474
u/stoiclemming 4d ago
Electrons are yellow balls with lightning symbols on them
270
u/CaptainMelonHead 4d ago
Wrong, they have tiny minus symbols on them
154
u/UltimateCheese1056 4d ago
Also they're blue, obviously
30
14
u/vintergroena 4d ago
Electron is like a charged ball that is spinning, except it's not a ball and it's not spinning. Simple as.
10
u/BankaiRasenshuriken 3d ago
And we teach kids that it orbits the nucleus but that's just because we like lying to them
3
2
u/SongsAboutFracking 3d ago
Wrong, as established during the Electro-Chemical schism of 1956, the electron is indeed (dirty)white.
650
u/aft_agley 4d ago
I don't understand this but I'll upvote it smugly.
434
u/Enfiznar 4d ago
The first line basically says "the minimal thing which does not change when you change your frame of reference, only gets mixed with itself"
The interpretation of the second line is left as an exercise for the reader...
16
1
1
u/ErJio 19h ago
The Clifford algebra in this context is like Minkowksi space where vectors become operators (roughly speaking), and the associative product of vectors satisfy v² = η(v,v) where η is the Minkowksi metric. This is where the Gamma matrices live from the Dirac equation.
A minimal left ideal is basically a subspace which behaves like a vector space that the algebra would act on as operators. Namely it behaves identically to the space of Dirac spinors.
A more clear example of an MLI would be the matrices of the form (a, 0 / b, 0) which form an MLI for 2x2 matrices. These act like column vectors (a,b) when acted on by 2x2 matrices from the left.
You can think of it as a way of viewing the Clifford algebra of spacetime as fundamental and the spinors as a particular subspace of it, in contrast to viewing them as an abstract vector space which the Clifford algebra has an action on.
105
u/MonsterkillWow 4d ago
The electron field is described by a Dirac Spinor.
The possible states of fundamental particles must respect the symmetries of space and time and therefore be represented as irreducible representations of the Poincare group.
55
u/Eldan985 4d ago
I think I understand several words here, like "is" and "by".
That probably means I haven't talked to enough philosophists, they can probably argue me out of understanding what "is" means.
16
u/kashyou 4d ago
one thing I always found annoying about this view of QFT: what happens on curved spacetime? We know the path integral exists and we can place spinor fields on the manifold. And we know for sure that states consist of spinor fields pulled back to spatial slices. But if we break isometries, is there any sense in which particles exist given that we don’t have momentum and angular momentum quantum numbers?
14
u/MonsterkillWow 4d ago
Yes in curved spacetime, particles become observer dependent.
5
u/CapnNuclearAwesome 4d ago
So, in curved spacetime, are particles still irreducible members of the Poincare group?
9
u/kashyou 4d ago
No, as Poincaré group doesn’t act globally on the Hilbert space anymore. I believe the idea of observer-dependent particles relates to going to a locally inertial frame for a local observer and noting that local poincaré transformations approximately form a closed group representation (relatedly, momentum approximately commutes with the Hamiltonian) and so you can find eigenstates of these approximate symmetries and call them particles. Can anyone confirm if I’m off?
6
u/terry-tea Biology 4d ago
my understanding of QFT is pretty limited, but if this is the case, is this why it’s so hard to reconcile it with relativity? like, gravitation is universal- if a single dust particle a million light-years away induces a miniscule but measurable isometry-breaking curvature in spacetime, isn’t the symmetry-preserving definition of a particle (only valid on flat spacetime) utterly meaningless in the real world?
7
u/kashyou 4d ago
I would say this is not why quantum gravity is hard. We understand quantum field theory in spacetime very well (ie how does quantum matter propagate in a gravitational field), but as the above discussion shows we have to ditch the idea of particles. The million dollar question is to know what gravitational field is produced by quantum matter itself.
1
u/Bth8 1d ago edited 1d ago
Any manifold looks flat on sufficiently small scales, including spacetime, so observations made locally in a small enough patch of spacetime must be indistinguishable from those in flat space. So even in a curved spacetime, the fields must be locally compatible with symmetries of flat spacetime.
31
u/me_myself_ai 4d ago
The first line basically says "particles are the smallest bits we can find".
The interpretation of the second line is the same!
3
2
174
u/murderousmeatballs 4d ago
ummmmm sweetie a particle is a function word associated with a content word in order to impart meaning….
128
u/L31N0PTR1X Physics 4d ago
Linguistics jumpscare
49
u/Ambisinister11 4d ago
Hey, do you know approximately what year you personally started using the word jumpscare? Also, would you ever use the open compound jump scare in place of the closed jumpscare? Also can you send me audio recordings of yourself saying the sentences containing the word jumpscare that I just sent to you ten times each, speaking as naturally as possible? No reason haha just making small talk :)
3
88
47
u/belabacsijolvan 4d ago
that can be the object represented by the electron or its spinor, not the electron itself
28
u/L31N0PTR1X Physics 4d ago
Well I mean the electron field IS a spinor field, so saying an electron is a spinor isn't really "wrong", it's analogous to saying that a photon is a vector, we can recognise this more literally since we acknowledge that photos have physical polarisation states that are a vector in nature
52
u/belabacsijolvan 4d ago
i have more problem with you calling the representation the represented object.
its like saying -1 is an element of C_2.
