Widdekind

http://www.bnl.gov/bnlweb/pubaf/pr/pr_display.asp?prid=05-38 BNL links their article to a RealPlayer animation, of the perfect fluid generated, during high-energy gold ion collisions. They seem to say, that in "off center collisions", an ultra-dense, compressible, inviscid quark-gluon fluid is produced: | | <--- |xxxxxxxxxxxxxx| ............................| ---> ............................| Note that the gold nuclei are "pancaked", according to their extreme "lorentz contraction", due to their relativistic trans-luminal velocities. The "fluid" seems to show "vortices", i.e. "eddy currents", in the collision-produced "stream" of QGP. Note that the (edges of the) nuclei seem to "pass through each other", whilst leaving a "stream of debris" behind the collision. I understand, that that phenomenon, like two worlds colliding, and actually generating more (molten) rock mass, than they began the encounter with, is a direct demonstration, of the conversion, of collision Kinetic Energy (KE), into a "stream" of new massive quarks (KE --> mqc2) & gluons. Also, I understand, that that demonstrates "color confinement" of quarks, i.e. as the colliding nuclei "rip through" each other, and "rip out" each others' quarks... those "snapped" gluon bonds rapidly "regenerate" into new quark-antiquark pairs, within the "debris stream". So, I understand, that that "debris stream", trailing between the colliding nuclei after they "pass through" each other, is plausibly Electro-Magnetically & Strongly charge-neutral, i.e. only quarks - antiquarks, in bound meson-like pairs. If the debris stream was composed, of quasi-bound mesons, could that explain the "correlations" observed, in the motions, of the quarks, compared to the antiquarks, i.e. "they move the same b/c they're bound into mesons" ?? Perhaps the "off-center" collision, "rips out quarks", which become "color confined", into quark-antiquark mesons, rotating with non-zero angular momentum ? The animation talked about, and depicted, pairs of quark-antiquarks, co-spiraling, in vortices. So again, what if those quark-antiquarks were co-spiraling, b/c the were bound, into rotating mesons ? Naively, such seems physically feasible -- an off-center collision, imparts a rotation, into debris particles, which spin around, as if in an eddy current. The researchers said, that they had expected to see a gas, of non-interacting quarks -- perhaps 4TK is not enough, to "punt quarks free & clear", but instead, their baryons only "melt" and a few quarks are "extruded out" still enmeshed in glue ??

Particle physics describes Does that imply, that, de facto, gluons have mass ?

According to Nambu's book Quarks, the Higgs mechanism treats the fabric of space-time like a "super-conducting material", exhibiting "skin effects", analogizing the short range of propagation of EM fields in SCs, to the short-range propagation, of massive boson fields, in space-time. Does that mean that the "vacuum energy" is a little like an "ocean of water", within which background "water molecules" can "break apart", into "OH-, H+", i.e. matter & antimatter ?? Or, would the ionization of iron, into soluble Fe++ ions, be like the "ionization" of electrons, into neutrinos, which are "much more soluble in spacetime", i.e. have much reduced mass, and propagate much more readily ??

