Why is Schrödinger’s cat not just dead OR alive?

In quantum theory there is a thought experiment called Schrödinger’s cat-experiment. The idea of the experiment is that there is a cat in a closed box (don’t try this at home or at all!) together with a flask filled with poison which would, if released, instantly kill the cat. Next to the flask there is a hammer whose position is determined by some kind of mechanism involving the nucleus of an atom. The details of the mechanism do not concern us here: what is important for us is that if the atomic nucleus decays then the hammer will fall, the poison will be released and the cat dies. If the nucleus doesn’t decay, then the flask remains unbroken and the cat remains unharmed.

Suppose that, at a given moment after the lid has been closed, we don’t know whether the atom has decayed or not, and hence whether the cat is alive or dead. Quantum mechanics tells us* that as long as the box is closed and we cannot say that the cat is either dead or alive, we must assume that the cat is in a ‘superposition’ of a live and a dead state. Does that mean that we must assume that the cat is both dead AND alive?! That would be bizarre!

Schrodingers_cat.svg
Fig 1. Schrödinger’s cat.

Why can’t we just assume that although we are uncertain as to whether the cat is alive or dead, the actual state of affairs is that the cat is either alive or dead? Why do quantum theorists resort to this vague concept of superposition?

To understand the answer to this question we look at a different thought-experiment from earlier in the history of quantum theory (this experiment has actually been carried out in the 1980s): the double slit-experiment. This experiment shows that particles sometimes don’t behave as particles, but as waves. Physicists call this wave/particle-duality.

2slit
Fig 2.

The experiment works as follows. A lasergun fires a stream of photons at a screen with two slits in it. Behind the screen with the slits is a second screen, which can detect individual photons that hit it (this second screen may be thought of as a photographic plate).

If we fire the gun repeatedly, an interference pattern emerges on the second screen. Nothing is odd about that. It just shows that the photons fired from the gun behave as waves: they pass through both slits so that at each slit a new wave is created, and these two new waves interfere with each other to create the interference pattern on the optical screen (see figure 2).

Now we set the lasergun to fire at a very low rate (say, only one photon per second). We can then see the individual photons hit the second screen one by one. What kind of pattern would we expect this time? Well, if the individual photons hit the second screen one by one (as particles would), each of them must be passing one of the two slits, right? And if that were the case, then we’d just get two bright stripes behind where the slits are.

But that is not what happens. If we let the photons accumulate on the second screen, then the individual bright dots gradually form the interference pattern that we saw earlier: again there is a pattern of alternatingly bright and dark bands!

If you don’t believe me (and I wouldn’t if I were you), take a look at the video-clip below to have Anton Zeilinger (who actually did the experiment) tell you the same thing.

Now return to Schrödinger’s cat. We were wondering why we can’t just assume that the cat in the experiment – even though we can’t know for certain – is either alive OR dead. What would a no-nonsense (“cats can’t be alive and dead at the same time!”) approach look like in the context of the double-slit experiment? In the context of the double-slit experiment it would mean that we say “nah, particles can’t pass through two slits at the same time, that’s what waves do. If the photons in the double-slit experiment hit the screen as individual particles (one by one), they must pass through only one of the slits.”

bohm traj
Fig 3. Bohmian particle trajectories.**

Well, we could adopt such a stance, but then we would have a very hard time accounting for the emerging interference pattern.

We could of course assume that every photon passes through only one slit, and then mysteriously splits into many copies of itself which hit the second screen in different places, so as to produce a pattern that looks like an interference pattern. Or we could assume that the laws of motion for particles in the experiment are (or appear to be) different from what we’re used to in the macroscopic world (a proposal for such alternative motion is shown in figure 3).

We could make either of these assumptions, but then we’d have to give up on our intuitions about either energy conservation or particle motion. It seems doing away with nonsense in quantum mechanics is a bit like ‘whack-a-mole’: the moment you press it down in one place, it re-emerges in another.

We now see why quantum physicists are reluctant to assume that Schrödinger’s cat is either alive or dead. Quantum physicists resort to the concept of superposition to describe interference patterns like that in the two-slit experiment. But by using the word ‘superposition’ they do not (or at least, should not) claim to know what is going on.

whackamole
Fig 4. Doing away with nonsense in quantum mechanics is a bit like ‘whack-a-mole’: the moment you press it down in one place, it re-emerges in another.

 

*) At least, as quantum theory is usually interpreted.

**) Trajectories of particles in the Bohmian interpretation of quantum mechanics

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One thought on “Why is Schrödinger’s cat not just dead OR alive?

  1. During the lecture yesterday, one of the students asked me: “okay, so I get that quantum mechanics is weird, but you’re not saying that WE, in this room, are both alive and dead until somebody opens the door, right?!” I replied that that *is* the belief that quantum mechanics forces upon us. I would like to elaborate on that.

    What quantum mechanics tells us is that as long as a system is not observed, it can be in two states at the same time. But that goes only for an outside observer (the one opening the door). An observer inside the system (one of us) is in either of the two possible states.

    And yet what happens (whether we see a superposition or one of the two possible states) is not merely a matter of perspective: the different states really exist at the same time (they have real effects on each other; that’s what the double slit-interference tells us).

    So I must admit that my answer was too quick. I should have asked: what do you mean by ‘WE’? If by WE you refer to the superposition of states, then, yes, WE are both alive and dead.

    On the other hand, perhaps you meant ‘WE’ as referring to a number of alive people (which is just one of the states; not the whole superposition), and in that case it’d be a contradiction to say that WE are both alive and dead at the same time.

    Like

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