Tuesday, January 24, 2017

Killing the cat?

This graphic from New Scientist, and conversations last night at the Science Museum, got me thinking. Using Schrödinger’s cat as a way to illustrate the differences between interpretations of quantum theory is a nice idea. But it suffers from the flaw that challenges the entire thought experiment. In order to be able to talk about the scenario in quantum terms, we need to be able to express it in quantum terms. But we can’t, because “live cat” and “dead cat” are not well-defined quantum states.

What, you can’t tell a live cat from a dead cat? Nonsense! Well yes, it is; but that’s not we’re asking here. What quantum property is it, exactly, that characterizes the superposition state, and that will enable you, unambiguously and in a single shot, to distinguish the two classical states? Live and dead are not quantum variables, and I’m not at all sure that they can be correlated even in principle with quantum variables that can be placed in superposition states.

Schrödinger’s point was not, in any case, that these are two different states of a macroscopic object, but that they are logically exclusive states. The paradox lies not in “two states at once”, but in “two contradictory states at once”. He was pointing not to “weird behaviour” predicted by quantum theory, but to logical paradoxes.

And this is why the Many Worlds Interpretation doesn’t resolve the problem. Yes, it looks as though it does: both outcomes are true! As New Scientist puts it here, “The universe splits. Your cat is dead, but in a parallel world it remains alive.” (Or, as Rowan Hooper points out, vice versa.) But wait: your cat? Who is you? Whose cat is it in the other world?

Brian Greene, in The Hidden Reality, tells us: that is you too! They are both you. Oh, so that sentence reads “Your cat is dead, but your cat remains alive.” Greene isn’t troubled by the fact that this is not how “you” works. But nevertheless, this is not how “you” works.

David Deutsch and Max Tegmark say, ah language! What should we trust more, language or maths? Contingent sounds, or timeless equations? But here language is articulating something that underpins maths, which is logic. Schrödinger realized that, but his point seems to be forgotten (by some). I don’t have time to go into it here (my forthcoming book will), but individual identity is a logical construct. You can’t wish it away with fantasies about “other yous”. I am trying to resist the topical urge to suggest that the Many Worlds interpretation offers us “alternative facts”, but that is terribly hard to do. So folks, the second option here is far more problematic than it looks.

What about the first? Let me say first of all that in neither the Copenhagen nor the Many Worlds interpretation is the cat “simultaneously alive and dead”. Not only is there no way of expressing that in quantum mechanics (at least, no one has articulated one), but in any event the proper statement of the situation is that “We can say nothing about the state of the cat, other than that live and dead are both possible outcomes of an observation”. That might sound like a pedantic distinction, but it will not be possible to make sense of quantum mechanics without it.

Now, I would hesitate to call the Copenhagen interpretation the “standard” interpretation, since there is no consensus, nor even a majority view, about which is the correct interpretation of quantum mechanics, at least among those who think about foundational issues. What’s more, the “Copenhagen interpretation” is not a single thing: Heisenberg expressed it differently to Bohr, and Wheeler had his own view too, as did others. However, I think Bohr would have said something like this: after observation, we have acquired now information that has changed our view of the cat’s condition (assuming it can be expressed in quantum terms at all) from an indeterminate to a determinate one. Some Copenhagenists, such as Pascual Jordan, spoke of this in causative terms: our observations produce the results. In that view, it seems acceptable to say that “Your measurement killed the cat” (although since we cannot say that it was previously alive, we might need to say more strictly “Your measurement elicited a dead cat”). But I’m not at all sure that Bohr would have seen causation at work in the measurement, as if “wavefunction reduction” is a physical effect that kills the cat. (That’s really the third, “objective collapse” option, which is given the least problematic representation here.) I think Bohr might have said something along the lines that “Observation allows us to speak about the classical state of the cat. And look, it is a dead one!”

So, which way will you vote? Bear in mind, however, that there are other option available, not all of them mutually exclusive. And that you won’t be able to prove that you’re right, of course.