The number of stars, of mass [math]M[/math], decreases with increasing mass, according to a power-law, [math]N(M) \propto M^{-\alpha}[/math], where [math]\alpha \approx 2[/math]. And, the lifetime of stars, defined by the stars' ratio of mass to luminosity, decreases with increasing mass, according to a power-law, [math]\tau(M) \propto M / L(M) \propto M^{-\beta}[/math], where [math]\beta \approx 2[/math]. (Note that the mass-to-light ratio, observed by astronomers, is a direct measures, of the effective age, of the stellar population.) Er go, the number of stars, of lifetime [math]\tau[/math], can be calculated [math]N(\tau)d\tau = N(M)dM[/math] [math]N(\tau) = N(M) \frac{dM}{d\tau} \approx M^{-2} \left( \frac{d\tau}{dM} \right)^{-1}[/math] [math]\propto M^{-2} \left( M^{-3} \right)^{-1} \propto M[/math] [math]\therefore N(\tau) \propto \tau^{-\frac{1}{2}}[/math] To normalize that lifetime distribution density [math]N_{tot} \equiv \int_{\approx 0}^{\tau_{max}} C \tau^{-\frac{1}{2}} d\tau \approx 2 C \sqrt{\tau_{max}}[/math] [math]\therefore C = \frac{1}{2} \frac{N_{tot}}{\sqrt{\tau_{max}}}[/math] [math]\therefore N(\tau) = \frac{1}{2} \frac{N_{tot}}{\tau_{max}} \left( \frac{\tau}{\tau_{max}} \right)^{-\frac{1}{2}}[/math] Now, as a star population ages, all stars with lifetimes shorter than that age, will already have evolved off of the MS. So, at age [math]\tau_0[/math], [math]N(\tau_0)[/math] is the number of stars, then evolving off of the MS. Now, for "young" stellar populations, dominated by big, bright, blue OB stars, that rate will equal the number of SNe, generated by those OB stars, then evolving off of the MS, and undergoing SNe. And, for "old" stellar populations, dominated by sun-like stars, that rate will equal the number of PNe, generated by those G-like stars, then evolving off of the MS. Qualitatively, since [math]N(\tau) \approx \frac{1}{2} \frac{N_{tot}}{\tau_{max}} x^{-\frac{1}{2}}[/math], younger star populations will have many more stars leaving the MS per year, cp. "star-burst galaxies"; and older star populations will have gradually ever fewer stars leaving the MS per year. Quantitatively, our galactic disk contains [math]\approx 400 \times 10^9[/math] stars; is [math]\tau \approx 10 Gyr[/math] in age; and the maximum stellar lifetime, of minimum mass stars [math]M_{min} \approx 0.1 M_{\odot}[/math], is [math]\tau_{max} \approx 1000 \; Gyr[/math]. Thus [math]N(\tau) \approx 1/yr[/math], i.e. this simple picture, of a single-aged stellar population, predicts the formation of approximately 1 PN / yr. Now, PN persist for [math]\approx 10^4 yr[/math]; and there are [math]\approx 10^4[/math] PN in our galaxy. Assuming equilibrium, that implies a rate of formation, of PNe, of approximately 1 PN / yr. Yet, billions of years ago, that rate of PNe generation, would plausibly have been higher. Are PNe more common, in galaxies, observed at high redshift ?? Given the number of stars in some population [math]N_{tot}[/math]; and assuming a minimum star-mass, i.e. maximum star-lifetime [math]\tau_{max}[/math] then the number of PNe (assuming equilibrium, and a 'known' lifetime for PNe, e.g. 104yr) implies the age of the star population.

Thanks for the links. Are you saying, that, being "composite bosons", formed from the combination of magnetically-attracting (spin-anti-parallel) electrons, CPs are "extra stable" vs. scattering / decohering, upon encountering defects, in their propagation media, i.e. "CPs are self-sealing" (very approximate analogy) ? At RF, space has negligible optical density, and negligible optical depth, i.e. RF photons rarely interact with "space gas & dust", even across cosmological distances. And, if RF photons do not interact with such "defects in their propagation medium", i.e. gas & dust in space, then they do not decohere; and they would not 'disentangle'. Er go, transmitting entangled RF photons, "through the water hole", seems feasible.

I don't understand what you are saying. I'm trying to say, that, according to the 'Right-Hand Rule', to generate that 'solenoidal' magnetic field, of that bar-magnet, in that diagram, via actual currents of actual charged particles, would require those currents to be 'solenoidal', i.e. spiraling around the central axis; and, that charged particles, in that 'solenoidal' field, near that bar-magnet, where the field lines "wrap back around" essentially straight-and-parallel to that bar-magnet, would spiral around those field lines, in much the same sense, as the charged particles, which generated the field, in the first place Er go, the generating charges are "spiraling around" the central axis, emanating a magnetic field, that induces nearby charges, to "spiral around" the field lines, in much the same "dance", as the generating charges.

According to the Big Bang theory, our universe began in a small, dense, hot state. So, in that early "quark-gluon plasma", the separation distance, between quarks, was small. So, as our universe expanded & cooled, that QGP cooled, "condensing" into "color-less, color-neutral" bound quark groupings, i.e. baryon 'triplets'. Then, as our universe expanded further, those bound quark groupings simply receded from each other, increasingly beyond the reach & range of the Strong 'color' force. I'm trying to say, that all quarks are bound, into groupings, today, because all quarks became bound, into those groupings, billions of years ago, when our universe was tiny. If our universe had, somehow, begun in a very expanded, diffuse state, similar to present epoch, perhaps then, in theory, you could have isolated quarks, "emanating" attractive Strong force-fields, that simply "couldn't reach" the other quarks, quantum-mechanically huge distances away. I'm trying to say, that perhaps the observational fact, that all quarks are bound into tight groupings, today, is itself observational support, for the Big Bang theory, i.e. that our universe began, billions of years ago, in a compact state, within which all quarks were well within the range & reach, of other quarks' Strong-force-fields, so that all quarks emerging from the compact state, had already become bound, into tight groupings (and from which no quarks have ever since been 'isolated') ??

