/sci/ - Science & Math

[Anonymous No.15552208]

I don't understand spin. Why does spin have to be half-integer +1/2 or -1/2? Why can't you call it up and down or +1 and -1 or 1 and 0? Can you have other fractions of spin e.g. 1/3?

[Anonymous No.15552268]

>>15552208
Spin is only half-integer for fermions

[Anonymous No.15552341]

>>15552208

[Anonymous No.15553310]

>>15552341
>even
shouldn't that be integer?

[Anonymous No.15553340]

>>15552208
Spin is the dimensionality of a particle's range of motion in spacetime. It's 1/2 for fermions because they have freedom of motion with respect to time in the forward direction, but not the reverse. However, note that I am not a physicist, nor do I know of any physicist that endorses the above interpretation.

[Anonymous No.15553990]

What's the relationship between spin and gravity?

[Anonymous No.15553999]

The Stern-Gerlach experiment

[Anonymous No.15554218]

>>15552208
Don't try, most of quantum mechanics is untested fairytales and is just a mathematical jerkoff competition

[Anonymous No.15554236]

>>15553340
>Spin is the dimensionality
Spin representations are 2-dimensional, not 1/2-dimensional.

>>15553999
Stern-Gerlach only implies that spin is binary, not that it's half-integer.

[Anonymous No.15554258]

>>15554236
>Spin representations are 2-dimensional, not 1/2-dimensional
I think you're conflating the magnitude of the space within which spin occurs with the magnitude of the spin itself. Spin is a function of Hausdorff dimension 1/2 mapped onto a space of topological dimension 2.

[Anonymous No.15554261]

>>15554258
>Spin is a function of Hausdorff dimension 1/2
Please redpill me on this statement.

[Anonymous No.15554267]

>>15553310
Yeah, it's lazy language, an even amount of halves=integer. Used because electrons.

[Anonymous No.15554269]

>>15552208
Spin is just angular momentum. When you consider angular momentum in quantum mechanics it turns out it must be quantized in multiples of some smallest value which is proportional to Planck's constant (which has the same units as angular momentum). This smallest unit is what people refer to as spin 1/2, but you can have much greater values than this, and at the macroscopic level angular momentum appears continuous.

>Why does spin have to be half-integer +1/2 or -1/2?
It can be multiples of this

>Why can't you call it up and down or +1 and -1 or 1 and 0?
Not 1 and 0 because it is literally angular momentum. You could call it +1 and -1 if you redefined the unit, it is just convention.

>Can you have other fractions of spin e.g. 1/3?
No

[Anonymous No.15554273]

>>15554261
It's nonsense. There is no connection between spin and Hausdorff dimension

[Anonymous No.15554274]

>>15554261
Well for one I am obviously only referring to spin-1/2 fermions with that statement. It means that fermions' distribution over time within a given frame of reference is a fractal.

Hausdorff dimension is a measure of how well a curve fills the space within which it is embedded. For ordinary curves it matches with Lebesgue dimension, i.e., a point has Hausdorff dimension 0, a line has Hausdorff dimension 1, etc. For fractal curves, their Hausdorff dimension is a non-integer.

[Anonymous No.15554288]

>>15554273
>There is no connection between spin and Hausdorff dimension
If the confidence with which you make this claim is merited, you should have no difficulty answering >>15553990

[Anonymous No.15554298]

>>15554274
I'm familiar with Hausdorff dimension. I'm not aware of its role in describing fermions. Do you have any text for me to read?

[Anonymous No.15554308]

>>15554288
>>15553990
Yes, I have no difficulty. General relativity is a classical theory, and gravity is coupled to spin 1/2 particles by coupling a spin 1/2 field to a metric. Then Einstein's equation holds with the energy momentum tensor expressed in terms of the fermion fields. To couple the spin 1/2 field to a metric you need to write the metric in terms of vielbeins (so it is compatible with the gamma matrices that appear in the fermion action), but this is no major difficulty and it is covered in every good GR textbook.

