Widdekind

David Griffiths' Intro. to Elem. Particles (pp. 180,192) shows that the Color Force is modulated by a spin-spin splitting, proportional to roughly [math]150 MeV / \hbar[/math] in mesons, and [math]50 MeV / \hbar[/math] in baryons. It is not clear to me, whether this is an electro-magnetic, or chromo-magnetic interaction. The ratio appears to be about 3:1, and their is only 1 pair in a meson, and 3 pairs in baryons (???).

Thanks for the link ! Can virtual photon emission, by electrons in atoms, be regarded as the (quantum equivalent of) the Larmor radiation, of the electrons, accelerating around in the attractive potential well of their nucleus ? Can you view the Hydrogenic wave functions, and their ensuing "electron clouds", as a "Bohr-model atom plus virtual photons" ?? If the electron needs to reabsorb its own virtual photons, their emission time must be comparable to the electron's crossing time, for its particular orbit. Thus, solely to order-of-magnitude, and using the H.U.P., the time & energy uncertainty, in these virtual photon self-absorption events is: [math]\Delta t \approx \frac{\Delta x}{\Delta p / m_e} \approx \frac{m_e}{\hbar} \Delta x^2[/math] [math]\Delta E \approx \frac{\hbar^2}{m_e \, \Delta x^2}[/math] Thus, the energy uncertainty, "dumped" into the virtual photon field, is comparable to the K.E. of the emitting electron, and, hence (Virial Theorem), to the total bound-state energy of the emitting electron, [math]\Delta E \propto E[/math]. Could such an energy-uncertainty causes higher energy, excited electronic states, to "bleed over", into other orbitals of similar energy, and help account (Overlap Integrals, Transition Matrix Elements) for the spontaneous transitions, of excited electrons, into lower energy orbitals ? Emission / Absorption as "Promotion / Demotion" of (Virtual / Real) photons This strongly suggests, that photon absorption represents the "demotion", of an incident real photon, into a "bound" or "hang-around" virtual photon. Perhaps an electron's cloud of virtual photons is the repository housing all the incident photons it has ever absorbed ?? What happens, to the virtual photon cloud, when the electron's wave function discontinuously "re-adjusts", during the wave function collapse caused by a Measurement ??

The classical electron radius assumes that the electron's mass arises from electro-static self energy. This is an assumption, and need not be physically accurate at all. Is there is any evidence that the c.e.r. is physically meaningful ? Intriguingly, the Compton wavelength is the radius an electron would have to have, were it limbs spinning at the speed of light, in order to account for its spin angular momentum. Solely to order-of-magnitude: [math]\hbar \approx (m r^2) \omega \approx (m c^2) / \omega[/math] [math]\hbar \omega \approx m c^2[/math] This is the "baseline" phase frequency, of electrons, according to the Klein-Gordon Equation. Is this physically significant ?

The projectile can, apparently, be a photon as well: Apparently, too, were one able to detect the electron before the photon, the wave function collapse of the former would trigger that of the latter, so that any residual patterns, in the electron's wave function, would still be observable. (??)

So, in theory, Bohmian HV would allow, for an "[math]\vec{A}[/math] manipulating apparatus" (of suitable size & sophistication), far away from an electron diffraction experiment, to affect the electrons in said experiment, in a non-local way. It would do so, by suitably adjusting [math]\vec{A}[/math] along each electron path, so that all the paths running through the apparatus wound up with constructively interfering phases (instead of being "good zeros" which is what would happen typically). (?)

(thanks for the response) Just noting patterns, from the Classical Electron Radius (Rc), to Compton Wavelength ([math]\Lambda_C[/math]), to Bohr Radius (aB): [math]R_c \propto e^2[/math] [math]\Lambda_C \propto 1[/math] [math]a_B \propto 1/e^2[/math] [math]R_c \propto 1[/math] [math]\Lambda_C \propto \hbar[/math] [math]a_B \propto \hbar^2[/math] Of course, this is merely a restatement of the previously proferred pattern. I thought that [math]\Lambda_C[/math] was the characteristic amount by which electrons lengthen the wavelengths of incident photons, sort of the "inertial impact" of electrons on photons (?).