I understand, that the "singlet" gluon amounts, in effect, to an "all white (& anti-white)", i.e. "color-less" gluon, having no forceful effect what-so-ever: [math]g_s \approx g_{\bar{r}r} + g_{\bar{y}y} + g_{\bar{b}b} \approx g_{\bar{W}W} \approx g_{BW}[/math] Could such a Strong-force "color-less", "black-and-white" gluon be compared, to a Weak-force "neutral current", i.e. [math]Z^0[/math] ?? I understand, that when gluon bonds "break", they "rip" at the "juncture" between their color & anticolor, creating a new quark & antiquark, having those color & anticolors: [math]g_{\bar{r}r} \rightarrow \bar{q}_{\bar{r}}'q_r'[/math] I understand, that the new quark & antiquark become bound into new hadrons: [math]q_r : g_{\bar{r}r} : q_y q_b \rightarrow q_r \bar{q}_{\bar{r}}':q_r' q_y q_b \rightarrow q_r\bar{q}_{\bar{r}}'+q_r' q_y q_b[/math] The resulting meson [math]q_r\bar{q}_{\bar{r}}'[/math], is a pion, which "burps" from one baryon, to a neighboring baryon. The residual Strong nuclear force seems to stem, from the stressing & breaking, of intra-nucleon gluon bonds.

If you take the negative root solution, then [math]\beta \rightarrow 0[/math] as [math]r \rightarrow 0[/math], i.e. the massive force carriers are "weaker", and the force "softens", at shorter ranges. Plotting that F(x) solution reveals, that the force is zero at zero range, and increases in strength linearly, up to the maximum "cut off" range, whereat the force strengthens "steeply". Now, qualitatively, that behavior resembles that of the Strong "color" force, which is weak ('asymptotic freedom') at short range, but increases sharply near its maximum range. And, qualitatively, taking the negative over the positive root, sounds similar, to the difference between "non-Abelian gauge fields", e.g. Strong force, vs. "Abelian gauge fields", e.g. EM. If so, then the Strong force could be modeled, via massive gluons. For what reason(s) do scientists say, that gluons are mass-less, e.g. "have they weighed one" ? Naively, if the maximum range of the Strong force is [math]r_0 \approx 3 fm[/math], then the implied gluon mass would be [math]m_g \approx 100 MeV[/math].

Might gluons have mass ? If so, then only EM photons would be mass-less, i.e. massive force-carriers would be the rule, not the exception. By what means do experimenters conclude, that gluons have no mass ? I understand, that "what is so special" about the Weak interaction, is that its eigenstates are not orthogonal, to those of (all?) the other interactions, i.e. the Weak-mixing angle. I cannot explain "why" that is so, but I understand that that is "what" differentiates the Weak interaction, from (all?) the others.

