Widdekind

According to this presentation, [math]\sigma_{W^+ \rightarrow \bar{e}\nu} \approx 3 nb[/math] [math]\sigma_{W^- \rightarrow e\bar{\nu}} \approx 2 nb[/math] [math]\sigma_{W^+ \rightarrow \bar{l}l} \approx 0.5 nb[/math] where all of the above figures are, subsequently, divided by an "acceptance factor" of [math]\approx 0.5[/math], to derive "total" cross sections. Naively, perhaps the square-roots, of those figures, represent estimates, of the linear range, of the Weak interaction, via those pathways ? If so, then those cross-sections represent ranges, of approximately 0.1-1 10-18m = 0.1-1 m-fm.

what are you saying, "that's where the information has been QT'd" ?

Is the photon's "obliviousness", to the Weak interaction, what "shields" photons, from decay, into neutrinos, i.e. [math]\gamma \rightarrow \bar{\nu}\nu[/math] ? Otherwise, if neutrinos mass <1eV, then every photon more energetic than infra-red would be unstable to neutrino decay ?

gluons are the force-carriers, of the Strong interaction. gluons carry Strong "color" charge, and so can generate more, of the very field, that they mediate. (imagine if photons carried electric charge, then they, too, could generate EM fields, even as they propagated them.)

