Quantum Superposition Paradox

Superposition is a weird thing, and there's definitely disagreement over how to think about it. Mostly, there is disagreement over whether or not it literally represents multiple realities. That is to say, when Schrödinger's cat is in a superposition, is it both alive and dead at the same time?

It's hard to talk about that without getting into metaphysical debates (see my entry on the measurement problem). While metaphysics is good to get into, it'd be nice to avoid that, at least initially.

So maybe a good starting place for talking about the interpretation of superpositions are logical sentences about them.

Multiple Realities

For example, if it's true that 'Schrödinger's cat is in a superposition state', does that logically imply the statement 'the cat is alive' as well as the statement 'the cat is dead'. More symbolically, is it the case that

'Superposition' -> ('alive' & 'dead') ?

I'd wager that this view of superpositions is widely held. Most will probably think of superpositions as implying multiple realities in the very meaning of the term. This would be an a priori assertion, and it would agree with the phrasing above.

Opposed to this view would be the belief that there is no true logical relation that looks like the one above. One could argue, for example, that superpositions could possibly imply multiple realities, but that it would have to be decided empirically. This would mean that the above logical statement wouldn't always be true, and that it would depend on the circumstances.

See how much cleaner that is than normal? I don't have to talk about metaphysical things, but still get to articulate something providing some insight.

Contradictory Realities

The second half of this is what relationship is between the states of life and death. Do they contradict? If so, the statement

~('alive' & 'dead')

is directly contradictory with the superpositions statement above. In other words, one of these two statements must be false.

This second statement certainly seems natural to accept as well. We certainly think of life and death as being mutually exclusive states. But what could show that they really are mutually exclusive states, and not just compatible states that appear incompatible to our mistaken intuition?

More formally, maybe we can say that mutually exclusive pairs of physical states will create two conflicting set of predictions, both of which can't be true. For example, a macroscopic object can be both falling and electrically charged. There is no reason why these two physical states should make conflicting predictions, so a physical object can be in both states at the same time.

(I think the full story of why this is the case looks like this: since a system is said to be in a physical state only when it fits a physical model, and physical models are what we need to make predictions, having a contradiction in the predictions of two models applied to the same system suggests an error somewhere further up in reasoning. Either a model was applied that should not have, or there was an error in how one or more of them were applied. Feynman describes using this very line of thought to call out the existence of errors in other physicist's reasoning and impress others without working through all of the math. It's in Surely You Must Be Joking Mr. Feynman p.244-5. The fact that the statement could be wrong either because an incorrect model was applied or a correct model was incorrectly applied means that this second statement has an a priori sense to it and an empirical sense to it.)

Two mutually exclusive states would give predictions that contradict. For example, having a macroscopic object (not currently under quantum effects) be both charged and not charged would create contradictions. There would be two sets of predictions created by the two possible situations: when the object is charged and when it is not, and those predictions could differ significantly. Therefore, only one of them can be true, and a well designed experiment will typically decide between the two.

So are quantum states different? Do quantum effects somehow make states that are normally mutually exclusive so that they are not in the right circumstances?

An interpretation that would argue that this statement is false is the many-worlds interpretation. While classical states like 'alive' and 'dead' are mutually exclusive, in the quantum realm they are not. The simple fact for this being that they exist in separate worlds. It's not a contradiction to say that the cat is both dead and alive because the dead cat exists separately from the alive cat, and it is this world-splitting aspect of quantum mechanics that keeps these two states from producing contradictory predictions.

So yeah, I dunno how helpful this approach will be, or if there is any literature on breaking it down this way. I'm calling it the quantum superposition paradox, which seems appropriate, but I don't know if there would be a better name for it.