Standard Model already reveals Hyperspace ?

[Widdekind]

space-time hyper-spatial thickness comparable to Compton wave-length of Z⁰ bosons ?

 

As photons increase in energy, their wave-lengths decrease. And, at the energy-equivalents, of massive particles, those wave-lengths are sub-atomic in scale (~10^-13m for electrons). And more, massive matter is made up of (approximately?) point-particles. Taken together, such suggests that there's something special, about ultra-small scales, relating to the transition from energy to matter. Moreover, that E² = m² + p² suggests, via resemblance to Pythagoras' Theorem, some sort of rotation is involved, in the transition from mass-less energy, to massive matter.

 

Therefore, positing that space-time has some hyper-spatial 'transverse' thickness, perhaps the EM oscillations, of ultra-high-energy photons, can, at some size scale, stop 'sliding through' the thin space-time, like EM wafers through a parallel-plate wave-guide, and 'rotate' into the 'transverse' hyper-spatial dimension. Then, those oscillations would 'slop back & forth', 'laterally', and create standing waves, localized in space-time. To wit, massive matter particles, possessing a 'restable' rest mass.

 

At what size scale would such occur? 'The clue' seems to be, the relation between mass-light (photons), and massive light (Z⁰ bosons). If photons, of ~90 GeV, can 'twist laterally', and start oscillating in the 'transverse' hyperspatial dimension, then the (Compton) wave-length size-scale, associated with the Z⁰, being about 10^-18m, could conceivably correspond to the hyper-spatial thickness, of our space-time.

 

 

 

matter-antimatter detonations briefly 'bubble' space-time, in hyper-spatial dimension ?

 

Matter (& antimatter) particles are point-like. Per previous, perhaps they have size-scales of order 10^-18m, the hyper-spatial thickness, of space-time. When two such quasi-point-particles collide, and explode, producing 'paper-thin-pancake' pairs of photons, ~10⁵x larger in spatial extent, perhaps the sudden & localized release, of all that energy, causes the "skin" of space-time, to "bubble out", briefly, into both the "inward" & "outward" hyper-spatial directions.

[Widdekind]

Perhaps the relation E² = m² + p² actually represents, an easily visualizable quadratic sum, of a 'hyper-spatially transverse' momentum (m, rest mass), plus the standard 'thru-spatial' momentum (p). Massive matter oscillates 'in & out', hyper-spatially, at its Compton frequency/wavelength, accounting for its rest mass (mc² = hf_comp). To get that particle moving through space, that momentum arrow has to 'tip over' more & more, so that its total momentum/energy, is the quadratic sum, of the hyper-spatial, & spatial, terms.

 

If rest mass derives from the 'transverse', hyper-spatial oscillation of particles' wave functions, then, when space-time is curved, the (rest-mass-)Energy eigenstates, of said hyper-spatial oscillations, would change. Thus, the curvature of space-time, do to mass, would fundamentally alter that mass, "adding back in" additional effects, into GR ("mass tells space-time how to curve, curved space-time tells mass how to move... and mucks with the masses (=hyper-spatial Energy levels) too"):

 

Edited May 25, 2011 by Widdekind

[Widdekind]

A hyper-spatially "thick" space-time fabric, would have two "sides", like an ice-cream sandwich, an "in-side" skin, and an "out-side" skin. That duality, and an apparent Flatland-analogous-ability of space-time-embedded matter to "rotate" around that hyper-spatial "in-out" axis in either a "left-handed" or "right-handed" sense, seems qualitatively consistent, with the existence of two types of mirror-image-matter (matter vs. anti-matter).

