/sci/ - Science & Math

>>9918853
>sub-atomic/atomic
>meaning and reason
It doesn't work like that, it just exists. tl;dr It's fun to imagine.

>>9918853
yeah, you're on the right track

take neutrinos for example
we only see left-handed neutrinos in all the experiments we've done so far. what this means is that if a neutrino is coming toward you, it will always be spinning clockwise from your perspective. (and if it's going away from you, it's always spinning counterclockwise from your perspective) so that's the definition of a left-handed chiral particle.

if you were to ever see a neutrino coming at you and spinning counterclockwise from your perspective, then that's a new discovery because all known neutrinos are left-handed.

so now the puzzling part is what you mentioned:
if that left-handed neutrino is coming toward you, spinning clockwise from your perspective, then, if we assume it has a mass, that means it should be possible in principle to accelerate backward until you're moving faster than the neutrino. once you are moving away from the neutrino faster than it's coming toward you, then in your frame of reference, you see it moving away from you now. but now, by definition, it's right handed -- it continued to look like it was rotating clockwise from your perspective, but it changed from moving toward you to moving away from you.

so the chirality of a particle does depend on relativity -- a left-handed particle can look right-handed if you change your relative motion.

the real puzzle is why all neutrinos are left handed experimentally. if they were massless, then there is no problem: you can never move fast enough to change whether it's going toward you or away from you, it'll always be coming toward you. but unfortunately there is strong evidence that says neutrinos have a mass (you see a neutrino of one type, e.g. a muon neutrino, change into e.g. electron neutrino, and that would be possible if they had no mass.)

>>9918853

yeah, you're on the right track

take neutrinos for example
we only see left-handed neutrinos in all the experiments we've done so far. what this means is that if a neutrino is coming toward you, it will always be spinning clockwise from your perspective. (and if it's going away from you, it's always spinning counterclockwise from your perspective) so that's the definition of a left-handed chiral particle.

if you were to ever see a neutrino coming at you and spinning counterclockwise from your perspective, then that's a new discovery because all known neutrinos are left-handed.

so now the puzzling part is what you mentioned:
if that left-handed neutrino is coming toward you, spinning clockwise from your perspective, then, if we assume it has a mass, that means it should be possible in principle to accelerate backward until you're moving faster than the neutrino. once you are moving away from the neutrino faster than it's coming toward you, then in your frame of reference, you see it moving away from you now. but now, by definition, it's right handed -- it continued to look like it was rotating clockwise from your perspective, but it changed from moving toward you to moving away from you.

so the chirality of a particle does depend on relativity -- a left-handed particle can look right-handed if you change your relative motion.

the real puzzle is why all neutrinos are left handed experimentally. if they were massless, then there is no problem: you can never move fast enough to change whether it's going toward you or away from you, it'll always be coming toward you. but unfortunately there is strong evidence that says neutrinos have a mass (you see a neutrino of one type, e.g. a muon neutrino, change into e.g. electron neutrino, and that would be impossible if they had no mass.)

The standard model says that neutrinos should have left chirality. This means the spin vector points in the opposite direction to the momentum. However, if the neutrino moves slower than light, then it would be possible to obtain via Lorentz transformation an inertial frame in which the velocity is pointing in the other direction, in the direction of the spin. This is called right chirality and the standard model says neutrinos can't have it. Therefore, the 2015 Nobel result that neutrinos have mass disproves the standard model. Massive particles always travel slower than light and then it is possible to speed past the neutrino in a spaceship at still subluminal speed such that its velocity vector recedes from your rear view window, meaning that, relative to your own velocity, the neutrino has right chirality.

>>9919390
it doesn't disprove the SM

the SM required a small modification that was anticipated long before the nobel work on neutrino oscillations

the SM is totally fine with this minor add-on that was needed, stop being a larper. SM is a champ, still 99.999999% right, and asshats like you like to blow out of proportion anything that makes normies think "wow these string theory guys are doing important work" so you can collect your grants

>>9919403
Is the modification self-consistent? I doubt it, and I think there is no self-consistent theory with massive neutrinos.

