Widdekind

According to the Borexino Princeton Group, Neutrino Oscillations behave differently, in high density media, at high energies: What effects would this have had, on Neutrinos, at ultra-early epochs, at ultra-high red-shifts, associated with Primordial Nucleo-Synthesis ?

Back at the Big Bang, the expansion of the universe was infinitely rapid, [math]H(t=0) \rightarrow \infty[/math]. This is visualizable, as the vertical, 'infinitely steep', asymptote, of the Cosmic Scale Factor, plotted as a function of time, simply in 1D: or, as a more attention-grabbing 'surface-of-revolution': Thus, at the "bottom of space-time", back at the Big Bang, the fabric of space-time becomes asymptotically flat, with a flat, planar, tangent surface. Is that a way of "visually explaining" the cosmological 'Flatness Problem' ??

According to figure 10, from a redshift of z ~ 1, that which is observed to span 4 days, "here-and-now" at earth, actually occurred over only 2 days, "there-and-then", at the source, in the source-frame. Whilst Prof. Perlmutter is referring, in said cited source, to SNIa, surely the same "stretch factor" affects GRBs, as well. Perhaps this has some impact, on the "short-burst" vs. "long-burst" debate ?? All else being equal, more cosmologically distant GRB Hyper-Novae (HN) will appear to have longer, more slowly evolving, light-curves... could those durations be used, to estimate, the red-shift, of the source-emitter HN ???

Oops -- [math]\int_0^{\infty} r^2 \times \frac{e^{-2r}}{r^2} dr = \frac{1}{2} \rightarrow 1[/math], so that our probability density has an extra factor of two (2), and so our WF has an extra factor of square-root-two (21/2). And, so, the spatial integral, of the original WF itself, integrates to [math]\int_0^{\infty} r^2 \times \sqrt{2} \frac{e^{-r}}{r} dr = \sqrt{2}[/math]. Thus, the WF spatially integrates to square-root-two (21/2) times that of the probability density. Now, this same "square-root-two (21/2) result" appears to be the case, for a spreading Gaussian wave-packet, as well. For, according to Pan 2009, a spreading Gaussian WF has the form: [math]\Psi \propto \frac{1}{\sqrt{1 + i t}} e^{-\frac{x^2}{1+i t}} = \frac{1}{\sqrt{1 + i t}} e^{-\frac{x^2}{1+ t^2} \times (1 - i t)} [/math] Substituting [math]u \equiv \frac{x}{\sqrt{1+t^2}}[/math], that integral computes to: [math]\frac{\sqrt{1+t^2}}{\sqrt{1+it}} \int_{-\infty}^{\infty} du \; e^{-u^2 \times (1 - i t)} = \frac{\sqrt{1+t^2}}{\sqrt{1+it}} \times \frac{\sqrt{\pi}}{\sqrt{1 - i t}} = \sqrt{\pi}[/math] according to an online integrator. And, thus, the probability density, [math]\Psi^{*} \Psi[/math], integrates to: [math]\frac{\sqrt{1+t^2}}{\sqrt{1+it} \times \sqrt{1 -it}} \int_{-\infty}^{\infty} du \; e^{-u^2 \times 2} = \frac{\sqrt{\pi}}{\sqrt{2}}[/math] Again, the WF spatially integrates to "square-root-two (21/2) times" that of the associated, squared-modulus, probability density (PD). CONCLUSION ?? The WF has a "constant mathematical reality", which underlies that of the associated, squared-modulus, PD. The WF is "mathematically conserved", in overall, aggregate, spatially-integrated value. And, not implausibly, the WF may generally integrate to "square-root-two (21/2) times" as much, as its associated PD.

