Widdekind

I understand, that there are three "physical" or "mass" eigenstates [math]\left( \nu_1, \nu_2, \nu_3 \right)[/math], which form three super-posed combinations [math]\left( \nu_e, \nu_{\mu}, \nu_{\tau} \right)[/math], when neutrinos are generated, via Weak interactions, into Weak eigen-quantum-states.

I understand, from perusing Riccardo Barbieri's book Lectures on the ElectroWeak Interactions, that the Higgs hypothesis, for the manifestation of "mass", assigns, to every point in space, a complex-valued scalar field [math]\phi(\vec{x})[/math], whose vacuum expectation value is [math]v \approx 200 \; GeV[/math]. But, particles interact with that field. And, if that field is "perturbed", from its equilibrium value; then a potential energy is generated: [math]\phi(\vec{x}) \sim v \left(1 + h(\vec{x}) \right)[/math] [math]V(\vec{x}) \sim -1 + 4 h^2 + 4 h^3 + h^4 = \left(1 + h\right)^2 \left( \left(1 + h\right)^2 - 2\right)[/math] By some means, the hypothesized Higgs potential well manifests the "mass" of particles. Can particles be considered to "oscillate" in the quartic Higgs potential, vaguely resembling quadratic potentials, of classical QM, with the eigenstates associated with the various fermions, and their three 'generations' ?? Trying to "force fit" some semblance of structure, to the masses, of the standard particles, I observe the following crude correspondences (masses in MeV subscripted, "bare" masses for u,d quarks employed): [math]u_{1.5} \begin{array}{c} \times 1000 \\ \longrightarrow \end{array} c_{1500} \begin{array}{c} \times 100 \\ \longrightarrow \end{array} t_{170,000}[/math] [math]d_{4.5} \begin{array}{c} \times 100 \\ \longrightarrow \end{array} s_{500} \begin{array}{c} \times 10 \\ \longrightarrow \end{array} b_{4500}[/math] [math]\nu_1 \begin{array}{c} \times 20? \\ \longrightarrow \end{array} \nu_2 \begin{array}{c} \times 2? \\ \longrightarrow \end{array} \nu_3[/math] [math]e_{0.5} \begin{array}{c} \times 200 \\ \longrightarrow \end{array} \mu_{100} \begin{array}{c} \times 20 \\ \longrightarrow \end{array} \tau_{1800}[/math] I observe that "extrapolating the trends", implies hypothetical "higher generation" particle states: [math]u_{1.5} \begin{array}{c} \times 1000 \\ \longrightarrow \end{array} c_{1500} \begin{array}{c} \times 100 \\ \longrightarrow \end{array} t_{170,000} \begin{array}{c} \times 10?? \\ \longrightarrow \end{array} superT_{1,700,000} \begin{array}{c} \times 1?? \\ \longrightarrow \end{array} hyperT_{2,000,000}[/math] [math]d_{4.5} \begin{array}{c} \times 100 \\ \longrightarrow \end{array} s_{500} \begin{array}{c} \times 10 \\ \longrightarrow \end{array} b_{4500} \begin{array}{c} \times 1?? \\ \longrightarrow \end{array} superB_{5,000}[/math] [math]\nu_1 \begin{array}{c} \times 20? \\ \longrightarrow \end{array} \nu_2 \begin{array}{c} \times 2? \\ \longrightarrow \end{array} \nu_3[/math] [math]e_{0.5} \begin{array}{c} \times 200 \\ \longrightarrow \end{array} \mu_{100} \begin{array}{c} \times 20 \\ \longrightarrow \end{array} \tau_{1800} \begin{array}{c} \times 2?? \\ \longrightarrow \end{array} super \tau_{4,000}[/math] First, "down-type" fermions (d,e, isospin T3=-1/2) seem to "max out" near 5 GeV, with leptons (e) "dropping down" in mass ~2x more per generation. Second, "up-type" fermions (t) seem to "max out" near 2 TeV. And, 2 TeV is the energy scale, at which "a theory without a Higgs boson leads to a saturation of unitarity; or, more precisely, to a loss of perturbativity, at an energy [math]E \approx 4 \pi v \left[\approx 2 \; GeV \right][/math]" (Barbieri, p.26). Are the energy scales ~5 GeV (T3=-1/2) or ~2 TeV (T3=+1/2) significant? How do they relate to the hypothetical Higgs field ?

If humans gradually cultivated various food crops, over hundreds to thousands of years; then could not the same tried-and-true tactic be applied, to cultivating salt-water crops, which could be irrigated, with ocean water ? I.e. take "durum wheat", grow it for hundreds of years, in increasingly saline conditions, and gradually cultivate "beach wheat" ? (Can humans consume sea-weeds ?)