Neutrinos only interact Weakly. Er go, neutrinos are generated into Weak eigenstates, which are "mixtures" of the canonical mass eigenstates; and neutrinos remain in those Weak eigenstates, until detection. For example, electron neutrinos [math]\nu_e[/math] are a mixed Weak eigenstate, representing a mixture of the neutrino mass eigenstates [math]\nu_1, \nu_2, \nu_3[/math], specifically [math]|\nu_e> \approx 0.9 |\nu_1> + 0.5 |\nu_2>[/math] The following analysis employs normalized units [math]c \rightarrow 1[/math]; and assumes that the neutrino mass eigenstates, are also eigenstates, of mass [math]\left( \hat{m} \right)[/math], momentum [math]\left( \hat{p} \right)[/math], & squared-energy [math]\left( \hat{E}^2 \right)[/math]. take 1 How can such a Weak eigenstate possess a well-defined energy & momentum ? For, if [math]m \equiv \alpha m_1 + \beta m_2[/math] [math]E \equiv \alpha E_1 + \beta E_2[/math] [math]p \equiv \alpha p_1 + \beta p_2[/math] then [math]E^2 = m^2 + p^2[/math] [math]\left( \alpha E_1 + \beta E_2 \right)^2 = \left( \alpha m_1 + \beta m_2 \right)^2 + \left( \alpha p_1 + \beta p_2 \right)^2[/math] [math]\begin{array}{c} \alpha^2 E_1^2 + \beta^2 E_2^2 \\ + 2 \alpha \beta E_1 E_2 \end{array} = \begin{array}{c} \alpha^2 m_1^2 + \beta^2 m_2^2 \\ + 2 \alpha \beta m_1 m_2 \end{array} + \begin{array}{c} \alpha^2 p_1^2 + \beta^2 p_2^2 \\ + 2 \alpha \beta p_1 p_2 \end{array}[/math] [math]\therefore E_1 E_2 = m_1 m_2 + p_1 p_2[/math] But w.h.t. [math]E = \gamma m[/math] [math]p = \gamma m \beta = \beta E[/math] So [math]E_1 E_2 = m_1 m_2 + p_1 p_2[/math] [math]\gamma_1 \gamma_2 = 1 + \gamma_1 \beta_1 \gamma_2 \beta_2[/math] [math]\gamma_1 \gamma_2 \left(1 - \beta_1 \beta_2 \right) = 1[/math] [math]\left(1 - \beta_1 \beta_2 \right)^2 = \left(1 - \beta_1^2 \right) \left( 1 - \beta_2^2 \right)[/math] [math]\begin{array}{c} 1 + \beta_1^2 \beta_2^2 \\ - 2 \beta_1 \beta_2 \end{array} = \begin{array}{c} 1 + \beta_1^2 \beta_2^2 \\ - 2 \beta_1^2 \beta_2^2 \end{array}[/math] [math]1 = \beta_1 \beta_2[/math] [math]\therefore 1 = \beta_1 = \beta_2[/math] But, neutrinos have mass, i.e. [math]\beta_{1,2} < 1[/math]. take 2 Are "Weak neutrinos", i.e. neutrinos in Weak eigenstates, "off mass shell" ? For, if: [math]|\nu_e> = \alpha |\nu_1> + \beta |\nu_2>[/math] then is the mass expectation value: [math]<m_{\nu_e}> = \left( \alpha^* <\nu_1| + \beta^* <\nu_2| \right) \hat{m} \left( \alpha |\nu_1> + \beta |\nu_2> \right)[/math] [math]= |\alpha|^2 <\nu_1|\hat{m}|\nu_1> + |\beta|^2 <\nu_2|\hat{m}|\nu_2>[/math] [math]= |\alpha|^2 <m_1> +|\beta|^2 <m_2>[/math] [math]\equiv |\alpha|^2 m_1 +|\beta|^2 m_2[/math] [math]\therefore m_{\nu_e} \approx \frac{3}{4} m_1 + \frac{1}{4} m_2[/math] or is the momentum expectation value: [math]<p_{\nu_e}> = \left( \alpha^* <\nu_1| + \beta^* <\nu_2| \right) \hat{p} \left( \alpha |\nu_1> + \beta |\nu_2> \right)[/math] [math]= |\alpha|^2 <\nu_1|\hat{p}|\nu_1> + |\beta|^2 <\nu_2|\hat{p}|\nu_2>[/math] [math]= |\alpha|^2 <p_1> +|\beta|^2 <p_2>[/math] [math]\equiv |\alpha|^2 p_1 +|\beta|^2 p_2[/math] [math]\therefore p_{\nu_e} \approx \frac{3}{4} p_1 + \frac{1}{4} p_2[/math] or is the squared-energy expectation value: [math]<E_{\nu_e}^2> = \left( \alpha^* <\nu_1| + \beta^* <\nu_2| \right) \left[ \hat{p}^2 + \hat{m}^2 \right] \left( \alpha |\nu_1> + \beta |\nu_2> \right)[/math] [math]= |\alpha|^2 <\nu_1|\left[ \hat{p}^2 + \hat{m}^2 \right]|\nu_1> + |\beta|^2 <\nu_2|\left[ \hat{p}^2 + \hat{m}^2 \right]|\nu_2>[/math] [math]= |\alpha|^2 <E_1^2> +|\beta|^2 <E_2^2>[/math] [math]\equiv |\alpha|^2 E_1 +|\beta|^2 E_2[/math] [math]\therefore E_{\nu_e}^2 \approx\frac{3}{4} E_1^2 + \frac{1}{4} E_2^2[/math] ??? If so, then Weak neutrinos are "off mass shell", i.e. [math]E_{\nu_e}^2 \ne m_{\nu_e}^2 + p_{\nu_e}^2[/math], i.e. [math]m_{\nu_e}^2 + p_{\nu_e}^2 = \left( |\alpha|^2 m_1 +|\beta|^2 m_2 \right)^2 + \left( |\alpha|^2 p_1 +|\beta|^2 p_2 \right)^2[/math] [math]= \begin{array}{c} |\alpha|^4 m_1^2 +|\beta|^4 m_2^2 \\ + 2 |\alpha|^2 |\beta|^2 m_1 m_2 \end{array} + \begin{array}{c} |\alpha|^4 p_1^2 +|\beta|^4 p_2^2 \\ + 2 |\alpha|^2 |\beta|^2 p_1 p_2 \end{array}[/math] [math]= |\alpha|^4 E_1^2 +|\beta|^4 E_2^2 + 2 |\alpha|^2 |\beta|^2 \left( m_1 m_2 + p_1 p_2 \right)[/math] [math]= |\alpha|^2 \left(|\alpha|^2 \right)^2 E_1^2 +|\beta|^2 \left( |\beta|^2 \right)^2 E_2^2 + 2 |\alpha|^2 |\beta|^2 \left( m_1 m_2 + p_1 p_2 \right)[/math] [math]= |\alpha|^2 \left(1 - |\beta|^2 \right)^2 E_1^2 +|\beta|^2 \left(1 - |\alpha|^2 \right)^2 E_2^2 + 2 |\alpha|^2 |\beta|^2 \left( m_1 m_2 + p_1 p_2 \right)[/math] [math]= \left( |\alpha|^2 E_1^2 +|\beta|^2 E_2 \right) - |\alpha|^2 |\beta|^2 \left( \left( E_1^2 + E_2^2 \right) - 2 \left( m_1 m_2 + p_1 p_2 \right)\right) [/math] [math]= E_{\nu_e}^2 - |\alpha|^2 |\beta|^2 \left( \left( E_1^2 + E_2^2 \right) - 2 \left( m_1 m_2 + p_1 p_2 \right)\right) [/math] [math]= E_{\nu_e}^2 - |\alpha|^2 |\beta|^2 \left( \left( m_1^2 + p_1^2 + m_2^2 + p_2^2 \right) - 2 \left( m_1 m_2 + p_1 p_2 \right)\right) [/math] [math]= E_{\nu_e}^2 - |\alpha|^2 |\beta|^2 \left( \left(m_1-m_2 \right)^2 + \left(p_1-p_2 \right)^2 \right) [/math] [math]\approx E_{\nu_e}^2 - \frac{3}{16} \left( \left(m_2-m_1 \right)^2 + \left(p_2-p_1 \right)^2 \right) [/math] If so, then [math]E_{\nu_e}^2 > m_{\nu_e}^2 + p_{\nu_e}^2[/math], i.e. "electron neutrinos are energy rich" (by a few eV ?).

