quantum wave-particle duality

[Darkpassenger]

In quantum wave particle duality what is need to make the wave turn to a particle. I understand that observation alone will turn the wave to a particle but what is the magnesium in observation that makes it turn. Is it just the fact that another particle is present or what?

[ydoaPs]

Wave-particle duality is really just something we use to frighten children and undergraduates. Everything is a (quantum) wave, period. The only sense in which we have point-like particles, is that when we measure their position, we find that we get an error on that position which is only limited by our measurement. We teach undergrads that the wavefunction has collapsed into a position eigenstate, but this isn't quite correct, since it has collapsed into a superposition of position eigenstates, localized around a point, with an variance given by the error of our measurement. So even right after a position measurement, particles are still waves.

[Darkpassenger]

OK I think I get it now, the wave only collapses when we measure it to give us a position to measure. Otherwise we wouldn't be able to measure the position if it were a wave. Although the position can only be measured to with in a given allowance for error because it is waving and not a stationary position. correct?

[Widdekind]

Material objects are, quantum mechanically, "Matter Waves", which Localize upon "measurement" interactions

 

Quantum Mechanics relies, at root, upon the Schrodinger Wave Equation [or, relativistically, the Klein-Gordon Equation] to evolve the Wave Functions of material quantum objects. To wit, Quantum Mechanics treats material quantum objects as "matter waves", which can be Localized, or Delocalized, depending upon environmental conditions, to which they are subjected. The act of "measurement" induces the Localization of matter waves, called the "collapse of the Wave Function". But, besides being "compressed", the matter wave remains a matter wave -- which it must, to remain compatible, with the governing Wave Equation of Quantum Mechanics.

 

According to von Neumann, a quon [quantum object] follows not one law of motion, but two. Everywhere in the universe, proxy waves [Wave Functions] are expanding (called "Type I process" by von Neumann). However, in the measurement act, and nowhere else, proxy waves contract to a definite result (a so called "Type II process"). After contraction, these entities are still proxy waves -- they never turn into classical objects [point particles]...

 

Physicists call von Neumann's Type II process "the collapse of the Wave Function"; it's also called the "quantum jump". Von Neumann's all-quantum description will not work, unless such a collapse really occurs, as a physical process, in every quantum measurement.

 

N.Herbert. Quantum Reality, pp. 146-147.

 

 

Measurement radically alters the Wave Function, so that it is now sharply peaked about [a point]. We say that the Wave Function collapses, upon measurement, to a spike at the point... It soon spreads out again, in accordance with the Schrodinger [Wave] Equation... There are, then, two entirely distinct kinds of physical processes: "ordinary" ones, in which the Wave Function evolves in a leisurely fashion, under the Schrodinger Equation; and "measurements", in which [math]\Psi[/math] suddenly & discontinuously collapses...

 

What if I made second measurement, immediately after the first? ... A repeated measurement (on the same particle) must return the same value. Indeed, it would be tough to prove that the particle was really found at [a point] in the first instance, if this could not be confirmed by immediate repetition of the measurement... Since the Wave Function soon spreads out again, in accordance with the Schrodinger Equation, the second measurement must be made quickly.

 

D.J.Griffiths. Intro. Quantum Mech. (2nd. Ed.), pp. 16-17.

 

 

Scrodinger laid down the basis of modern quantum mechanics [1925] with an equation describing waves of matter... In Schrodinger's matter wave, the mathematical representation of the wave is called the "Wave Function". In some real sense, the Wave Function of an object is the object. In quantum theory, no atom exists in addition to the Wave Function of the atom...

 

Quantum probability waviness [Wave Function], on the other hand, is objective -- it's the same for everyone. The Wave Function is the whole story: the quantum description of the complete physical situation has no atom in addition to the Wave Function of the atom. As a leading quantum physics text has it, the term "Wave Function of an atom" is a synonym for "the atom".

 

If someone looked in a particular spot, and happened to see the atom there, that look would collapse the spread-out Wave Function of the atom, to be wholly at that particular spot, for everyone... Someone looking immediately thereafter would find the atom at the place where the first looker found it.

 

Rosenblum & Kuttner. Quantum Enigma, pp. 70-77.

 

 

Classical, "particle" behavior, of material objects, arises from Localization

 

When matter waves are spatially confined, in deep attractive potential wells (e.g., electrons in atoms), they acquire a large statistical spread of momentum. This flows from the identification of momentum with the spatial gradient of matter waves [math]( \hat{p} \rightarrow -i \hbar \vec{\nabla} )[/math], and agrees with the Heisenberg Uncertainty Principal. It is this combination, of Localized confinement, and ensuing momentum spread, which gives matter waves their "outward pushing" ("hard elbows") and apparent solidity. Such "solid" states of matter, are the only ones, with which humans have common contact or conception.

