Anonymous at Thu, 27 Mar 2025 19:28:31 UTC No. 16630069

>>16630067
your fish friend is adorably handsome
what is its name?

Anonymous at Thu, 27 Mar 2025 19:32:16 UTC No. 16630074

Imagine partitioning space into a bunch of tiny cells. The state of a fermion is basically given by which cell it is in (and whether the spin is up and down). Momentum can be taken into account by building localized wave packets out of a superposition of nearby cells.

The point is that a fermion somewhere on a distant planet isn't taking up any of the cells for wavepackets of the fermions over here, so we can treat them as distinguishable. This has nothing to do with entanglement.

Anonymous at Thu, 27 Mar 2025 21:27:56 UTC No. 16630181

>>16630067
pauli exclusion has to do with the inability of fermions to stack their wavefunctions
the 1/2 spin of electrons partially defines the region of space that they have exclusive rights to
a condensate is the inverse, where many boson wavelengths are able to exist simultaneously in overlapping regions

Anonymous at Fri, 28 Mar 2025 04:53:07 UTC No. 16630543

>>16630074
>>16630181
what defines the tiny cell size, i.e region when the exclusion principle kicks in?
Nothing in particular? I know that the position uncertainity of a subatomic particle can be huge, in the order of meters and doesnt have to be tiny just because quantum

Anonymous at Fri, 28 Mar 2025 04:54:08 UTC No. 16630544

>>16630069
mr hands

Anonymous at Fri, 28 Mar 2025 05:57:02 UTC No. 16630583

>>16630181
>electrons
what is an electron? As I understand it we do not really know, you simply have to look at the equations that describe its properties there is no real world analogy, correct?

Anonymous at Fri, 28 Mar 2025 06:07:59 UTC No. 16630592

>>16630067
technically, you always have to antisymmetrize your fermion wavefunctions, so it's always in effect.
if you are making position measurements in freespace, the eigenbasis is compoased of deltas.
the measurement process will have some uncertainty associated with it, so a measurement won't collapse to a delta (it can't, as deltas aren't normalizable), but instead a small spread around the measured point.
numerically, you need to start worrying about the exclusion principle when your the accuracy of your position measurements is on the same scale as the expected measured distance between particles.

Anonymous at Fri, 28 Mar 2025 06:57:34 UTC No. 16630628

>>16630592
The reason i started to ask myself this was due to the existence of composite bosons such as helium nuclei. I didnt and still dont understand why they behave like bosons and not like just 4 independent fermions, or at least 2 identical protons and 2 indentical neutrons. But then realized similar things happen with fermions when multiple particles act collectively like one system. Then realized bosons can act as a single system by the billions, as in condensates, and fermions do so up to a poit in composite particles.
Is it just physical proximity? When the wavefuctions overlap enough, then its a system?

Anonymous at Fri, 28 Mar 2025 07:42:47 UTC No. 16630658

>>16630628
>composite bosons such as helium nuclei
you are asking an excellent question.
i've asked myself the same question, because i don't understand in what way composite particles can act as boson, as i've read in my QM texts.
that being said, i do know that the components are still fermions and obey the exclusion principle. helium nuclei don't all pile up in the same location in space, like photons can.

Anonymous at Fri, 28 Mar 2025 07:50:09 UTC No. 16630663

>>16630658
rubidium atoms (whole atom) behaves as a boson, you see it being used in many experiments. Its bosonness only kicks in when its cold tho

Anonymous at Fri, 28 Mar 2025 08:22:55 UTC No. 16630680

>>16630658
>helium nuclei don't all pile up in the same location in space, like photons can.
one thing that boson atoms can do is to have all the same energy, unlike having a typical maxwell-boltzmann energy distribution. Like, if average energy is 1 eV per atom, that will also be the actual energy. A bunch of atoms moving at the same (low speed). In that sense they are "same state". I do wonder if you can compress a bose-einstein condensate to a high density, i figure with a small volume comes a lower uncertainty in position and with that comes a greater spread of speeds, i.e heats up.

Anonymous at Fri, 28 Mar 2025 14:34:58 UTC No. 16630893

>>16630544
>mr hands
fr fr, like what is up with that?!? evolving before our eyes.

Anonymous at Fri, 28 Mar 2025 15:19:15 UTC No. 16630923

>>16630543
Neutron stars are a good example. Electrons are forced to be so close together it becomes favorable for them to be captured by protons to become neutrons, while the rest becomes a literal free flowing sea, which doesn't force them to occupy any orbitals (and energy levels).
>>16630583
Carriers of the electromagnetic force.

Anonymous at Sun, 30 Mar 2025 12:00:58 UTC No. 16632548

>>16630067
>If you have two electrons really far away from each other, you can just think about them as independent particles doing their thing. When they are close together, they start getting the quantum effects like "cant be in the same state".
Except when you have phase transition into superconductivity, you get boson concensation, and the electron are paired into Cooper pairs, within the coherence length.

Anonymous at Sun, 30 Mar 2025 12:12:51 UTC No. 16632565

>implying there are 2 electrons

Anonymous at Sun, 30 Mar 2025 12:13:54 UTC No. 16632567

>>16630067
trick question, it resolves automagically if you recall that you cannot actually be outside a reference frame

Anonymous at Sun, 30 Mar 2025 17:10:52 UTC No. 16632822

>>16632567
>next trick question

Anonymous at Sun, 30 Mar 2025 17:15:02 UTC No. 16632832

>>16632822
>next electron

Anonymous at Mon, 31 Mar 2025 08:16:24 UTC No. 16633541

>>16630923
>electrons
>Carriers of the electromagnetic force.
Please stop posting and go back to high school

Anonymous at Mon, 31 Mar 2025 08:28:29 UTC No. 16633546

>>16630067
Study the theory of an electron gas with statistical mechanics, if you actually want to know.

Anonymous at Wed, 2 Apr 2025 20:25:36 UTC No. 16635409

>>16630543
Sorry I didn't come back to this for several days, but I'll reply in case you're still around.

The tiny cell size is nothing physical, it is just a convention. You can turn it into a legitimate single particle basis if you include the momentum levels of the particles within the cell (working this out is just the same problem as the infinite square well that is in every QM textbook). The point is that if the cell size L gets small, the momentum level spacing, which is on the order of hbar/L, gets large. So it costs more energy to put additional fermions in a smaller cell rather than a larger one.

The point I was trying to make was just that if you have N_1 particles localized in one region of space, and N_2 particles localized in another region of space, this means that the N_1 particles are only occupying single particle states that are completely orthogonal to any of those occupied by the N_2 particles. And if this is the case then the two sets of particles can be considered to be distinguishable as far as statistics goes. Once you start to consider particles which are not localized precisely so some of the states of the N_1 particles overlap with the N_2 particles, then the exclusion principle "kicks in" so to speak.

Anonymous at Wed, 2 Apr 2025 23:35:25 UTC No. 16635527

>>16630067
no one knows. the universe is actually a hologram and everything is connected to everything else

Anonymous at Thu, 3 Apr 2025 18:33:27 UTC No. 16636295

>>16635527
Wrong and (longest sigh this side of the Andromeda) falsifiable.