From wikipedia, I understand the following re: QT: an entangled pair of particles is generated, sharing some property, e.g. spin, such that s1* + s2* = S12 the sender transmits the 'second' particle, to a remote receiver the sender entangles the 'first' particle, with an 'information' particle; and makes a measurement, of their combination, causing wave-function collapse, s1*,s2* --> s1, s2, s.t. i + s1 = Si1 er go, the sender now knows, the quantum state, of the 'second' particle, at the remote receiver, s2 = S12 - s1 = S12 - (Si1 - i) = i + (S12-Si1) the sender transmits the 'offset factor', S12-Si1, to the remote receiver the remote receiver 'subtracts off' that 'offset factor', from their 'second' particle, to recover the 'information', s2 - (S12-Si1) = i I understand, that QT can effect communications encryption. For, when transmitted, s2 carries no meaningful information. And, if transmitted, the 'offset factor' S12-Si1 is meaningful information, but exclusively in application, to but one quantum 'particle', in all of the entire universe, i.e. s2, presumably possessed by the intended remote receiver. Er go, potential eavesdroppers would only intercept "meaningless undifferentiated quantum randomness", or "meaningless-for-them quantum certainty". Is this simple picture accurate (if approximate) ?

neutral Electro-Weak bosons undergo "hyper-oscillations" ? The observed "mixed" neutral Weak bosons [math]\left( \gamma, Z^0 \right)[/math] are mixtures, of the unobserved "unmixed" [math]B^0, W^0[/math]. Now, all Weak bosons have rest-mass. And, the [math]B^0, W^0[/math] are the "canonical" mass eigenstates, of the neutral Weak bosons. Er go, the "mixed" Weak eigenstates, [math]\gamma, Z^0[/math], are super-positions of those mass eigenstates. Thus, if mass eigenstates represent momentum hyper-states, i.e. relativistic photons "bouncing back and forth" in a 1D square-well potential through the "hyper-thickness" of the space-time fabric; then the neutral Weak bosons, as mixtures of the stationary states, would plausibly "slosh from side to side", i.e. "from the upper surface to the lower surface of the rubber sheet", via a beat-frequency effect, arising from the frequency interference, between the stationary states, of which their super-positions were composed. Such is an "anti-symmetric contrast", to the charged Weak bosons, which are themselves mass eigenstates; but which "mix" fermions into mixed Weak eigenstates. I.e. in neutral Weak interactions, the neutral Weak bosons exert no "hyper-forces" on fermions, but absorb "hyper-forces" themselves; but in charged Weak interactions, the charged Weak bosons exert those "hyper-forces" onto the fermions, so altering their "mass", i.e. hyper-momenta.