[Widdekind]

[rough draft]

 

If our space-time has a 'hyper-spatial thickness', in the 'in-out' direction (a little like an ice-cream sandwich); and if massive quantum particles oscillate, transverse to spacetime, in that 'in-out' direction (accounting for their rest-mass); and if powerful explosions, within spacetime, briefly 'blister' spacetime, 'bubbling' apart the 'ice-cream-sandwich crusts'; then powerful explosions might modify the rest-masses of quantum particles, residing in sections of space-time, whose 'hyperspatial skin' was so affected. Such powerful explosions might induce Surface Waves, in the skin of spacetime, which would propagate away from the explosion site, albeit at presumably dissipating intensities. Such Surface Waves would modify the rest-masses of quantum particles, as the waves passed 'above-and-below' (through the ice cream sandwich crusts) the 'matter in the middle' actually inside spacetime (the ice cream). Such 'Hyper-surface Waves' might propagate at speeds dramatically different from c, which is only The Speed Limit, for 'matter in the middle'. And, such 'Hyper-surface Waves' might be exploitable, for sending signals across space (vibrating the ice-cream sandwich crust, instead of the ice-cream).

[Ophiolite]

Would this be better suited to a blog, or does it not really matter where people don't read it?

[insane_alien]

Would this be better suited to a blog, or does it not really matter where people don't read it?

 

all of widdekind's posts are like this. It is getting quite annoying.

[Moontanman]

I rather like his posts, I seldom have anything to add but it's wild reading.... be interesting if some of them prove to be true... makes me want to learn the language of math just so i can understand what he is asserting...

[Ophiolite]

Mixing word salad with spurious maths is not something, in my opinion, to be liked. Couple it with poor communication skills and you have a bad advertisement for science.

[mississippichem]

I rather like his posts, I seldom have anything to add but it's wild reading.... be interesting if some of them prove to be true... makes me want to learn the language of math just so i can understand what he is asserting...

 

Don't learn the math. You will quickly cease to enjoy his posts. Ignorance can be bliss sometimes. Curiosity killed the cat to utilize two cliches in one post

[Widdekind]

The quadratic form, for quantum particle energy,

 

E

²

= m

²

+ p

_x

²

+ p

_y

²

+ p

_z

²

suggests, prima facie, that the rest-mass term m², can be interpreted, as a further, and fourth, dimensional momentum term, 'p_w²', representing motion orthogonal to standard spatial dimensions. And, that is strongly suggestive, of hyper-dimensional momentum-carrying-motion, in the 'in-out' dimension, of the (supposed) hyper-spatial 'thickness', of spacetime. Given that the rest-mass is constant, its interpretation as a 'hyper-momentum' implies, that the particle is residing in a 'stationary state', existing as a 'standing wave' spanning 'across' spacetime, through the 'in-out' hyper-dimension. And, such suggests, that quantum particles, confined within our spacetime, are kept in such confinement, by a 'hyper potential', in whose local minimum, matter & energy, in our spacetime, are 'shackled'.

 

Now, if our spacetime has a hyper-spatial 'thickness', and if our spacetime represents an attractive hyper-potential well along that 'in-out' dimension, then what shape is that 'hyper-potential' ? Mathematically, many potential wells, Taylor-expanded about their local minima, can be described, to lowest order, as quadratic 'harmonic' potentials V = 1/2 k x². And, it is well known, from elementary QM, that the energy eigenstates, of such quadratic potential wells, create a 'ladder' of levels, all being odd multiples, of the lowest, ground-state, energy: E = E₀, 3 E₀, 5 E₀, etc. Therefore, if an electron (say), is an energy wave, oscillating 'across' spacetime, through the hyperspatial 'in-out' dimension of spacetime 'thickness', in a quadratic attractive potential; and if its ground-state energy happens to be its observed rest-mass-energy of 511 KeV; then we would expect to see 'excited hyper-states' of electrons, with apparent rest-masses of roughly 1.5 MeV, 2.5 MeV, 3.5 MeV, etc. Such states are not, seemingly, observed. Yet, an intriguing explanation offers itself. For, by the time an energy-injecting event, has enough energy to 'hyper-excite' an electron, then that event embodies an amount of energy, equivalent to an even multiple of the electron rest-mass energy, which would preferentially produce electron-positron pairs.

