Widdekind

Can I ask, is it possible, that 'global' Cosmic spacetime is 'spinning', rotating around the central 'time-like' axis ??? What if the 'original singularity' had had a rotational spin ???

Thanks for your reply. Technically speaking, is not any system, which processes (sensory) information, a "data (info) processing unit" ? That's the limit of my meaning, in this case, I am not suggesting "cell's are smart" (per se)... only that cells (1) have sensors (w/ which they interrogate their environment); (2) process sensor-data (w/ basic, primitive, pre-defined pathways, apparently). Would you not agree, w/ such strict & limited definitions ? (The only "sentience" I am attributing, to single cells, is such limited sensory-information processing, "a limited feeling" for the cell's environment, as it were. Yet, that "small amount of sentience" still separates a "bag full of chemicals working together", from inert physical phenomena, like a clump of chemicals stuck together in a rock, say.) The only question I would further ask is, where does the following analogy break down: eyes (Earth animals) == chemo-receptor (single Cells) optic nerve pathway == chemical pathway triggered by CR (above) brain 'sensor-data-processor' == ??? What I'm asking is, at some point, information stops being transmitted & relayed (= "optic nerve"), and begins being processed (= "brain"). Where in a single Cell's chemical pathways, is information processed, and behavioral actions determined / decided ("swim left / right / straight, turn around, etc."). Thanks again for your time to respond.

I respectfully disagree. The surface of sphere is 2D, so its "down-projection", to 1D, must be a 1D object -- to wit, a line. The "down-projection" of a 2D spherical shell, is a 1D linear ring. Your diagram looks to me, like it projects the 2D surface of a spherical shell, onto a 2D disk-planar shape. That is not really a down-projection, which would lose 1 full dimension (-1D).

So the near-integral relationship between Earth-system's (sidereal) months & years is purely coincidence ?

ROUGH DRAFT Consider organelles, inside "sovereign" cells. A vescicle, for example, seems to be a "beaker" w/in the cell, w/in which chemical cocktails are "brewed" by the combination of sugars, enzymes, proteins, etc. Such an organelle, ultimately, can be described by a Wave Function which -- a little like an electron whose spatial WF can be complex, but still has the two spinor-states (up/down) -- which describes that organelles functionalities. To wit, a vescicle might have several "states" -- "open up", "close off", "shake & bake" (as it were). Then, by "volitional WFC", the "sovereign" cell can -- by invoking the "Quantum Magic" phenomena -- "articulate" the states of that organelle, "switching" it from "gear to gear" (car transmission analogy), by causing & controlling the organelles WFC processes. The "information-bearing pattern", of the self-sovereign cell, then, might be a record of the "states", of all of its "subordinate" organelles & substructures, which are "gear-shifted" from state-to-state, as per the "will" of the self-sovereign cell.

In my naive understanding, single Celled organisms swim through their lives, "smelling / tasting" various chemical gradients, and thereby orienting themselves and their movement strategies. How do single Cells "taste" chemical gradients -- do they use chemo-receptors, on opposite sides of their membranes, to get a "forked-tongue" effect, and "smell in stereo" like snakes ? If you consider such chemo-receptors as "sense organs", what, inside the cell, is the "sensory data processor" -- to wit, the Cell's "proto-brain", which translates "taste" into movement instructions ?? If, in higher animals, the "seat of cognition" seems associated with the physical brain ("sensory data processor"), is there some similar sense, in single Cells, such that the Cell's "sensory data processor proteins" (if one would allow the broadest of brush strokes) are the "control center" or "HQ" of the Cell ???

Thank you very much for the informative reply !

In round numbers, a lunar sidereal month (360 degrees rotation, not the same as New Moon to New Moon), is 28 days, and there are almost exactly 13 such sidereal months per Earth orbital year. Might this mean, that the Earth-Moon system, is "semi-locked", into some sort of "orbital resonance", between their mutual orbit (4 weeks), and mutual solar orbit (52 weeks) ??

Would a beam of neutrinos, arcing across the Cosmos, over Cosmological distance & time scales, "redshift", their Wave Functions spreading out with the expansion of the underlying spacetime fabric ? Would neutrinos' slight masses affect their physics any ??