calculating masses, for Weak-eigenstate quarks ?? If [math]\left( \begin{array}{c} d_W \\ s_W \\ \end{array} \right) = \left( \begin{array}{cc} cos(\theta_W) & sin(\theta_W) \\ -sin(\theta_W) & cos(\theta_W) \\ \end{array} \right) \left( \begin{array}{c} d \\ s \\ \end{array} \right)[/math] then is not the 'expectation value', of the masses, of the Weak-eigenstate quarks (in MeV), assuming that the Weak mixing-angle is [math]\theta_W \approx 30^{\circ}[/math] [math]\left( \begin{array}{c} <m_{d_W}> \\ <m_{s_W}> \\ \end{array} \right) = \left( \begin{array}{cc} cos^2(\theta_W) & sin^2(\theta_W) \\ sin^2(\theta_W) & cos^2(\theta_W) \\ \end{array} \right) \left( \begin{array}{c} <m_d> \\ <m_s> \\ \end{array} \right) \approx \frac{1}{4} \left( \begin{array}{cc} 3 & 1 \\ 1 & 3 \\ \end{array} \right) \left( \begin{array}{c} 300 \\ 500 \\ \end{array} \right) \approx \left( \begin{array}{c} 350 \\ 450 \\ \end{array} \right) [/math] and [math]\left( \begin{array}{c} <m_{u_W}> \\ <m_{c_W}> \\ \end{array} \right) \approx \frac{1}{4} \left( \begin{array}{cc} 3 & 1 \\ 1 & 3 \\ \end{array} \right) \left( \begin{array}{c} 300 \\ 1500 \\ \end{array} \right) \approx \left( \begin{array}{c} 600 \\ 1200 \\ \end{array} \right) [/math] If so, then the Weak-eigenstate quarks are intermediate in mass, between their closest-corresponding "canonical" quarks. (Note that the inverse matrix involves negative numbers??) How would this affect the "exo-thermy" or "endo-thermy" of quark Weak decays ? For example, the Weak kaon decay [math]K^0 \rightarrow \bar{\mu}\mu[/math] begins with the "collapses", of the kaon's [math]s, \bar{d}[/math] quarks, in "mutually compatible" Weak eigenstates. Naively, the "lower flavor" decay pathway "ought" to be energetically favored I understand, that the Weak-boson generating interactions are: [math]\bar{u}_W d_W \longleftrightarrow W^{-}[/math] [math]\bar{c}_W s_W \longleftrightarrow W^{-}[/math] et vice versa. For some reason, no 'flavor-changing neutral currents (FCNC)' occur, as if "the strangeness goes with the (electric) charge". Please ponder the "Weak mixing", of the hypothesized [math]W^0, B[/math] unified-EW bosons, into [math]Z^0, \gamma[/math]. Given that [math]m_Z > m_W[/math], whilst [math]m_{\gamma} \rightarrow 0 \ll m_W[/math], perhaps, via that mixing, "the [math]Z^0[/math] gains mass, whilst the [math]\gamma[/math] loses mass" ?? And, if "the [math]Z^0[/math] has something more than the [math]W^0[/math]", and if "the [math]\gamma[/math] has something less than the [math]B[/math]", then perhaps: [math]W^{+} = W_0 + \{+1\}[/math] ("loaded with positive electric charge") [math]W^{-} = W_0 + \{-1\}[/math] ("loaded with negative electric charge") [math]W^0 = W_0 + \{ \}[/math] ("unloaded") [math]Z^0 = W_0 + \{+1\} + \{-1\}[/math] ("double loaded") [math]\gamma = B - \{+1\} - \{-1\}[/math] ("double unloaded" ??) What might a hypothetical "non-specified (mass &) electric charge packet", i.e. [math]\{+1\}, \{-1\}[/math], represent ?? Seemingly, they are associated with mass, and with electric charge, but not with Weak charge, or Strong "color" charge. An intimate connection, between mass & electric charge, seems suggested, e.g. in flavor-changing charged currents, both mass & charge change. And, saying that [math]B = \gamma + \{+1\} + \{-1\}[/math] seems possible, i.e. "a [math]B[/math] would be a doubly-charge-loaded [math]\gamma[/math]". Somehow, photons "forsake all charges, both positive & negative", and so "opt out of mass-inducing interactions" ?? Could that, qualitatively, characterize the hypothesized Higgs interaction ?? And, why would not such hypothetical "massive charge packets" not be able to exist alone, i.e. what would they "lack w.r.t. particles", i.e. "charge must be confined within particles" -- could there be some sort of similarity, to color-confinement, in the Strong interaction ?? Stated another way, without Weak mixing: [math]W^{+} = W_0 + \{+1\}[/math] ("loaded with positive electric charge") [math]W^{-} = W_0 + \{-1\}[/math] ("loaded with negative electric charge") [math]W^0 = W_0 + \{ \}[/math] ("unloaded") [math]B = \gamma + \{+1\} + \{-1\}[/math] ("double loaded" ??) but with Weak mixing: [math]Z^0 = W_0 + \{+1\} + \{-1\}[/math] ("double loaded") [math]\gamma = B - \{+1\} - \{-1\}[/math] ("fully unloaded" ??) Pictorially, the "double charge load" has been transferred, from the [math]B[/math], to the [math]W^0[/math], rendering the former a [math]\gamma[/math], and the latter a [math]Z^0[/math]. Naively, if [math]m_Z \approx m_W + 10 GeV[/math], then perhaps the "massive charge packets" mass [math]m_{\{\pm1\}} \approx 10 GeV[/math] ?? Naively, perhaps then [math]m_B \approx 20 GeV[/math] ??

The Weak Force eigenstates are not the same, as the "true" or "mass" eigenstates, of the other Fundamental Forces. So, during Weak interactions, i.e. upon the emission or absorption of Weak bosons [math]\left( W^{\pm}, Z^0 \right)[/math], particles' wave-functions "collapse" into "conformance", with the Weak force, i.e. into Weak eigenstates. And, those Weak eigenstates, e.g. [math]\left( \nu_e, \nu_{\mu}, \nu_{\tau} \right) [/math], are "mixtures" of the "canonical" eigenstates, e.g. [math]\left( \nu_1, \nu_2, \nu_3 \right) [/math], e.g. [math]\nu_e \approx 0.9 \nu_1 + 0.5 \nu_2[/math]. In particular, neutrinos only interact Weakly. Er go, after every interaction neutrinos do undergo, they "emerge" from the Weak interaction, in a Weak eigenstate, i.e. [math]\left( \nu_e, \nu_{\mu}, \nu_{\tau} \right) [/math], which are mixtures of the "true" mass eigenstates, e.g. [math]\left( \nu_1, \nu_2, \nu_3 \right) [/math]. And, each of those "true" mass eigenstates, has a different rest mass, and so a different speed, for the same energy. Thus, the "true" components, of neutrinos, constantly interfere with themselves, producing "beats", i.e. neutrino flavor oscillations.