If, from the Big Bang, N photons were initially generated (having no net charge)... and those N photons pair produced N fermions, and N anti-fermions (having no net charge)... then those particles & anti-particles, could have mutually interacted, via random processes, e.g. W-boson exchange, to produce random numbers, of photons (from annihilations); and neutral particles, which would then "opt out" of the intense EM interactions, attracting the other particles to their mutual dooms. And, there are two such ways to "charge neutralize", and "opt out" -- form neutrons (or anti-neutrons), or form neutrinos (anti-neutrinos). Most matter & antimatter annihilated. But, randomly, there would plausibly have been "a few survivors" on "either side". However, the "side" that produced more neutrons, would necessarily have produced fewer neutrinos, et vice versa. So, perhaps there is no matter / anti-matter asymmetry, i.e. the number of surviving fermions = number of surviving anti-fermions -- even though there is an matter / anti-matter difference, for the former primarily "neutronized", whilst the latter primarily "neutrino-ized" ? If so, then from "the fires of creation" came a blizzard of blistering photons, and a dusting of neutral particles, namely anti-neutrinos, and neutrons, whose charge neutrality had allowed them to "opt out" of annihilation. The matter neutrons became our baryons, i.e. "the foreground actors", whilst the anti-neutrinos became "background". Is it possible, that our cosmos is replete, with a background of anti-neutrinos ? Would that imply that protons should decay, via anti-neutrino absorption ? But does not observed charge neutrality, imply numerical symmetry between the matter & antimatter, which carry equal & opposite charges ?

If the gluon is a "Strong photon"; and if photons can pair produce leptons, e.g. [math]\gamma \rightarrow \bar{e}e[/math]; then is gluon "fission" into quarks, the Strong interaction equivalent, of pair production ? (Note, I understand, that single photon "fission" can only occur, in the intense EM fields, near large nuclei -- but gluons "live" in such intense environments, so, naively, I'm "comparing apples w/ apples".) Also, if you can have [math]\bar{e}e \rightarrow \gamma \gamma[/math], i.e. "complete matter/antimatter annihilation"; then can you have [math]\bar{e}e \rightarrow \bar{\nu}\nu[/math], i.e. "incomplete" annihilation (e.g. via double W-boson exchange) ??

I understand, that a particle can have a momentum expectation value [math]\langle \hat{p} \rangle = 0[/math], indicating that the "centroid" of the wave-function is stationary. The HUP demands, however, some "uncertainty", i.e. some mathematical statistical spread, in momentum. Er go, a particle which is "stationary" is a super-position, of numerous momentum states, representing equal amounts of momentum, flowing forward as backward, left as right, up as down.

I understand, that "color", having three "hues", is mathematically equivalent, to quarks having a "spin S=1 like" property. Perhaps you could conceive of "color" as an "orientation", i.e. xyz, i.e. quarks are "x-oriented", "y-oriented", "z-oriented" ? I understand, that "color" is as intrinsic of a property, as spin, i.e. all quarks must have some "color" state, at all times.

I understand, that neutrinos are generated, exclusively by Weak interactions; and, therefore, neutrinos are generated, exclusively into Weak eigenstates [math]\left( \nu_e, \nu_{\mu}, \nu_{\tau} \right)[/math], which are super-posed "mixtures", of the canonical mass eigenstates [math]\left( \nu_1, \nu_2, \nu_3 \right)[/math]. Somehow, those different mass eigenstate components, of the neutrino's wave-function, evolve at different rates, due to said different masses; and that the resulting "beat frequencies" are observed, as neutrino oscillations. How should this be understood ? For, in the rest-frame of a massive neutrino, surely the various components, of its wave-function, would not separate apart; rather, the wave-function would surely remain more-or-less "clumped together". And if so, then would not the wave-function, of that same neutrino, in some other reference frame, in which the neutrino was moving rapidly, be the "clumped together" wave-function, of the particle, in its own rest-frame, relativistically "boosted" by some velocity near that of light ? If so, is not the constraint, on the various components, of a neutrino's multi-faceted wave-function, that they all must be propagating, with the same velocity [math]\beta = const, \gamma(\beta) = const.[/math] ? You mentioned SN1987a -- did those neutrinos arrive "all together in one pulse", or did they arrive gradually, over hours / days ? For, if they arrived as a "clump", then surely their wave-functions had not become "smeared through space", as would surely be the case, if the various components, of the neutrino wave-functions, were propagating at different speeds. I.e. if a neutrino is a little like a "motorcade of three cars", then all three "cars" "drive" at the same speed ? Again, otherwise, if not, then one of the "cars" would pull ahead; one of the "cars" would lag behind; and the neutrinos would become "smeared out thru space", with one "flavor" of "car" detected for the first few hours/days; then the next "flavor"; then the next. The neutrinos generated by SN1987a were electron neutrinos. Whereas, the neutrinos generated for the CERN-SG experiments, were muon / tauon neutrinos, i.e. different "flavors" of neutrinos, from those generated by SN1987a. Could that "flavor" difference account for the discrepancies ?

Would you please clarify that ? Are there actually decays, that produce more fermions than anti-fermions ? Or, are we ignoring (anti)neutrinos in such statements ?