 

Thus, the to-date absence, of observations, of excited hyper-states, of electrons (or other fundamental particles), can be accounted for, by the pre-emptive preference, of physics, for pair production, over (alleged) hyper-spatial excitation. Perhaps careful, balanced-and-omni-directional stimulation, of a ground-state electron, in a deep 'Fermi sea' of electrons (e.g., in a metal), wherein all neighboring electron states are already occupied, might impede pair production (at least, on the electron side?), which would, then, allow energy blasts, of multiples of ~1 MeV, to excite electrons into 'anomalously heavy', supra-normal, rest-mass states??

 

Note, too, that the fact, that our spacetime's supposed hyper-potential well, can attractively bind both particles & anti-particles, whose charges are all opposite-if-equal, might mean, that the 'in' and 'out' skin-like-layers of spacetime, are equal-but-oppositely charged. If so, then the 'inside skin', and 'outside skin', of spacetime are a little like parallel-plate capacitors, carrying equal-but-opposite charges. Such a scenario would produce a potential, which was anti-symmetric, 'across' spacetime, through its 'in-out thickness':

 

---^v----

If so, electrons & positrons (say) would be separately attracted, to opposite 'sides' of that potential well, with the former attracted to the 'inside edge', and the latter the 'outside edge' (say). Moreover, the appearance of distinct 'generations' of particles (e.g., Muons & Taons) in the Standard Model, could be accounted for, by the higher-order terms, deviating from simple quadratic form, in the 'hyper-potential', as one moved away from the two local extrema. Again, near those extrema, Taylor expansions of the (alleged) hyper-potential are closely approximated by a quadratic, harmonic oscillator form, producing the standard energy 'ladder' of levels. But, at some point, as particles are hyper-excited to near 'ionization' energies, higher-order terms perturb the simple previous picture, producing unstable-and-distinct semi-stationary solutions, interpreted as Muons & Taons (say). Note, that, in this picture, particles & anti-particles 'ionize' in opposite hyper-spatial directions, each ionizing 'off into hyperspace', hyperspatially 'away' from the opposite 'side' of spacetime.

 

Comparison of electrically uncharged Neutrinos, to electrically charged Electrons / Muons / Taons, seemingly suggests, that the hyper-potential depends strongly on particle charge. Similarly, subsequent comparison to quarks, seemingly suggests, that the hyper-potential also depends strongly on particle color-charge. If so, then perhaps one 'hump' of the hyper-potential, is positively electrically-charged x 'white' color-charged, whilst the other is negatively electrically-charged x 'black' color-anti-charged ? Then, by inspection, we observe, from the Standard Model, that:

 

[math]m \approx \left( 0.5 MeV \times -q_e \right) + \left( 5 MeV \times q_c \right)[/math]

Thereby, the mass excess, of bottom-quarks over top-quarks, can be explained, if:

 

1. all Matter exists in the 'positive Electrical potential (+), positive Color potential (white)
   
2. all Antimatter exists in the 'negative Electrical potential (-), negative Color potential (black)'
   

Thus, for bottom-quarks, the Color and Electrical potentials contribute in concert, to its larger mass; whereas, for up-quarks, the dominant Color potential is opposed by the subordinate Electrical potential, slightly reducing its mass. Note, though, that this prescription implies, that Matter & Antimatter exist in 'opposite pockets' of the hyper-potential, preferring 'opposite sides' of the fabric of spacetime, the one preferring the 'in-side' half, the other the 'out-side' half. Note, too, that, since there is more Matter than Antimatter in this Cosmic spacetime fabric; and since the 'out-side' surface, of the same, is larger than the 'in-side' surface (slightly today, perhaps more so soon after the Big Bang, when spacetime was highly curved); then, perhaps Matter occupies the ever-so-slightly-larger 'outside pocket', and oppositely.

[Widdekind]

At low energies (1^st generation), when the wave-functions, of fundamental particles (u^+2/3,d^-1/3,e^-1), would be (hypothetically) 'hyper-spatially narrow' (confined close to the w=0 hyper-spatial 'mid-hyper-plane of spacetime'), then the quantum behavior appears to be dominated by the Color Force, so that the quarks resemble each other, in mass, much more than either resembles an electron. But, at high energies (2^nd-3^rd generations), when the wave-functions would 'hyper-spatially spread out' (away from w=0, in both the 'in' and 'out' directions), then the (allegedly) 'hyper-spatially excited states' of electrons (i.e., muons & taons) and down-quarks (i.e., strange & bottom) are much more similar, in terms of mass, than either are to the 'way-out-in-a-league-by-itself' up-quark excited hyper-states (i.e., charm & top).