W0 would be a 'Flavor-Changing Neutral Current' ?? If both the [math]W^{\pm}[/math] bosons can change 'flavor', then would not the already-hypothesized [math]W^0[/math] boson change 'flavor' too? I.e. would not the [math]W^0[/math] be a FCNC ? Somehow, the "mixing" of the already-hypothesized [math]W^0, B[/math] bosons, of the unified EW force, into the [math]Z^0, \gamma[/math] bosons, of the separated EM & W forces, "suppresses" FCNCs, by "balancing" the effects, of the [math]W^0, B[/math] ?? I understand, that the eigenstates, of both the [math]Z^0, \gamma[/math], are the "canonical", "mass" eigenstates, of EM & S interactions, i.e. emission / absorption, of either [math]Z^0, \gamma[/math] "conforms" the wave-functions of 'particles', into "collapsed" eigenstates, of the non-Weak forces. If so, then the [math]Z^0[/math] is "merely heavy light".

Once 'mated together', CPs are bosons. And, in 'super-conductors', such bosons can encounter defects, without decohering. Perhaps such SC phenomena, could be applied, to space communications, so that photons (bosons) could encounter space dust ('defects') without decohering ?? For the former, 'decoherence' would be the breaking apart, of the CP, with each electron scattering off from some defect. For the latter, 'decoherence' would be ... the photons scattering of from some space dust. I.e. the behavior, of different bosons (CPs, photons), upon 'decoherence' is different. But, before decoherence, whilst coherent, in both cases S=1 bosons encounter 'defects', in their propagation media. So, if the former can "weather the rough ride", then perhaps the latter could too, with sufficient "QM magic" ??

virtual photons have mass ? Consider two 'particles', separated by a distance [math]r[/math], that are interacting through some force, via massive force-carrying bosons, which propagate at a speed [math]v < c[/math], so that [math]r = v \Delta t = c \Delta t \beta[/math]. Recall, for massive particles [math]p = \gamma m_0 v[/math], i.e. [math]c p = \gamma E_0 \beta = E \beta[/math]. Thus: [math]F \equiv \frac{\Delta p}{\Delta t} \approx \frac{\Delta E \beta}{c \Delta t} = \frac{\hbar c}{\left( c \Delta t \right)^2} \beta = \frac{\hbar c}{r^2} \beta^3[/math] Now [math]\Delta E = \gamma E_0[/math] [math]\approx \frac{\hbar}{\Delta t} = \frac{\hbar c}{r}\beta[/math] Let [math]r_0 \equiv \frac{\hbar c}{E_0}[/math] [math]x \equiv \frac{r}{r_0}[/math] Then [math]x = \frac{\beta}{\gamma} = \beta \sqrt{1-\beta^2}[/math] So [math]\beta(x)[/math] is a solution of [math]\beta^4 - \beta^2 + x^2 = 0[/math], i.e. [math]\beta^2 = \frac{1 \pm \sqrt{1 - 4 x^2}}{2}[/math] By analogy, to the case of mass-less force-carrying bosons, we take the positive solution, so that [math]\beta \rightarrow 1[/math] as [math]x \rightarrow 0[/math], i.e. the force intensifies, and the force-carriers become increasingly energetic, with decreasing distance, between the interacting 'particles'. Also, massive force-carriers are limited to a maximum range, [math]x = 1/2[/math], i.e. [math]r = r_0/2[/math], beyond which they cannot reach, before their "borrowed" energy must be "repaid". At that maximum range, force-carrying bosons propagate at minimum speed, [math]\beta^2 = 1/2[/math], i.e. [math]\approx 0.7 c[/math]. Er go, forceful interactions are always relativistic, i.e. [math]v \sim c[/math]. Thus [math]F \approx \frac{\hbar c}{r_0^2} \frac{\beta^3}{x^2}[/math] [math]\beta^2 = \frac{1}{2} + \frac{\sqrt{1 - 4x^2}}{2}[/math] [math]\therefore F \approx \frac{F_0}{x^2} \times \left( \frac{1}{2} + \frac{\sqrt{1 - 4x^2}}{2} \right)^{\frac{3}{2}}[/math] So [math]F \rightarrow 1/r^2[/math] as [math]r \rightarrow 0[/math], where [math]\beta \rightarrow 1[/math]. Er go, forces mediated by massive bosons exhibit an inverse-square-law behavior, at short ranges, with a "cut-off" at longer ranges, i.e. are qualitatively "Yukawa-like". Perhaps, as the energy [math]E[/math], at which 'particle' collisions are conducted, increases, the "effective mass" of massive force-carriers decreases, i.e. [math]E_{0,eff} \approx E_0 - E[/math] ? If so, then the maximum effective range of interaction [math]r_{0,eff}[/math], approximately separating the "short range" region wherein [math]F \approx 1/r^2 [/math], from the "beyond range" region wherein [math]F \approx 0[/math], increases with collision energy [math]E[/math] Note that forces are never stronger than [math]F \propto 1/r^2[/math], but, at higher energies, "you get more of that potential". No, our universe offers "venture capital" to "aspiring entrepreneurs", to make a business analogy. For, an energy "loan", of amount [math]\Delta E[/math], may be "borrowed", from the background, for a time [math]\Delta t \approx \hbar \ \Delta E[/math], according to the Heisenberg Uncertainty Principle (HUP), before the "loan" must be "repaid". Only by such "lending" can low-energy 'particles', in our cold cosmos, at present epoch [math]\left( T \approx 3K \right) [/math], "finance" the generation, of "expensive" Weak Force bosons, whose rest-mass-energies are 80-90 GeV. I understand, that Fundamental Forces, are conveyed, between fermions f1,2, by force-carrying bosons B, which are generated by a transmitting 'particle' f1; and later absorbed by a receiving 'particle' f2 [math]f_1 \begin{array}{c} B \\ \longrightarrow \\ \end{array} f_2[/math] Perhaps the "force of attraction" is "generated" by particles, and "conveyed" by force-carriers ? In analogy, a transmitting radio dish, sends a signal, which is received by another radio dish, some-where-and-when-else. Or, fundamental 'particles' are constantly "chatting" at each other, via "walkee-talkees" or "cell phones", where the first particle "talks", then a signal is sent, which "plays out" to the other particle.

