Okay, to get back to the predicament of Schroedinger's cat, the reason we can't apply normal logic and say the cat is either alive or dead and we don't know which until we look is because quantum logic defies normal logic. The cat is in a superposition of states of being alive and being dead. In the state vector notation of quantum mechanics, this can be written
where in this equally probable two-state example, α = β = 1⁄√2. In Lectures on Quantum Mechanics, page 26, Gordon Baym discusses the difference between the classical either/or case and the quantum "unique superposition" case (which Gary Zukav noted the strangeness of by calling it a "thing in itself"). Instead of a cat Baym is talking about a single photon and how it's a superposition of polarization states:
|Φ> = α|Ψalive> + β|Ψdead>,
where in this equally probable two-state example, α = β = 1⁄√2. In Lectures on Quantum Mechanics, page 26, Gordon Baym discusses the difference between the classical either/or case and the quantum "unique superposition" case (which Gary Zukav noted the strangeness of by calling it a "thing in itself"). Instead of a cat Baym is talking about a single photon and how it's a superposition of polarization states:
“It is very important to realize that the statement ‘the photon is either in state |Ψ1> or |Ψ2>, but we don’t know which,’ is not the same statement as ‘the photon is in a superposition of |Ψ1> and |Ψ2>.’ … The point is that when we say that a photon is in a state |Φ> that is a linear combination of states |Ψ1> and |Ψ2>,
|Φ> = α|Ψ1> + β|Ψ2>,
then we are implying that the relative phase of the coefficients α and β is certain. For example, if |Ψ1> = |x> and |Ψ2> = |y>, then if α = 1⁄√2 and β = i ⁄ √2, clearly |Φ> = |R>, but if if α = 1⁄√2 and β = – i ⁄ √2, then |Φ> = |L>, which is a state completely different from |R>. The relative phase must be fixed to specify the linear combination uniquely. On the other hand, when we say that a photon is either in state |Ψ1> or |Ψ2>, but we don’t know which, then we are implying that there is no connection between the phases of these states, and hence no possibility of interference effects, which depend critically on delicate phase relations…”
The state |R> represents right circular polarization, |L> represents left circular polarization, and, of course, i is the square root of negative one. Who would have thought this could be so much fun?!
The state |R> represents right circular polarization, |L> represents left circular polarization, and, of course, i is the square root of negative one. Who would have thought this could be so much fun?!
