Re:What’s Going on During Wave Function ‘Collapse’
by cygx on Friday July 05, 2019 @04:05PM
(#20365423)
My mistake: I should have said can't. Schrödinger time evolution is linear and unitary, ie once you split off branches that have factors living in different eigenspaces, they can no longer interact.
It is true that branches may in principle join again - however, that cannot be detected by nature of the process.
Re:What’s Going on During Wave Function ‘Collapse’
by lisper on Friday July 05, 2019 @04:44PM
(#20365740)
> once you split off branches that have factors living in different eigenspaces
And how exactly does that happen?
The answer is: it doesn't. The orthogonality of different branches is an approximation. It's a very good approximation because decoherence is a phenomenally efficient process, but it's an approximation nonetheless. The universal wave function always resides in the same Hilbert space because, as you yourself pointed out, Schrödinger time evolution is linear and unitary.
The key word there is "tend". The branches can interact (via interference) it's just the the technological challenges of demonstrating this become more pronounced as you add degrees of freedom. The limits of falsifiability here are technological, not limits in principle. To be considered unfalsifiable (in the Popperian sense), a theory has to be unfalsifiable in principle, not just in practice.
In fact, interference has already been experimentally demonstrated on some very large systems, and work on quantum computing is progressing rapidly enough that post-quantum cryptography is a serious concern. The falsifiability of the universal wave function is at a similar stage as the falsifiability of gravity waves was a few decades ago.