If a cat can be in a superposition of being dead and alive, why can't a statement be in a superposition of being true and false?
“Be in superposition” is a sloppy way of saying “is a physical system whose wavefunction can be written as a linear combination of orthogonal basis vectors”. A statement isn’t a physical thing so it doesn’t have a wave function so cannot possibly qualify.why can't a statement be in a superposition of being true and false?
There's the statement at the heart of Russell's paradox:If a cat can be in a superposition of being dead and alive, why can't a statement be in a superposition of being true and false?
That's in a superposition of true or false, in the sense that it's neither one nor the other.
It can. Put a sign inside the box with the cat that says the cat is alive.
No, my sign had unconditional "the cat is alive" on it, so we don't wonder what's written on it. We wonder about the truth of it before any physical measurement is taken, and that truth (my bold) is not a physical thing, so the point in the OP is arguable, I agree.However, as @Halc points out above, we could have a sign upon which we have written some statement about the cat. That sign is a physical thing like the cat, so now we have the same problem as the original Schrodinger’s cat: instead of wondering whether the cat is dead or alive before we open the box, we wonder what’s written on the sign (we can imagine a robot in the box that monitors the cat’s health and writes the sign if it dies)
As I posted, the sign say "the cat is alive". We write that with a sharpie or whatever before closing the box. Later, once the measurement of the decay is taken and the mechanism triggered accordingly, the physical state of the box is in superposition of a live cat with a true sign and a dead cat with a false sign. That makes the sign definitely in superposition of being true and false.Does the sign always say "the cat is alive", even if the cat is found dead when the box is opened?
A reasonable point. We've already measured what it says, so putting it in the box doesn't change that. We've measured what it says, but until we've opened the box, the truth of the sign is arguably in superposition of being true or false. So I'm with you on that, but it isn't a physical relationship compared to the same sign being in there entangled with the cat, so that might disqualify it as being in such a state.And why must the sign be inside the box?
Indeed, superpostion does not require 50/50 odds. It implies the various states, unmeasured, are capable of interfering with each other from a certain observer's perspective. I don't know how not to make it a relation with a potential measurement. I also don't know how one might measure interference from the cat being in superposition of dead and alive. They've put some macroscopic (visible without aid) objects into such states, but a cat? No. It's not a practical scenario except by discussing a cat on another planet that is isolated by virtue of being outside the past light cone of the observer.It seems the sign just has a certain probability of being true, say 60% true and 40% false. But is that the same as being in a superposition of being true and false?