Widdekind

The energy-time [uncertainty] relation is usually interpreted, in a practical sense, to signify that the lifetime of an emission (the amount of time taken for the intensity of the light emitted to decay to some separate proportion of its initial intensity) will be uncertain by an amount related to the uncertainty in its energy. The uncertainty in the lifetime can be translated into an uncertainty in the exact moment of emission of a quantum particle. In other words, the more sharply we can measure (in time) the lifetime, and, hence, the moment of creation, of a quantum particle... the more uncertain will be its energy, and vice versa.

 

Jim Baggott. Beyond Measure, pg. 38.

The wave train produced by a single quantum "transition" is demonstrably one or two feet long [1-2 ns]; th time an atom requires to radiate this wave train is about the same as the lifetime of an excited state.

 

W.H.Cropper. The Quantum Physicists, pg. 99.

The photon picture of light suggests, that the process of light emission is rather like firing a bullet from a gun, while that of light absorption is similar to a bullet hitting a target. This image correctly predicts, that an atom emitting or absorbing a photon reacts by recoiling.

 

Hey & Walters. The New Quantum Universe, pg. 144.

Math:

For the atom, of mass m, emitting a photon of energy E = h f, w.h.t.:

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 ?

Since the early 1990s, interference experiments with atoms have been performed. The first experiment directed a beam of helium atoms at a tiny gold screen, in which two slits had been cut. These slits were separated by only about a millionth of a metre -- roughly the wavelength of visible light. A movable detector observed the arrival of individual helium atoms, and gradually the familiar interference pattern emerged. This is exactly analogous to the electron interference experiments... Similar experiments with more massive atoms than helium have also now been performed.

 

Hey & Walters. New Quantum Universe, pg. 45.

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 ??

I have a theory where an electron is a part of photon oscillators. Such is their intrinsic coupling in my construction.

Gluons can "quantum split" into quark-antiquark pairs.

Photons can "quantum split" into electron-positron pairs.

Could there be some kind of connection* ??

Yes, I think so, except I do not like the term collapse.

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.]).

If you scatter a projectile from an atom (a bound relative motion state), then the final atomic state is a superposition of all excited atomic states allowed by the energy conservation law. These excited states may include the ionized states (free relative motion of atomic components).

General Principle of QM -- collisions do not cause "collapses" (??)

Among all interactions between a macroscopic object & various other systems, very few are actually measurements. The window of a bubble chamber is bombarded continuously by air molecules, and none of these collisions ends in a measurement. One must therefore specify what is peculiar in the interactions giving rise to a measurement.

 

R.Omnes. Interpretation of QM, pg. 329.

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 ?

Yes in principle and no in reality. To obtain entanglement one has to use the conservation laws. For that the initial atomic state and that of a projectile have to be well determined (by the preparation devices). After scattering the projectile energy loss should be measured very accurately to judge in what energetic state is the target atom in the final state. Resolving the projectile energy is a very hard problem. So in practice it is not done. In practice it may be easier to observe the target atom state directly (traces of ion and electron) or indirectly (atomic radiation).

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 ??

If you scatter a projectile from an atom (a bound relative motion state), then the final atomic state is a superposition of all excited atomic states allowed by the energy conservation law. These excited states may include the ionized states (free relative motion of atomic components).

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:

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..

Theory -- Schrodinger Wave Equation (SWE)

[schrodinger] viewed an atomic electron, not as a particle, but as a collection of wave disturbances, in an electro-magnetic field. He proposed, that the electron's particle-like properties are really manifestations of their purely wave nature. When a collection of waves, with different amplitudes, phases, and frequencies, are super-imposed, it is possible that they may add up to give a large resultant wave, located in a specific region of space. Such a super-position of waves is commonly called a wave 'packet'. Schrodinger argued that... the movement of a wave packet through space might, therefore, look to all intents and purposes, like the movement of a particle. This is in many ways analogous to the relationship between geometrical optics (or ray optics) and wave optics. According to this view, the dual wave-particle nature of subatomic particles is replaced by a purely wave interpretation, with the wave functions representing the amplitudes of a field...

 

A wave packet can persist for an appreciable time, only if its dimensions are large compared with the wavelength. When confined to move in a small region of space, tightly grouped super-positions of waves, in a wave packet, are expected to spread out rapidly, dispersing into a more uniform amplitude distribution.

 

Jim Baggott. Beyond Measure, pp. 31-32.

In typical electron double slit experiments, electrons have de Broglie wavelengths 10²-10⁷ times smaller than their spatial spreads, suggesting considerable coherence times:

A wave packet is a wave [function] corresponding to each electron. The length of an electron wave packet, in a field-emission electron beam, is [math]1 \; \mu m[/math]... Interference only occurs, when two electrons come as close as [math]1 \; \mu m[/math] ['back-to-back'], but the average distance between electrons is 1 m [~3 ns between emissions], at the shortest, in our electron beam, even when we use the brightest field-emission electron source. [Thus] the probability that two electrons overlap is extremely small...

 

In a typical electron diffraction [Double Slit] experiment, [the distance between the two slits] [math]d = 3 \AA[/math] and [math]\lambda = 0.04 \AA[/math]. Therefore the divergence angle of the electron beam should be less than 7 x 10^-3 rad = 0.4 degree. It is not difficult to obtain such a degree of the divergence angle of the electron beam. But, when we want to get an interference pattern, from two slits separated by a macroscopic distance, say, [math]d = 10 \; \mu m[/math], then [math]\alpha < 2 \times 10^{-7} rad = 1.2 \times 10^{-5} degrees[/math]. We have to use a highly collimated electron beam...

