On: Carlo Rovelli on challenging our common-sense noti...

[antidesitter]

What do you mean by “unitary evolution is a theory where nothing changes”?

[mathgenius → antidesitter]

For any two state vectors, |u> and |v>, unitary evolution preserves the amplitude <u|v>:

<u|U^\dag U|v> = <u|v>.

[monktastic1 → mathgenius]

Sure, if U operates on both |u> and |v>, their inner product doesn't change. But why does this mean that "nothing ever changes?" |u> can evolve independently of |v>, after all.

OTOH, I can understand the argument that nothing ever happens. One reasonable requirement for something to happen is that it should not be able to "unhappen," which is why some are looking for the possibility of irreversible decoherence.

[mathgenius → monktastic1]

" |u> can evolve independently of |v> "

This is not unitary. Quantum theory has two parts: unitary evolution, and measurement processes. That's it.

[monktastic1 → mathgenius]

Eh? If U is a unitary operator that can act on |u>, then U @ I is a unitary operator on the state |u> @ |v>, producing U|u> @ |v>. Can you explain what you mean?

[antidesitter → mathgenius]

Doesn’t that assume |v> evolves the same way |u> does (according to U)?

[mathgenius → antidesitter]

Anything else is not unitary evolution.

[antidesitter → mathgenius]

What do you mean?

Let u and v be qubits. Apply a Hadamard gate to u while leaving v unchanged. Then they have evolved independently (but unitarily): u according to H, and v according to I.