Summer School 2024 - Quantum Physics

[@AssumptionsofPhysicsResearch]

Index and slides available at assumptionsofphysics.org/presentations/2024SummerSchool.html (Video quality came out a lot lower than expected)

[@pdelong42]

I'm at ~37:00 presently - this is the first time I've actually seen anyone describe the processes of unitary evolution and measurement in-terms of motion around a Bloch sphere. Sure, static states were defined that way, but never the processes themselves. Perhaps it was tacitly left as an exercise for the student. Anyway, thanks! That helps my mental model tremendously, and I'll be looking at things with that in mind from now on.

[@AssumptionsofPhysicsResearch]

I had never seen that either... it's all stuff I developed myself. You may want to look at the videos I posted on the geometry of quantum mechanics on the other channel: they cover a bit more stuff.

[@Kram1032]

1:08:00 The problem with high precision position measurements is going to be, that you require very high energies to even measure them. Say, you might use gamma rays to measure your particle's position and since gamma rays have a very short wavelength, you can set up an interference type experiment that allows you to locate your particle extremely well. But that same gamma ray will also cause quite a substantial kick to the particle, drastically changing its trajectory or possibly even breaking it apart in the process. So at that point you can't really easily measure its position on the next time step as you have no idea where it went in the first place. Especially when we take serious the idea of the inability to put markers or labels on our simplest particles: If you pump that much energy into the system, you can't even be sure that you're still looking at the same particle even if you *do* find a particle again. It's possible in principle that you have created it, right? (The probabilities depend on the particle of course. With anything complex like an atom that's basically not gonna happen, but if you are trying to track electrons, it's gonna be easier.) It's hard to imagine an extremely high resolution measuring method that doesn't involve extreme energies which, in turn, disturb momenta.

[@Kram1032]

1:28:00 So the half-spin issue ("there are only Bosons and Fermions") is a result of us living in more than 2 spatial dimensions. If you take seriously the notion that you can not distinguish individual identical particles (i.e. two electrons or two photons etc.), you find that you can't know for sure whether they pass through each other or bounce off each other upon collision. Literally nothing gives away which particle is which post-collision! So you can describe your particles in a phase space. Using two particles in 1D, you can take all their possible paths to be the Euclidean 2D plane. Each point in that plane describes the current 1D position of the first as well as the current 1D position of the second particle. But since you can't distinguish the two particles, states where you swap their positions are the same. I.e if your coordinates are (1, 3) that's the same as (3, 1) meaning one particle is in position 1 unit right from the origin, and the other is 3 units right from the origin. But if you do that equivalence (1,3) = (3, 1), that means you essentially set up a boundary along the diagonal x=y. And you can reduce the redundant paths (the Euclidean plane is a double cover of state space) by reflecting particles off that 45°-diagonal. If you do the math, you'll find, that this causes a phase shift, i.e. you change the spin. At this point, that's completely unconstrained: You get "anyons" which may have any spin what so ever. If you allow the particles an extra degree of freedom, operating in 2D, you *still* can find anyons. But once you go to 3D, you get an issue: Because you can then flip the plane in which your two particles operate through the 3rd dimension, your spin suddenly becomes observer-dependent for arbitrary phase shifts. However, if you demand observer independence, you suddenly recover the condition that spins can only be moving in halves. So the three conditions you need to make this work are: 1. Indistinguishability of your particles 2. observer independence 3. a sufficient number of degrees of freedom. Would that suffice for your reverse physics approach?

[@AssumptionsofPhysicsResearch]

I'll need to put more brain power in understanding the argument... but this would exactly be along the lines of what I am looking for. The fact that spin must be in three dimensions is actually something we already have (it comes from the fact that the 2 sphere is the only symplectic manifold). If I understand correctly, the observer independence is just "at-equal-time", right? Also, the final conclusion is just that spin are multiples of 1/2, not they must have the different statistics, right? (I'd be surprised if you get the different statistics, because all proofs I saw requires relativity)

[@Kram1032]

@@AssumptionsofPhysicsResearch it's probably not as in-depth as you'd want it, but at least as a starting point, the latest video of PBS Space Time dealt with this exact thing I don't know but I'm guessing yes, the assumption is at-equal-time. And as far as I know, yes, it's just about the multiples of 1/2. Maybe the statistics linger in there though: The argument requiring observer independence kinda is a relativistic notion, right? I'm not well-versed enough to really tell you much more than I already said though. Hope you or your team finds some good arguments here :)

[@manuderezzo]

I like a lot the idea of putting ensambles and entropy as the basis. It's quite different from more usual approaches. I can see that many laws can be recovered much simpler this way, which is great. Are there any predictions one could check experimentally?

[@AssumptionsofPhysicsResearch]

For now, it's mainly a way to reorganize the current theories. So the "predictions" we want to get our are classical theory on one side and quantum theory on the other side (give the appropriate and meaningful assumptions). Part is also getting the map between physics and math right.