 

When one attribute's realm suddenly contracts [e.g., Position], its realm of conjugate possibilities explosively expands [e.g., Momentum].

 

N.Herbert. Quantum Reality, pg. 147.

 

 

"Particle" effects typically occur when position is Localized... and the "wave packet" collapses.

 

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

 

 

Considered as a [matter wave], the electron fills its atom to the brim... In each atom[,] something seems smeared out to fill the atom[,] something we call the "probability cloud"[,] "electron Wave Function", or "quantum stuff"... The whole world is made of it... These waves of possibility have tangible consequences... Try, for instance, to push your hand through the nearest wall... Each atom's possibility wave pushes back at you. Pretty substantial, aren't they?

 

... Atoms don't drift through one another like mist, but stack up more like billiard balls, each one pressing against his nearest neighbor's probability cloud... The [math]\Psi[/math] wave for an individual system is evidently something solid enough to sit on.

 

N.Herbert. Quantum Reality, pg. 124.

 

 

 

Estimation of "solid" matter Bulk Modulus from compression of Quantum objects

 

From Heisenberg's Uncertainty Principle (3D), w.h.t.

 

[math]\Delta p_i \approx \hbar / x_i[/math]

 

[math]\Delta p^2 = \sum \Delta p_i^2 \approx \frac{3 \hbar^2}{\Delta x^2} \; \; \; (\Delta x_i \equiv \Delta x \; \forall i)[/math]

 

[math]KE \approx \frac{\Delta p^2}{2 m} \approx \frac{3 \hbar^2}{2 m \Delta x^2}[/math]

Now, Work = Force x Distance. And, as pressure is applied to our quantum object, confined in its 3D "box", it compresses slightly. The Work done, by the applied pressure force (on all 6 faces of the "box"), increases the Kinetic Energy of the quantum object:

 

[math]W = F \times d = ( P \times \Delta x^2 \times 6 ) \times \delta x = \delta KE[/math]

 

[math]\delta KE = \frac{\partial}{\partial ( \Delta x )} \frac{3 \hbar^2}{2 m \Delta x^2} \delta x = \frac{3 \hbar^2}{m \Delta x^3} \delta x[/math]

 

[math]\therefore P = \frac{\hbar^2}{2 m \Delta x^5} = \frac{\hbar^2}{2 m \, V^{5/3}}[/math]

And, so, w.h.t.:

 

[math] K \equiv -V \frac{\partial P}{\partial V} = \frac{5 \hbar^2}{6 m \Delta x^5}[/math]

For [math]m = m_e[/math] and [math]\Delta x = 1 \AA[/math], w.h.t. [math]K \approx 10^{12} Pa[/math], which is well within an order-of-magnitude, of measured Bulk Moduli, for standard substances (K = 100s GPa).

 

As pressure is inexorably increased, the electronic Wave Functions become increasingly compressed. Ultimately, the "squishy" & "springy" electron waves can, under inordinate pressure, be compacted down to subatomic, and even nuclear, size scales (~1 fm). When the Wave Functions of electrons are made to so significantly overlap the Wave Functions of nuclear protons, the former can (apparently) be absorbed by the latter, forming Neutronium (which would probably "pop" back out, to standard sizes, were pressure reduced, perhaps obviating the possibility of producing Neutronium armor plating).

Edited August 10, 2010 by Widdekind

[Darkpassenger]

What is the purpose for the wave to collapse (other then to get a generalized measurement), is there a reason that it doesn't stay in one form or the other?

[Widdekind]

What is the purpose for the wave to collapse (other then to get a generalized measurement), is there a reason that it doesn't stay in one form or the other?

 

Visualization of Wave Function collapse in Double-Slit experiment

 

Electrons:

 

As soon as an electron is fired from the source it begins to spread out, and to propagate as a wave that can pass through both sides of the biprism [double slit]. The electron wave is represented by a mathematical quantity, called wave function [math]\Psi[/math], whose behavior is determined by the Schrodinger [Wave] Equation. When detected, however, electrons are always detected as indivisible particles.