I don't expect you or OP understood what I just said, but just let me reiterate that I understand spin, and it has nothing to do with Hausdorff dimension

[Anonymous No.15554315]

>>15554298
>Do you have any text for me to read?
No, as I mentioned in >>15553340 I know of no physicist who endorses this idea. It's just a pattern that I've noticed. I am still figuring it out. I'd be happy to explain further but if you're only interested in authoritative published information then there would be no point, so you tell me.

[Anonymous No.15554317]

>>15554315
Your own idea? Nice. Can you show me the math please? I'd be genuinely interested.

[Anonymous No.15554321]

>>15554308
>General relativity
Care to look at the pic and attempt to answer the question in its context?

[Anonymous No.15554326]

>>15554317
I will try, but it's 95% in my head so it will take time, please bear with me.

[Anonymous No.15554329]

>>15552208
Nobody knows for real but in theory it comes from group theory. From the classification of representations of the lorentz group.

[Anonymous No.15554336]

>>15554321
I did. Elementary particles are described in terms of fields, which have different transformation properties depending on the spin, and it is straightforward to couple these to gravity.

You asked me to answer that as some kind of confidence test, and you didn't expect I would be able to answer but I am. None of this has anything to do with Hausdorf dimension

[Anonymous No.15554349]

>>15554336
>and it is straightforward to couple these with gravity
Then why is there no unified theory yet?

[Anonymous No.15554365]

>>15554349
Saying how the fermion action is coupled to the metric isn't the whole story. If you want to describe a quantum spin 1/2 particle in a classical gravitational field this gives the answer. If you want to describe gravity being quantum too, this gives part of the answer. There needs to be additional higher order terms in the effective action beyond the Einstein-Hilbert action and some of these will include the fermion field too. String theory works along this lines, but as I'm sure you know there is no experimental support.

In any case, asking me to give you a unified theory of fermions and quantum gravity in order to test whether I understand spin is asking too much. Spin is just quantized angular momentum, as I explained earlier in a much easier to understand post than this.

[Anonymous No.15554395]

>>15554317
Time as an abstract notion can be modeled as a single dimension, such as by a real number line. But time as we experience it is not smooth in the way that the real number line is. For two events A and B, such that A precedes B, you could measure the distance from A to B in some way analogous to the Euclidean distance between two points a and b, a < b on the real number line. However, on the real number line, the Euclidean distance from a to b is equal to the Euclidean distance from b to a. The same is not true for events in time A and B. Since, in our experience, one cannot travel backwards through time, the distance from B to A is either infinite or undefined. Intuitively, if time is a single dimension, and we can only move one way through that dimension, then we have only a half degree of freedom with respect to the time dimension.

I noted a correlation between my observation that I experience only a half degree of freedom with respect to time, the fact that the Hausdorff dimension of the zeroes of a Weiner process in one dimension is 1/2, and half-integer spin. From there it was just "what if this is more than mere coincidence?" speculation. As mentioned by another Anon in a previous post, spin is defined with respect to two dimensions. Assuming the above correlation is not a coincidence, then spin-1/2 marks a half-degree of freedom with respect to time, thus time accounts for one of the two dimensions with respect to which spin is defined. If it's the time dimension of Brownian motion (Weiner process) in a single (spatial) dimension, then the second dimension with respect to which spin is defined is space. (1/2)

[Anonymous No.15554398]

>>15554317
But if space is only one dimension, then why do we experience it as three-dimensional? Because, some process unpacks space over time (Planck timescale) into the three dimensional space which we experience over a MUCH greater timescale. That process is the three fundamental interactions -- strong, weak, and electromagnetic -- whose force carriers have spin 1, corresponding to a full degree of freedom with respect to space.

I'm going to go play with my kids now but I will post more later. Please feel free to ask questions in the meantime. (2/2)

[Anonymous No.15554404]

>>15554395
>>15554398
Interesting thought but I'm not mathematically convinced yet. Could you write down the argument more rigorously?

