Widdekind

Math: For the atom, of mass m, emitting a photon of energy E = h f, w.h.t.: [math]a = \frac{F}{m} \approx \frac{p}{\Delta t} = \frac{ h f }{c \, \Delta t}[/math] [math]\therefore a \approx \lambda_{C} \frac{f}{\Delta t}[/math] For a hydrogen atom [math]( \lambda_{C} \approx 1.5 fm )[/math], emitting a 3 eV photon, the acceleration is about 108 Gs (terran standard). is this correct ?

If Helium atoms are normally about [math]1 \AA[/math] across, how can their wave functions "puff up" roughly ten-thousand times, to about [math]1 \mu m[/math] ?? What about the Hydrogenic solutions, to the SWE? What happened to atoms being bound states, composed of many particles, of sizes comparable to the Bohr radius ?? If atoms can "balloon" up like that, why don't they do so all the time ??

Gluons can "quantum split" into quark-antiquark pairs. Photons can "quantum split" into electron-positron pairs. Could there be some kind of connection* ?? * Were one to view photons, as localized 'packets', of oscillating electrically positive & negative aether particles (+/-)... then could one view gluons, as localized 'packets', of (triply) color positive & negative aether particles (blue/orange, red/green, yellow/purple) ??

I would gather, that the principal objection to wave function "collapse", is the super-luminal instantaneity, of such "quantum jumps" ? Even Erwin Schrodinger, a founding father of QM, hated "these damned quantum jumps" [direct quote]. Never-the-less, even so, suspending disbelief on such super-luminality, for 10 seconds [9... 8... 7... ], are there any other (major) objections, to regarding wave functions as real, and their "collapses" as equally real (if disconcertingly discontinuous) ? If you regard the [math]\Psi[/math] as real, then wave functions expand (Type 2 process, SWE) and contract (Type 1 process, "quantum jump"), a little like a squid splaying its tentacles, and then squirting away, as it swims (cf. particle tracks, thru cloud chambers). Were one want (desperately, perhaps) to view the [math]\Psi[/math] as real, one would require some kind of "two-component medium" (a little like the O2 & N2 in Earth air), thru which light & matter waves would propagate, and whose coupled oscillations were [math]\pi / 2[/math] out-of-phase (the complex-valued SWE can be recast, as two real-valued, if coupled, PDEs -- the "imaginary" number "i" merely amounts to a convenient accounting trick). The [math]\Psi[/math] (for a single particle) assigns to every point in space two real numbers, whose positive & negative values could correspond to "over-" & "under-" densities, in the "two-component aether" (at which point, I appeal to John Bell, who admitted the possibility of this position [brown&Davies. Ghost in the Atom.]). General Principle of QM -- collisions do not cause "collapses" (??) And, double-slit experiments, performed with sliding slit-barriers, which are "kicked" & displaced some distance to the left & right, as the electron matter waves penetrate the slits, en route to the macro-detector screen (D) -- wherein they are absorbed into one of the micro-detector phosphor grains (d) -- still show interference effects, essentially similar to that seen with a fixed slit-barrier (zero "kick" displacement) (T.Bastin. Quantum Theory & Beyond, pp. 43-44.). And, moreover, every "entanglement" interaction involves a direct collision, with wave functions overlapping. Thus, if 'particle' collision caused "collapse", then "entanglements" could never occur, in the first place.

Could you say, that the "evanescent tail" of the electron [math]\Psi[/math], extending (slightly) up & off the surface of one of the blocks, would "enter" an available Molecular Orbital in the other block, and thereby form into a new, both-block-spanning Molecular Orbital ?

Atomic radiation would constitute an "optical micro-signal" (s), which could, in principle, be amplified into a "macro-signal" (S), which human scientists could observe. That would also constitute an "irreversible act of amplification", which would "register" the phenomena, and coincide with wave function collapse, to quote physicist John Wheeler. Would, then, if only in theory, the (optical) micro-signal also collapse the entangled scatterer into a specific state of its own ?