Would fabricating a high-temperature super-conductor, require engineering, a large energy difference, between the Cooper-pairs' lowest-energy ground state; and their first available, vacant, excited state ?

I understand, that according to GR theory, all mass-and-energy curves the fabric of space-time, i.e. "the fabric of space-time perceives all matter & energy in the same way", or "everything is effectively a photon to space-time".

In the book Quarks, by Nambu, the author says that the theory of the Higgs field, likens space, to a "super-conductor", i.e. a Bose-Einstein Condensate. I want to understand, what the author is implying, e.g. "space is like a BEC, with a ~1MeV band gap, between the ground state, and lowest available [math]\left(\bar{e}e\right)[/math] excited state"? I'm trying to understand Nambu's book Quarks, about whose analogies, I may be confused.

Do the following "rules" apply, to interpreting FDs ? each & every emission, or absorption, of a force-carrying boson, represents a "forceful interaction", i.e. wave-function "collapse", which "conforms" fermions "emerging from the interaction", into eigenstates, of the force, of the interaction, e.g. EM, W, S (er go, "ghosted out" super-position states can only exist, in between wave-function "collapses", i.e. in between interactions) when force-carrying bosons decay, into "con-joined fermion pairs", e.g. [math]g \rightarrow \bar{q}q[/math], those fermions emerge from the interaction, in an entangled state (which is also an eigenstate, of the force, of the interaction), cp. Cooper pairs, i.e. one boson (force-carrier) decays into one boson (entangled fermion pair) when boson-like, fermion pairs interact with other fermions, via other bosons, entanglement is "broken", and the "conjoined fermion pair" separates, into (mutually consistent) separate fermions

I understand, that you waving your laser pointer, from one direction, through to another, is a little like you "spraying a burst of photons with your laser AK". And, those photons fly away from you, in all directions, as if you "had detonated a photon flash grenade". I.e. you are the source of all the "information"; and various "targets" can receive their inbound photons, at various different times; but they themselves aren't doing any active communication FTL, they're just "happening to passively receive your laser shrapnel" whenever they happen to do so.

If all massive fermions have 3 'flavors' or 'generations', then might massive bosons also have two or more 'flavors' or 'generations' ? Would the [math]B^0, W^{\pm}, Z^0[/math] constitute such a 'series' ??

In classical QM, when 'particles' propagate into a 'classically forbidden' region, wherein their energy E < V, then their wave-functions decay away exponentially, [math]\propto e^{-\left(\frac{V-E}{\hbar c}\right)x}[/math]. And, when 'particles' are "borrowed into existence", per HUP, then, in some sense, they represent a negative energy, w.r.t. the zero-energy vacuum, from which they were "borrowed". Does that cause their wave-functions, to "decay exponentially", explaining their finite propagation range, cp. Yukawa potential ??

According to Wikipedia, Z0 bosons decay, to fermion-antifermion pairs, in "branching ratios", proportional, to those fermions' "effective Weak hyper-charges", i.e. not their Weak charges YW = 2(Q-T3), but a "mixed" factor, involving the Weak mixing angle, YW,Z0 = 2(xQ-T3), where [math]x = sin^2(\theta_W)[/math]. By contrast, W+,W- bosons decay to fermions, without such "bias". I understand, that if "there was no Weak mixing", i.e. x = 0, that the Z0 would "unmix", back into the W0; and that, therefore, the W0 would couple to fermions, only proportional to their iso-spin T3, whose magnitude (1/2) is the same for all fermions. I understand, that if "there was full Weak mixing", i.e. x = 1, that the Z0 would "become" the B; and that therefore the B must couple to fermions, in proportion, to their canonical Weak hyper-charge YW. I understand, that if "Weak mixing was reversed", i.e. [math]\theta_W \rightarrow \theta_W'[/math], such that [math]sin^2(\theta_W) \rightarrow cos^2(\theta)[/math], that the Z0 would "become" the photon; and that, therefore, the photon must couple to fermions, in proportion to another "biased" Weak hyper-charge derivative, i.e. [math]Y_{W,\gamma} = 2 \left( cos^2(\theta_W) Q - T_3 \right)[/math]. Accordingly, assuming [math]\theta_W \approx 30^{\circ}[/math], w.h.t.: mass q Qb Qg Qz Qw C u 4 +2/3 +1/3 0 -2/3 -1 +1 d 5 -1/3 +1/3 +1/2 +5/6 +1 +1 v >0 0 -1 -1 -1 -1 0 e 0.5 -1 -1 -1/2 +1/2 +1 0 So, up-type quarks barely couple, to photons, i.e. [math]Q_{\gamma,u} \approx 0[/math] ??