[Anonymous No.15554673]

>>15554395
>>15554398
Continuing:
I think (but again, making no claims to expertise) that what I'm describing here is a Minkowski space on a quantum scale. The inertial reference frame is the "layer" in which spin-1/2 fermions are embedded. "Beneath" that is the Higgs field (?), "anchoring" the inertial reference frame. "Above" is the field in which the spin-1 bosons are embedded. That field moves over the inertial frame of reference at c, re-ordering the fermions embedded within it, which on a macro scale is perceptible as the passage of time.

If gravitons exist, then they're in a separate, "higher" spin-2 layer, and (under this interpretation of spin) would operate retrocausally in some sense, having (unlike fermions) a full degree of freedom with respect to time. However, the gravity in effect within a given inertial reference frame might also be explicable as the resultant of the spin-1 forces' work upon the complement of the inertial reference frame with respect to the inertial reference frame's closure with respect to the universe (which may just be the complement of the inertial reference frame with respect to the universe).

[Anonymous No.15554676]

>>15554365
I'm the Anon who posted >>15554288, but not the Anon who posted >>15554349, just to be clear.
>asking me to give you a unified theory of fermions and quantum gravity in order to test whether I understand spin is asking too much.
In >>15554273 you state with certainty that there is no connection between Hausdorff dimension and spin. Not "no connection in any current theory," but categorically no connection. If you don't understand spin well enough to give an account of how spin on the quantum scale gives rise to gravity on the macro scale, then I don't recognize your epistemic authority to make that claim, and I don't think the Anon who posted >>15554349 does either.

>>15554404
Could you write down the argument more rigorously?
Probably, with enough time and effort. Can you give me a compelling reason to invest that time and effort, given that I already have an established career, have no interest in changing that to physicist or mathematician, and could more profitably commit the same time and resources to other endeavors?
Solving puzzles is fun. Talking about how to solve puzzles is kind of fun. Writing puzzle-solving documentation is boring and I don't think it would pay well.

[Anonymous No.15554681]

>>15554676
>Can you give me a compelling reason to invest that time and effort, given that I already have an established career, have no interest in changing that to physicist or mathematician, and could more profitably commit the same time and resources to other endeavors?
For the highest, most virtuous and most intellectual purpose: debate on 4channel.

[Anonymous No.15554721]

>>15554681
In that case, given that rigor is not synonymous with formalism (rather, formalism is a tool for ensuring rigor), I invite you to match effort for effort and offer specific criticisms of >>15554673 such that I might further improve my argument's rigor to a standard acceptable to the average Kyrgyzstani glass-blower.

[Anonymous No.15554731]

>schizophasia thread
everyone post their collection of memorized soience buzzwords and jargon

[Anonymous No.15554771]

>>15554676
>If you don't understand spin well enough to give an account of how spin on the quantum scale gives rise to gravity on the macro scale, then I don't recognize your epistemic authority

Spin is something on the "macro" scale (meaning large compared to some quantum gravity scale, so we can define a classical background spacetime) by its nature. It is just angular momentum which is associated to spatial rotations. Whatever theory of spin you have must deal with the fact that we already understand how spin works on this "macro" scale where spacetime is classical and matter is quantum, and on this scale there is absolutely no connection to the Hausdorff dimension. Is that epistemologically aware enough for you?

[Anonymous No.15554788]

>>15554731
some (very) low-effort OC for you, Anon

[Anonymous No.15554809]

>>15552208
>Why does spin have to be half-integer +1/2 or -1/2?
Because quantum numbers go in full steps and the math works out such that you have a range of -n, -n+1...n-1, n for the angular momentum quantum numbers. The spin allows n to be an integer or half-integer. But notice that for an integer n, say 1, you would have three values -1, 0, 1, while 1/2 gives two values. Turns out that's exactly what's needed to explain something like the Stern-Gerlach-experiment where silver atoms are split into two piles by a magnetic field.
It means the one outer electron silver has can only take one of two spin values, depending on which the whole atom is deflected up or down. If spin was integer there would be three piles.

[Anonymous No.15554842]

>>15554395
Not even wrong

[Anonymous No.15554884]

>>15554842
Reviewbrah looking classy here.

