Demystifier said:
Well, maybe I have misunderstood something, but I view quantum logic as denying of validity of the classical logic. On the other hand, classical logic seems so fundamental to me that I am not ready to accept that it might be wrong. For example, a statement must be either true or false ...
I think you have misunderstood something, but I have now realized that I had too. I had previously thought of quantum logic
only as an approach to quantum theory that starts by letting a specific mathematical structure (some kind of lattice, I don't know the details) represent the set of experimentally verifiable statements. If that's all quantum logic is, then it's not very different from the other well-known approaches. For example, the traditional approach is to associate a complex separable Hilbert space with the set of operationally defined "states". Another option, which seems very popular these days, is to associate a unital C*-algebra with the set of operationally defined "observables". What all of these approaches have in common is that they associate a mathematical structure with a set of "things in the real world" that can be defined operationally.
There's certainly nothing radical about quantum logic so far, and it doesn't even seem to have anything to do with interpretations. The "experimentally verifiable statements" are either true or false, so who cares if that mathematical structure isn't a Boolean algebra, right? What I didn't realize before I started writing this is that there's more than one way to think of an experimentally verifiable statement. Compare e.g.
"If we measure the position of the particle, the result will (with probability 1) be in the interval (0,1)"
with
"The particle's position
is in the interval (0,1)"
As long as we keep our statements in the first form, then quantum logic is just a more complicated way to arrive at the same thing as the traditional approach, and possibly make some interesting insights along the way. (Yes, I understand that statements of the first kind can't be verified by measurements on a single system; we need an ensemble). But if we take our statements to be of the second kind, then I think you're right. This
is an interpretation of QM that rejects some aspects of classical logic. (The distributive property: A and (B or C)=(A and B) or (A and C)). This does seem like a fairly radical interpretation, but is it really more radical than many worlds? If we insist on realism, it seems that we have to choose between many worlds or quantum logic. (My choice is to drop realism, but you know that already).
Note that even if we strongly disagree with this interpretation, that's not a reason to dismiss quantum logic as an approach to quantum theory. It actually seems like a good place to start if we ever want to find some sort of generalization of QM. For example, we may not
have to let that mathematical structure be isomorphic to the lattice of subspaces of a complex separable Hilbert space.
Count Iblis said:
The MWI implies that time does not exist. The early universe before we existed is simply a component of an eternal wavefunction. In fact, you can take the early universe in which we supposedly do not exist, expand it in another basis and obtain today's universe from it. So, it isn't even true that we don't exist in the early universe.
My first thought was that this is crazy talk, but then I thought about it and I think you're right. That's actually what the MWI says. Of course, that doesn't mean that it's not crazy.
Dmitry67 said:
It is called a block time.
It is not a property of MWI, but of ANY deterministic theory, BM for example.
No Dmitry, it's not. This goes far beyond that. In the MWI, the time evolution of the omnium is a curve in a Hilbert space. The state of the omnium "now" is a point on the curve. This point has a bunch of components in any given basis. Now consider a point much earlier on the curve. You can always find a basis such that
that point has the same components. That means that it can be intepreted as describing the same thing. However, since the time evolution curve in general takes off in a different direction at that point (relative to the basis vectors) than it does at the "now" point, the observers described by that state would experience very different dynamics. Probably so different that they all die instantly.
Also, I think you have the wrong idea about the "block time" stuff. For example, it's not the "block" property of Minkowski spacetime that makes SR deterministic. It's the fact that equations of motion are always such that there's a unique solution for each initial condition.