 

What happens to the wave function, when the electron is detected ? The wave function, spread out in space, is considered to shrink to a spot, as soon as it is detected. The wave should be concentrated at the spot. However, we cannot predict precisely where the wave function shrinks. We can, instead, only know the probability of finding electrons at a certain point. The square of the absolute value of the wave function, [math]| \Psi |^2[/math], provides the probability distribution, of finding where the electrons are found to arrive.

 

A.Tonomura. The Quantum World Unveiled by Electron Waves, pg. 52.

Atoms:

 

The

atom

's

wave function

is localized in space, as it leaves the gun, but spreads out as it travels towards the slits... As the

wave function

reaches the slits, it begins to squirt through both of them simultaneously. On the other side, the two pieces of the

wave function

form a super-position which has a very different looking probability distribution (due to interference between its two pieces). By the time the

wave function

reaches the screen, the distribution is such that the

atom

has a high probability of reaching certain places, and no probability of reaching others. Although the

atom

will only manifest itself in one place, statistically, many

atoms

, each with a similar probability distribution, will build up to form the pattern seen.

 

Jim Al-Khalili.

Quantum

, pp. 86-87.

 

 

Overlap Integrals underlie "collapse" phenomena

 

The probability amplitude, for a "quantum jump" transition, from one current & actual state [math]\Psi[/math], to another potential & possible state [math]\Phi[/math], is equal to the "matrix element" or "Overlap Integral", of those two states:

 

[math]a = \; < \Phi | \Psi > \; = \int d^3 x \; \Phi^{*} ( \vec{x} ) \Psi ( \vec{x} )[/math]

The probability, then, of the transition, is equal to the modulus squared, of the probability amplitude, p = |a|².

 

Now, the wave functions, of electrons in double-slit experiments, frequently span some "several inches" across, as the fly forward towards the detector screen (Rosenblum & Kuttner. Quantum Enigma, pg. 75). Consider such relatively large, macroscopically scaled, distended & delocalized wave functions, "spread out over inches". And, consider the comparatively coarse-grained resolutions, of typical detector screens, which utilize phosphor particles (Herbert. Quantum Reality, pg. 58), typically [math]5-10 \mu m[/math] across. Then, for all practical purposes, of macroscopic experimental measurement, we can approximate the (nano-scopic) bound-state electron orbital [math]\Phi_{ \vec{ R } }[/math], in a (micro-scopic) phosphor particle, at position [math]\vec{ R }[/math] on the detector screen, and into which the electron's wave function [math]\Psi_e[/math] could conceivably "collapse" and be absorbed, as a Dirac Delta Function [math]\delta^3 ( \vec{R} )[/math], placed at the appropriate (coarse-grained) particular position on said screen. The probability amplitude, for the "quantum jump" transition, then, is:

 

[math]a ( \vec{R} ) = \; < \Phi_{ \vec{ R } } | \Psi_e > \; = \int d^3 x \; \Phi_{ \vec{ R } } ( \vec{ x } ) \Psi_e ( \vec{x} )[/math]

 

[math] \approx \int d^3 x \; \delta^3 ( \vec{R} ) \Psi_e ( \vec{x} )[/math]

 

[math] = \Psi_e ( \vec{R} ) [/math]

And, the (full-fledged) probability of the transition is:

 

[math]p( \vec{ R } ) = | a ( \vec{ R } ) |^2 = | \Psi_e ( \vec{R} ) |^2[/math]

Thus, the probabilities, of wave function "collapses", are simply the standard "Matrix Elements" or, equivalently, "Overlap Integrals", governing the "quantum jumps" between states available to the quantum system in question (here, electrons). This, then, highlights a crucial concept -- "quantum jumps", like the Localization of wave functions upon "collapse", involve an interaction, between the current state of a quantum system, and another state, with which said system comes into "contact", defined by the physical overlap of the current & actual wave function, with that of the potential & possible future wave function. The more the current & actual wave function overlaps that of the second state (usually bound, in a deep attractive potential well), and the more similar the present state is to the possible future state, the larger the Matrix Element or Overlap Integral will be, and the larger is the likelihood of the "quantum jump" transition, from the former, to the latter.

 

In my understanding, since such Localizations absorb a formerly free electron, into a now-bound orbital, the electron, losing energy (c.f. Recombination in ionic plasmas), must emit a photon. Since a photon is a quantum of electromagnetic energy, photons can only be created whole, in integer numbers. Thus, a large & delocalized electron wave function, must "collapse" into a single bound-state orbital, in order to emit a single & whole photon. If the electron were to "collapse", into some super-position of many bound-state orbitals, scattered across the surface of the detector screen, then it would have to emit many "partial photons". But that is impossible, so the electron must "choose" one particular place to appear, and from where it emits its photon.