[Anonymous No.15554956]

>>15554771
>Spin is something on the "macro" scale (meaning large compared to some quantum gravity scale, so we can define a classical background spacetime) by its nature.
The fact that spin is evident at macro scale doesn't make it an inherently (by its nature) macro-scale phenomenon. On the contrary, the fact that it is also evident at the quantum scale (spin quantum number) means that it can't be an inherently macro phenomenon. An inherently macro-scale phenomenon would disappear at the quantum scale, like a constant of integration disappears when differentiated. (Gravity could be such an inherently macro-scale phenomenon.)
>Whatever theory of spin you have must deal with the fact that we already understand how spin works on this "macro" scale where spacetime is classical
A scalar value (spin quantum number) in two-dimensional spacetime (described in >>15554673) becomes a vector (intrinsic angular momentum) when mapped (by interplay of spin-1 bosons) to four-dimensional (classical) spacetime. Where's the problem?
>on this scale there is absolutely no connection to the Hausdorff dimension
I think you'd need to demonstrate that it isn't a factor of the mapping above (or else that such a mapping isn't possible) to actually prove that statement.

[Anonymous No.15554961]

>>15554842
Where did you think I got the idea?

[Anonymous No.15554966]

>>15554956
You didn't understand my non-standard use of macro. I mean macro with respect to quantum gravity. You don't need to understand quantum gravity to describe something like the Zeeman effect of a hydrogen atom in a gravitational field, but you do need to understand quantum mechanics.

[Anonymous No.15554981]

>>15554966
I don't believe you're arguing in good faith, because I recognize your style of writing from previous threads, but feel free to prove me wrong by making a good-faith effort of explaining how the Zeeman effect of a hydrogen atom in a gravitational field is inconsistent with what I've said.

[Anonymous No.15554995]

>>15554981
> inconsistent with what I've said.
I didn't bother to read much of the description of your theory sorry. But it seems to rest on the fact that the Hausdorff dimension of a Wiener process in 1 spatial dimension is 1/2 (this is true). But you never demonstrated any link between this appearance of 1/2 and the 1/2 appearing in a spin 1/2 particle which is something having to do with angular momentum. You also demonstrate a misunderstanding when you say "As mentioned by another Anon in a previous post, spin is defined with respect to two dimensions." That anon was referring to Hilbert space dimension and you seem to be talking about spatial dimension. This is why I stopped reading.

[Anonymous No.15555032]

>>15554995
>it seems to rest on the fact that the Hausdorff dimension of a Wiener process in 1 spatial dimension is 1/2
Your "rest on" assumption is incorrect.
>this appearance of 1/2 and the 1/2 appearing in a spin 1/2 particle
Correct, I haven't proven a connection. It's a coincidence which gives me reason to suspect that the mapping described in >>15554956
>A scalar value (spin quantum number) in two-dimensional spacetime (described in >>15554673 (You) #) becomes a vector (intrinsic angular momentum) when mapped (by interplay of spin-1 bosons) to four-dimensional (classical) spacetime.
is one-dimensional Brownian motion, with fermions being the particles in motion and the "interplay of spin-1 bosons" being the fluid (or possibly vice versa). But my interpretation of spin quantum number doesn't rely upon that being the case.
>That anon was referring to Hilbert space dimension and you seem to be talking about spatial dimension
The formalism used to describe the dimensions in question don't change their quantity, but also lolno it's not a spatial dimension in the sense of length or width or height, it's a one-dimensional self-extracting compressed representation of all three.

[Anonymous No.15555627]

>>15554961
And where's the connection...?

[Anonymous No.15555787]

>>15555627
>degrees of freedom within a quantum-scale Minkowski space
>quantum degrees of freedom
No connection at all, Anon.

[Jealous No.15555800]

>Why does spin have to be half-integer +1/2 or -1/2?
The relevant Schrodinger's equations admit solutions only when spin steps in half-integer increments. It's a mathematical artefact in that way, but the fundamental cause is that the structure of the MCM unit cell has two modular "halves." In that, the modules are associated with halves of integer units of spin, which has units of action, etc...