Two surfaces, in intimate contact, for 'prolonged' periods, become "cold welded", as electrons from each surface, bond to the other. Is this a manifestation of Quantum Tunneling effects ? If two perfect crystalline lattices were brought together, with perfectly smooth faces, would they "meld together", into a single block ??

Wow, does that involve "entanglement", of the scattering projectile, with the atomic wave function(s) ? If, then, the scatterer is later "observed", does such "measurement" cause the entangled atomic wave functions to collapse, into one particular state (ionized or otherwise) ?

Can QM admit the possibility of particle states, which are super-positions, of bound-states (E<0) and free (plane-wave, E>0) states ?? I understand, that for a free particle (E>0), incident on a potential well, to become bound into that well (E<0), would require a discontinuous, von Neumann Type 1 Process, "quantum jump" -- with an associated photon emission. Now, imagine that the Overlap Integral (< F | B >), between the free state (F) and bound-state (B), was (say) 10%, so that the Transition Probability was 10%2 = 1%. Imagine, further, that that 10% portion of the Wave Function were to "quantum jump", down into the bound state, "on its own" (emitting a 1% strength photon). Would not the application, of a discontinuous "jump" process, to a previously continuous Wave Function, necessarily introduce discontinuities, into said Wave Function ("at the edges", where the Localized bound-state "ended") ? And, aren't all Wave Functions required to be smooth & continuous, so as to furnish well defined second derivatives ? It seems, qualitatively and w/o mathematical rigor, that, insofar as a discontinuous "quantum jump" transition is required, to "arrest" a free-state (E>0, spatially varying phase) wave packet, into a bound state (E<0, spatially uniform phase), then the only way to apply that discontinuous process, to the free 'particle', and still wind up with a smooth, continuous, & computable wave packet, would be to apply that said discontinuous "jump" procedure, to the whole wave function, completely "relocating & repackaging" the same, down into the potential well. Any application, of a discontinuous procedure, in a 'pieces parts' manner, might necessarily introduce mathematically impossible discontinuities into the wave function.

If spatially extended, De-Localized, fundamental 'particles' are possible, you could, in theory, treat the Wave Function as a real, tangible, (two-component) entity, whose amplitude squared represented (essentially) the mass & charge density of the 'particle'. Perhaps, if fundamental 'particles' need not react, to external stimuli, as elementary units, then a real tangible Wave Packet for a 'particle' could be compatible with what you've said. What about 'Delayed Choice' experiments? How could even a super-luminal Bohmian HV 'pilot wave' retroactively choose "which way", after it had already passed the initial beam splitter ?

I understand, that QED is built upon the assumption of true, zero-size, point-particles, in order to keep compliant, with (Einsteinian, aetherless, absolute-rest-frame-less) Relativity [Davies & Brown. Ghost in the Atom, pp. 48-9]. If all particles have finite size, as intuitively seems much more realistic, then all elementary quantum objects must possess instantaneous "internal" communications capacity:

Theory -- Schrodinger Wave Equation (SWE) In typical electron double slit experiments, electrons have de Broglie wavelengths 102-107 times smaller than their spatial spreads, suggesting considerable coherence times: Experiment -- Double Slit apparatus Please ponder a beam of electrons, 'boiled' out of a metal wire filament, and accelerated through a double slit barrier, towards a macroscopic detector array (D), composed of microscopic detector particles (d), such as phosphor grains or CCD cells. The electrons, initially Localized, and, hence, 'particle' like, in the electron gun, rapidly De-Localize, spreading out across space, after being 'boiled' out of the heated filament. After diffracting through the double slit barrier, and ignoring any reflected waves, the transmitted electron matter waves rapidly reach the macro-detector (D), whereat they 'collapse', Re-Localizing randomly into one of the micro-detectors (d): The collapse, of the electron's matter wave, is associated with the generation of a micro-signal (s), such as photon emission from a phosphor grain, or photon absorption in a CCD cell. This micro-signal (s) can, in principle, be amplified, into a macro-signal (S), which would be observable, by (human) scientists. In practice, wave function collapse is associated with optical (photonic) registrations (micro-signal generations).