 

 

 

In "Interactionless Isolation", quantum objects' Wave Functions always evolve deterministically (Type I process)

 

Isolated quantum micro-systems are always "un-collapsed" Matter Waves:

 

The quantum state of any isolated physical system in the [sic] world never fails to evolve in perfect accordance with the linear dynamical equations of motion [e.g., Schrodinger Wave Equation]... We know, by experiment, that no collapses ever occur at the level of isolated microscopic systems...

 

Isolated microscopic physical systems have never yet been observed not to behave in accordance with the linear dynamical equations of motion, the fact that such systems, in other words, have never yet been observed to undergo collapses...

 

Purely microscopic systems... so long as they remain isolated from outside influences, always evolve in accordance with the dynamical equations of motion.

 

Albert. Quantum Mechanics & Experience, pp. 83,93,111.

It is, as yet, a mystery (to Mankind), as to what specifically prompts "collapses" (Type II process) to interrupt, or punctuate, the deterministic evolution of the Wave Function (Type I process). As an attempt to connect these two types of evolution processes, please ponder, that, at all instants of time, the Overlap Integral, of a Wave Function, with itself, is always one. This fact flows from the very probability "normalization", of the Wave Function, [math]< \Psi^{*} | \Psi > \; = \int d^3 x \; \Psi^{*} ( x ) \Psi ( x ) \equiv 1[/math]. Thus, the Matrix Element, describing the probability of the "self-collapse" transition, [math]\Psi \rightarrow \Psi[/math], is always one.

 

Now, in "interactionless isolation", there are no other possible quantum states to occupy, and no Matrix Elements & Overlap Integrals to compute. Hence, there is no possibility of transitions, to any other quantum state, than that currently occupied by the quantum object. In essence, there is nothing to "compete" with the self-collapse process [math]\Psi \rightarrow \Psi[/math], of probability one.

 

However, upon interaction, the Wave Function of a quantum object begins to contact, and overlap, available alternative states [math]\phi_i[/math] (e.g., localized, bound-state orbitals, in a detector screen). Suddenly, for the first time (since the quantum object's last Wave Function collapse event), there are one, or more, Matrix Elements & Overlap Integrals, of positive-definite value, [math]0 < p ( \Psi \rightarrow \phi_i ) = | < \phi^{*}_i | \Psi > |^2[/math]. This produces the curious effect, that the total transition probability, of the quantum object, from its current state ([math]\Psi[/math]), to any of its available states ([math]\Psi, \phi_i \; \forall i[/math]), including itself, now exceeds one [math]\left( p(\Psi \rightarrow \Psi) \equiv 1, \; p(\Psi \rightarrow \phi_i) > 0 \; \forall i \right)[/math]. Perhaps, then, it is specifically to avoid these "impossible probabilities", that causes the collapse of Wave Functions, to "prune off" possibilities, and keep every quantum object's total transition probability "sufficiently close to" one (?)*.

 

*

One might imagine, that, say, as an electron "splats" against a phosphor-particle coated detector screen

(in roughly

10

^-14

s

from "tip to tale")

, its

Wave Function

starts to "tunnel into" the awaiting, available, bound-state orbitals, in those phosphor particles. Then, the

Matrix Elements

, for transitions to those states, start to increase, from zero (when the electron was in "interactionless isolation", far from the screen) to positive-definite values (as the electron "splats" onto the screen). But, soon, the electron's reflected wave will start to "bounce back", off of said screen. At that point (after ~

10

^-14

s

), the electron's

Wave Function

will "ebb away", reducing the

Overlap Integrals & Matrix Elements

with those bound-state orbitals, in the phosphor particles. Thus, the probabilities of transitions, into those bound-state orbitals, will begin to fall, declining back down to zero. And so, were one to plot these transition probabilities, as functions of time, over the

dozen or so femtoseconds

of the "splatting"

interaction

, one would see a hill-shaped function (

p: 0 --> peak --> 0

). What, then, would actually "

trigger the dice roll

", to determine if the electron's

Wave Function

localizes into, or dis-localizes away from, those bound-state orbitals (the

Type II process

) ? Perhaps it is that "probability-peaking" process -- as interactions begin, and transition probabilities begin to climb from zero, the

Wave Function

is "put on notice", as the electron's "portfolio of investments" begin to accrue & accumulate increasing probabilities. But then, this "stand-by mode" is interrupted, when one of those "investments" (

Transition Matrix Elements

) "maxes out". When the electron "senses" that some "investment" has "panned out", and peaked in its probability,

then

the electron "rolls the dice", and either

Localizes

into, or

Dis-localizes

away from ("prunes off" the relevant "tunneling" transition wave), that bound-state orbital. (?)

