A few years ago, the lovely Eva Longoria made a forgettable movie in which she played a ghost who died on her wedding day and came back to haunt her husband.
One scene had her hovering face to face with her husband, over his bed.
I thought about that scene after reading Anil Ananthaswamy's 23 July New Scientist article about quantum particles losing their identity (the "Cheshire Cat" phenomenon), which concludes with the question: "What does it mean for an atom to be separated from its properties?"
While the article allows that "No one quite knows" the answer, we might be closer to understanding what the question means when experimenters "succeed in measuring the electric dipole moment of a neutron by separating it from its magnetic moment."
Not surprisingly, experimentalists interpret their data on the conventional quantum assumptions of superposition and entanglement. That's where the ghost of Eva Longoria's character comes to my mind:
I don't remember how the hovering-over-the-bed scene actually appeared in the movie, but let's imagine that Eva's ghost is dressed in a flowing nightgown for maximum ghostly effect. Were she standing upright, we would see that gravity confines the hem of her gown more or less uniformly around her calves. Were she not a ghost, we know that were she lifted from the floor and placed horizontal over the bed, her gown would droop toward the bed; that's the way that gravity works. Assuming that a ghost is an object already independent of its (former) physical properties, then the orientation of the gown should not change when the ghost rotates from vertical to horizontal -- why?
Nothing physical is happening. Importantly, though, the way that we know nothing physical is happening, is that the property of orientation drives our measurement schema; i.e., whether it's an experimenter's orientation of measurement direction, or the orientation of a property (gravity), the effect of the choice of orientation is always independent of the object being measured.
This alone is enough to make Yakir Aharonov and Jeff Tollaksen's finding of time symmetry in the quantum domain important and foundational. Using the technique of weak measurement, "Aharonov and Tollaksen found that past and future can lead to a particle and its properties going their separate ways. The quantum Cheshire cat was born." Aharonov's mathematics had shown that a strong (classical) measurement on a particle with spin 1/2 or - 1/2 may be allowed a spin of 1.00 when measured weakly. (Ultimately, this means that fermion, or fractional spin, particles are integrated with boson particles that have integer spin values. Past and future, as in classical mechanics, are time symmetric.)
Peter Geltenbort (Institut Laue-Langevin)comments: "The only thing that cannot be separated from a particle is its mass. What defines where the particle lives is its mass; everything else is like the smile of the cat. You can separate it from the cat."
As one can also separate the behavior of the ghost's garment from the ghost, because it's the behavior of objects -- classical or quantum -- that we measure, and not "where the particle lives." After all, mass lives in all conditions of spacetime with its properties differing in proportion to the measured behaviors.
So assuming that ghosts are not physical, we can't actually detect them even when we might think that they hover right over us -- suppose, though, that weak measurement lets us detect the "drooping hem" independent of the hypothetical nonphysical ghost. That surely qualifies as a physical effect, and leaves us no choice but to conclude that the ghost is metaphysically real, i.e., a rationally objective phenomenon. So it is that Johannes Kofler (Max Planck Institute of Quantum optics) nails the foundational question with compact precision:
"The interpretation of these measurements is non-trivial, even tricky. The Cheshire cat paradox arises only when you give a physical meaning to the observed weak values -- which is challenged and debated in the community."
And Aephraim Steinberg (University of Toronto) argues: "I think it's easy to overinterpret that language. "I'm not going to claim that when I dig up a dinosaur bone today, it causes that dinosaur to have gotten killed 65 million years ago. I wouldn't say that the future is influencing the past. I'd say that information about the future gives us information about the present or the past."
The demarcation that Prof. Steinberg draws, however, is not necessary if the measurement (examining the bone) is accompanied by a metaphysical reality. That is, just as the ghost is not physical but metaphysically real, the measurement is physical, not metaphysical. That describes time symmetry at every scale -- the moon is really there when no one is looking, and so are an infinity of unphysical moons. Not in linear superposition as time asymmetry would have it, because the unphysical manifest only in a measure of physical properties that are bosonic, i.e., in which any number of particles may occupy the same point in space. (No two fermions can occupy the same space.)
It continues to amaze me that Joy Christian is the only physicist I know who takes metaphysical realism seriously -- by seriously, I mean with a precise mathematical measurement framework -- by using the key principle of orientability that is native to topology. If the only thing that cannot be separated from a particle is its mass, it follows that its measured orientation is the only thing that cannot be separated from a metaphysically real topology. And what we find with the n-sphere topology n > 3, is the number line R^3 of dimension 3, is compactified by a single point at infinity. Eva's ghost can rotate on her horizontal axis to any degree, and yet the "hem" of her gown will maintain the same vertical orientation (and forget that she is "entangled" in the gown; since she isn't physical, she can't be entangled with anything). The physical measurement tells us that Eva's ghost lives in many worlds, while we live only in this one, possibly without ever recognizing what a lonely existence it is.
Tom