A wave-function has a momentum expectation value, at every point in space, which is proportional to the gradient of the wave-function, at that point: [math]\propto \left( - \imath \hbar \frac{\partial}{\partial x} \right) \Psi(x) [/math] In analogy, a wave-function is a little like a flock of birds, flowing through space, with each "bird", at each point in space, having some momentum, at that point in space.

I understand, that "wave-function collapse to a point" is, rigorously, an exaggeration, which has never, actually, been observed. For example, in double slit experiments, the incident photon / electron wave-function "collapses", into one of many phosphor grains, coating the detector screen. But, those phosphor grains are [math]\approx 1 \mu m[/math] in size, characteristically. Thus, the wave-function "collapses", from a macro- or meso-scopic scale, to a micro-scopic scale, but, by no means, to "a point". I also understand, that the Schrodinger Wave Equation, is an approximation, to the more rigorous, and relativistically accurate, equations (e.g. Dirac equation, Klein-Gordon equation). Thus, the SWE implicitly embodies simplifying assumptions, whose omission could cause confusion. In particular, in the full relativistic equations, a particle's rest-mass-energy (mc2) defines that particle's intrinsic phase frequency. That could be included in the SWE, as [math]E \rightarrow E + mc^2, \omega t \rightarrow \left( \omega + \frac{mc^2}{\hbar} \right) t[/math]. Thus, a particle with zero KE, or even a negative bonding energy, still has a positive frequency (unless the negative bonding energy exceeds its rest-mass energy, which only occurs, in relativistically deep gravity wells). I understand, that that phase frequency is physically real, as the phase of wave-functions can be measured, e.g. Aharonov-Bohm effect. Thus, the wave-function, of a particle at rest, is still "spinning its phase", even if "its just sitting there", e.g. in its own rest-frame.

I understand, that the calcite / quartz crystal induces polarizations [math]\vec{P}[/math] into photons, differentially, according to their momenta [math]\vec{p}[/math]: [math]\vec{p} \longrightarrow \vec{P}[/math] And, the detector screens used, can detect polarization, as a function, of position on the screen, i.e. [math]\vec{P}(x,y)[/math]. Then, "working backwards", [math]\vec{p}(x,y) \longleftarrow \vec{P}(x,y)[/math] Now, all of those quantities are statistical distributions, accumulated, over many many repeated trials, i.e. each photon fired lands somewhere on the screen (x,y), with some polarization (P), implying some momentum (p). After many many trials, many photons will have landed at each spot on the screen (x,y); each having had various polarizations (P); each of which implied various momenta (p). You repeat the experiment, many many times, until you have large numbers of detections, at each point on the screen (x,y), from whose polarizations (P[x,y]), you can infer some average mean momentum (<p(x,y)>). Supposedly, you can mathematically show, that those average values <p(x,y)> converge towards the actual original wave-function's momentum at that point.

I understand, that an anti-neutrino has a "Weak hyper-charge" of +1, whereas a neutrino has a "Weak hyper-charge" of -1. Naively unifying W+EM (hyper)charges, into a "charge doublet" (QW,qEM); then anti-neutrinos would have the vector (0,+1); neutrinos (0,-1). Via absorption of W+ bosons, anti-neutrinos can be "charged up" into anti-electrons (+1,+1). Via absorption of W- bosons, neutrinos can be "charged down" into electrons (-1,-1). I understand, that Weak hyper-charge is a "good quantum number", i.e. conserved in every interaction; and, that anti-neutrinos & neutrinos are exactly as distinct, as anti-electrons & electrons (or anti-matter & matter) ? I understand, that neutrinos, as fermions (s = 1/2), can exist in two states, i.e. "right-handed" (sz = +1/2) and "left-handed" (sz = -1/2), where the z-axis is defined to be parallel to the particle's linear momentum. Likewise for anti-neutrinos. If so, then RH neutrinos are no more equivalent, to LH anti-neutrinos, then "spin-up" electrons are to "spin-down" anti-electrons. I understand, that the Dirac equation implies the existence of four species of each fundamental particle, i.e. RH/LH for M/AM, none of which represent exactly the same quantum states.

I understand, that our universe, at present epoch, is comprised of matter particles, in the following (approximate) ratios: [math]7 e^{-} + 7 p^{+} + 1 n^0 \longrightarrow 6 H + \frac{1}{2} He[/math] Now, if our universe began as "pure raw energy", i.e. photons; and if those photons pair-produced matter / antimatter, e.g. [math]\gamma \rightarrow \bar{e}^{+}e^{-}[/math]; then matter / antimatter "must" have emerged in equal (equally enormous) quantities. Then, negatively charged matter [math]\left( e^{-}, d^{-\frac{1}{3}}\right)[/math], and positively charged anti-matter [math]\left( \bar{e}^{+}, \bar{d}^{+\frac{1}{3}}\right)[/math], "must" have exerted powerful forces onto each other, the only "escape" from which, was charge neutalization, i.e. neutrinos or neutrons. If "anti-matter" formed more (anti)neutrinos; then "matter" would have formed more neutrons, i.e. [math]\bar{f}^{+}f^{-} \longrightarrow \bar{\nu}^0n^0[/math] whichever form of matter produced more neutrons would have become the basis, for all modern "baryonic matter" structures; whereas the other form of matter, producing more neutrinos, would have "ghosted out of the action". Er go, whichever form of matter neutronized > neutrino-ized, i.e. "anti-matter" or "anti-anti-matter", all future baryonic structures, including earth & humans, would necessarily have formed from that matter component, i.e. Anthropic Principle "kicks in". Later, as our universe cooled, the "neutronium plasma" of [math]n^0[/math] evidently decayed mostly to [math]p^{+} + e^{-}[/math] (plus more anti-neutrinos), until approximately 7/8 neutrons had produced protons & electrons, which eventually coalesced into neutral H.