Please consider the Hydrogen 1S ground-state Wave Function (WF), [math]\propto \frac{e^{-r}}{r}[/math]. If that WF is normalized, so that its modulus squared integrates to one, [math]\int r^2 \times \frac{e^{-2r}}{r^2} dr \rightarrow 1[/math], then the WF itself integrates to two, [math]\int r^2 \times \frac{e^{-r}}{r} dr = 2[/math]. (Of course, that 'direct WF integral' is only the amplitude, to be multiplied by the appropriate complex exponential of the ground-state energy-frequency, [math]\propto e^{-13.7 \, eV \, \times t}[/math].) QUESTION: For a general 'wave packet' -- which 'spreads through space', over time, according to its evolution, as described by the SWE -- would not the 'direct integral', of the WF itself, actually increase over time ?? For, whilst a highly spatially concentrated WF, and its square, aren't dramatically different -- [math]x \approx x^2[/math] when [math]x \approx 1 \, or \, 0[/math] -- conversely, a low-and-flat, spread-out WF, will be much higher in absolute value, than its square. If so, then the spreading of the WF, actually increases the "overall integrated aggregate amount", of WF present, even if its squared-modulus remains normalized. If so, then, in some sense the SWE "grows" the WF, over time, even though the WF2 remains normalized to one.

Please consider, a 'cosmological photon', crossing our cosmos, through cosmological distances, over cosmological time-scales. For billions of years of time, through billions of light-years of space, that photon exists in "phantasmal form", "ghost evolving" across the cosmos, according to the Type II von Neumann evolution, of its 'wave function' (WF), governed by the SWE. Then, suddenly, on the other side of space, after eons of time, that photon -- which went 'AWOL' from its emitting source system, billions of years before, billions of light-years away -- "collapses" into definite, measured, observed existence, inside some human space-surveying telescope. The WF associated with that photon vanishes; viewed as a simple quantum system qs, that same system is destroyed, violating local, "intra-system" energy conservation; even as that energy is transferred over, to the telescope. QUANTUM STEALTH ? If a simple quantum system qs, consisting of a single photon, can cross cosmological distances, over cosmological times, in "phantasmal form", without ever being detected or observed, so much as a single time; then, in theory, a (much) more complex quantum system QS could also cross our cosmos, in "ghost ethereal form". Thus, in theory, an advanced "quantum coherent space-craft" (space probe, space ship, 'star destroyer'), could "ghost evolved" its way through space-and-time, at conventional velocities (v < c) according to the SWE, but in a completely quantum-un-detected, quantum-un-observed, quantum-un-measured manner. If some 'science-fiction' be permitted, solely for sake of emphasis, an "alien invasion fleet", could "ghost out" in some distant star system; cross this cosmos, to earth; and then "pop" back into existence, with 'star destroyers' "collapsing" into observable reality, over every major earth city, simultaneously... without warning, with "quantum stealth". Is such not so, in theory ??

According to Maoz' Astrophysics in a Nutshell, our space-time is isotropic, on size scales exceeding 100 Mpc. The observed 'super-void' is, apparently, 1 Gpc across, 10x that size.

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].

Quantum Wave Function "collapse", upon Measurement / Detection, always involves some signal, which "registers" the WFC / M / D, to the rest of our space-time. WFC / M / D often involves a spatial localization, into a vacant-and-available bound state, in an attractive potential well. Yet, charged particles, accelerating due to their interactions, can also emit energy-carrying photons. Generalizing, WFC / M / D seems to involve "Force Interactions" (e.g., EM), and the creation-and-emission (or absorption-and-destruction) of the corresponding Force Carriers (e.g., photons). Therefore, total particle number is not conserved. To wit, WFC / M / D seems to involve multi-particle interactions, and is not something isolated systems spontaneously undergo, on their own. Crudely, the "total energy", of a system of particles, as expressed by their "system Hamiltonian" H = KE1 + KE2 + ... + V, is constant, during typical Type II evolution, wherein energy is only "spread around", or "diffused amongst", or exchanged between, the interacting quantum particles. In such circumstances, interacting-and-energy-exchanging particles can "Entangle". Yet, during Type I evolution, energy is utterly expelled from the system (or, incorporated into the system), and so the "total energy" discontinuously changes. Thus, Type I WFC / M / D seems to involve a system of force-interacting particles, which "changes gears", "down-shifting" into a lower energy mode (or, "up-shifting" to a higher energy mode), such that [math]H_i \ne H_f[/math]. In such circumstances, the particles "WF Collapse". In sum, there seems to be some sense of: Type I evolution discontinuous "quantum jump" Wave Function "collapse" discontinuous energy change energy not conserved particle number not conserved: Force-Carrier particle created/destroyed, effecting "registration signal" to surrounding space-time Type II evolution continuous energy exchanged "in house" only energy conserved Wave Functions "Entangle" Are these statements appropriate ? Seemingly, if so, then there is no such thing as a "partial registration signal". To wit, by the time that some energy-carrying photon is created (say), and expelled from the system as a registration signal to the rest of our cosmos, then that system has already undergone WFC / M / D. Thus, there is never any such thing, as a "partial registration" -- such signals are either sent, or not sent, in their entirety. To wit, Wave Function Collapse = Measurement = Detection = Registration WFC = M = D = R Otherwise, there seems to be the sense of potentially "infinite recursions", of Entanglements, with partially-present prior Registration-Signals, with no "out", to "clear the table", for a "new hand of cards". Also, and perhaps more importantly, you would, then, actually have "half photons" (or, generally, "partial Force Carriers"), whose total Wave Function, integrated over all space-time, would only add up to some fraction, less than one whole, of a particle. Thus, WFC, upon M/D, seems to preserve the "Quantum Integrability", of quantum particles (specifically, the Force-Carriers created/destroyed, in the process).