 

Thus, qualitatively, this hyper-spatial hypothesis alleges, that the up-quarks are, ultimately, distinct from down-quarks & electrons, b/c (supposedly) for up-quarks, their Color Force attraction to the 'matter-out-side' of spacetime is opposed by their EM Force attraction to the 'antimatter-in-side' of spacetime; whereas, for the others, all attraction forces are complimentary. And, quantitatively, up-quarks do indeed evidence unique behavior, if only at high (excited hyper-spatial) energy. And so, there is at least a conspicuous coincidence, between the qualitative claims of this hyperspatial hypothesis, and actual quantitative observations.

 

Keeping in mind, that the Compton-wavelength is the characteristic range of any fundamental force (Bernstein. Intro. to Cosmology), then the Color Force is far shorter range, and far more confined, than the EM force. Perhaps, then, the CF is also so confined, in the 'in-out' hyperspatial dimension? For, then, in guestimating the shape, of the hyper-potential, combining contributions from the CF & EMF, perhaps the former is delta-function-like, whereas the latter, although shallower & flatter, is far broader?? Such a scenario could create conditions, wherein, at higher energy / generation, up-quarks became "bound to both sides of spacetime", conceivably accounting for the colossal energies of charm & top quarks. Thus, this hyper-spatial hypothesis predicts, seemingly testably, that, by virtue of such "straddling the hyper-span of spacetime", up-quarks (up-anti-quarks) will be, someway-somehow, "more interactive with antimatter" (matter), than down-quarks & electrons (down-anti-quarks & positrons), who "keep to their own side of the tracks".

 

 

[Widdekind]

Crudely, and completely qualitatively, if our space-time fabric resides in a 'hyper-space' of higher dimension; and if our space-time fabric has a 'hyper-thickness'; then that fabric has two 'hyper-faces', an 'inside surface', and an 'outside surface'. And, that dual nature, is qualitatively consistent, with the dual nature of charge (+/-), and matter-antimatter.

 

 

Furthermore, if particle rest mass represents 'transverse standing wave oscillations', 'across' our space-time fabric, in the 'in-out' hyper-dimension; and if the three 'generations' of matter, in the 'Standard Model' represent three successive states of 'hyper-excitation' (H₀, H₁, H₂); and since the three 'generations' of Neutrinos have such similar masses; and since those Neutrinos 'flavor oscillate' between those states; and since, in practice, all Quantum particles, being localized in space, have some spread in momentum [math]\Delta p[/math], and hence energy as well [math]\Delta E[/math]; then perhaps Neutrino Oscillations occur b/c, in practice, Neutrinos are created with Energy spreads [/math]\Delta E[/math] that exceed the minute differences between the rest-mass-energies, of the three Neutrino 'flavors', [math]\Delta E > E_{\nu_{\tau}}-E_{\nu_e}[/math].

[Widdekind]

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:

 

E

²

= m

²

+ p

²

....

= p

₀

²

+ p

²

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".

Edited January 14, 2012 by Widdekind

[Widdekind]

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.

[Widdekind]

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" (p_w), in a "hyper-dimension" (w), orthogonal to the three spatial dimensions (xyz), i.e. E² = m² + p², s.t. m = p_w.

 

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 EM_xyz, and hyper-space-like W_w, 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 EM_xyz interactions; but are coupled, to hyper-space-like W_w interactions. And, electrons are coupled, to space-like EM_xyz interactions; and are coupled, to hyper-space-like W_w 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 EM_xyz interaction, from the hyper-spatial W_w 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] ??

 

• charged bosons "double couple" ??