I meant to say, manipulate the phase factors, of various paths, by manipulating [math]\vec{A}[/math] along those paths. You yourself said that "the phase factors do [depend on [math]\vec{A}[/math]]". So, by suitably manipulating [math]\vec{A}[/math], you could manipulate the phase, and hence action, associated with those paths. Wouldn't that, then, affect the particle's dynamics, via the principle of least action (action minimization) ?

Electro-dynamic potentials ([math]\vec{p} \rightarrow \vec{p} - e \vec{A}[/math]) affect particle momentum, and hence (path integrated) phase, yes? With suitably sophisticated micro-manipulation, of electromagnetic fields, then, one could -- conceivably, if but barely so -- "micro-manage" the phases, of all those paths passing through one's "territory". Since, as you said, most far-out paths are "good zeros anyway", then such "coherent phase manipulation" could conceivably create a "united voting block", which could exert unexpectedly profound influence, on remote events, non-locally, yes (like a small symphony being "heard" over a cacophonous babbling din) ??

Wow, what about coherent light, like lasers ? Can CED describe lasers, or is QM required, for such BE condensates ? The Bohr Radius ([math]\hbar^2 c^2 / (e^2/4 \pi \epsilon_0) m_e c^2[/math]), Electron Compton Wavelength ([math]\hbar / m_e c[/math]), & Classical Electron Radius ([math]e^2 / 4 \pi \epsilon_0 m_e c^2[/math]), all increase by factors of the Fine Structure Constant (so that the Compton Wavelength is the geometric mean of the other two). Is this significant ?

I recently read, that, when a wave function collapses, to an energy state (say) which is degenerate, having numerous states of the same energy, then the collapse occurs into the subspace spanned by those degenerate energy eigenstates (ie, into a super-position of them?). I got the impression, that it was not into any single degenerate energy state, but into some SP of the group of them. Doesn't this amount to a "partial wave function collapse", like those seen in Renninger Negative Result Experiments ? There seems to be some sense, in which WFC is "as little as possible", collapsing only down into as large a subspace of the original, as can be consistent, with observation / measurements imposed upon the system. Is this (crudely) correct ?

If a photon is a wave packet, of finite spatial spread, then the Heisenberg Uncertainty Principle (HUP) imposes some spread in momentum, as well. But, for photons, energy is proportional to momentum, so there should be some corresponding spread in energy... and, hence, by the Energy-Time version of the HUP, another corresponding spread in the lifetime of photons. What's wrong ??

If the "expectation value" for a quantum 'particle's' momentum is [math]< \vec{p} > = <\Psi | \hat{p} | \Psi >[/math]; and if the momentum operator is [math]\hat{p} \equiv -i \hbar \vec{ \nabla }[/math]; and if the wave function [math]\Psi[/math] is exclusively real (as in the Hydrogen 1S state); then what ensures that the expectation value <p> winds up being a real number ? EDIT: I suppose you could always decompose the wave function, into the momentum basis, wherein each plane wave would contribute a real-valued-amount of momentum (??).

(thanks again for the replies) From the value of the Fine Structure Constant, we know that: [math]\hbar c \gg e^2 / 4 \pi \epsilon_0[/math] by over two orders of magnitude. So, does that tell us, that electro-magnetic phenomena are "fully quantum" phenomena, "well inside" or "well under" the scope of the quantum scale ?