I guess I don't understand. If "raw energy" had numerous "mass states" to "choose from", why wouldn't the "raw energy" occupy more, of the lower energy states, per the Boltzmann factor ? By like logic, more leptons would plausibly have been generated, than quarks. What do I not understand ? If matter-antimatter asymmetry does not arise, from their (pair) production by photons, i.e. the EM; then I must look to the Weak & Strong Forces. And, are not both of the latter as matter-antimatter symmetric, as the EM Force ? [math]\gamma \longrightarrow \bar{e}{e}[/math] [math]W^{-} \longrightarrow \bar{\nu}_e{e}[/math] [math]g \longrightarrow \bar{q}{q}[/math] From whence arises the matter-antimatter asymmetry? Has said asymmetry been "hidden", "deposited" into a plethora of non-interacting anti-neutrinos, "masked" by their prolific "high profile" electron kin ? Speaking of such slight asymmetries, the anti-could, hypothetically, mass more than the proton, by up to "four parts in 100 million", i.e. 40eV. So, it is possible, that anti-matter masses slightly more, e.g. "a neutrino masses worth", than matter ?

The following videos seemed informative:

I understand, that the Strong "color" force increases with distance, out to some maximum effective range (~1 fm), and up to some maximum effective strength (~1 GeV/fm = 10tons). I understand, therefore, that "color confinement" presupposes, that the considered quarks, were already quite close to each other, i.e. "all in the same bag" (cp. 'Bag Model'). For such "quarks in a crew", the harder you try to tug on one quark, the harder that quark's colleagues tug back. But, I also understand, that, out past some maximum effective range (~1 fm), even the Strong "color" force then begins to decline with distance, presumably approximately as 1/d2, given that the SF is modeled mathematically as a "gauge field" (Nambu. Quarks).

What if you liken 'massive' particles, to high-energy photons ? As repeatedly observed, above the various pair-production energy thresholds, e.g. ~1 MeV for e+e-, 'matter' and 'energy' freely inter-convert. Thus, the appearance of distinction, between the two, is an artifact of our "cold", i.e. low-energy, universe (in which low-energy photons lack the energy to "excite" into "mass states"). Accordingly, perhaps the ambient background vacuum, could be analogized, to a Bose-Einstein Condensate ?

Assume that anti-matter must be created, by some process which converts available energy, into anti-matter. If you could create that conversion, with 100% efficiency, then your anti-matter would, including cost-of-production, be no more energy-efficient, than the process, with which you generated your anti-matter. Er go, anti-matter would plausibly make a "super-potent, super-expensive rocket fuel", for specialized systems, e.g. military. However, anti-matter would not plausibly be a generally applicable power source, needing (assumedly) a prior, pre-required power-source "up-production-stream".

Is the following chart accurate, especially regarding the Weak charges QW ? mass q Qw C u 4 +2/3 +1/3 +1 d 5 -1/3 +1/3 +1 v >0 0 -1 0 e 0.5 -1 -1 0

Are anti-matter particles ever-so-slightly more massive, than matter particles ? I understand, that our universe contains 7x as many protons, as neutrons, because the former are less massive, and so were 7x more numerous, at the temperature, when baryons became bound into nuclei, i.e. Boltzmann factor [math]e^{-\frac{\Delta E}{k_B T}}[/math]. If the matter-antimatter asymmetry, related to the baryon-to-photon ratio [math]\eta \approx 10^{-10}[/math], arose when the universe was approximately the temperature-equivalent of Weak bosons [math]\approx 100 GeV[/math], then a massive difference of a few eV, conceivably comparable to neutrino masses, could account for the matter-antimatter asymmetry ?