If we recall that: Type I evolution = "Quantum Jumps" = "Wave Function Collapse" = Measurement / Detection Type II evolution = SWE then, can we not claim, that (1) all behavior is Quantum; (2) so-called 'Classical' behavior is Quantum 'Type I' behavior, whereby WF "collapse" constantly re-localizes macro-scopic systems of particles into definite states of existence ? To wit, there is no such thing as 'Classical' behavior, but, rather, all behavior is Quantum (Type I or Type II evolution); and, so-called 'Classicality' is simply 'the Type I half of QM behavior' ??

I was wondering whether, with a sufficiently slowly generated ("slowly spun off, slowly woven") photon, one could exploit Quantum non-locality to "stretch" a photon's wave packet, all the way across the cosmos, in some super-luminal way. [math]\Delta x \Delta p \approx \hbar[/math] [math]\Delta E \approx \frac{c \hbar}{\Delta x}[/math] For [math]\Delta x[/math] = 1 Gpc, [math]\Delta E \approx 10^{-32} eV[/math], an ultra-pure, nearly mono-chromatic, light source. And, that would require a generation time, of [math]\Delta t \approx \hbar / \Delta E \approx \Delta x / c[/math]. To wit, [math]\Delta x \approx c \Delta t[/math], and no "sneaky super-luminality" appears to be possible upon this particular path. What would be "weird", would be that the Wave Function would physically span the space between source & destination, being a "bridge" of photon WF. But there are probably a slew of reasons why such a suggestion is Quantum physically impractical.

May I please request a clarification -- physical phenomena are not actually exactly instantaneous, but occur over some "spread" or "uncertainty" in time, [math]\Delta t[/math]. Then, per the HUP, [math]\Delta E \Delta t \ge \hbar[/math] -- where also, for photons, [math]\Delta E = c \Delta p[/math] -- the finite-and-non-zero "generation time" implies that even individual photons are not pure-and-mono-chromatic. To wit, a photon "wave packet", being localized in space, will have some spread in momentum-and-energy. Moreover, all of the other quantum particles involved, in the photon-emitting process, will also be "wave packets", presumably partially localized in space, and so also having their own momentum spreads. Thus, momentum conservation, for the system, will involve some "slop" or "blur", [math]\left( p_1 + \Delta p_1 \right) + \left( p_2 + \Delta p_2 \right) \rightarrow \left( p_1' + \Delta p_1' \right) + \left( p_2' + \Delta p_2' \right) + \left( p_{\nu} + \Delta p_{\nu} \right)[/math]. Is this not so ? Were it the case, that [math]\Delta p_{\nu} \ll p_{\nu}[/math], then would not [math]F_{recoil} = dp/dt \approx p_{\nu}/\Delta t_{\nu} \approx E_{\nu}/c \times \Delta E_{\nu} / \hbar[/math], so that [math]F \propto E_{\nu} \Delta E_{\nu}[/math] ? Physically, such would seemingly say, that higher energy, 'harder' photons obviously 'kick' more; and, more mono-chromatic, 'pure' photons, with lower [math]\Delta E_{\nu}[/math], taking longer to generate or 'erect', would smooth out and so slow down that 'kick' ("photons slowly spun off"); and, more multi-chromatic, 'colorful', photons, with higher [math]\Delta E_{\nu}[/math], which were more quickly created -- and which, being more spread in momentum, would be more localized in space -- would concentrate, compress, and so increase the 'kick' ("gun-slung generated & fired from the hip like a BB-sized bullet"). Cannot photons 'accelerate', "in frequency", red-shifting up-and-out-grav-well, or blue-shifting down-and-in-grav-well ?