Typically, interacting Wave Functions do not "collapse", but become "entangled", entering a single state for all of the entangled particles. "Measurement" destroys this singular entangled state, causes all of the entangled Wave Functions to collapse, and, thereby, puts all of the particles into individually separate states ("product states"): Would wave function collapse coincide with "free" ("externally oriented") vertices, in Feynman Diagrams, of the interactions, associated with (electron) Localization ?? Such "free" vertices would beget full-fledged photons ("micro-signal (s)" generation), which would leave the locale of the original interaction, and thereby (potentially) inform the rest of the universe, of the "measurement" outcome of that interaction (representing the "registration" of the phenomena, as demanded by Bohr & Wheeler).

According to David Griffiths' Introduction to Elementary Particles, the ("chromo-electrostatic") color-potential, between two quarks, is often modeled using Hooke's Law (F = - k x). And, according to Michael Creutz's Quarks, Gluons and Lattices (pg. 3): If the Flux Lines are conserved, would the "bag of gluo-electric flux", which squeezes down when stretched, but pancakes out when compressed, generate a Hooke's Law force ?? (This simple picture does not account for the powerful "chromo-magnetism" force, which Griffiths also discusses, separately.)

I wanted to double check -- matter must be rather rugged, if it can commonly accommodate hundreds of millions of Gs (!!). I guess that's why the can put payloads, in surface super-gun shells, and sling the same into space.

When atoms in a crystalline lattice interact, vibrationally, via phonons, do they exchange virtual photons (making the interaction, ultimately, an "optical", electromagnetic phenomena) ??

[math]\therefore \frac{G M_V m_p}{R_H} \approx \frac{e^2}{4 \pi \epsilon_0 \; a_B}[/math] The LHS contains two terms, which both depend upon time (MV, RH). But, there ratio is (approximately) independent of time: [math]M_V \approx \frac{4 \pi}{3}R_H^3 \rho_{crit}[/math] [math]\rho_{crit} \equiv \frac{H^2}{8 \pi G} = \frac{c^2}{8 \pi G R_H^2}[/math] And so: [math]\frac{M_V}{R_H} \propto \frac{R_H^3}{R_H \times R_H^2} \propto 1[/math] [math]\therefore \frac{G M_V m_p}{R_H} \approx \frac{e^2}{4 \pi \epsilon_0 \; a_B} \; \; \; \forall t[/math] Such seemingly suggests, that (1) the cosmos is close to critical; (2) constants are constants. Both such suggestions seem rather reasonable, yes?

A proton is a bound-state, of a system, of 3 quarks. Roughly speaking, we can decompose the wave function, into a [math]\Psi_{CM}[/math] and [math]\Psi_{rel}[/math]. And, the [math]\Psi_{rel}[/math] is the standard nucleon wave function, producing a probability "cloud" ~1 fm across. But, then, that relative wave function can be "sliced", and "spread", a little like smearing around a deck of cards. Each "card / slice" represents a whole & complete, but only partially probable, nucleon, centered at a given CM coordinate. (If the proton is certainly centered at some CM coordinate, that's a little like "telescoping" the deck of cards, back into a single stack.) So, the proton can enter a "spatial super-position state", where the whole proton, is partially probable, at many spatial locations simultaneously. If you could prepare two opposing proton beams, each of which produced protons in such de-localized states, they could "reach out", and have at some positive, if partial, probability, of interacting, w/ other protons, which otherwise would miss each other by a wide margin. Presumably, high energy p-p reactions, would cause both proton's to "collapse" into some pair of particular, punctiform, point-particle like states, which would react "normally", and scatter. But perhaps you would get, overall, more p-p (i.e., potentially fusing) reactions. "Preferencing" wave function collapse ?? The work functions, or inner potentials, of various materials, range from 10-30 eV (Tomonura. Quantum World Unveiled by Electron Waves, pg. 61) What would happen, if you did a Double-Slit experiment, with a macroscopic detector array (D), composed of two types of micro-detectors (d), which had dramatically different inner potentials? For example, although the apparatus would remain electrically neutral, so as not to alter the evolution of the electron [math]\Psi[/math], the incident electrons could minimize their energy by another < 20 eV, if they "chose" to "collapse" on one side of the screen (say). Would the "goal", of energy minimization, "preference" or "optimize" the electron's behavior, such that more than half of the hits might be on one side of the macro-detector vs. the other, even though their wave functions were not altered in any way?