In decays, wherein one particle "breaks apart" into two or more other particles, is relativistic four-momentum conserved through the decay, i.e. [math]p^{\mu}_i = p^{\mu}_f = p^{\mu}_1 + p^{\nu}_2 + ...[/math] ?? And, if four-momentum is conserved, is not its "squared interval" [math]p^2 = p^{\mu}p_{\mu}[/math] (= m2 for one particle) ??

Is there an easy way of visualizing the effect? "Everybody knows", that relativistic boosts "collapse" the moving observer's x,t "grid", a little like some form of folding fence. So, "everybody knows", that relativistic observers' "lines of simultaneity" (t=const) "slash diagonally across" some fiducial stationary observer's grid. And, exaggerating for simplicity, FTL signals that were infinitely FTL would "zip" along lines of simultaneity, covering immense distances, in negligible time. So, someone moving relativistically "to the right", firing an FTL beam "to the left", would look like they had "communicated backwards in time" (to the stationary observer). Quantum non-local instaneity, exploiting entangled wave-functions, which had previously been propagated conventionally, could possibly avoid violating Causality, if the original luminal signal was "pregnant with the possibility" subsequently manifested, cp. "consistent histories". In the following figure, events Q&R could hypothetically manifest some seemingly supra-luminal "synchronicity", had they both been synchronized, Causally, from the vertex at the intersection of both events backwards light-cones. Perhaps exploiting quantum entanglement would be somewhat similar to such a "synchronization"?

Not quite ? I get the impression, that, in the limit of weak perturbations, the averages of the data distributions that you gather, asymptotically converge, to the what the wave-functions, of all of the assumedly identical photons, "really would have been doing", in the absence of any perturbations. If so, then sometimes "the perturbation kicks the particle one way", and other times "the other way", so that you get a broad distribution of actual data... but the mean in the middle is (mathematically provable to be) the "original unperturbed behavior".

Thank you very much for the link. Physorg cited the experiments as well. Perhaps the strong measurement interaction, at the photon-absorbing detector screen (which destroys the incident photons), between the incident photon wave-function & said screen, "starts" as soon as wave-function begins to impinge upon the screen, so that wave-function having a shorter path-length to said screen, has a "head start" on wave-function flowing in, from farther away ? I found this nature article. I understand, that a "weak measurement" does not cause wave-function "collapse", at least not very often. (Wave-functions that did "collapse", due to the "weak" perturbing influence, obviously would not propagate further through the experimental apparatus, on through to the main detector, i.e. they would represent "losses" of input signal strength, e.g. photons being absorbed by the apparatus, heating it up.) Naively, for the photons of the two top-prize-winning "weak measurement" experiments, from the article, if those photons are prepared, into some state [math]|s>[/math], which is then "weakly perturbed" by some "weak measurement", represented by some "operator" A, then [math]|s> \longrightarrow |s> + \epsilon A |s>[/math]. The [math]\epsilon[/math] parameter measures the "strength" of the perturbation, and can be adjusted. For example, for the top-prize experiment, the "weak measurement" perturbation was a calcite crystal, which polarizes photons, differentially, according to their momenta. Presumably, the thicker the calcite crystal, the "stronger" the perturbation. So, by "shaving the crystal down", until it was wafer thin, the [math]\epsilon[/math] parameter could be reduced. Somehow, a subsequent "strong measurement", which does cause the collapse of the wave-function (or, all that manage to make it that far through the apparatus), can then infer properties of the unperturbed wave-function, e.g. momentum [math]\vec{p}[/math], from the "proxy" of the "weak measurement", e.g. polarization. After many many many trials, by some "law of large numbers", the average momentum, as implied by the average polarization, measured through space, one detector plane at a time (each detector plane measures p(x,y); then the detector plane is moved, and many many more trials are conducted, at the new value of z --> p(x,y,z)). After the facts, ex post facto, of many many trials, you can build up a picture, of what the average photons' wave-functions "were doing" or "had looked like". I feel like "flowery language" over-complexifies the physics, and makes me much less capable, of comprehending the quantum mechanics, which I would want to think, that I otherwise could.