A 'disk' is a solid circular 2D planar shape. There are no 'disks' in the above figure. In the original, 'unaugmented' figure from NASA, space is represented by 1D, and time by 1D, and the curvature of the resulting 2D spacetime is indicated by the 3D perspective -- hence the term (1+1)D in 3D. Again, 1D space, being curved, 'closes' in on itself, in a closed loop -- in 1D, space is a circle, or ring. It is hollow. By extension, 2D space, being curved, 'closes' around, into a spherical shell -- in 2D, space is a hollow spherical shell. In 3D, closed curved space is the 3D hyper-spherical surface, of a 4D hyper-sphere (or, hyper-ball). Again, it is hollow. That higher dimensional, interior region, is part of Hyperspace, the higher dimensional space through which spacetime can be considered to curve. Being 'closed off', within & inside the fabric of spacetime, one could call it "Interior Hyperspace", or simply "Sub-space" -- which is what, to my knowledge, it happens to be called, in the StarTrek sci-fi show (when Federation HQ sends a subspace signal to the Enterprise, on the other side of space). This is an important point to keep clear for comprehending ST diagrams: the Visible Universe (VU) is the backwards light-cone, it is a 2D spherical shell (centered on Earth) at every time-slice, so that the "time-stack" of the 2D spherical shells is a (2+1)D "onion" of such shells, "blurred over" across the time dimension (a little like a deck of cards "smeared over" to the side) The Causally Connected Universe (CCU) is all the spacetime interior to the VU / lightcone, it is the "time stack" of the 3D (hyper-spatially warped) "spheres" (or "balls") out to the VU (hyper-)surface, so that the CCU "time-stack" is a (3+1)D section of space-time I suppose one could call these the "Seen Universe" and the "Known Universe", or some such. Note that the book Geometry, Relativity, & the 4th Dimension says that, since mass curves space, and since the combination of matter & anti-matter must yield flat empty space (after mutual annihilation), then matter & anti-matter must cause spacetime to curve in opposite hyper-spatial directions. To wit, if matter in a closed Cosmos causes spacetime to "pinch" outward, into Exterior Hyperspace ("convex hyperspatially outward"), then anti-matter would "pinch" inward, into Interior Hyperspace (Subspace). The impression is given, that, since a closed Cosmos has a "baseline preference" (my words) for being "convex outward / concave inward", that that preference translates into the observed preference for matter over anti-matter, seemingly suggesting a kind of confirmation of the closure of the Cosmos.

Yes, our VU is the (3D hyper-)surface of Earth's backwards light-cone, cutting backwards (in time) across Cosmic spacetime. The latter is 4D, and Earth's backwards light-cone is a 3D 'slice' of that spacetime fabric. Please note, that the correct term is "our VU", not "the VU", since our VU is the backwards lightcone 'slice', of global Cosmic spacetime, from Earth's particular present position. To wit, VU's vary with both space & time of 'starting inquiry'. I myself have struggled for years, to keep track, of all these details, but they can & do add up, to make or break clear comprehension of the (core) concepts. The VU is indicated as a thick, solid, light blue line, on the unaugmented (1+1)D in 3D spacetime diagram. On the 'augmented' spacetime diagram, which 'overuses' the 3Ds we have available for visualization, 'augmenting' the circular loop of space (1D curved around in 2D), at each time slice, into a sphere (2D curved around in 3D) as a translucent overlay. In the 'augmented' spacetime diagram, Earth's backwards light-cone is the 'stack' of 'rings' on the surfaces of those (2+0)D in 3D spherical surfaces. The interior of those 'rings' is shaded, simply to show, the region of the universe in Causal Contact with Earth, on any given time-slice. On any given time-slice, (A) in the 'unaugmented' ST diagram, the part of our VU lying on that time-slice, consists of two 0D points, on the 1D circle of space; (B) in the 'augmented' ST diagram, the part of our VU lying on that 'augmented' time-slice, consists of a 1D 'ring', on the 2D sphere of space. Similarly, in full (3+1)D in 5D (?) spacetime, the part of our VU, intersecting any given 3D hyper-sphere of space, is a 2D sphere (spherical shell).