Arthur Eddington discovered conspicuous coincidences, amongst the ratios, of various physical & cosmological constants, for our cosmos (Wolff. Exploring the Physics of the Unknown Universe, pp. 173-4), including: [math]\frac{time \, since \, the \, Big \, Bang}{time \, for \, light \, to \, cross \, a \, hydrogen \, atom} \approx 10^{36}[/math] [math]\frac{electrical \, repulsion \, between \, two \, protons}{gravitational \, attraction \, between \, two \, protons} \approx 10^{36}[/math] [~1042 for electrons] [math]\frac{mass \, of \, visible \, cosmos}{mass \, of \, proton} \approx 10^{79}[/math] [~1082 for electrons] The last ratio, is conspicuously close, to the square of either of the previous pair (Pirani & Roche. Introducing the Universe, 154-155) -- and, hence, to their product. Now, noting that RH = c TH, w.h.t.: [math]\frac{R_H}{a_B} \approx \frac{e^2 / 4 \pi \epsilon_0}{G m_p^2}[/math] [math]\therefore \frac{G m_p^2}{a_B} \approx \frac{e^2}{4 \pi \epsilon_0 \; R_H}[/math] This says, the the GPE of two protons, at an atom's width apart, is comparable, to the EPE of two protons, at a Hubble Radius (!). And, from the product, w.h.t.: [math]\frac{R_H}{a_B} \times \frac{e^2 / 4 \pi \epsilon_0}{G m_p^2} \approx \frac{M_V}{m_p}[/math] [math]\therefore \frac{m_p \times e^2}{4 \pi \epsilon_0 \; a_B} \approx \frac{m_p \times G M_V m_p}{R_H}[/math] [math]\therefore \frac{G M_V m_p}{R_H} \approx \frac{e^2}{4 \pi \epsilon_0 \; a_B}[/math] This says, quasi-classically, the GPE binding protons to the visible cosmos, at the macroscopic scale, is closely comparable, to the EPE pushing protons apart, at the atomic, microscopic scale. Thus, there is seemingly some sort of "balance", between the forces of contraction (gravity), and those of expansion (electro-static repulsion). Doesn't this seem reasonable?

(Thanks again for the clarifications) Is it possible, to put protons, into de-localized spatial superpositions ([math]\Psi_R[/math]), yet at high energy ?

Succinctly stated, as I understand it at least, atomic wave functions can "quantum split", into spatial superpositions (which can overlap, or be widely separated, according to conditions applied in the apparatus of experiment). Could you apply something similar, for "thermal protons", in fusion processes ? The delocalized charge distribution, and multiple parallel proton-proton interactions, might increase the likelihood of fusion events??

(thanks for the responses!!) So, its the CM wave function which does the diffracting ? If the whole atom "puffed up", wouldn't that dramatically reduce the depth of the potential well, and, so, radically reducing the ionization energies of the atoms ??

According to M.D.Fayer's Absolutely Small, Molecular Bonding Orbitals, in diatoms, form from the spatially symmetric (in-phase) -- and, hence, spin anti-symmetric -- addition, of the originally individual atoms' valence electron orbitals. Now, when the diatomic molecule has formed, therefore, the electrons will be "phase-locked", fully in-phase. Yet, presumably, the individual atoms entered the interaction with random, and completely uncorrelated, "phase offsets". Does this imply, that those phase differences, manifest themselves, initially, in the formation, by the valence electrons, of a super-position state, of some Bonding Orbital (BO) + some Anti-Bonding Orbital (ABO) ? Then, some sufficient "act of measurement", causes the super-position state to "collapse", into the energetically favored BO, and an optical (photon) "micro-signal" is generated, which, in the words of Wheeler, "irreversibly registers" the event ??

Yes, thanks for the correction