 

The wavelength of electrons, accelerated up to 100 KeV, is only [math]0.04 \; \AA[/math].

 

Akira Tonomura. The Quantum World Unveiled by Electron Waves, pp. 19,24,59.

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 electrons start as particles at the electron gun, and finish as particles when they arrive at the detector, but the arrival pattern of electrons, observed at the detector, is as if they traveled like waves in between... We conclude, that electrons show wave-like interference, in their arrival pattern, despite the fact that they arrive in lumps, just like bullets. It is in this sense that we can say, that quantum objects sometimes behave like a wave, and sometimes behave like a particle...

 

In the double slit experiment[,] although electrons appeared to 'travel like waves', they 'arrived in lumps like bullets'. The square of the wave function gives the probability of arrival, at any place on the detector array [D]... When the arrival of an electron is detected, by a flash at one of the detectors [d], the previously spread-out probability wave function of this electron obviously collapses down to the region bounded by this detector. How this collapse happens is not governed by the Schrodinger equation. This collapse or 'reduction' of the wave function is the mystery of quantum mechanics...

 

Before we record the arrival of this electron, its position is indefinite, and, according to quantum mechanics, all we know is specified as a wave of probability extending over all of the detectors [d's]. After a flash, at a particular detector [d], we suddenly know the location of the electron. Instead of a spread-out wave function, the probability amplitude has apparently 'collapsed' all of the potential electron positions down to one. This is the famous quantum jump. Although Schrodinger's wave equation accurately describes the spread of the quantum probability wave of the electron, it does not predict the quantum jump of the electron to a particular location of quantum state. This is the heart of the so-called 'quantum measurement' problem.

 

Hey & Walters. New Quantum Universe, pp. 14-15,158-160.

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).

We gain information, about the microscopic world, only when we can amplify elementary quantum events, like the absorption of photons, and turn them into perceptible macroscopic signals, involving the deflection of a pointer on a scale, etc. Is this process, of bridging between the microworld and the macroworld, a logical place for the collapse of the wave function ? ...

 

Bohr recognized the importance of the 'irreversible act' of measurement, linking the macroscopic world of measuring devices, and the microscopic world of quantum particles. Some years later, John Wheeler wrote about an 'irreversible act of amplification'... "no elementary phenomenon is a phenomenon until it is a registered (observed) phenomenon".

 

Jim Baggott. The Meaning of Quantum Theory, pp. 156,178.

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 ?

This is not "a valid interpretation" but a fact.

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

Total cross-sections measure the overall strength of an interaction. At low energies total cross-sections for strongly interacting particles show peak due to resonances, and in many instances, an overall drop as the collision energy rises. At larger energies, however, a new feature comes into play, first noticed by experimenters at the Serpukhov proton synchrotron 90km south of Moscow, back in 1971. There's an across-the-board rise -- in proton-proton, pion-nucleon, kaon-nucleon collisions, and more besides -- in cross-section, with increasing collision energy. It's as though particles expand and become more opaque at high energies.

 

Watson. Quantum Quark, pg. 367.

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?

It is popular but not correct explanation because it may still imply some probability of creating separated quarks in pairs. In fact, the only "explanation" is the quark definition as charged species in bound states. In other words, gluons are always meant to be inplace.

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):

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,

Now:

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:

However, such instantaneous "internal communication", through the wave function, could account for the elementary nature of fundamental quantum objects:

Such a "realistic" interpretation of the wave function was initially favored by Schrodinger himself:

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".

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]

A wave represents an ensemble of measurements...

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:

What is the electron radius r₀ ?

Particle-Wave "Duality"

"Particle" = spatially Localized wave function

"Particle" effects typically occur when position is localized; in other words, when a quantum event occurs, latency is actualized, and the "wave packet" collapses.

 

R.I.G.Hughes. Structure & Interpretation of Quantum Mechanics, pg. 303.

Particles... are spatially confined, local, & individual...

 

R.G.Newton. Thinking about Physics, pp. 54-55.

Wave = spatially De-Localized wave function

The property of entanglement ... is not at all odd for waves, extended in space as they are, but ... seems strange for particles... Entanglement of particle-events that are spatially separated... is counter-intuitive, and strikes us as weird, b/c our intuitive grasp of corpuscles is that they are individual & localized. We have no instinctive feeling for mutual dependency of bounded objects, while we have little difficulty understanding the interdependency of extended entities like waves, which may overlap.

 

R.G.Newton. The Truth of Science, pg. 184.

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:

The splitting of a coherent beam, of spin 1/2 particles, by means of a Stern-Gerlach apparatus, into two separate beams, of spin down & spin up, respectively, does not by itself constitute a measurement -- the two partial beams, still coherent, may be recombined to form a beam like the original one; each still in a pure state, they are properly described by a state vector or wave function, and their superposition is, again, a state vector. A measurement (of a spin projection of particles) is performed only when we identify particles in one (or both) of the beams and count them; the two beams must now be described by a density operator. Treating the constituents as particles is what destroys the coherence [by inducing wave function collapse].

 

R.G.Newton. The Truth of Science, pg. 184.

Quantum objects can be both free (E > 0, De-Localized plane-wave like wave function), or bound (E < 0, Localized wave function).

Non-locality means, that a wave package, a single physical particle, or several entangled particles, are spread across a given space at the same time (instantaneously).... A photon or electron can be met at the same time in New York or Paris. Only when measured will particles be localized, they are arrested, the wave function of the particle collapses.

 

Günter Nimtz, Astrid Haibel. Zero Time Space, 120-121.

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.