[Jealous No.15555805]

>>15555800


Sixty-Six Theses: Next Steps and the Way Forward in the Modified Cosmological Model
>https://vixra.org/abs/2206.0152
>http://gg762.net/d0cs/papers/Sixty-Six_Theses__v2-20220726.pdf
The purpose is to review and lay out a plan for future inquiry pertaining to the modified cosmological model (MCM) and its overarching research program. The material is modularized as a catalog of open questions that seem likely to support productive research work. The main focus is quantum theory but the material spans a breadth of physics and mathematics. Cosmology is heavily weighted and some Millennium Prize problems are included. A comprehensive introduction contains a survey of falsifiable MCM predictions and associated experimental results. Listed problems include original ideas deserving further study as well as investigations of others' work when it may be germane. A longstanding and important conceptual hurdle in the approach to MCM quantum gravity is resolved. A new elliptic curve application is presented. With several exceptions, the presentation is high-level and qualitative. Formal analyses are mostly relegated to the future work which is the topic of this book. Sufficient technical context is given that third parties might independently undertake the suggested work units.

[Jealous No.15555808]

>>15555800
>>15555800

[Jealous No.15555813]

>>15555800
>>15555800
>>15555800

[Anonymous No.15555842]

>>15555787
as far as I can make out in the best faith possible, you're confusing or rather conflating the degree of freedom and the values the degree of freedom can take.
An electron has spin as a DOF that can take 2 possible values +-1/2 (because >>15554809
). That has nothing to do with the DOF being "half-dimensional".

It's like arguing that a classical coordinate like the position on a line that's 0.8324 meters long is thereby in a 0.8324-dimensional fractal space.

[Anonymous No.15555892]

>>15555842
>as far as I can make out in the best faith possible, you're confusing or rather conflating the degree of freedom and the values the degree of freedom can take.
thank you for your good-faith response, I sincerely appreciate it. I don't think that I am guilty of the conflation you say, but I can see how it would appear that way.

For a particle in an inertial reference frame, represent the spin quantum number as a tuple (x,y) where x can take values {0, 1/2, 1} and y {0, 1}, such that x + y = (spin quantum number). Then for elementary particles in the Standard Model:
Spin(Higgs boson) = (0,0)
Spin(fermion) = (1/2, 0)
Spin(photon) = (0, 1)
Spin(gluon) = (0, 1)
Spin(W boson) = (0, 1)(?)
Spin(Z boson) = (0, 1)(?)
Spin(graviton) = (1, 1)
Both x and y represent values for a quantum degree of freedom, while their positions within the tuple (x,y) represent the degree of freedom itself. Ergo, no conflation.

From what I understand Pauli was referring only to electrons, and so he was referring only to the x side of the tuple. The "two possible values" he gave it are what's now represented as sign (+/-) when the spin quantum number is resolved (on the macro scale) to intrinsic angular momentum, where the sign indicates the direction of the momentum. For my purposes that sign is irrelevant, as when I speak of spin (and unless otherwise noted) I am referring to scalar called "spin quantum number," not the vector called "intrinsic angular momentum."

[Anonymous No.15555898]

>>15555892
Whereas the W and Z bosons are massive, I'm not sure that those particular tuples are accurate. They might be (1/2, 1/2). Interesting thought.

[Anonymous No.15556479]

bump

[Anonymous No.15556505]

>>15554269
No, indeed angular momentum has it's own spin like properties, but spin turns out to be another degree of freedom in particles.

[Anonymous No.15556547]

>OMG I'M SO SMART!!!
>MY IQ IS HUGE!!!
>I HAVE SO MUCH MEMORIZED EXCLUSIVE SOIENCE JARGON
>AND THIS THREAD GIVES ME THE OPPORTUNITY TO POST IT
>EVERYONE IS GOING TO KNOW HOW SMART I AM AFTER I POST MUH SOIENCE CATCHPHRASES AND MEMEWORDS
>I FUCKING LOVE SOIENCE SOOOO MUCHH!!!
>I'M GOOONNAAA QUANTUUUUUUUUUUUUMMMM!!!!!!