Thank you very much for the response

In the Quantum 'eraser' experiment, Quantum-Entangled photons are created; and, then, manipulations applied to one such Entangled photon, evoke "sympathetic metamorphoses", in its Entangled partner. And, these "sympathetic responses" are manifested "Quantum quickly", apparently instantaneously, in zero measured time: Is the following an accurate picture of the physical phenomena ? In this writer's understanding, all "Quantum quick" -- to wit, instantaneous & non-local -- phenomena occur completely "intra-Wave-Function", within one single WF, through the "tenuous tails" of probability, that always connect the "pieces of probability", of a spatially sundered WF. If so, then the BBO crystal, utilized in the QEE, would seemingly create two mutually co-entangled "half-and-halved" photons, per the proceeding picture: Quantum "Detection", would involve a simultaneous "active measurement", of one "half-photon-cum-full-photon" (which WF "collapsed" into the detector), with a co-occurring "null anti-measurement", of the other "half-photon-now-not-here-and-so-there" photon (whose WF "collapsed" out-and-away-from the detector, i.e., into the "not-here-in-the-detector" state), as this writer currently comprehends the concept (simultaneous "Measurement", of one, and "Null Measurement", of other): Are these pictures appropriate? And, if manipulations applied to one Entangled "photon packet", instantly & non-locally communicate complimentary responses, in the other Entangled "photon packet", then, could you create "steerable lasers", by causing the course of the one to "veer left", and so inducing the other to "veer right", and so on?? (To wit, could you create, if we would allow, "wire-guided, gyro-jet" lasers ??)

Muon-to-Electron Neutrino Oscillations have been observed twice. What causes NO ? If, in practice as opposed to theory, every Quantum system has some spread in Energy [math]\Delta E[/math]; and if such spreads, or "line widths", were wider than the spacings between the "lines" themselves, [math]\Delta E > E_{\nu_{\tau}}-E_{\nu_e}[/math]; then would that explain NO ?? To wit, in practice, it is impossible to produce a "pure mono-chromatic, mono-energetic, mono-flavor" neutrino beam, so that every neutrino manufactured, is inherently some super-position, of the three ever-so-closely-energy-spaced neutrino "flavor" states ??

I found this thread, on Phyiscs Forums, citing these online sources: http://www.science20.com/news_releases/electron_caught_on_film_for_the_first_time http://www.physorg.com/news122897584.html

Don't position operators, of some spatial direction, commute, with momentum operators, of other-and-orthogonal directions ? Does that permit, or deny, the above-proposed "spaghetti-strand wave function" ?