(1) Living quantum systems can cause & control Wave Function Collapses At deepest root, all physical systems are quantum systems. And, living cells are "self-measuring" quantum systems -- "at its most fundamental level, the living cell is a quantum system, which measures its own internal state" (McFadden. Quantum Evolution, p.164). Thus, quantum systems that are "alive" can cause, or "self-trigger", their own Wave Function Collapse events (quantum evolution by von Neumann Type I process). Moreover, modern human science has hinted that quantum Wave Function Collapse, normally an unbiased random process, can be biased, so that quantum possibilities, latent in the quantum system's Wave Functions, can be willfully, or volitionally, selected, in a non-random way. For example, Carl Sagan did not dismiss "that by thought alone, humans can (barely) affect random number generators in computers" (Haisch. Purpose-Guided Universe, p.38). And, some scientists have suggested, that (human) Consciousness can cause & control the "quantum jump" (or, Wave Function Collapse) process (Goswami. Quantum Activist (DVD); Eysenck & Sargent. Explaining the Unexplained, p.136-149), suggesting specifically that "Consciousness [can] influence internal state-vector [Wave Function] collapse" (ibid., p.146). (2) Preferenced selection, of quantum possibilities, into actualized realities, is the "Miracle" of Life -- "if it can, then it will" Imagine, if only for a few moments, that there truly is some "Miracle Magic" quantum phenomena, by which quantum possibilities, latent within a Wave Function's super-position state, can be selected, in an active & non-random way. By such "Miracle Magic" means, as soon as some event became quantum mechanically possible, no matter how unlikely, that event could be made manifest, as a well-defined actual reality. And, as it happens to happen, such a "Miracle Magic" phenomena, is already popularly attributed to Life processes, with the popular expression, "if it can, it will", and, "where there's a Will, there's a way". Therefore, it could be construed self-consistently, if somewhat circularly, that the popularly perceived "Miracle of Life" is the "Miracle Magic" quantum phenomena, by which the picking of possibilities can be preferenced, to actualize even unlikely events, "without waiting" for those possibilities to become probable. Life, then, would be able to Willfully "deal cards from the deck", without "drawing cards randomly". To wit, Life is a skillful "mechanic" card cheat. Alternatively, Life has "the luck of the Irish", whereby if a fortuitous event is quantum mechanically possible, it is automatically made manifest*. To wit, whenever some quantum event could occur "if the stars aligned", Life can miraculously make "those stars so align". * Cf. Murphy's Law, whereby latent quantum possibilities are preferentially selected, but male-volently, not bene-volently. So, if good-willed WFC underlies Life, then the ill-willed WFC (allegedly) observed in Murphy's Law suggests the same as some sort of "death (or, kill) process".

Thanks very much for all the responses. Please ponder the following scenario: Take some simple cell Put it into "torpor / sleep" Invasively, but non-lethally, "rip out all of its protein molecules" (say) Invasively, but non-lethally, "replace all the removed protein molecules" with artificially synthesized duplicates Wake up the cell Q: Does the cell care (about being given a complete "blood transfusion exchange" [in rough analogy]) ?

Fig. 1 -- Visible Universe (VU) and corresponding forward-projected Hubble Volume (HV) indicated. Note that documentaries, like NGC's Journey to the Edge of the Universe (DVD), explore the former, not the latter. Mankind has no news about the current conditions in the HV, being only aware of the archaic pasts of that present. Fig. 2 -- 'Augmented' time-slices of (2+0)D overlain. Time-slices of Cosmic spacetime do not simply "expand like a balloon", but rather "expand like a balloon whilst 'sliding down through the time hyper-dimension'". Higher-D time-slices also show, that most Cosmic real-estate exists, relative to Earth's position at an (arbitrary) Cosmic 'hyper-pole', near the Cosmic 'hyper-equator', at relative 'hyper-latitudes' near 90 degrees, a "quarter turn around the rim of the cup" of Cosmic spacetime. (This is true even more, in full (3+0)D.) Thus, most E.T.I.s who do exist, would exist, "half way to the other side of space", from Earth, which would probably be far out beyond our own HV. Fig. 3 -- Repeat of previous figure, highlighting HV, on current time-slice of Cosmic spacetime, on 'augmented' (2+0)D time-slice surface.