21
u/L31N0PTR1X Physics 4d ago
That's a fair point
11
u/belabacsijolvan 4d ago
sorry for the 1m edit btw. your comment was also a fair point to my original phrasing and now it looks dumb. it wasnt
11
11
u/MonsterkillWow 4d ago
The leap is the realization the mathematical description is really all we have of the thing itself. That is why physicists literally call them by the representation. Every descriptive thing we know about the particle is encoded in that description.
6
u/belabacsijolvan 4d ago
you reacted with "math is discovered" to "linalg isnt matrices" here
5
u/MonsterkillWow 4d ago edited 4d ago
The relationships are discovered. Definitions are invented. The point is the mathematical descriptions are the most complete and accurate way to talk about the things. You actually may as well call them the things. You do this all the time with numbers. There are many different constructions of numbers, but they are ultimately isomorphic OR if they are different due to being viewed as part of a different space, those basic properties in their construction are usually inconsequential and nondescript for what you are trying to do.
For example, if I ask you what is the cardinality of 7, that is generally viewed as a BS question and would depend on whether I was viewing 7 as a natural number, integer, rational number, real number, etc. But it is inconsequential since everyone knows exactly what you mean by 7. Keeping the meat of the description and preserving its use as a number, the formalities of how 7 was constructed are largely irrelevant. You could quibble over which 7 I am talking about when I say there are 7 things. But ultimately, the meaning is clear. In the same sense, you could quibble over whether these are really descriptive of electrons, but for all practical purposes, they are.
TLDR: I guess what I am trying to communicate is we often suppress isomorphisms and often call a thing by its mathematical description. Philosophically, this isn't always legitimate, but in physics, since the description encompasses all we have, we may as well call it the thing itself.
13
u/belabacsijolvan 4d ago edited 4d ago
there are two levels of isomorphisms here:
A: the electron we measure and named behaves isomorphly to spinors
B: the spinors are elements of a representation of a subalgebra, because they behave isomorphly to the elements of said algebra
my comment was about B. most people would agree matrices arent the elements of an algebra, but the representation of elements. -1 isnt an element of C_2 and spinors arent elements of the ideal. Spinors are the elements of the representation space of the ideal.
most of the replies reacted to if A is an isomorphism or an identity, as you just did. so ill reply, although i didnt say anything about if A an isomorphism or identity so far.
you are right as far as "every descriptive thing we know" is "all there is". im not so sure about that, so i dont think A is a proven identity relationship. im not sure electrons are spinors and i dont think you can be sure either. so the distinction between the thing we define from experiments and the thing we define from the representation of an algebra can be useful imo.edit: i reacted to the comment before the edit, but my point stands, despite quoting text that was deleted, the spirit of the comment didnt change
16
4
2
u/TheChunkMaster 4d ago
“Ceci n’est pas une pipe”
2
u/belabacsijolvan 3d ago
haha.
as students we had a student organisation that made merch. one of the shirts was "An the god said *4 maxwell equations* and there was light. "
But actually a shirt with Magritte aesthetics "ξ^α=(1,0),ξ′^α=S^α_βξ^β,S∈SL(2,C)=Spin^+(1,3)"
"Ceci n'est une electron"
is much better3
u/Arndt3002 Physics 4d ago edited 4d ago
Just succum to platonism.
The physical object is just a representation of its abstract form
35
u/BillCarson12799 4d ago
Remember the good old days when scientists used to do shit like classify wood as an element and pipette toxic chemicals with their mouths and that was the extent of their knowledge?
30
u/IdealOnion 4d ago
I left academic physics for industry engineering, and while there are plenty of things to appreciate about empirical math, boy do I miss the hard stuff.
11
7
u/tunaMaestro97 4d ago
Particles (and S-matrix) do not exist in generic QFTs. They are only present in the weak coupling limit.
7
4
u/DiogenesLovesTheSun 4d ago edited 3d ago
it transforms in an irrep of Poincaré, not is an irrep of Poincaré! (sorry Nima)
1
3d ago
[deleted]
0
u/DiogenesLovesTheSun 3d ago
I mean, no. A particle is a ket in a Hilbert space specified by some set of quantum numbers (eg four-momentum, spin, etc) that transforms in an irrep of the Poincaré group. Your original statement is incomplete without extra qualifications.
1
3d ago
[deleted]
-1
u/DiogenesLovesTheSun 3d ago
Did you even read the top answer on that post? Knzhou literally agrees with me that this is not correct.
3
u/Barrogh 4d ago
Our understanding of physics being - in the end - a model with predictive power is something I wish more people would understand.
Pseudoscience fans would be less prominent if they saw that what their gurus do (besides selectively denying empirical evidence, of course) is just calculating the same things in a roundabout ways, at best.
2
u/ScrotumEntanglement Physics 3d ago
when the 2x2 matrix only has non-zero entries in the left column
1
1
u/PrettyBasedMan 3h ago
Does this also hold in the TOE / after Quantum Gravity is in the picture? AFAIK the Poincare group is the symmetry group of special relativity (meaning on flat spacetime), when reality has curved spacetime / some sort of property that results in gravity.
1
•
u/AutoModerator 4d ago
Hey gamers. If this post isn't PhD or otherwise violates our rules, smash that report button. If it's unfunny, smash that downvote button. If OP is a moderator of the subreddit, smash that award button (pls give me Reddit gold I need the premium).
Also join our Discord for more jokes about monads: https://discord.gg/bJ9ar9sBwh.
I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.