On Fri, Oct 4, 2024 at 9:21 AM PGC <[email protected]> wrote:
> When a quantum system interacts with an environment the combined system > develops into an entangled state where system and environment become > entangled through their interaction, resulting in the superposition of > correlated states. This does not require the environment to physically > duplicate. This naturally emerges from the unitary evolution governed by > the Schrödinger equation. > It does require environment duplication if you want the different outcomes to each entangle separately. The “branching” into multiple outcomes is a way to conceptualize the > resulting entangled superposition, with each “branch” corresponding to a > different outcome, with the system and environment in correlated states. > > Also, I thought the tensor product is bilinear (linear in each of its > arguments). So for quantum states, the following would be a standard > operation: > > (∣a⟩+∣b⟩)⊗∣e⟩=∣a⟩⊗∣e⟩+∣b⟩⊗∣e⟩ > > The distributive law applies due to properties of tensor products. Yes, we > have nonlinear functions but linear operators. There’s potential for > confusion here, as the Hamiltonian includes terms that are nonlinear > functions of position and momentum. > But does the distributive law apply to quantum states? We can represent the situation as a tensor product, but a tensor product of what? The things we write down may not be physical reality. Bruce Iirc these functions are however constructed from linear operators and, > when properly defined, result in linear operators themselves. Linearity for > me refers to the way operators act on quantum states within a Hilbert > space. Obviously this is essential for the superposition principle. I’m a > tourist here, but nonlinear operators seem exotic. Linearity of QM is > essential for consistency of the theory/accurate predictions. > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLQYOFyivg3gioJF-ZbGuvP%3DK6SyW3uUieYO5ctSQmqNow%40mail.gmail.com.
