On the website of the American Association for the Advancement of Science, a physicist recently wrote:
Suppose you have a quantum particle of light, or photon. It can be polarized so that it wriggles either vertically or horizontally. The quantum realm is … hazed over with unavoidable uncertainty, and thanks to such quantum uncertainty, a photon can … be polarized vertically and horizontally at the same time. If you then measure the photon, however, you will find it either horizontally polarized or vertically polarized, as the two-ways-at-once state randomly ‘collapses’ one way or the other.
This two-ways-at-once state is called “superposition”. The idea is that something can be in more than one state (or “position”) at one time, i.e. a super-position.
However, saying that a photon can be polarized vertically and horizontally at the same time, or that it can be in a “two-ways-at-once” state, looks extremely suspicious. It’s hard to know what such a statement means, if anything. After all, language is based on logic (it wouldn’t work otherwise) and logic is based on the law of contradiction: proposition P cannot be both true and false, assuming that P has a single, precise meaning.
The proposition that photon p is polarized vertically at time t has a single, precise meaning. So does the proposition that photon p is polarized horizontally at time t. Yet these statements certainly look contradictory. It looks as if we have to give up the law of contradiction in order to accept them both.
To avoid the contradiction, however, it might be preferable to say that a photon can be in an indeterminate state, in which its polarization is neither vertical nor horizontal. It’s potentially in either state, but it’s not in either one until its state is measured (or otherwise affected), at which point the photon randomly ends up in one state or the other.
Viewed in probabilistic terms, the fate of Schrödinger’s cat doesn’t seem to be a problem (to me anyway). It was alive when it was put in the box and presumably remained alive unless it was poisoned as the result of a random sub-atomic event. We don’t have to say that the cat is now both dead and alive (or in some twilight state). It’s just a cat that may have died and there is a certain probability that it did.
But then there is the famous double-split experiment. This experiment shows that photons don’t behave like cats (or dogs) or, in the philosopher J. L. Austin’s phrase, “medium-sized dry goods”. A single photon travels through two slits and creates a wave-pattern on the other side, even though common sense tells us that the photon can only travel through one slit or the other. The bizarre but reasonable conclusion is that the photon actually takes every possible path through the two openings, not just in theory, but in fact.
Fortunately, there isn’t any contradiction in saying that the photon goes through slit 1 and slit 2 at the same time, since saying that it goes through slit 2 doesn’t conflict with saying that it also goes through slit 1. In similar fashion, photons can be polarized horizontally and vertically at the same time, because that’s the kind of thing that can happen to the crazy little bastards (i.e. sub-atomic particles).
We are used to saying things like “a person can’t be in two places at the same time” (many episodes of Law and Order are based on that premise). Logic tells us that if the number 5 is odd, it can’t be even. Logic and experience tell us that if Miss Scarlet was in the billiard room, she wasn’t in the conservatory. That’s how numbers and people work. Photons don’t work that way. It’s extremely strange, but not incomprehensible and not contradictory.