The RHIC 'particle' collider, at BNL, has smashed gold nuclei together, thereby generating intra-nuclear temperatures, of [math]4 TK \approx 400 MeV[/math], as measured by the "color of light" emitted, from the collision region, immediately after impact. Prima facie, nuclei, and individual nucleons, can & do have internal temperatures. Indeed, [math]4 TK[/math] temperatures correspond, to the "dressed" quark masses, inside nucleons, i.e. [math]m_{q,eff} \approx \frac{1}{3} m_P[/math]. Perhaps quarks, gluons, and virtual quark-antiquark pairs, inside nucleons, equilibrate to the same ambient temperatures, of the nucleon's environment (and "boil out" of nucleons at temperatures [math]\ge 4 TK[/math]? For example, quarks carry EM charge, and so they could interact, with ions & electrons, in astrophysical plasmas. Perhaps the nucleons, within the gas & dust, in deep space, have equilibrated, to [math]\approx 3K[/math] ??

Z0 bosons Z0 bosons convey momentum, energy, & spin: Z0 bosons are generated, with appreciable probability, only at high energies, comparable to the rest-mass-energy of the boson, i.e. 100GeV = 1015K: From whence arises that energy-dependence, of the interaction cross-section? It resembles the Rayleigh-Jeans limit, i.e. [math]\frac{E}{M_Z} \rightarrow \frac{k_B T}{M_Z c^2}[/math], but would not the super-massive W-bosons correspond to the "ultra-violet limit" ?? "running" range of Weak interaction ? If Weak bosons have rest-masses [math]E_0 = m_0 c^2[/math]; and if a 'particle' experiment is performed at some energy [math]E[/math]; then is not the range, of the Weak interaction, calculated according to: [math]\Delta t \approx \frac{\hbar}{\Delta E}[/math] [math]\gamma E_0 = \Delta E + E[/math] ("loan + cash-on-hand") [math]r = t v = \frac{\hbar c}{\Delta E} \left( 1 - \left( \frac{E_0}{\Delta E + E} \right)^2 \right)^{1/2}[/math] [math]= r_0 \frac{1}{x} \sqrt{1 - (x+f)^{-2}}[/math] where: [math]r_0 \equiv \frac{\hbar c}{E_0}[/math] [math]x \equiv \frac{\Delta E}{E_0}[/math] ("loan") [math]f \equiv \frac{E}{E_0}[/math] ("cash-on-hand") For [math]f \ll 1[/math], the function [math]r(x,f)[/math] is maximized at [math]x_{max} \approx \sqrt{2} \left( 1 - f \right)[/math], whereat [math]r_{max} \approx \frac{r_0}{2} \left(1+\frac{f}{\sqrt{2}} \right)[/math]. For [math]f \geq 1[/math], [math]x_{max} \rightarrow 0[/math], and [math]r_{max} \rightarrow \infty[/math], i.e. once 'particles' can "pay their own way", the potential range of interaction is no longer limited, by a need "to pay back the Heisenberg bank". Perhaps that explains the large 'resonances', in the interaction cross-sections, when the 'particle' experiment is 'tuned' to the bosons' rest-mass-energy, i.e. at [math]f = 1, E = E_0[/math] ? Note, the above approximations seem to remain accurate, if imprecise, for the entire range of [math]0 \leq f < 1[/math].