Please ponder the process of simple Cell Division, in simple single-celled organisms. Presumably, the single cell starts with some mass (m), "eats" biologically important molecules, "fattening up" on those "parts", until it masses about twice its original mass (m --> 2m). Then, it uses those "parts" to duplicate all of its cellular systems, and divides, into two daughter cells, each of approximately the original mass (2m --> m+m). QUESTION: Imagine being able to track all of the individual atoms, inside the single cell. Imagine being able to 'tag' those atoms, labeling them as "original" or as part of the "parts" supply. Then, when the cell uses the "parts" to duplicate all of its cellular systems, do the "original" and "parts" atoms get mixed and mingled; or, after Cell Division, do all of the "original" atoms remain together, in one of the daughter cells, whereas all of the "parts" atoms were assembled, into the the other daughter cell ??? In some sense, in the "bio-molecular dance of Life", the original single cell is a little like a dance floor, full of active bio-molecule "dancers". Then, the cell "eats", consuming "parts", which are a little like new bio-molecule "dance students", who enter the dance floor, and (somehow) become "partnered" with the original "dancers" already on the "dance floor". The "original dancers" then "instruct the new students in the waltz dance". And then all the "partnered pairs" separate, in two distinct "dance squads", at opposite ends of the "dance floor". When that happens, does the "original dance squad" remain together ??? Does the "original roster" remain the same ??? Or, do the active bio-molecule "dancers" swirl around the "dance floor", and all the "trainers" & "trainees" stay stuck together, 'on the same team' ??? (thanks very much in advance, for any kind of clarification, of any of the considered concepts)

Please ponder a hypothetical closed Cosmos ([math]\rho > \rho_{crit}[/math]), composed completely of matter ([math]\Omega_M > 1[/math]). In (1+1)D, its spacetime diagram (x,t) would be spheroidal, 'circuloidally' [eliptically ?] closed in time (lines of longitude), and closed in space (lines of latitude). Now, denser universes don't expand out as big, or for as long, as more rarified (but still cosmically closed) universes. Thus, the Radius of Curvature for Time, and the Radius of Curvature for Space, for a cosmically closed, matter only, universe, seem like they would be closely correlated. Is this so, and is there any (simple) relation between the two ?

To my understanding, the "Visible Universe (VU)" is the backwards lightcone, of Earth, on the present time-slice of spacetime (shown above in a (1+1)D in 3D visualization). Whereas, the Hubble Volume (HV) is that spatial section, along the current time-slice of spacetime, corresponding to, and coming forward in time from, the VU (an arc-length, along the spatial circle, of the present time-slice, of that "vase" of (1+1)D in 3D spacetime).

I am grateful for the linked & cited source. In some sense, the struggle between "Chaos & Order (Structure)" [set vs. Osiris, as it were] is deeply rooted in the fabric of physics.

Passive Sensory Systems will be woefully slow & inadequate Passive visual sensors, which "wait for lagging light" to slowly percolate across the cosmos, and "deign to finally inform" Mankind, of "cosmic politics", will be woefully inadequate, for figuring out, what actually is occurring, across the cosmos. In theory, the Hyper-Civilizations, of alien Hyper-Species, could be billions of years old, at present, and yet the light from their fledgling "Apollo Programs" wouldn't be seen in the skies of Earth, for billions & billions of years to come. Most of the "meat of the onion of [expanding, closed] spacetime" is above & beyond the Backwards Light-Conoid of Earth.

Lacking Rest Mass, photons vanish upon Measurement Living (and Conscious?) quantum systems can "craft" Wave Function Collapses of own sub-systems It is completely consistent, with current conceptions of quantum physics, to claim that (human) Consciousness can (A) cause; (B) control the "quantum jump" (or, T1 Wave Function Collapse) process: "truly random events in the brain [afford] greater scope for Consciousness to influence internal state-vector [Wave Function] collapse" (Eysenck & Sargent. Explaining the Unexplained, pp.136-149; cf. Amit Goswami's The Quantum Activist [DVD]). Indeed, (human) Consciousness can be considered as a "downward causing" epi-phenomena of brain activity, which, whilst being "compliant" & "consistent" w/ quantum mechanics, so that brain activity always obeys physical laws, actually exerts subtle influences on that brain bio-activity (neuronal firings, protein foldings & unfoldings, etc.) [Parrish. Nothing I See Means Anything, pg.80+]. And, such subtle influences could be explained, as Consciousness causing & controlling -- to wit, "crafting" -- wave function collapses (electron tunnelings across neuronal synapses, electronic configurations creating protein folding structure, etc.). The "magic" of mind, then, would "lurk" within these "quantum jump" processes. Spatial, and temporal, cross-correlations of the same, occurring across the brain, would be the "footprint" of Consciousness, in the biological tissues of the (human) brain. In sum, Decoherence effects, quite crucial to quantum processes, reflect the usual & customary condition, of quantum 'particles', being embedded in "random & uncontrollable" Environments (Greenstein & Zajonc. Quantum Challenge.). However, it is consistent with current comprehensions of quantum physics, that Living, Coherent, & Conscious quantum systems, by providing an "ordered & structured" Environment for their quantum sub-systems to Entangle with, can "leverage" that order, to "order & craft" their own internal Wave Function Collapse processes ("random WFC from random Env., ordered WFC from ordered Env."). Would a Localizing electron, WFC-ing into a vacant & available bound-state orbital, about some nucleus, need to Entangle with that nucleus, in a "synchronized WFC" process, a little like a "docking maneuver" between space-craft ???