VH21 is optically thick, so self-absorption masks most of its mass ? For radiative transfer, 'inbound' along a line-of-sight, 'back' towards the observer, through some emitting-and-absorbing medium, the light intensity (energy per time, per emitting-area-perpendicular-to-LOS, per solid-angle-towards-observer, per frequency band, measured in Jansky's [Jy]) increases by emission, and decreases by self-absorption: [math]\frac{dI_{\nu}}{ds} = \epsilon_{\nu} - \kappa_{\nu} \, I_{\nu}[/math] Generally, the emission & self-absorption coefficients, are functions of the light frequency, as well s the emitting-and-absorbing medium's particle-number-density & temperature. Simplistically, then, if the medium is assumed to be uniform in both density & temperature, then the radiative transfer equation can be easily integrated, to calculate the 'observer-bound' light intensity, emerging from the 'observer-facing' surface, of the medium: [math]\frac{dI_{\nu}}{ds} = \kappa_{\nu} \left( \frac{\epsilon_{\nu}}{\kappa_{\nu}} - I_{\nu} \right)[/math] Letting [math]B_{\nu} \equiv \epsilon_{\nu} / \kappa_{\nu}[/math], and assuming that the medium is not 'back-lit' at the frequencies of interest, w.h.t.: [math]\int_{I_0=0}^{I_L} \frac{dI_{\nu}}{B_{\nu} - I_{\nu}} = \int_0^L \kappa_{\nu} ds[/math] From a few further, quick calculations, w.h.t.: [math]I_L = B_{\nu} \left( 1 - e^{-\kappa_{\nu} L} \right)[/math] Now, the afore-going formula displays two important 'regimes' of behavior. First, if the medium is 'optically thin' ([math]\kappa_{\nu} L \ll 1[/math]), then [math]I_L \approx \epsilon_{\nu} L[/math]. Second, if the medium is 'optically thick' ([math]\kappa_{\nu} L \gg 1[/math]), then [math]I_L \approx B_{\nu} = \epsilon_{\nu} \kappa_{\nu}^{-1}[/math]. Thus, when the medium is transparent, then emissions along the entire 'inbound' LOS, 'back' towards the observer, contribute to the detected flux. But, when the medium is opaque, then only emissions from close to the observer-facing surface contribute to the detected flux. So, an opaque medium has a 'skin depth' ([math]\kappa_{\nu}^{-1} \ll L[/math]), whose length must replace that of the full LOS length through the medium, in the afore-going forumla [math]\left( I_L = \epsilon_{\nu} L \rightarrow \epsilon_{\nu} \kappa_{\nu}^{-1} \right)[/math]. Consider, then, an isolated (non-back-lit) HI cloud, with the afore-assumed simplistic structure (uniform, isothermal), emitting 21cm radio-frequency radiation. Imagine, too, that the cloud has a cross-sectional area [math]A[/math], total depth-thickness [math]L[/math], and emits, across this Cosmos, ultimately into a human radio antenna, at a distance [math]D[/math], having an effective cross-sectional area [math]a[/math], and so sub-tending a 'receiving solid-angle' of [math]\Omega = a/D^2[/math]. If the emitting cloud is diffuse, and so radio transparent, then the human radio detector will receive a flux of: [math]F = \epsilon_{\nu} \times A \times L \times \Omega[/math] Now, the emission coefficient is quickly, and comprehendably, calculated, as: [math]\epsilon_{\nu} = \frac{h \nu_{21}}{4 \pi} \times \Gamma_{21} \times \left( \frac{3 n_H}{4} \times \phi(\nu) \right)[/math] interpreted as the photon energy [math]h \nu_{21}[/math], emitted isotropically into [math]4 \pi[/math] steradians, at the 21cm spontaneous emission rate-per-particle [math]\Gamma_{21}[/math], by the [math]3/4[/math] of the hydrogen-atoms-per-volume [math]n_H[/math] that are expected to be in the excited-and-emission-capable state (according to the Boltzman Distribution, in the Radio Limit), and reduced by a further factor -- the 'frequency line-width' [math]\phi(\nu) \approx 1/ \Delta \nu[/math] -- characterizing the 'Doppler-induced de-synchronization', of the emitting-and-self-absorbing hydrogen atoms, by virtue of their various relative motions (thermal & bulk, e.g. rotational), which shift their rest-frame frequency responses (both emission & absorption), 'out of reach' of each other, so 'optically thinning apart' the cloud (even for the same physical density). Therefore, if the emitting cloud is optically thin, then the eventually-human-detected flux is proportional to the total cloud Hydrogen mass: [math]F \propto \left( n_H \times A \times L \right)[/math] [math]\propto \left( n_H \times Volume \right) [/math] [math]\propto M_H[/math] Conversely, if the emitting cloud is optically thick, then the eventually-human-detected flux is only proportional to a fraction of the total cloud Hydrogen mass: [math]F \propto \left( n_H \times A \times \kappa_{\nu}^{-1} \right)[/math] [math]\propto \left( n_H \times Volume \times \frac{\kappa_{\nu}^{-1}}{L} \right) [/math] [math]\propto M_H / (\kappa_{\nu} L)[/math] Now, in practice, human radio Astronomers prefer to convert their 'line widths', from frequency to velocity, according to the Doppler Shift formula [math]v_r = c \left( 1 - \nu / \nu_{21} \right)[/math], the differentiation of which yields [math]1/\Delta \nu = \lambda_{21} / \Delta v[/math], recalling that [math]c = \nu \lambda[/math], to convert from frequency to wave-length. And, by Kirchoff's Law, in the Radio limit, w.h.t.: [math]B_{\nu} \approx \frac{2 h \nu^3}{c^2} \frac{k T}{h \nu}[/math] s.t., again converting from frequency to wave-length: [math]\kappa_{\nu} = \frac{\lambda_{21}^2}{8 \pi} \Gamma_{21} \frac{3 n_H}{4} \frac{\lambda_{21}}{\Delta v} \left( \frac{h \nu_{21}}{k T} \right)[/math] Therefore, the 'skin depth', for HI clouds, is: [math]\mathcal{L} \equiv \kappa_{\nu}^{-1} \approx 20 \; thousand \; lightyears \times \left( \frac{\Delta v}{100 \; km/s} \right) \left( \frac{n_H}{1 \; atom/cm^3} \right)^{-1}[/math] In particular, the "dark disc" of "dark spiral galaxy" VH21 has [math]\Delta v \approx 200 \; km/s[/math]. And, its cold-and-neutral Hydrogen gas has temperatures conceivably comparable, to the CNM phase, of standard spiral galaxies' ISMs. So, if VH21's Hydrogen gas is also similarly dense, [math]n_H \approx 20-50 cm^{-3}[/math], then VH21 could be very optically thick, with a skin-depth [math]\mathcal{L} < 1 \; thousand \; lightyears[/math]*. And if so, then human-received 21cm emissions, from VH21, arising only from the earth-facing surface layers of the HI halo, would have been dramatically dimmed, by internal self-absorption. That, in turn, would lead to large mathematical under-estimates, of VH21's Hydrogen gas mass, along the lines of those recently reported. Could, then, VH21 be optically opaque, to 21cm emissions, so masking most of its mass, of Hydrogen gas ? * If our own Milky Way galactic disc were similarly 'foggy', at optical frequencies, then the Orion Nebula might not be visible from earth.

