Recent content by QuarkyMeson

I mean, just so you know I agree with you. I don't think span preservation for quantum states is a good definition of invariance. The 0 vector isn't a quantum state. Your example shows that information has leaked out of the system into the environment, this is hardly what I would personally call...

Yeah, see Scotts post here for more information: Given a finite volume and finite amount of energy there are only a finite number of possible states.

Yes, a big caveat to all this is that the universe is truly infinite and that energy is also randomly and uniformly distributed. It appears to be so, but we will never know for sure. I called out the observable universe wrt the notion that there is only a finite number of configurations for our...

If the universe is infinite and matter is distributed randomly and uniformly, patterns have to repeat. This is because there’s a limit to how many ways you can arrange particles inside a single observable universe. Once you run out of unique arrangements, nature is forced to start repeating them.

This is a misconception. When people say it's like a particle or wave it doesn't mean it's actually either. It's just in general, sometimes it better to model quantum objects as one or the other, but it remains a quantum object described by a quantum state. In fact, when you actually learn...

I guess that makes sense. You already have engines and a fuel tank so the weight savings (if any) of adding in a parachute system instead of carrying more fuel to land probably isn't worth the extra complexity.

In QM we can look at two different update rules: $$|\psi\rangle \mapsto U|\psi\rangle$$ with ##U## unitary. This evolution of the state vector is deterministic and preserves norm: $$\|U|\psi\rangle\|=\||\psi\rangle\|$$ Alternatively, for say a measurement, each possible outcome is associated...

Like before, a global measurement of the screen’s total momentum gives which-path information only if the two recoil states are distinguishable. In a symmetric two-slit experiment where the screen merely receives a kick to the left, that kick is tied to the particle’s outgoing transverse...

The universe appears homogeneous and isotropic on large scales. The lower bound for the size of the universe is much much larger than the observable universe. If the universe is truly flat and homogeneous than it's infinite with infinite energy (or finite energy with some weird 3-torus thing and...

This is basically what you're asking: https://arxiv.org/pdf/cond-mat/0101157 A global momentum measurement of the screen only yields which-path information if the recoil states are distinguishable. When they are, interference visibility drops accordingly. This occurs because the uncertainty...

I mean, you just kind of make it up and pick a definition for it so everyone is on the same page. You could argue for exact invariances, such that ##A\in SU(2)## or ##A\in U(2)## up to global phase (like the paper). You could say it's invariant up to some scalar (when I hear this I normally...

The delta between Griffiths and Jackson isn't that large. Jackson goes into more detail on certain topics, like BVP, chapters 10, 15, 16 and 17 don't really have a straight Griffiths analogue but that doesn't matter for what OP is looking for. They're much better off just reading relevant papers...

It's kind of a given that they don't. Even after reading all of Jackson this would be true. You plug in the holes as you're reading.

Why land boosters at all though? Why not just parachute them down if you want to refurbish them? The shuttle used to just drop them in the ocean and recover them, that's probably less idea with all the transportation costs and salt water/mechanical damage. I guess I just don't see why you...

##(A \otimes A )\ket{\Psi^-} = \det(A)\ket{\Psi^-}## in the above context is always true. The proof is trivial. For invariance you need to define exactly what that means. I briefly looked at the linked paper and I don't fully understand it, but it looks like they're exploiting SU(2) rotations...