I understand, that the AB effect relies directly upon the Potentials, which "underlie" the so-called E&B fields. It is the Potentials (V, A) which appear in the Hamiltonian, of the SWE. Quantum 'particles' respond directly to the Potentials. (The "fields" derived therefrom are only useful in the Classical limit, of Ehrenfest Theorem expectation values, d<x>/dt = -<p>/m, etc.)

Technically, "civilized" means "city dweller" (Latin civis, townsman). A city is an aggregation of cooperating organisms, displaying some semblance of labor specialization, and validating the biology maxim that "aggregation precedes specialization". In some sense, the cells making up an organism already constitute a "civilization". An actual "civilization", then, is an "organism of organisms". Seemingly, initially, a sufficient & steady supply of energy (food surplus) is required, to bring about the initial aggregation, of organisms, into continuous contact (e.g. cities at the center of farm fields [on Earth]).

(1) 'Measurement' = Wave Function Collapse (2) All 'Measurements' are, ultimately, spatial position Localizations According to GRW, "outcomes [of (Quantum) Measurements] are typically recorded in the position of something". (3) Localizations = Wave Function Collapses into attractive Potential Wells (w/ photon emission "registration" of event) Free particles' Wave Packets steadily spread out across space (von Neumann Type 2 evolution, according to SWE). Spatial Localization requires an attractive Potential Well. When a quantum 'particle' (e.g. electron) encounters an attractive potential well (e.g. nucleus, with vacant bound orbital(s)), it may "choose" to bind, via wave function "collapse" (Type 1 evolution), with a probability proportional to the (squared modulus of the) Overlap Integral, between the incident free 'particles' wave function [math]\Psi[/math], and the available vacant bound-state orbital wave function [math]\Phi[/math] -- to wit, [math]P \propto | < \Phi | \Psi > |^2[/math]. (4) "Dice Roll" for Wave Function Collapse occurs upon initial Particle-Potential Interaction, before "organization" of Reflected & Transmitted waves When an incident wave packet encounters an interfering potential barrier, the wave function "piles up", and a tunneling "feeler wave" threads through that potential barrier instantaneously, in zero time. Over the course of approximately one period, of the particle's phase oscillations, Reflected & Transmitted waves are "organized", out of the "piled up" incident wave packet. (Nimitz & Haibel. Zero Time Space.). We observe, that, immediately upon encountering an "interfering potential", quantum "weirdness", in the form of instantaneous, zero-time phenomena, occurs. Speculatively generalizing this phenomena, we infer, that any & all such quantum instantaneity occurs, as soon as the particle's wave packet "piles up" upon the newly encountered (potential-)energy discontinuity. In particular, upon encountering an attractive potential well, with available vacant orbitals, any quantum instantaneous wave function "collapse" occurs, during that initial interaction period, before any Reflected or Transmitted waves are fully "organized", out of the wave packet "pile up". Only if, and after, the "dice roll" for quantum binding fails, so that Type 2 evolution is never "exited", are Reflected & Transmitted waves fully & finally "organized". Once so "erected", [math]\Psi_R[/math] and [math]\Psi_T[/math] propagate away from the (potential-)energy discontinuity, according to the SWE. Note that this wave packet "pile up" period represents the peak, of the Overlap Integral, and Transition Probability, from the incident free state, to the available vacant bound state. For, before the interaction, when the wave packet is far from the potential well, there is little overlap. Likewise, after the interaction, when the Reflected & Transmitted waves have propagated away from the potential well, there is (again) little overlap. But, in between, upon "piling up" at the potential, the incident wave function finds maximum overlap, with any available vacant binding orbitals. The time frame, for non-deterministic Type 1 evolution, when the particle's evolution "exits" conventional Type 2 evolution according to the SWE, for instantaneous wave function "collapse", is that initial "pile up" period, immediately upon the initial encounter, by the particle, with the (potential-)energy discontinuity, in its environment. In some sense, an (attractive) energy discontinuity, and the spatially Localized bound orbital which it "offers", can "trigger" the "exiting" of conventional T2 evolution, for non-conventional T1 "collapse" evolution. (5) On "collapse", the Wave Function is "rectified" to spatially uniform phase, representing the particle's "arrest", into the Rest Frame corresponding to the attractive Potential Well (with an emitted "registration" photon carrying off the excess energy & momentum) In measurement & wave function collapse, the wave function is "arrested" (Nimitz & Haibel, ibid.). This is necessary, to bring the particle to rest, in the Rest Frame of the attractive potential well, into which it Localizes. Typically, an emitted photon represents the "registration" of the event, required by John Wheeler*. The creation of such a photon also represents the "quantum creation", of the "third body", beyond electron & nucleus, necessary for compliance with the conservation of energy & momentum. * This "quantum micro-signal" can, in principle, be amplified, into a "macro-signal" comprehensible to some (human) scientist. However, whether said (human) scientist bothers to amplify, after the fact, that original "quantum micro-signal", has no retro-active influence, upon the original interaction, which has already occurred, as an event "permanently recorded (or etched)" in space-time, before it is even, in principle, possible to amplify said event's micro-signal. Einstein's Moon still exists, even when Earth-bound human eyes, light-seconds away, happen to be averted. In all cases, that the particle is "arrested", and brought to a halt in some Rest Frame, indicates the importance of particle Rest Mass. In particular, the Rest Mass represents the "persistent" part of a wave function, which survives the stresses of (non-local, instantaneous) wave function collapse (and "phase rectification"). Since photons have no rest mass, their "arrest" represents their destruction.

