how do they interact? Will they form a sort of shell of a boson with spin of zero or one (antiparallel/parallel cases)?

    Suppose we do this for many, many electrons.

    The masses will add but the spins can be made to cancel. What happened to conservation laws?

    Can this be done with hadrons? Can we separate out their constituent quarks’ color charges?

    Can this be done with macroscopic quantum objects like fermionic condensates?

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  9. 9. glang 9:18 am 02/14/2012

    ‘Purring or meowing’ is so much better than ‘living or dead’. As for the more technical things … meow? :-)

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