>>9919411
i'm pretty sure all the possible modifications that get you neutrino oscillations are self consistent. see-saw mechanism is a nice one that i'm pretty sure nobody has found any problems with

http://pdg.lbl.gov/2016/reviews/rpp2016-rev-neutrino-mixing.pdf

please provide a ref for what you're saying. i'm under the impression after reading bits and pieces of the PDG article that there are at least several self-consistent approaches

http://pdg.lbl.gov/2016/reviews/rpp2016-rev-neutrino-mixing.pdf

>>9918853
Let [math](\mathcal{H},D)[/math] be a Dirac theory on a Reimannian manifold [math]M[/math]. Suppose [math]\operatorname{dim}M[/math] is even, then the spinor bundle [math]\mathbb{S}\rightarrow M[/math] admits a skew-symmetric "chirality operator" [math]\gamma = i \prod_{i=1}^{n}\gamma_\mu \in \operatorname{End}(\mathbb{S}) \cong \operatorname{Cliff}^{n,1}(\mathbb{C})[/math] which satisfies [math]\{\gamma,\gamma_\mu\} = 0[/math], and hence [math]\{\gamma,D\} = 0[/math]. This allows the decomposition of the Hilbert space [math]\mathcal{H} = \mathcal{H}_+ \oplus \mathacl{H}_-[/math] into chirality eigenspaces [math]\mathcal{H}_\pm[/math] such that [eqn]D = \begin{pmatrix} 0 & D_+ \\ D_- & 0 \end{pmatrix}[/eqn].
For any principal gauge [math]G[/math]-bundle [math]P\rightarrow M[/math] compatible with the spinor bundle, its representation in [math]\mathcal{H}[/math] then admits a chiral central extension [math]\tilde{G}[/math] by [math]\mathbb{Z}_2[/math] (this is why models with chiral symmetry have universality classes labeled with [math]\mathbb{Z}_2[/math]), and the resulting associated vector bundle [math]P\times_G \mathcal{H} \rightarrow M[/math] acquires gauge transformations [math]\operatorname{End}(P\times_G \mathcal{H}) \cong \operatorname{Map}(M,\tilde{G})[/math].
For instance, if [math]G = U(1)[/math] corresponds to the EM gauge group that mediates local charge conservation, then the chirality operator allows a central extension [math]\tilde{U}(1)[/math] that acts as [math]e^{\pm i\varphi}[/math] on [math]\mathcal{H}_\pm[/math], meaning [math]\mathcal{H}_+[/math] is the "particle Hilbert space" while [math]\mathcal{H}_-[/math] is the "hole space". On the other hand if [math]G = SU(2)[/math], then we may make [math]U^{(\dagger)} \in G[/math] act on [math]\mathcal{H}_\pm[/math]; this means that [math]\mathcal{H}_+[/math] is the "parallel-spin" space while [math]\mathcal{H}_-[/math] is the "antiparallel-spin" space.
Hope this clears up the confusion.

>>9919431
probably this is correct, i donno, fucking theorists, but anyway it is not at all helpful.

anytime somebody brings up Z(2) or U(1) in their descriptions of why physics works, i basically say "ugh mathematician, i'm sure you studied your books, but there's a reason you guys suck at physics -- physics is about thinking physically, not your group theory buzzwords"

ITT: People who don't understand the fucking difference between chirality and helicity.

Helicity is the projection of spin along the direction of motion. (Depends on observer in massive case.)

Chirality comes from the spinor solutions of the Dirac equation. When you mirror the system/particle (parity operation, x -> -x, p -> -p) you find that the two halves of the spinor "swap places", therefore you may call one half left and the other right.

In the massless limit, these two are identical for all observers.

In the massive case, it is possible for a left-chiral neutrino to have positive or negative (left or right) helicity.

>>9919411
>Is the modification self-consistent? I doubt it, and I think there is no self-consistent theory with massive neutrinos.
Yes, it is. Neutrinos are only affected by weak force, thus only left neutrinos are coupled. You can add right neutrinos without a problem because they will not be charged under any of the forces (as the term responsible of the weak interaction project them out, as happens with other particles).
As they are now massive (although there is still the possibility of having two massive neutrinos and one massless neutrino, has we have only measured the mass difference between them), there is no problem with the Higgs mechanism as the mass term will be a usual Dirac mass term.

>>9919431
based yukari poster, always enjoying your posts

>>9918853

Can i be the first to tell you.

THEY ARE SPINNING.

>>9921214
Nothing is actually spinning there.