[Anonymous No.15556754]

>>15556505
Spin is internal angular momentum, period.

Spatial rotations (or their covering group, more precisely) are represented as unitary operators in quantum mechanics, and the Lie algebra associated to the spatial rotation group is represented by Hermitian operators. These Hermitian operators are basically the definition of angular momentum in quantum mechanics. The spin operators are connected to spatial rotations in exactly this way.

[Anonymous No.15557227]

>>15556505
No, spin is just an intrinsic angular momentum

[Anonymous No.15557242]

>>15556754
>>15557227
>internal
>intrinsic
What does this mean with respect to angular momentum? Sounds like a cope. "It doesn't spin in the physical sense but it's vaguely mathematically related to angular momentum, let's just call it intrinsic."

[Anonymous No.15557246]

>>15554731
This, the mental cases and their delusions of intellectual grandeur are cringe af

[Anonymous No.15557279]

>>15557242
>vaguely mathematically
It has the same dimensions as angular momentum.

[Anonymous No.15557286]

>>15557279
My dick has the same dimension as my leg. Doesn't mean they're the same. At least you could have argued with Lie algebra representations, but appealing to dimensions is lower than midwitted.

[Anonymous No.15557301]

>>15557286
On the contrary, the penis has been refereed to as "the third leg" for centuries.

[Anonymous No.15557409]

>>15557286
>My dick has the same dimension as my leg. Doesn't mean they're the same.
They're both measured by 'length' in this case. Are you too retarded to understand the difference between a measure and the thing measured?

[Anonymous No.15557567]

>>15552268
>half-integer
no such thing, fuck off

[Anonymous No.15557622]

>>15554809
>If spin was integer there would be three piles.
This isnt a good explanation because photons only take 1 out of 2 spin values despite having 3 possible values. The reason their actual spin isnt zero is caused by having zero mass. I dont remember the logical argument.
Just saying that detecting 2 spin values doesnt automatically mean its spin 1/2 because photons have spin 1 and you only detect them in 2 spin states

[Anonymous No.15557629]

>>15557242
Its a superfluous adjective.
Its just angular momentum, its quantized like energy. People are ok with hydrogen atoms and their ground state so guess what the minimum angular momentum isnt zero. That's all.

[Anonymous No.15557690]

>>15557242
NTA and not a physicist, but:
>intrinsic
it's a property of the particle rather than the space in which the particle is embedded
>internal
if I'm right in guessing that this is a reference to inner product space, then this means a scalar returned by an operation that takes two vectors as arguments
>it's vaguely mathematically related to angular momentum
I'm going to assume you've at least studied calculus.
Let f(x) = x^3 + 5. Take the first derivative of f and you have f'(x) = 3x, the 5 disappears and the 3 is demoted from exponent to multiplier. (The 5 disappearing means it isn't intrinsic at this level.) Take the second derivative and you have f''(x) = 6x, from there f'''(x) = 6. Now this is an extremely simplified example, but if f(x) is analogous to intrinsic angular momentum, then f'''(x) is analogous to the spin quantum number. Less vague?

[Anonymous No.15557698]

>>15557690
correction:
f'(x) = 3x^2

[Anonymous No.15557829]

>>15557567
Honestly curious, are you disputing the existence of rational numbers or do you just object to the terminology?

[Anonymous No.15557859]

>>15555805
jonathan tooker is a crank
this board is pathetic

[Anonymous No.15557865]

>>15557567
https://en.wikipedia.org/wiki/Plate_trick

[Anonymous No.15557866]

>>15557859
>this board is pathetic
good thing you're here to bitch about it, that's sure to improve the situation

[Anonymous No.15557911]

>>15557690
Its just angular momentum, same old angular momentum with no extra words

[Anonymous No.15557912]

>>15557865
Most reddit trick that doesnt prove anything at all. Go one and logically connect these plate and belt tricks with electron spin without just claiming its self evident

[Anonymous No.15558008]

>>15557690
What I meant by vaguely related is the following: Angular momentum is the infinitesimal generator of rotation, i.e. a Lie algebra representation of so(3) corresponding to a representation of SO(3). Spin(3) is a double cover of SO(3). Of course that implies that the Lie algebras are isomorphic. However, the representation of Spin(3) is physically not rotation but only in a handwavy sense a "square root of rotation" at best. So in what sense can its infinitesimal generator still be labeled "angular momentum"? Do you have another calculus analogy to help my understanding?