"Optically Cloaked" dark cloud in Virgo Virgo-HI-21 (VH21) seems to be a "dark spiral galaxy", with a "dark disc" spanning some 50 thousand light-years across. VH21 resides in the Virgo galaxy cluster, about 50 million light-years away: VH21 appears to possess a flattened, rotating galactic disc, typical of spiral galaxies (jb). Seemingly seen from the side, or 'edge-on', that disc is full of the diffuse, cold-and-un-ionized Hydrogen gas, otherwise common in the discs of ordinary, luminous, star-spangled spiral galaxies (register). But, sans stars, VH21 is only observable, from the faint, radio-frequency emissions (with a wave-length of 21 cm), of those cold clouds of neutral Hydrogen: HI halo surrounding VH21 (with unassociated foreground dwarf galaxy at left), whose "dark disk", seen edge-on, is 50 thousand light-years across (cf. UGC 10043) Now, those emissions imply, firstly, that the total mass, of Hydrogen gas, in VH21, is over 100 million solar masses; and, secondly, that the Hydrogen gas -- and so, assumedly, the dark disk in which they reside -- is rotating rather rapidly, spinning through space, with a speed, relative to the apparent center-of-mass, of ~100 km/s. And, such swift spin speeds imply, in turn, that VH21 must mass nearly 100 billion solar masses, nearly 1000x more than the emission-observable Hydrogen alone (or else self-gravity could not keep the galaxy together). Moreover, that amount of mass is also required, to account for the 'bridge' of cold-and-neutral Hydrogen, stretching half-a-million light-years, from VH21, to NGC 4254, resulting from a close encounter a quarter billion years ago (Minchin 2008). HI bridge between VH21 (upper left) & NGC 4254 (lower right), half-a-million-light-years away (cf. Milky-Way-to-Fornax (local dwarf galaxy, not remote galaxy cluster, seen in the same stretch of sky, from earth)) For comparison, VH21 is half as wide; spins half as fast; and, has one-tenth of the mass (both of gas alone, and overall, including DM), as our own Milky Way galaxy (astronomy). Also, these radio-band observations, of VH21, are most consistent, with a 'barred spiral' classification (SBc), similar to our own Milky Way (see below). Now, anomalously, VH21 betrays the presence of precisely zero stars. Again, no stars have been detected, within the VH21 "dark spiral galaxy". Instead, HST images, of a square patch of sky, 50,000 light years on a side, and centered on VH21's position, detected only 119 old red giant stars -- "the number found in a typical region, of the same size, in intergalactic space" (NS). Meanwhile, VH21 itself "contains no starlight down to a very low surface-brightness level" (NAIC). Again, "not a single star is shining from this massive region of space" (UT). Thus, at optical frequencies, "this object remains in-visible" (phs). VH21's Hydrogen gas also emits no currently-human-detectable x-rays, consistent with completely cold-and-neutral conditions (T < 1000 K) (Bonamente 2008)*. * VH21's Hydrogen 'ISM' is cold, comparable in temperature, to the 'Cold Neutral Medium' (CNM) phase, of standard spiral ISMs. Yet, that Hydrogen is diffuse, comparable in calculated density (M = 100 M*; D = 50 Kly, H = 1-10 Kly), to the typical Super-Novae-shock-heated 'Hot Ionized Medium' (HIM) phase. Thus, VH21 apparently possesses the mass, of a major galaxy; and, even, the stable spinning structure, of a spiral galaxy. Yet, VH21 is optically non-visible, emitting no currently-human-detectable star light. And, VH21 appears to be completely cold, as if neither star formation, nor ensuing super-novae, have heated its Hydrogen 'ISM' in eons. Seeing a dark galaxy —- a galaxy without any stars -— is like seeing a city without any people. We want to know why nobody lives there. Prof. Robert Minchin (Cardiff University, UK) VH21 "dark spiral galaxy", range 50 million light-years Optical-band image VH21 "dark spiral galaxy", range 50 million light-years Optical-band image, over-lain with Radio-band (21 cm) detected intensity contours NGC 4945, barred spiral galaxy (SBc), range 13 million light-years disc, seen edge-on, spans 75 thousand light-years "the type of galaxy that astronomers would have expected to see, based on the measurements taken" -- JB References: http://arxiv.org/PS_cache/arxiv/pdf/0706/0706.1586v1.pdf http://arxiv.org/PS_cache/astro-ph/pdf/0502/0502312v1.pdf A Dark Hydrogen Cloud in the Virgo Cluster Swift XRT Observations of VIRGOHI 21

