How can atoms do Double-Slit Experiments ??

[Widdekind]

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 ??

[Darwinsbulldog]

Higher energy states.

[Bob_for_short]

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 ??

 

A compound system is described with its center of inertia variables, say, R, and relative motion variables, say, r.

The wave function of relative motion depends on r. It determines the atom size. The center of inertia coordinate R determines the CI position in space. In QM the total wave function factorizes, so the CI wave function may be a plane wave or a wave packet, depending on preparation device. In case of a plane wave you may obtain an interference picture but it does not mean that an atom "balloons".

Edited August 28, 2010 by Bob_for_short

[swansont]

Hint: It's mentioned in the section on deBroglie waves. Waves diffract when they go through narrow openings, and can interfere when they go through a pair.

[Widdekind]

(thanks for the responses!!)

 

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

[swansont]

I think the difficulty here is you are trying to hang on to classical concepts at the same time as you apply quantum ones. The ionization energy is dictated by the attraction between the electron and the nucleus, not the size of the deBroglie wave.

[Bob_for_short]

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

There are two de Broglie waves - one describing the relative electron-nucleus motion in an atom (atomic size) and the center of inertia de Broglie wave (position of the atom as a whole). It is the latter that determines the interference or diffraction features, and it depends on the preparation device (source).

[Widdekind]

Succinctly stated, as I understand it at least, atomic wave functions can "quantum split", into spatial superpositions (which can overlap, or be widely separated, according to conditions applied in the apparatus of experiment).

 

Neutrons slowed to thermal energy (< 1eV) have wavelengths around 10^-10m, comparable to the size of an atom. The 'size', or 'fuzziness', of such a neutron, is tens of thousands of times larger than the size of a nucleus. It cannot reveal any details of the inside of a nucleus, but it can "reach out" to interact with nuclei that, according to a classical calculation, it is missing by a wide margin. In doing so, it reveals specific features of the neutron-nucleus interaction at zero angular momentum [interaction causes "collapse" of neutron w.f. at point of contact w/ nucleus, causing "head-on" collision??]. Moreover, if the neutron is slowed sufficiently, it can interact with more than one nucleus at a time, and can be diffracted by the array of nuclei in a sample of material. This reaching out is also important in nuclear fission. A slow neutron can find a nucleus of uranium 235, and stimulate a fission event, even if its trajectory would seem to bypass all the nuclei.

 

Kenneth W. Ford. The Quantum World, pg. 213.

Could you apply something similar, for "thermal protons", in fusion processes ? The delocalized charge distribution, and multiple parallel proton-proton interactions, might increase the likelihood of fusion events??

[swansont]

 

Could you apply something similar, for "thermal protons", in fusion processes ? The delocalized charge distribution, and multiple parallel proton-proton interactions, might increase the likelihood of fusion events??

 

Protons need to overcome or tunnel through the Coulomb barrier in order to fuse. Slowing them ensures it must be tunneling, and that probability decreases as you lower the kinetic energy.

[Bob_for_short]

Protons need to overcome or tunnel through the Coulomb barrier in order to fuse. Slowing them ensures it must be tunneling, and that probability decreases as you lower the kinetic energy.

 

Absolutely correct. Again, if you have at least two interacting particles, there are relative distance r = r1 - r2 and the interaction potential depends on it, and the center of inertia coordinate R. Equations for R and r are separated. Equations for r may describe bound states in case of attractive potential and even reactions (a complex potential with an imaginary part). So the interaction is the main thing - it determines the overlapping, if any.

[Widdekind]

Absolutely correct. Again, if you have at least two interacting particles, there are relative distance r = r1 - r2 and the interaction potential depends on it, and the center of inertia coordinate R. Equations for R and r are separated. Equations for r may describe bound states in case of attractive potential and even reactions (a complex potential with an imaginary part). So the interaction is the main thing - it determines the overlapping, if any.

 

(Thanks again for the clarifications)

 

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

[Bob_for_short]

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

 

Quantum mechanics answers these questions. If I knew what you want to know...

Edited August 30, 2010 by Bob_for_short

[Widdekind]

Quantum mechanics answers these questions. If I knew what you want to know...