Thanks for the response

Q: In classical QM, free particles have positive energy & frequency (plane waves), whilst bound particles have negative energy & frequency (Hydrogen wave functions). Is this transition, from positive to negative frequency, significant (e.g., given that anti-matter has inverted frequencies) ?? A (??): No. Technically, the classical (scalar) Schrodinger Wave Equation (SWE) is the classical limit, of the (scalar) Klein-Gordon Wave Equation (KGWE), which incorporates the rest-mass-energy of the quantum 'particles'. Accounting for that rest-mass-energy, the SWE would be modified as follows: [math]\hat{E} \Psi = \hat{H} \Psi \; \; \; \rightarrow \; \; \; \hat{E} \Psi = \left( \hat{H} + m c^2 \right) \Psi[/math] Now, it can be shown, by simple substitution, that the addition of a spatially uniform & constant potential energy (V), to the Hamiltonian, multiplies the wave function by a corresponding time-varying phase factor (e-i V t / h). And, mathematically, one can consider the 'particle' rest-mass-energy as precisely such a spatially uniform & constant potential energy (V = m c2)*. Thus, when one accounts for the rest-mass-energy, the 'particle' frequency increases markedly, to a "new baseline", centered around the rest-mass-frequency, which is that corresponding, and complementary, to the 'particle' Compton Wavelength (h f = h c / l = m c2). * Could considering a quantum 'particle' rest-mass-energy, as a spatially constant & uniform potential energy, correspond to the Higgs field (interaction with which supposedly gives mass to particles) ??? For example, for an electron, m c2 = 511 KeV, so that the mere transition, from a free state, to a Hydrogen 1S state (say), with E = -13.7 eV, makes little "dent" in the electron's "hyper-fast" phase frequency. Indeed, the lowest energy, 1S, Hydrogenic bound states, for the first (and, hence, unscreened) electrons added to a bare nucleus, having Z protons, is - Z2 x 13.7 eV. Since an electron's rest-mass-energy is nearly 40,000 times larger (m c2 / E0 = 37300), than the (magnitude of) the Hydrogen 1S state's binding energy, one would need an ultra-trans-uranic nucleus, with nearly 200 protons (> 193), to create electro-static potential wells deep enough to actually "invert" the electron's phase-frequency*. * The largest naturally occurring elements have ~100 protons. One could construe such coincidences (200 roughly equals, but safely exceeds, 100) as an argument for "fine tuning" [cf. Bernard Haisch. Purpose-Guided Universe]. Thus, using the standard, un-mass-energy-modified, SWE, amounts, mathematically, to a "Frequency Modulation (FM) signal analysis", where you "skim off" the "carrier frequency" (h f0 = m c2), and consider only the relative phase frequency (f - f0). So, simply b/c the relative phase frequency becomes negative, in bound states, need not imply that the electron's overall "actual" phase frequency has been "inverted", by becoming bound.