Would Bohmian point-particles, having positive mass, but zero radius, be Black Holes ?

What if you used a "high" intensity split-beam, of BBO-crystal correlated photons. Their polarizations are random, but correlated. This constant "carrier" signal would be sent, from some central source, out to two "talk stations", as per PP. The "talkers" each have their own polarizers & detectors. Imagine that one of the "talkers" is closer to the central source, so that the "close talker" drives the wave function collapse (WFC) process. Now, if the "close talker" does not insert his polarizer, into his "feed" signal, the other, "far talker", will always get random & un-polarized light. If the "close talker" now inserts his polarizer, he causes WFC, into either H or V. The "close talker" cannot, of course, control this random & unpredictable von Neumann Type 1 WFC process. Never-the-less, by making his measurement, of H or V, the "close talker" ensures WFC, one way or the other, for the "far talker's" photons. Thus, the "far talker" is now receiving random but polarized light. So, if the "far talker" always rotates his polarizer, then, in the former random-and-un-polarized case, he always gets a constant 50% thru-put. But, when he's receiving random-but-polarized light, his thru-put will cycle periodically from 0 to 100%. By convention, "50% = dit" (or 0), and "0-100% = dah" (or 1), and you've got FTL Morse Code (or Binary). This system works only one way, from "close talker" (shorter leg) to "far talker" (longer leg). This system would be quite cumbersome, work only one way, and require a "high" intensity "feed" or "carrier" signal, so that large ensembles of photons could be counted, continuously, to observe the statistics soundly. But, assuming the reality of WFC, and the "active" nature of Measurement in QM, I don't see where it wouldn't work, theoretically. What am I missing ?

Many physicists ascribe to other pictures, including "Many Worlds" and "Hidden Variables" (e.g. Bohm), yes ?

Please ponder the low-energy limit. There, the wave functions of the collision particles are relatively de-localized & diffuse. As the two diffuse probability "clouds" come together, and begin to merge & overlap, at any given moment, the total Transition Matrix Element (TME), computed from the overlap integral as [math]| <\Phi | \Psi > |^2[/math], is low. But, at high-energy, the Lorentz contraction "pancakes" the wave functions, into "dense disks" perpendicular to the direction of motion. When these "dense disks" of probability collide, like "lead plates", the overlap integrals automatically "max out", making for larger TMEs. Moreover, at higher & higher energies, the colliding wave functions "bore into" the other particle's electrostatic potential well more & more easily, having less & less time to "adapt" and "deflect away", so that interactions are more & more "intimate", "immediate", at "point blank", w/ more wave function overlap (lead plate on lead plate), and less wave function dispersion, away from the intervening area of high potential. Is this what explains the phenomena?

If a quark is bound to other (anti-)quarks, that whole system of particles is completely confined in a "bag", whose "skin" is the "slime" of glue, that "epoxies" them together. In order to extract a quark, you must stretch the "slime skin" of the "bag". Eventually, the "bag" tears, and, where it rips, "in the middle", the gluon's color creates a quark (on one side of the rip), while its anti-color creates an anti-quark (on the other side of the gap). I understand, that there is a "slow stretch mode" (my words), wherein gluons can "spawn" more glue, and gradually lengthen the bond; and, a "fast tear mode" (my words), wherein hard-hit quarks can "rip free" straight away, before the glue "tendons" have time to self-generate more glue (from the input mechanical stretch energy). This is why, at higher & higher energies, quarks look lighter & lighter -- they "rip free" trailing less & less glue. Apparently, it looks like, as you asymptote towards infinite incident energy, free quarks would "rip free & clear", completely, and "bare quarks", of mass-energy equivalent 4-5 MeV would be (briefly) born. Is this an accurate (if not particularly precise) picture ? Could you, in theory, create an "infinitely" long glue "tendril" gluon bond, by "slowly stretching" the bond, sufficiently slowly, for sufficiently long ? Here's another picture, from Hey & Walters' New Quantum Universe (pg. 270): Uploaded with ImageShack.us

