FrediFizzx wrote: ↑Wed Sep 25, 2024 6:25 pm
Joy Christian wrote: ↑Wed Sep 25, 2024 1:09 pm
FrediFizzx wrote: ↑Wed Sep 25, 2024 12:42 pm
So, you agree that probability waves exist as mathematical objects. Is that correct? If so, then we can have probability based superposition. Do you agree?
I understand what probability is. And I understand what quantum superposition is. But what is "probability based superposition"?
It is what quantum superposition is basically. Say that the coefficients of the up and down states of the qubit are equal at 1/sqrt(2). Then there is a 50 percent probability that the qubit is either up and a 50 percent probability that it is down. Does that mean that the qubit is up and down at the same time? I don't think so.
You are talking about two different things.
First, there is a superposition of up and down states, with, in general, complex coefficients a and b. So we have
Psi = a x up + b x down.
This is a qubit state in which up and down states exist at the same time, at least according to the quantum computing guys. To them, Psi exists and it is as real as anything else.
Second, if we want to know the probability of the qubit being in the up state, then that is equal to |a|^2, according to the Born rule. But this is a separate postulate. It is not a part of the qubit itself. The qubit would have interference terms in addition to having the potential probabilities of |a|^2 and |b|^2.
So superposition and probabilities are two different concepts. In particular, Psi =/= |a|^2 and |b|^2 only.
.