I'm not a quantum physicist, but it seems like theoreticians always resolve to adding more dimensions when they can't solve a problem. In a way this sounds like string theory 2.0.
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.
> I'm not a quantum physicist, but it seems like theoreticians always resolve to adding more dimensions when they can't solve a problem.
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.
It does seem pretty weird to me. If you poured half of a cup of four dimensional water into a second container, you could certainly have more than a cup of fluid. Why? Because you measured a four dimensional object with a three dimensional container. If you turned the fluid it may take up more three dimensional space.
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.
I think I’m playing a little loose with words here. A measuring cup measures volume of a liquid, which is three dimensions. It is a three dimensional ruler. A ruler only measures one dimension, but it is built from an object, and that object has three dimensions.
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.
Ok I stand corrected (I'm just a lowly experimentalist ;). Is it correct to say that in a time-invariant system a unitary transformation conserves energy?
I have a very similar feeling, when i read about quantum superposition.
It feels like a super theoretical theory. If you don't measure something it can be either state, but if you measure something it has a state, just like a entangled other piece you did not measure before.
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 principle of superposition is that any addition of quantum states is also a valid quantum state. For example, you can have a system that has a state which is both "the particle is at x = 1m" and "the particle is at x = 2m". What really happens physically when you measure the position of the particle is not specified by the theory, but the Copenhagen interpretation says that one of those positions will be chosen depending on the coefficient in front of each state, e.g. if we have a state |psi> = 1/sqrt(2) |x = 1m> + 1/sqrt(2) |x = 2m> then we get either 1m or 2m with 50/50 probability. Then if we measure 1m we will find that afterwards the state will be |psi> = |x = 1m>. Again, what actually happens during this process is not well understood by physics yet, and also is one of the things that differentiates different interpretations of quantum mechanics, so yes that is "philosophy".
> 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.
No, certain interpretations (such as Many Worlds Interpretation (MWI)) say that "measurement" is just "interactions with the broader reality". Copenhagen says that "measurement" is a primitive feature of the theory that cannot be explained via such interactions. I.e. Copenhagen interpretation says that Quantum Mechanics cannot describe the physics of the photodiode entirely, since it cannot describe the measurement process. MWI says that measurement occurs due to decohering interactions with the environment
My go-to ELI5 explanation for entanglement: suppose you take an object, cut it along non-symmetry axis (e.g. cut a bill), place both halves in different envelopes. Upon opening one envelope (measuring) you immediately know what is in the other envelope. Not because of "spooky action at a distance", but rather due to prior knowledge of the system[s].
That is not correct though, at least not in the Copenhagen interpretation.
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.
so god doesn't following best practices and uses global interdependent variables.
maybe our universe was a PoC and the Universe 2.0 is going to be well refactored version.
Not quite, entanglement is indeed spooky action at a distance given bell’s inequality theorem showed that it can’t be local hidden variables (prior knowledge)
Also not quite, since that depends on your interpretation of quantum mechanics. For example, in the Many Worlds Interpretation there is not spooky action at a distance, since there is no wavefunction collapse in the first place, i.e. measurement does not cause a projection operator to occur, but instead occurs through unitary decoherence. Therefore, no spooky action at a distance (although it is still non local)
Yeah, each valid interpretation is consistent with the observations, but each is weird in its own way (usually some form of non-local, sometimes more out there like superdeterminism).
As a non-physicist, I found Jeffrey A. Barrett The Conceptual Foundations of Quantum Mechanics, Oxford UP 2019, quite interesting. It focuses on laying out the experimentally confirmed data that basically any theory and interpretation of QM must take into account and "explain" (unless there is something with the experiments or something groundbreaking new is found). It's understandable by laymen. However, at least my experience was that the more I read about QM, the weirder it appeared to me and the harder it was for me to grasp it conceptually.
Feynman : “The difficulty really is psychological and exists in the perpetual torment that results from your saying to yourself, "But how can it be like that?" which is a reflection of uncontrolled but utterly vain desire to see it in terms of something familiar. But nature is not classical, dammit, the imagination of nature is far greater than the imagination of man.”
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.