Perhaps, in charged boson interactions, the absorbing particle interacts, with both the "underlying neutral carrier" boson, conveying the charges of the emitter; and with the "loaded charge" directly residing within the boson. For example, in the re-orientation interaction [math]q_R q_Y \rightarrow q_Y g_{\bar{Y}R} q_Y \rightarrow q_Y q_R[/math]:

 

[math]F_{d_x d_y \rightarrow d_y d_x} \propto \hat{Q}_{d,x}^T \circ \hat{\gamma} \circ \hat{Q}_{d,y} + \hat{g}_{\bar{y}x}^T \circ \hat{Q}_{d,y}[/math]

 

[math]= \left( \hat{Q}_{d,x} + \hat{g}_{\bar{y}x} \right)^T \circ \hat{\gamma} \circ \hat{Q}_{d,y} [/math]

 

[math] = \left[ (e) \left( \begin{array}{cccc} +1 & -1 & -1 & -1 \end{array} \right) + (e) \left( \begin{array}{cccc} +2 & -2 & 0 & 0 \end{array} \right) \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) \left( \begin{array}{cccc} +3 & -3 & -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]= - 5 e^2[/math]

 

[math]= -\frac{5}{3} Q_l^2[/math]

or

 

[math]F_{d_x u_y \rightarrow d_y u_x} \propto \hat{Q}_{d,x}^T \circ \hat{\gamma} \circ \hat{Q}_{u,y} + \hat{g}_{\bar{y}x}^T \circ \hat{Q}_{u,y}[/math]

 

[math]= \left( \hat{Q}_{d,x} + \hat{g}_{\bar{y}x} \right)^T \circ \hat{\gamma} \circ \hat{Q}_{u,y} [/math]

 

[math] = \left[ (e) \left( \begin{array}{cccc} +1 & -1 & -1 & -1 \end{array} \right) + (e) \left( \begin{array}{cccc} +2 & -2 & 0 & 0 \end{array} \right) \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] = (e) \left( \begin{array}{cccc} +3 & -3 & -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]= - 6 e^2[/math]

 

[math]= - 2 Q_l^2[/math]

According to this guess, "extruded charge get to do double duty".

 

More simply, the force is conveyed by the "bare" boson; and "loaded on charges" merely "update the absorber for next time". According to a crude "space-time is a discrete quantum computer" conception, the latter "code" being simpler, seems preferable.

 

 

• 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.

Edited January 21, 2012 by Widdekind

[Widdekind]

mass "hyper-inertia" curves space-time ?

 

Mass, "tied into" the fabric of space-time, was "flung outwards", by the Big Bang. Mass could possibly have "hyper-inertia", tending to retain a constant "outwards hyper-momentum", until restrained by "elastic" space-time fabric:

 

 

 

 

estimating "hyper-thickness" of space-time, from first-generation quark masses ?

 

According to QM, 'particles' confined into 1D square potential wells, of finite energy "depth", have a finite number of bound states. And, the most energetic bound state tends to have an energy comparable to the depth of well. So, up-type quarks (m_top ~ 180 GeV) possibly experience a dramatically deeper well, than down-type quarks (m_down ~ 5 GeV). Yet, the "ground" states, of both types of quarks, i.e. u & d, have nearly identical masses, near 5 MeV. Now, in classically forbidden regions, where the particle energy, is less than the local potential energy, i.e. E < V, wave-functions decay exponentially. So, whether confined within a well of 5 GeV, or 200 GeV, in the low energy limit E << V, all bound particles are experiencing an effectively infinite square well potential. And, for infinite square well potentials, the wave-functions are driven to zero, at the potential "walls", i.e. the bound states are standing waves, with wave-lengths that are (essentially) integer multiples of the potential well width. If so, then the de Broglie wave-length, of u & d quarks, i.e. 10^-14m = 10 fm, would presumably be approximately the width of the well. Such a hypothetical hyper-spatial thickness, would be 10x the spatial breadth, of nucleons ("quarks are taller than they are wide"). Naively, a hyper-thickness of our space-time fabric, hypothesized to be "thin", should be "small", in comparison to spatial size scales. Using "dressed" quark masses, of mesons & baryons, which are 10-100x larger, would reduce the estimated hyper-thickness, to fractions of a fm.