According to Jim Baggott's Beyond Measure, in Bohm's HV approach, the "pilot wave", which is computed from the real part of the standard Wave Function, imposes upon the particle that "generates" (my word) the field, the momentum condition, that the particle's momentum is the gradient, of the phase, of the wave function. Now, what happens, in bound-state orbitals, like the Hydrogen wave functions? There, the L=0 Schrodinger-solution wave functions, have spatially uniform phase. Wouldn't that make the particle's momentum equal to zero? And, then, why wouldn't all S-state electrons plummet into their nuclei? Moreover, if, as in Bohm's HV approach, electrons are still regarded as actual point particles, then why, when they're "zipping" around in atoms, cutting across trillions of trillions of times per second, don't they rapidly radiate away energy, from all their accelerations?

thanks for the responses !

Whenever a wave function undergoes quantum splitting, such as the reflected & transmitted waves refracting from a potential barrier, "The two parts are, in practice, joined, b/c the wave function is never quite zero, just very small between them" [E.Squires. The Mystery of the Quantum World, pg. 29]. And, in quantum entanglements, "Something seems to be linking the two quons [quantum objects] instantly (faster-than-light)" [N.Herbert. Quantum Reality, pg. 170]. Indeed, once two particles have had any interaction, they do somehow remain linked as parts of the same indivisible system. Separated particles seem to be as connected as two ends of the same rod... the powerful rod-like connection has to be there, because Bell's sums say it is [J.Klaff. Bluffer's Guide to the Quantum Universe, pg. 33]. Now: The essence of a local interaction is direct contact... Body A affects Body B locally when it either touches B, or touches something that touches B... On the other hand, the essence of non-locality is unmediated action-at-a-distance. A non-local interaction jumps from body A to body B without touching anything in between... A non-local interaction is, in short, unmediated [Herbert, ibid., pp. 211-213]. So, when two quantum objects interact, inter-mingle, & entangle, then, even when they separate, their wave functions will remain "physically" linked, by a drawn-out & tenuous "tail" stretching between the two main "lumps" of probability. Could this "physical tendril", of mingled & entangled probability, mediate the instantaneous correlations, observed in EPR experiments ? If so, current interpretations of EPR correlations, as both "non-local" and "instantaneous", could be reduced, in "quantum weirdness", to "local" but "instantaneous", mediated through the "tendril" of entangled wave function, spanning from one "main lump" of particle probability, to that of its entangled twin. Possible rationale for quantum instantaneity Mainstream physicists are rather reticent to accept the "reality" of the wave functions of quantum objects: The fact that observing a quon "here" instantly changes the wave function "there" (where "there" may be billions of miles away) is another good argument for the fictitious nature of the proxy wave. If the wave function were real, it would have to change its shape drastically, over large distances, at faster-than-light speeds [Herbert, ibid., pp. 170-1]. However, such instantaneous "internal communication", through the wave function, could account for the elementary nature of fundamental quantum objects: There are serious logical problems with the quantum theory, when it applied to the electron, or other point-like particles. One of the important terms, in the mathematics of QED, is the "self-energy" of a charged particle, such as an electron, which has an electrical potential energy assumed to be given by V = e2/r. The self energy of a charged particle depends on the radius r according to 1/r. Thus, if the particle size is shrunk down to a point r --> 0, the self energy goes to infinity. Besides being impossible, the equation becomes useless. This is a problem. To avoid the infinity dilemma, one is tempted to abandon the idea of a point particle. But relativity will not allow this, as seen from the following argument. If a particle is elementary, it must react as a unit. However, if it has a finite size, and an electro-magnetic signal should arrive at one side, the other side must simultaneously know of the arrival of the signal, in order to react as a unit. But this implies that the signal travels with infinite speed, which is prohibited by relativity. The only way out, is to have a point particle. (Or, no particle at all, if you could find a way to represent mass & charge w/o it) [M.Wolff. Exploring the Physics of the Unknown Universe, pg. 132]. Such a "realistic" interpretation of the wave function was initially favored by Schrodinger himself: Schrodinger [initially] speculated, that an object's waviness was the smeared out object itself. Where, for example, the electron fog is densest, the material of the electron is most concentrated. The electron itself would, thus, be smeared over the extent of its waviness... If an actual physical object were smeared over the extent of its waviness, as Schrodinger initially thought, its remote parts would have to instantaneously coalesce to the place where the whole object was found [upon Measurement & Localization]. Physical matter would have to move at speeds greater than that of light [Rosenblum & Kuttner. Quantum Enigma, pp. 74-75]. Thus, quantum instantaneity could account, for the elementary nature, of spatially extended (De-Localized) quantum objects, in SR -- sidestepping issues of infinities in QED. This suggestion, of "quantum local instantaneity", avoids un-mediated non-locality, and (renormalizeable) infinities, in quantum physics, admitting only the "quantum weirdness" of instantaneous, FTL, influences, which are kept completely confined within the wave functions of singular quantum systems*. Such could be called "damage control for quantum weirdness". * This seemingly suggests, in turn, that, upon "collapse", wave functions "reel in", "slurping" the rest of the wave function in, from across the cosmos. This "drawing in", or "in-folding", could be compared to origami -- or, the Transformers, like Optimus Prime, which when "un-folded" was a large battle-station, but which could "fold up" into the shape of a smaller truck trailer. One could also consider swimming squid, in the seas (of Earth), which "flare open" to feed, but which rapidly "draw in" to squirt away.