eliminating "mass" in [math]\left(3 + \epsilon\right)D[/math] According to the equations of Quantum-Gravity, energy, momentum, & mass are equivalent, i.e. E = hf = cp = mc2. And, mass is mathematically equivalent, to a "hyper-momentum" (pw), in a "hyper-dimension" (w), orthogonal to the three spatial dimensions (xyz), i.e. E2 = m2 + p2, s.t. m = pw. Now, our space-time fabric plausibly has some "thickness", in a "hyper" dimension (w), orthogonal to the three spatial dimensions (xyz). Qualitatively, the hyper-dimension is plausibly "small", compared to the "large" spatial dimensions. Quantitatively, the "thickness" of the hyper-dimension, is plausibly comparable, to the range of the W interaction, i.e. ~10-18m; whereas the "breadth" of the spatial dimensions, is plausibly comparable, at present epoch, to the Hubble distance, i.e. ~1026m. If so, then, at present epoch, the spatial dimensions (xyz) are ~44 orders-of-magnitude larger, than the hyper-spatial dimension (w). But, in our ultra-early universe, the three spatial dimensions were smaller; and plausibly as small as the hyper-dimension. If so, then our ultra-early universe comprised four similar space-like dimensions (xyzw), through which particles propagated, at the speed-of-light (v=c), as mass-less fermions & bosons, per the SM. Afterwards, the three spatial dimensions stretched, with the Hubble expansion, thereby becoming bigger, than the hyper-dimension. Some particles, propagating primarily in the hyper-dimension, possibly became "trapped", as standing-waves, between the "inner edge" (w = 0-) and "outer edge" (w = 0+) of our space-time fabric, thereby acquiring "mass" ("trapped hyper-momentum"). Many particles, propagating primarily in the spatial dimensions, possibly "escaped into" the spatial dimensions, thereby remaining "mass-less", cp. fermion-to-photon ratio ~10-9. unifying EM/W interactions in [math]\left(3 + \epsilon\right)D[/math] At present epoch, the spatial dimensions (xyz) are possibly ~44 orders-of-magnitude larger, than the hypothetical hyper-spatial dimension (w). Such asymmetry, in [math]\left(3 + \epsilon\right)[/math] space-like dimensions, could possibly explain, the asymmetry, between the EM/W interactions. For, if so, then our ultra-early universe comprised four similar space-like dimensions, within which the "Electro-Magneto-Weak" (EM/W) interaction could possibly have occurred, without differentiation, between space-like EMxyz, and hyper-space-like Ww, interactions. Denote a particle's "EM/W" charge vector [math]\hat{Q} = \left( \begin{array}{cccc} q_x q_y q_z q_w \end{array}\right)[/math]. Any particle possessing EM/W charge, in some space-like dimension, couples to EM/W interactions, in that dimension, e.g. [math]\hat{Q}_{\nu} = -e \left( \begin{array}{cccc} 0 0 0 1 \end{array}\right)[/math] [math]\hat{Q}_e = -e \left( \begin{array}{cccc} 1 1 1 1 \end{array}\right)[/math] i.e. neutrinos are spatially un-charged, but hyper-spatially charged ("un-charged, hyper-charged"); whereas electrons are spatially charged, and hyper-spatially charged ("charged, hyper-charged"). Thus, neutrinos are un-coupled, to space-like EMxyz interactions; but are coupled, to hyper-space-like Ww interactions. And, electrons are coupled, to space-like EMxyz interactions; and are coupled, to hyper-space-like Ww interactions. The EM/W interaction is mediated, by force-carrying bosons. For example, the neutral EM/W interaction is mediated, by the [math]\gamma_{xyz}[/math], spatially; and by the [math]Z^0_w[/math], hyper-spatially. Thus, neutrinos are un-coupled to photons, but coupled to Z0's ("blind, hyper-sighted"). And, electrons are coupled to photons, and coupled to Z0's ("sighted, hyper-sighted"). Photons represent EM/W fields, oscillating spatially (xyz); Z0 represent EM/W fields, oscillating hyper-spatially (w). In the EM/W unification epoch, in our ultra-early universe, all four space-like dimensions were similar; and non-differentiated [math]\gamma/Z[/math]'s mediated a non-differentiated EM/W interaction, through all four space-like dimensions. Afterwards, the three spatial dimensions stretched, with the Hubble expansion, thereby becoming bigger, than the hyper-dimension. The resulting asymmetry differentiated the spatial EMxyz interaction, from the hyper-spatial Ww interaction. unifying S+EM/W interactions in [math]\left(3 + \epsilon\right)D[/math] By assumption, the S+EM/W interactions behaved similarly, in our ultra-early universe, i.e. "one single force" ultimately governs all interactions, between all particles. If so, then "one single charge" represents the coupling, of all particles, into that "one single force". Henceforth, denote the unified S+EM/W interaction force as "the force"; and unified S+EM/W charge as "the charge". Denote a particle's charge-vector [math]\hat{Q} = \left( \begin{array}{cccc} q_x & q_y & q_z & q_w \end{array}\right)[/math]. Any particle possessing charge, in some space-like dimension, couples to force, in that dimension. Now, forceful interactions are mediated, by force-carrying bosons, that represent oscillations of the force-field, in one or more space-like dimensions. So, force-carrying bosons may limit the ultimate strength of interaction, between two fermions, if the bosons do not carry force, in space-like dimensions, into which the emitting and/or absorbing fermions couple. I.e. the bosons are "stencils" that may "mask out" some space-like dimensions, to which the emitter and/or absorber were coupled. Mathematically, the charge-vector of the emitter, [math]\hat{Q}_e[/math]; and the charge-vector of the absorber, [math]\hat{Q}_a[/math]; are coupled through the boson's mediation-matrix [math]\hat{B}[/math], i.e. [math]\hat{Q}_e^T \circ \hat{B} \circ \hat{Q}_a[/math] Note that the boson mediation-matrix, of a neutral boson, must be normalized, i.e. [math]det\left(\hat{B}\right)=1[/math], to represent a "neutral messenger" that neither strengthens, nor weakens, the interaction-force it mediates. EM/W interaction For example, consider a forceful interaction, between two electrons, having charge (xyz) & hyper-charge (w); mediated by a photon, carrying force (xyz), but not hyper-force (w). Then their interaction can be mathematically represented as: [math]F \propto \hat{Q}_e^T \circ \hat{\gamma} \circ \hat{Q}_e[/math] [math] = (-e) \left( \begin{array}{cccc} 1 & 1 & 1 & 1 \end{array} \right) \left( \begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 \end{array} \right) \left( \begin{array}{c} 1 \\ 1 \\ 1 \\ 1 \end{array} \right)(-e)[/math] [math]= 3 e^2[/math] [math]\equiv Q_l^2[/math] We define the electron-electron interaction coupling, to be the "lepton standard strength" [math]Q_l^2[/math], compared to which other interactions may have fractional effective strengths, e.g. [math]\pm 1/3, \pm 2/3[/math]. S interaction Quarks carry one of three "colors" [math]\left( R Y B \right)[/math]. Equivalently, quarks carry one of three "orientations" (xyz). Accordingly, the exchange of "colors", between quarks, via gluons [math]\left( R \leftrightarrow Y \leftrightarrow B \right)[/math], can be recast, as the exchange of "orientations", [math]\left( x \leftrightarrow y \leftrightarrow z \right)[/math]. By analogy, to directional EM magnetic moments, such "orientations" could be called "Strong S-moments". If so, then in contrast to the "omni-directionality" of electron charge couplings (xyz); quark charge couplings are "un-directional" (x,y,z). Accordingly, denote the unidirectional charge-vectors, of variously oriented down quarks: [math]\hat{Q}_{d,x} = e \left( \begin{array}{cccc} +1 & -1 & -1 & -1 \end{array} \right)[/math] [math]\hat{Q}_{d,y} = e \left( \begin{array}{cccc} -1 & +1 & -1 & -1 \end{array} \right)[/math] [math]\hat{Q}_{d,z} = e \left( \begin{array}{cccc} -1 & -1 & +1 & -1 \end{array} \right)[/math] And, denote the unidirectional charge-vectors, of variously oriented up quarks [math]d \rightarrow u + W^{-}[/math]: [math]\hat{Q}_{u,x} = e \left( \begin{array}{cccc} +2 & 0 & 0 & -1 \end{array} \right)[/math] [math]\hat{Q}_{u,y} = e \left( \begin{array}{cccc} 0 & +2 & 0 & -1 \end{array} \right)[/math] [math]\hat{Q}_{u,z} = e \left( \begin{array}{cccc} 0 & 0 & +2 & -1 \end{array} \right)[/math] Note, by comparison to leptons, quarks can be considered "charge-loaded leptons", e.g. [math]\hat{Q}_{d,x} = e \left( \begin{array}{cccc} \left( \begin{array}{c} +2 \\ -1 \end{array} \right) & -1 & -1 & -1 \end{array} \right) = \hat{Q}_e + \{+2\}_x[/math] [math]\hat{Q}_{u,x} = e \left( \begin{array}{cccc} \left( \begin{array}{c} +2 \\ 0 \end{array} \right) & 0 & 0 & -1 \end{array} \right) = \hat{Q}_{\nu} + \{+2\}_x[/math] By extrapolation, anti-quarks can be considered: [math]\hat{Q}_{\bar{d},x} = e \left( \begin{array}{cccc} \left( \begin{array}{c} -2 \\ +1 \end{array} \right) & +1 & +1 & +1 \end{array} \right) = \hat{Q}_{\bar{e}} + \{-2\}_x[/math] [math]\hat{Q}_{\bar{u},x} = e \left( \begin{array}{cccc} \left( \begin{array}{c} -2 \\ 0 \end{array} \right) & 0 & 0 & +1 \end{array} \right) = \hat{Q}_{\bar{\nu}} + \{-2\}_x[/math] The origin, of quarks (and antiquarks), from leptons (and antileptons), in the unification epoch, in our ultra-early universe, can be attributed, to the conversion, of Positronium [math]P^0 = \left(\bar{e}e\right)[/math], into neutral pions [math]\pi^0 = \left(\bar{d}d\right)[/math], via gluon exchange: [math] \hat{Q}_{\bar{e}} + \left( \{-2\}_x + \{+2\}_x \right) + \hat{Q}_e \longleftrightarrow \hat{Q}_{\bar{d},x} + \hat{Q}_{d,x} [/math] [math]e \left( \begin{array}{cccc} +1 & +1 & +1 & +1 \end{array} \right) + e \left( \begin{array}{cccc} \left( \begin{array}{c} +2 \\ -2 \end{array} \right) & 0 & 0 & 0 \end{array} \right) + e \left( \begin{array}{cccc} -1 & -1 & -1 & -1 \end{array} \right)[/math] Accordingly, we identify gluons, which carry a "color & anti-color", i.e. "S-moment orientation & anti-orientation", as e.g. [math] g_{\bar{R}R} \longrightarrow \hat{g}_{\bar{x}x} = e \left( \begin{array}{cccc} \left( \begin{array}{c} +2 \\ -2 \end{array} \right) & 0 & 0 & 0 \end{array} \right)[/math] e.g. "Red to Yellow re-orientation" [math]\left( d_R \rightarrow d_Y + g_{\bar{Y}R} \right) \longrightarrow \left( \hat{q}_{d,x} \rightarrow \hat{q}_{d,y} + \hat{g}_{\bar{y}x} \right) [/math] becomes [math]e \left( \begin{array}{cccc} \left( \begin{array}{c} +2 \\ -1 \end{array} \right) & -1 & -1 & -1 \end{array} \right) \longrightarrow e \left( \begin{array}{cccc} -1 & \left( \begin{array}{c} +2 \\ -1 \end{array} \right) & -1 & -1 \end{array} \right) + e \left( \begin{array}{cccc} +2 & -2 & 0 & 0 \end{array} \right) [/math] Accordingly, gluons can be represented as "doubly doubled charged carriers", "loaded" with "doubly positive" & "doubly negative" charges, in one or more spatial dimensions (xyz). Similar to the absorption of [math]W^{\pm}[/math] bosons, the absorption of charged gluons, by quarks, effectively "re-colors" those quarks, i.e. "re-orients" those quarks' S-moments, into another spatial dimension. quark partial charges The "unidirectional" charging, of quarks, results in fractional effective charges, for quark-quark interactions, via photons, when compared to the "lepton standard strength" [math]Q_l^2 = 3 e^2[/math], e.g. [math]F_{d_x d_y} \propto \hat{Q}_{d,x}^T \circ \hat{\gamma} \circ \hat{Q}_{d,y}[/math] [math] = (e) \left( \begin{array}{cccc} +1 & -1 & -1 & -1 \end{array} \right) \left( \begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 \end{array} \right) \left( \begin{array}{c} -1 \\ +1 \\ -1 \\ -1 \end{array} \right)(e)[/math] [math]= - e^2[/math] [math]= -\frac{1}{3} Q_l^2[/math] or [math]F_{d_x u_y} \propto \hat{Q}_{d,x}^T \circ \hat{\gamma} \circ \hat{Q}_{u,y}[/math] [math] = (e) \left( \begin{array}{cccc} +1 & -1 & -1 & -1 \end{array} \right) \left( \begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 \end{array} \right) \left( \begin{array}{c} 0 \\ +2 \\ 0 \\ -1 \end{array} \right)(e)[/math] [math]= -2 e^2[/math] [math]= -\frac{2}{3} Q_l^2[/math] Note that "rapidly re-orienting" quarks are considered to exist in "color-less" super-positions, i.e. [math]<\hat{Q}_d> \approx (e) \left( \begin{array}{cccc} -1/3 & -1/3 & -1/3 & -1 \end{array} \right)[/math] [math]<\hat{Q}_u> \approx (e) \left( \begin{array}{cccc} +2/3 & +2/3 & +2/3 & -1 \end{array} \right)[/math] Thus, the fractional effective charges, of quarks, as compared to leptons (electrons), can be explained, as arising from hypothesized "charge unidirectionality" of the former, vs. "charge omnidirectionality" of the latter. Perhaps charge unidirectionality could be observed, in "high speed" interactions ?? Note, that such charge "smearing" renders the "instantaneous" down-quark-down-quark attraction, into a "time averaged" repulsion. Evidently, quarks may "tumble & spin around", only as a "single block unit", such that quarks do not experience the "smearing" of their hadronic neighbors' charges (lest all hadrons become unbound). How would you represent charged-boson interactions, e.g. [math]g, W^{\pm}[/math] ?? primordial particle The unification boson [math]\Gamma_4^{\pm}[/math] was the "grandmother" of all future particles, cp. pluri-potent stem cells in zygotes. All S+EM/W bosons must "converge" to a "common architecture", in the unification epoch. Perhaps the [math]\Gamma_4^{\pm}[/math] was a fully 4D photon, carrying the force in all four space-like dimensions; and "loaded" with both positive "field source", and negative "field sink", charges, coupling to each of those four space-like dimensions. I.e. the primordial particle was a boson "starter kit", an "all-in-one" package, capable of carrying the force in all space-like dimensions; and capable of generating the force into all space-like dimensions, by being imbued with field-source-charge, and field-sink-charge, coupling to all four space-like dimensions. The unification boson could have "split" into electron/anti-electron pairs: [math]\Gamma_4^{\pm} \longleftrightarrow \bar{e} e[/math] [math]e \left( \begin{array}{cccc} \left( \begin{array}{c} +1 \\ -1 \end{array} \right) & \left( \begin{array}{c} +1 \\ -1 \end{array} \right) & \left( \begin{array}{c} +1 \\ -1 \end{array} \right) & \left( \begin{array}{c} +1 \\ -1 \end{array} \right) \end{array} \right) \longleftrightarrow e \left( \begin{array}{cccc} +1 & +1 & +1 & +1 \end{array} \right) + e \left( \begin{array}{cccc} -1 & -1 & -1 & -1 \end{array} \right) [/math] Primordial matter & antimatter (electrons & positrons) could have communicated unification force, via 4D photons, i.e. "discharged" or "unloaded" neutral, unified [math]\gamma/Z \equiv \Gamma_4^0[/math]. Evidently, about this time, the spatial dimensions (xyz) became larger, than the still-small hyper-dimension (w). For, all ensuing "derived" bosons & fermions have asymmetric (3+1)D spatial-vs.-hyperspatial assymetries, e.g. [math]\Gamma_4^0 \rightarrow \gamma_{xyz} + Z^0_w[/math] ("light vs. hyper-light"), [math]\hat{W}^{\pm} = e \left( \begin{array}{cccc} \pm & \pm & \pm & 0 \end{array} \right)[/math] ("charged hyper-light"), cp. [math]\hat{\nu} = e \left( \begin{array}{cccc} 0 & 0 & 0 & 1 \end{array} \right)[/math] presumably appeared at this epoch. Could hypothetical [math]W_4^{\pm}[/math] have both "dis-charged" & "dis-hyper-charged" electrons, producing "not-even-hyper-charged" "ghost neutrinos" ?? Such "ghost fermions" would resemble hypothesized W.I.M.P. DM candidates.