If virtual photons can travel at supra-luminal speeds, then can EM interactions can be conveyed at such supra-luminal speeds? To wit, an electron "here" (Event 1), effects a proton "there" (Event 2), through space-like separations, in our space-time fabric ?

Prof. Aaron O'Connell: Making sense of a visible quantum object (8 minute video) COMMENT: I offer, that Prof. O'Connell's "Quantum Diving Board" enters a TRIPLE super-position state, in which it is, firstly, partially stationary ("still in the center"); secondly, partially oscillating up-and-down ("bouncing back-and-forth"); thirdly, partially oscillating down-and-up ("bouncing forth-and-back"). Classically, these are the three "modes" of oscillation available to the system -- none; in-phase; anti-phase. Note, too, that the "Diving Board" remains connected, back at its base, to a completely Classical, meso-to-macro-scopic scale, structure (the "pool" part, with the excavated pit, which permits the oscillating flexations, of the "board"). And so I offer, further, that that connection-to-the-Classical, is what constrains the Quantum behavior of the "board", to be able to enter a "ghosted out" Quantum super-position state, only out towards its "tip". In sum, Prof. O'Connell's "Quantum Diving Board" has three Classical "modes" of motion available, and, upon entering its Quantum "phantasmal super-position" state, it performs all three motions, simultaneously, thereby being "partially present", in three places, at one time.

I must have mis-spoken. The Wave Function I offered, was a momentum eigenstate in one direction, and position eigenstates in the other two. Was that Wave Function quantum mechanically allowed ?

EM fields are mediated by virtual photons. And, photons cannot escape BHs. So, how can BHs generate EM fields ?

What about a 'cyclic cosmos', wherein a prior incarnation, of our space-time, completely contracted, into a Big Crunch... from which 'super singularity', and through some sort of 'Hawking radiation' resembling mechanism, our current incarnation of space-time explosively expanded ?? If so, then the previous space-time, probably lacked a 'dark energy' expansion-acceleration phenomenon.

Would it be possible, to post a link to the SF, from this thread ?