Differing electro-negativities, of differing atomic nuclei, in hetero-nuclear di-atomic molecules, leads to unequal sharing, of the electrons' MOs. This is also consistent, with a "realistic" interpretation of the wave function, as the "smeared-out" (charge) distribution, of the electron, which "slews", "sloughs", or "skews" towards the more eletro-negative nucleus [M.D.Fayer. Absolutely Small]

That is the "Statistical Ensemble" interpretation of QM, yes? I understand that that is not necessarily the only valid interpretation.

(thanks for the reply) It seems, in a sense, that quantum spatial dispersion acts like a "pair of snowshoes", for quantum objects, so that they don't "poke holes in spacetime", and "fall down into the snow".

C.A.Bertulani's Nuclear Physics in a Nutshell (pg. 24) quotes the following formula for Vacuum Polarization in QED: [math]e^2® = \frac{e^2(r_0)}{1 + \frac{2 e^2(r_0)}{3 \pi} ln \frac{r}{r_0}}[/math] What is the electron radius r0 ?

Particle-Wave "Duality" "Particle" = spatially Localized wave function Wave = spatially De-Localized wave function Duality = Free (wave) / Bound (particle) When traveling freely, in (plane wave) momentum eigenstates, electrons display wave-like properties, in their spatially extended & De-Localized wave functions. But, when electrons are absorbed into (macroscopic) detector devices, which compel wave function collapse & Localization, the electrons appear to be particle-like: Quantum objects can be both free (E > 0, De-Localized plane-wave like wave function), or bound (E < 0, Localized wave function). Wave-Particle duality reflects the fact that quantum objects can exist in both bound & free, Localized & Delocalized, states. That the wave nature, of quantum objects, seems strange to humans, merely reflects the fact, that humans have little experience with free objects. Rather, instead, in almost all circumstances of common (human) experience, electrons (say) are bound & Localized into atomic & molecular orbitals.