[Anonymous No.15558215]

>>15557242
Intrinsic and internal are synonyms in this context. I'm the guy that wrote the post with a group theory explanation. If you don't understand it, just trust that there are people who do understand it, and it is a very deep reason why spin is literally angular momentum. This isn't gatekeeping btw, since you are welcome to study to the point at which it does make sense.

[Anonymous No.15558259]

>>15558008
I'm not the guy who brought up calculus, but this is what you seem to understand:
The physical rotation group is SO(3) in the sense that if you rotate the universe by 360 degrees nothing should change. Spin 1/2 is not a valid representation of SO(3) but it is a representation of Spin(3)=SU(2).

But then you are bothered by the fact that SU(2) is not the SO(3) we started with. But that's not quite how the logic goes. The idea is that in quantum mechanics we only care about projective representations, representations which are valid up to a phase. Spin 1/2 is a valid projective representation of the physical rotation group SO(3).

[Anonymous No.15559068]

>>15558008
I'm the guy who brought up calculus. I took one class in modern algebra back when Bush was in office and have done nothing with it since, so I won't pretend to be an expert on group theory, but the analogy wasn't entirely arbitrary. A Lie algebra is in a sense a derivative of a Lie group, see pic related.
I'm not familiar with infinitesimal generators of rotation, but the verbiage reminds me of infinitesimal generators of Feller processes. Which I'm also not an expert on by any means, I simply read recently that Brownian motion is an instance thereof.
>So in what sense can its infinitesimal generator still be labeled "angular momentum"?
In the sense that angular momentum is a group action of a Lie group to which that particular Lie algebra corresponds? I have no idea if that's true, but it sounds plausible and you're much handier at this than I, so maybe check that out.

[Anonymous No.15559126]

>>15553340
This is some fine pseudo physics but nothing constrains particle motion to travel forward in time. All equations of physics are valid under time reversal transformation

[Anonymous No.15559177]

>>15559126
2nd law of thermodynamics?

[Anonymous No.15559616]

>>15559126
>All equations of physics are valid under time reversal transformation
Really anon, ALL of them?

[Anonymous No.15559655]

>>15559616
not him but all deterministic are, statistical aren't.

[Anonymous No.15560009]

>>15557622
>photons only take 1 out of 2 spin values despite having 3 possible values. The reason their actual spin isnt zero is caused by having zero mass.
W and Z bosons have nonzero mass and still have spin 1, could you explain the difference?

[Anonymous No.15561093]

bump

[Anonymous No.15561403]

>>15560009
Spin works differently for massless particles since there is no rest frame.

[Anonymous No.15562750]

>>15561403
Okay but the question is, why do some particles that aren't massless have the same spin as particles that are massless?

[Anonymous No.15562872]

>>15562750
The idea that angular momentum about some axis must be quantized in half integer multiples of hbar is something general in quantum mechanics, and holds for both massive and massless particles.

A photon has +- hbar angular momentum about the direction of motion, and a W or Z boson also has a maximum of hbar angular momentum about any axis, hence we say both are spin 1. The difference is that the W or Z boson may also have an extra state with 0 angular momentum about their direction of motion.

[Anonymous No.15563194]

>>15562872
>The difference is that the W or Z boson may also have an extra state with 0 angular momentum about their direction of motion.
That's exactly what I was looking for, thank you. Is this a theoretical state, or has it been observed?

[Anonymous No.15563210]

>>15563194
It's been observed. It's also known as "longitudinal polarization."

[Anonymous No.15563218]

>>15563210
>It's also known as "longitudinal polarization."
Above and beyond, Anon, thanks again.