I understand, that when particles "interact", they have "detected" & "measured" each other, quantum mechanically, i.e. "interactions" cause wave-function "collapses", into eigenstates, of the interaction force (EM/W, S). Apparently, the eigenstates, of the EM,S interactions, are the "canonical" or "mass" eigenstates, e.g. me = 511keV. However, the eigenstates, of the W interaction, are special "weak" eigenstates, which are "mixtures", i.e. quantum super-positions, of the canonical mass eigenstates. Vaguely, [math]d_W \approx 0.97 d + 0.22 u[/math]; and [math]\left(\nu_e\right)_W \approx 0.9 \nu_1 + 0.5 \nu_2[/math]. Note that the neutrino mass eigenstates, [math]\nu_1,\nu_2,\nu_3[/math], should be depicted on the SM table of particles, to be consistent, with the other fermions, listed according to their mass eigenstates. However, b/c neutrinos only interact weakly, they are only generated into Weak eigenstates, whilst their pure mass eigenstates are not directly observed -- observing neutrinos requires them to interact, which requires the Weak force, which "collapses" all emerging neutrinos into Weak eigenstates. So, logically inconsistently, the SM table of particles lists every other fermion, according to their canonical mass eigenstates; but lists neutrinos according to their "Weak flavors", i.e. Weak eigenstates, [math]\nu_e, \nu_{\mu}, \nu_{\tau}[/math].