Does observed quark color confinement imply the Big Bang, i.e. all quarks began jointly immersed, in a common 'QGP', from out of whose expansion, they all emerged in groups ?

mass is 'hyper-momentum' ? If mass is equivalent to energy (E=mc2); and if energy is equivalent to momentum (E=cp); then perhaps mass is momentum (mc = p) ? If so, then mass can be interpreted, as a "hyper-momentum", i.e. linear momentum, in a "hyper-dimension", orthogonal to the three dimensions of space. And, that "hyper-dimension" can be interpreted, as the "hyper-thickness", of our space-time fabric, i.e. "the thickness of the rubber sheet" representing our space-time fabric: E2 = m2 + p2 ....= p02 + p2 Moreover, for massive 'particles' [math]m = \gamma m_0[/math] [math]\left(\frac{m_0}{m}\right)^2 + v^2 = c^2[/math] By like logic [math]v_0 \equiv \frac{m_0}{m}[/math] [math]v_0^2 + v^2 = c^2[/math] According to this picture, all 'particles' propagate, through the fabric of space-time, at the speed of light. However, mass-less particles propagate only through the spatial dimensions (v=c); massive particles at rest propagate only through the hyper-spatial dimension (v0=c); massive particles in motion propagate through all spatial & hyper-spatial dimensions (v02+v2=c2). Weak Force is "hyper-acceleration" ? Particles can increase, or decrease, their hyper-momentum (mass, i.e. 'flavor' or 'generation'), only via the Weak Force. Er go, only the Weak interaction generates "hyper-forces", through the hyper-spatial dimension, that impute "hyper-accelerations" to particles, which thereby increase, or decrease, in hyper-momentum, cp. Newton's First Law of Motion. Indeed, Weak Force bosons are the only force-carriers to possess hyper-momentum (mass), i.e. mass-less force-carriers, possessing zero hyper-momentum of their own, do not affect other particles' hyper-momenta. Note, 'flavor changing' Weak decays invariably involve the Weak Force's charged bosons (W+,W-), and never the Weak Force's neutral bosons (Z0). When particles undergo Weak interactions, their wave-functions "collapse", and they emerge from their interaction, "conformed" into a Weak Force eigenstate, which are linear combinations, of the canonical 'mass' eigenstates. Qualitatively [math]\left( \begin{array}{c} d_W \\ s_W \\ b_W \end{array} \right) \approx \left( \begin{array}{ccc} 0.97 & 0.23 & 0.00 \\ 0.23 & 0.97 & 0.04 \\ 0.01 & 0.04 & 0.99 \end{array} \right) \left( \begin{array}{c} d \\ s \\ b \end{array} \right)[/math] [math]\left( \begin{array}{c} e_W \\ \mu_W \\ \tau_W \end{array} \right) \approx \left( \begin{array}{ccc} 0.9 & 0.5 & 0.0 \\ 0.4 & 0.6 & 0.7 \\ 0.4 & 0.6 & 0.7 \end{array} \right) \left( \begin{array}{c} e \\ \mu \\ \tau \end{array} \right)[/math] Now, particles persist, within our space-time fabric, without "vanishing into hyperspace". So, the hyper-spatial thickness, of our space-time fabric, plausibly represents an approximately 1D square-well potential, trapping particles, within our space-time fabric. And, in 1D square-well potentials, linear combinations, of the mass-energy eigenstates, experience interference effects, and beat frequencies, i.e. 'flavor oscillations', due to which they "slosh from side to side". Er go, when particles experience the Weak "hyper-force", then their original, static, hyper-momentum 'mass' eigenstates, plausibly begin to "slosh back and forth", through the hyper-spatial dimension, as if the particles had, indeed, experienced an impulse, in that hyper-spatial direction. If so, then Weak bosons represent ultra-energetic (80 GeV), ultra-gamma-ray photons, "bouncing back and forth", through the "thickness" of our space-time "membrane".

You're denying the Big Bang theory, of a hot dense compact origin, of our universe, from which state, all quarks emerged, bound into color-neutral hadrons ?