Also it might not be clear to every one, but unitary also implies energy conservation, I assume isometry also conserves it otherwise it would be a pretty big ask to adopt it.
IANAP. It doesn't sound like string theory 2.0 to me; the dimension they added to accomodate their magical photon wasn't a new dimension of spacetime; it was a new dimension in the Hilbert space that they use describe the quantum state of the system. They explain that this is an "abstract space". I think the extra dimensions that ST requires are supposed to be actual dimensions of spacetime.
I share the doubts of the poster upthread who notes that the photon appearing on the way to Andromeda has no past, so is paradoxical already. I didn't understand that bit.
Like calculating the volume of a swimming pool from a single picture, you’re never going to get it right. You can get really close if you understand the behavior of 3 dimensional space quite well. Shadows, focal lengths, etc.
We (believe we) can only experience three dimensions plus time. So if the cup is four dimensional it may have topological holes we can’t see and yes, it will leak. Or it may be bigger or smaller on the inside, and we can put less or more of the fluid into the cup than we expect.
That’s not correct. It only implies that the Hamiltonian is Hermitian, and thus that any measured value for energy is a real number. As the article states, unitarity only implies conservation of information.
Noether’s theorem states that the time-translational invariance of the laws of physics implies the conservation of energy. Interestingly, this does not hold in general relativity.
Knowing nothing in-depth about this topic, it seems like a philosophical problem. The cat is dead and alive because you just don't know it. But it surely is one or the other, isn't it?
edit: maybe I'm confusing superposition and entanglement. I thought of these to be a similar problem in physics.
> The cat is dead and alive because you just don't know it. But it surely is one or the other, isn't it?
The Copenhagen interpretation says it is both dead or alive, or that the above particle really was in two places at once. Other interpretations, such as the Many World Interpretation (MWI), say different things. For example, MWI says that upon measurement the universe actually branches into many universes, one for each possible outcome, and that we live in one such universe (the universe with a living cat, for example), but that the state itself is not ontologically a mixture of those two orthogonal possibilities.
Entanglement is a very different beast. Basically it means that two systems interact such that measurements on them are highly correlated, i.e. by measuring something on system A you immediately know something about system B, even if they are very far apart. Again, how you interpret entanglement (i.e. whether or not "spooky action at a distance" actually happens) depends on your interpretation of quantum mechanics.
The reason is that the quantum state is supposed to be a complete representation of the system right now. It doesn't quantify our ignorance, it should actually correspond completely to the physical state of the system (check the PBR theorem for a strong justification of this)
Therefore, according to Copenhagen, the state really is collapsed for the other system upon measurement of the first. There is spooky action at a distance, because the entangled state does not encode our lack of information or ignorance, it encodes an actual physical thing.
The most common example is two entangled spin systems A and B in an initial state:
|psi> = 1/sqrt(2) (|upA upB> + |downA downB>)
if you then measure the spin of A and find it to be |upA>, you then know system B is in |upB>
BUT it wasn't |upB> all along, because |psi> before measurement is the complete physical state of the quantum system. |psi> is not an epistemological construct, it is an ontological one. It does not correspond to our lack of knowledge of the system, but the actual physical system.