 

Or, as a second supposed scenario, imagine an unpolarized photon, incident upon a

polarizer

crystal. As the photon encounters the

polarizer

, its

Wave Function

"splits" or "breaks", into two pieces -- a

transmitting wave

, and an

absorbing wave

. The

absorbing wave

is a little like the aforementioned "tunneling wavelets", of electrons, impinging upon phosphor grains, on detector screens. In this case, the photon's

absorbing wave

begins to interact with the valence electrons, of the atoms, in the

polarizer

. The electrons'

Wave Functions

are "ruffled", into super-positions, of their original ground-states, and new excited states, into which they

would

"quantum jump",

were

they "chosen" or "selected", to be the electron who absorbed the whole incoming photon, and its commensurate quantum of energy. Now, before the photon enters the

polarizer

, and encounters all those valence electrons, there is no probability, of any electronic excitation transitions. Then, as the photon's

transmitting wave

is transiting through the

polarizer

, the

interaction

, of the photon's

absorbing wave

, with all those valence electrons, causes all of their excitation transition probabilities to increase. Finally, as the photon's

transmitting wave

exits the

polarizer

, its "other half" (the

absorbing wave

) starts to ebb away, as well. Thus, the electrons' excitation transition probabilities begin to decrease. As before, the transition probabilities rise & fall (

p: 0 --> max --> 0

). So, again, the "natural cut-off trigger point", would appear to be, this "peaking" of the transition probabilities. It seems as if, when the valence electrons "sense" the perturbation, from the incoming photon's

absorbing wave

, they "let it ride", allowing the "investment" (of energy potential, from the photon's

absorbing wave

) to "grow"; then, when that "investment" starts to "decline in value", they "sell" (as it were), and "dice are rolled", to see, on a valence-electron-case-by-valence-electron-case, whether said valence electron "grabs" the photon (in which case, the photon's wave function collapses, and vanishes, depositing its energy into the now excited, and slightly

de

-localized, electron); or, whether it "misses" or "whiffs". If all the valence electrons "miss the catch", then the photon's

absorbing wave

has been completely

dis

-localized, and vanishes. Such leaves only the

transmitting wave

in existence, and the photon flies off, appropriately polarized.

 

Note that this picture predicts, that photons forced through longer & longer polarizers, would encounter more & more valence electrons, each of which would try to "grope" the photon's

absorbing wave

. Thus, fewer & fewer photons should "survive the gauntlet". But, this only says, that sufficiently long

polarizers

would transmit no light whatsoever, absorbing all photons, into their crystal structures, as thermal heat radiation (passing a laser through a

polarizer

heats it up).

Edited August 14, 2010 by Widdekind

[Widdekind]

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.

[Bob_for_short]

In quantum wave particle duality what is need to make the wave turn to a particle. I understand that observation alone will turn the wave to a particle but what is the magnesium in observation that makes it turn. Is it just the fact that another particle is present or what?

A wave represents an ensemble of measurements, not one. One measurement (a point or a spot) is a bit of information about the wave. So in a single experiment it is not a "wave collapse" that happens but information obtaining about the wave. With sufficient statistics you can get an idea about the wave, interference, etc.

 

You can look at this as at necessity to have many bits of information since the studied phenomena (wave behavior) is not elementary (is not reduced to one point while repeating observation).

Edited August 24, 2010 by Bob_for_short

[Widdekind]

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.

[Bob_for_short]

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

 

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

[Widdekind]

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 ?

[Bob_for_short]

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

 

Yes, that's true. Many Worlds, Many Gods, Hidden variables, etc., but it is not serious in my eyes.

 

In Classical Mechanics we have three coordinates with determinism but to observe these three coordinates in practice one exchanges with energy (photons) with internal degrees of freedom of a body. So the body is complex, not point-like. The internal degrees of freedom (relative motion of pieces of a body) is described with a plenty of other equations. They permit to get the right information about the center of inertia (3 coordinates) and sizes of the body. In QM, instead of additional set of equations, we have a wave equation covering "deviations" from the average (simplified, point-like) picture. This is much similar to those "internal motion equations" in CM. In both cases we need a lot of information to describe a phenomenon. This understanding saves us from searching for "wave function collapse" reason, hidden determinism, etc.

[Widdekind]

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.

[Sayonara]

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