If all bosons are spin S=1 particles; and if the Sz=0 state is suppressed, amongst mass-less bosons (i.e. all mass-less bosons have definite chirality, Sz = 1,-1); then can massive bosons exist in an Sz=0 state, i.e. can fermions exchange massive bosons without "spin flipping" ??

If neutral pions [math]\pi^0 = (\bar{d}d)[/math] can decay into "positronium" [math]P^0 = (\bar{e}e)[/math], via gluon exchange between the incident quarks; then, by time-reversal symmetry, can leptons also exchange gluons (when exposed to their anti-particles) ?

I understand, that a quantum 'measurement' is equivalent to a 'wave-function collapse', e.g. free electrons 'collapsing onto' free protons, in space plasma, emitting a 'recombination' photon. The center-of-mass rest-frame is not necessarily the same, as the earth rest-frame.

For clarity, then, the ZO neutral Weak boson has been dubbed "heavy light", and like light, is only able to alter another 'particle's' momentum / energy & spin. Yet, the Z0 couples to, and can decay into, neutrinos. So, then, the Z0 is "more than merely massive light" ?

'measurement' induces a 'wave-function collapse', "conforming" the collapsing wave-functions into certain states. The QT process exploits QE, to "conform" a wave-function, into a known state, without directly measuring-and-disturbing that state.