What does such fiber do, to "maintain polarization" ? Via what other mean(s), might you replicate that "maintenance" effect, i.e. "shepherding" of photons ? When you say "free space", I understand, that you are referring to ubiquitous space gas & dust, with which space-propagating photons would invariably "interact", and so, as you posted previously, "decohere" ? How do boson-like Cooper Pairs, in super-conductors, "maintain coherence", despite defects, in the super-conducting material, through which they propagate ? Might that make for some approximately-accurate analogy, to boson-like photons, propagating through "defect ridden" deep space ? Perhaps some "photon pair", combining a "spin-forward" right-handed photon, with a "spin-backwards" left-handed photon, super-posed with a suitable phase shift, e.g. [math]\theta = 0,\pi[/math] ??

I understand, that: From the wikipedia articles, I understand, that the Higgs mechanism is intrinsic to the EW unification model: Apparently, according to the Standard Model, the photon of EM "does not interact with the Higgs", i.e. photons have no mass. Does that mean, that according to the SM, photons do not gravitate ?

I understand, that wave-function "collapse" occurs, after each & every force interaction I, between "particle" quanta & "force" quanta, i.e. between fermions & bosons; and that that "collapse" conforms the "particle" quanta, emerging from the interaction, into eigenstates [math]|\phi_I>[/math], of the interaction force: In particular, I understand, that fermion "particle" quanta, which emit boson "force" quanta, need not "wait around", before "collapsing", whilst the emitted boson propagates away, towards some potential future interaction, with some other "particle", at some other place & time:

energy is "pluri-potent" ? All force-carrying bosons seem to be "pluri-potent", able to generate both matter & anti-matter, e.g. [math]\gamma \rightarrow \bar{e}e[/math] [math]W^{+} \rightarrow \bar{e}\nu_e[/math] [math]g \rightarrow \bar{q}q[/math] Now, photons & gluons are mass-less, er go "energy" can generate both "matter & anti-matter" ?

Logically, false assumptions can generate accurate predictions. Do I understand you to be acknowledging, that their EW Unification hypothesis assumes the existence, of the Higgs field; and, that, over 30 years later, the Higgs field has yet been experimentally verified ?

I understand, that after an interaction, between quanta, via a 'Fundamental Force', e.g. Weak & Strong, that the quanta, emerging from said interaction, have been 'conformed' into eigenstates, of said force. For example, after a down quark 'emanates' a W- boson, that quark emerges from that Weak interaction, in a Weak eigenstate, e.g. [math]u' \approx 0.97 u + 0.23 c[/math]. Then, only after a subsequent Strong interaction, e.g. with neighboring quarks in the same nucleon, would that quark's wave-function "collapse", into a Strong eigenstate, i.e. [math]0.96 \rightarrow u, 0.04 \rightarrow c[/math]. How does the 'energy barrier' eliminate the second possibility, i.e. "collapse" into a charm quark ? Note, neutrinos only interact Weakly. Er go, once neutrinos emerge, from a Weak interaction, in a Weak eigenstate, neutrinos remain in those Weak eigenstates, for-ever-more, until & unless their next Weak interaction. Meanwhile, [math]\nu_e, \nu_{\mu}, \nu_{\tau}[/math] are Weak eigenstates, and so are combinations, of the "true" neutrino Gravity mass eigenstates, e.g. [math]\nu_e \approx 0.9 \nu_1 + 0.5 \nu_2[/math]. Thus, emerging from the Weak interaction, depicted in the figure above, are a "Weak up" quark u', a "Weak electron" e-, and a "Weak electron neutrino" ve: [math]u' \approx 0.97 u + 0.23 c[/math] [math]e^{-}[/math] [math]\nu_e \approx 0.9 \nu_1 + 0.5 \nu_2[/math] Then, only subsequent interactions, with other quanta, via other forces, can "collapse" those emergent wave-functions, into eigenstates, of those other forces. Presumably, in the case of quarks, which readily & rapidly interact Strongly, such "collapses" occur "quickly". Is a "Weak electron", emerging from a Weak interaction, in the same quantum state, as a "normal", i.e. "EM electron" ? Note, neutrinos may interact Gravitationally. And, if neutrinos interacted via the Gravity force, then they would "collapse" into Gravity mass eigenstates, e.g. [math]\nu_e \rightarrow \nu_1[/math]. And, if neutrinos "collapsed" into a mass eigenstate, then they would have a fixed "flavor", i.e. they would not undergo "flavor oscillations". Er go, if Solar neutrinos undergo flavor oscillations, then they have not interacted Gravitationally, en route to earth, from the center of our sun ? Ipso facto, "free fall" trajectories, along geodesics, through curved space-time, do not constitute Gravity interactions. Presumably, any interaction, via any force, must impute some change in momentum, i.e. scattering. Perhaps a "quantum of curvature", in the fabric of space-time, i.e. a Graviton, must scatter other quanta, e.g. neutrinos, in order to have "interacted" Gravitationally ? Perhaps Gravitons, in the fabric of space-time, are like Phonons, in crystal lattices ? Perhaps, in regions of intense & rapidly varying gravity, e.g. cores of collapsing stars undergoing Super-Novae, Gravitons are generated, in the fastly flexing fabric of space-time, and scatter neutrinos, into "true" mass eigenstates ? In EM, EM radiation is attributed to EM quanta, i.e. photons. By analogy, perhaps G radiation is attributable, to G quanta, i.e. gravitons ? Perhaps gravitons obey E = h f ? If so, then gravitons with wave-lengths of km's would have energies of neV's, naively equivalent to temperatures of 10-5K. Perhaps super-cooled quantum detectors could absorb such low-frequency, low-energy gravitons ? The quantum coupling constant [math]\alpha_G \equiv G m_p^2 / \hbar c \approx 0.5 \times 10^{-38}[/math] is miniscule. I understand, that Weak bosons can decay, into both quarks & leptons. In the following figure, the EM charges carried, by charged Weak bosons, "enters into" one of the quanta, emerging from the decay, of the boson, e.g. [math]\left( -1 \right) + \nu_e \rightarrow e^{-}, \left( +1 \right) + \bar{u} \rightarrow \bar{d}[/math]. From the following figure, neutral Weak bosons would resemble one, or the other, of the charged bosons, except without the electric charge, and without the implied charge "entering into" any of the fermions:

I understand, that the "proof", of Electro-Weak Unification, won Profs. Salam, Glashow, & Weinberg the Nobel Prize for Physics, in 1979 AD. I understand, that their "proof" pre-supposed the existence, of the Higgs field, Higgs boson, & Higgs mechanism. How could Profs. Salam, Glashow, & Weinberg, win a Nobel Prize, in 1979 AD, over 30 years before one of their assumptions, was even "possibly glimpsed" ?

According to the article: What is the "factor that is PT-sensitive and yields the change of sign" ?? That factor would derive from the S.E.T., on the RHS of the GR equation ?? In Feynmann diagrams, anti-particles are always pictured "going backwards through time", is that T ?? I understand, that the Christoffel symbols are derived, from the metric tensor: [math]\Gamma \leftarrow g[/math] and, that the Einstein tensor is derived, from the Christoffel symbols: [math]R \leftarrow \Gamma[/math] and, that GR equates the ET, to the SET: [math]R \approx T[/math] Now, from a (3+1)D space-time perspective, PT 'merely' represents the inversion, of all space-and-time coordinates, i.e. [math]\forall \mu \in \{ x,y,z;t \}[/math]: [math]x_{\mu} \rightarrow -x_{\mu}[/math] and, [math]\partial_{\mu} \rightarrow - \partial_{\mu}[/math] Naively, since the Christoffel symbols involve an odd number of those derivatives (n=1), [math]\Gamma \rightarrow -\Gamma[/math] Naively, the 'equation of motion' in GR, for objects in free-fall, is crudely-and-rudely expressed, as: [math]0 = \frac{d^2 \vec{x}}{dt^2} + \Gamma \frac{d \vec{x}}{dt} \frac{d \vec{x}}{dt}[/math] Naively, if so, then both terms, of the 'EoM', involve an odd number of components (n=3), each of which individually inverts, under PT, so that: [math]\left( 0 = \frac{d^2 \vec{x}}{dt^2} + \Gamma \frac{d \vec{x}}{dt} \frac{d \vec{x}}{dt}\right) \; \longrightarrow \; \left( 0 = -\left(\frac{d^2 \vec{x}}{dt^2} + \Gamma \frac{d \vec{x}}{dt} \frac{d \vec{x}}{dt}\right)\right)[/math] Naively, I have come to conclude, that PT does not invert the EoM; and come into conflict, with Prof. Villata, per said cited article. Naively, moreover, the ET involves products, of even numbers, of those CSs & Ds (n=2), so that: [math]R \rightarrow R[/math] Naively, therefore, PT leaves the ET invariant. What about the SET? Naively, the SET has components, which are products, of even numbers of (time) derivatives (n=0,2), so that [math]T \rightarrow T[/math]. Naively, PT leaves the entire GR 'master equation' invariant: [math]\left( R \approx T \right) \; \longrightarrow \; \left( R \approx T \right)[/math] Naively, if all physical laws are CPT invariant, and if GR is PT invariant, then GR is C invariant. Naively, if so, then antimatter gravitates like matter, "no matter how you look at it", i.e. GR is symmetric w.r.t. "CPT by assumption, PT by proof, C by implication". Why does Prof. Villata say otherwise ??