 

A proton is a bound-state, of a system, of 3 quarks. Roughly speaking, we can decompose the wave function, into a [math]\Psi_{CM}[/math] and [math]\Psi_{rel}[/math]. And, the [math]\Psi_{rel}[/math] is the standard nucleon wave function, producing a probability "cloud" ~1 fm across. But, then, that relative wave function can be "sliced", and "spread", a little like smearing around a deck of cards. Each "card / slice" represents a whole & complete, but only partially probable, nucleon, centered at a given CM coordinate. (If the proton is certainly centered at some CM coordinate, that's a little like "telescoping" the deck of cards, back into a single stack.) So, the proton can enter a "spatial super-position state", where the whole proton, is partially probable, at many spatial locations simultaneously.

 

If you could prepare two opposing proton beams, each of which produced protons in such de-localized states, they could "reach out", and have at some positive, if partial, probability, of interacting, w/ other protons, which otherwise would miss each other by a wide margin. Presumably, high energy p-p reactions, would cause both proton's to "collapse" into some pair of particular, punctiform, point-particle like states, which would react "normally", and scatter. But perhaps you would get, overall, more p-p (i.e., potentially fusing) reactions.

 

 

"Preferencing" wave function collapse ??

 

The work functions, or inner potentials, of various materials, range from 10-30 eV (Tomonura. Quantum World Unveiled by Electron Waves, pg. 61) What would happen, if you did a Double-Slit experiment, with a macroscopic detector array (D), composed of two types of micro-detectors (d), which had dramatically different inner potentials? For example, although the apparatus would remain electrically neutral, so as not to alter the evolution of the electron [math]\Psi[/math], the incident electrons could minimize their energy by another < 20 eV, if they "chose" to "collapse" on one side of the screen (say).

 

Would the "goal", of energy minimization, "preference" or "optimize" the electron's behavior, such that more than half of the hits might be on one side of the macro-detector vs. the other, even though their wave functions were not altered in any way?

[Bob_for_short]

A proton is a bound-state, of a system, of 3 quarks. Roughly speaking, we can decompose the wave function, into a [math]\Psi_{CM}[/math] and [math]\Psi_{rel}[/math]. And, the [math]\Psi_{rel}[/math] is the standard nucleon wave function, producing a probability "cloud" ~1 fm across. But, then, that relative wave function can be "sliced", and "spread", a little like smearing around a deck of cards. Each "card / slice" represents a whole & complete, but only partially probable, nucleon, centered at a given CM coordinate. (If the proton is certainly centered at some CM coordinate, that's a little like "telescoping" the deck of cards, back into a single stack.) So, the proton can enter a "spatial super-position state", where the whole proton, is partially probable, at many spatial locations simultaneously.

 

If you could prepare two opposing proton beams, each of which produced protons in such de-localized states, they could "reach out", and have at some positive, if partial, probability, of interacting, w/ other protons, which otherwise would miss each other by a wide margin. Presumably, high energy p-p reactions, would cause both proton's to "collapse" into some pair of particular, punctiform, point-particle like states, which would react "normally", and scatter. But perhaps you would get, overall, more p-p (i.e., potentially fusing) reactions.

 

For a health reason, I cannot follow your reasoning about protons. Atoms are also compound systems. Atom-atomic collisions may be approximately described with a potential interaction. The cross section is given in http://arxiv.org/abs/0806.2635, formula (11).

 

 

"Preferencing" wave function collapse ??

 

The work functions, or inner potentials, of various materials, range from 10-30 eV (Tomonura. Quantum World Unveiled by Electron Waves, pg. 61) What would happen, if you did a Double-Slit experiment, with a macroscopic detector array (D), composed of two types of micro-detectors (d), which had dramatically different inner potentials? For example, although the apparatus would remain electrically neutral, so as not to alter the evolution of the electron [math]\Psi[/math], the incident electrons could minimize their energy by another < 20 eV, if they "chose" to "collapse" on one side of the screen (say).

 

Would the "goal", of energy minimization, "preference" or "optimize" the electron's behavior, such that more than half of the hits might be on one side of the macro-detector vs. the other, even though their wave functions were not altered in any way?

 

I did not get the point but the interference pattern will remain the same in my opinion. If the screens, slits, and detectors are some boundary conditions, then the material properties do not matter.

Edited August 30, 2010 by Bob_for_short

[Widdekind]

Other examples of de-localized atomic wave function states:

 

In May 1996, a group of experimenters at the National Institute of Standards & Technology (NIST) in Boulder, Colorado created what they called a 'Schrodinger cat'-like state, where the 'cat' in question was a single atom. After first trapping the atom, and laser cooling it down to as close to absolute zero as possible, w/o violating the uncertainty principle*, it was then zapped by a sequence of controlled laser pulses that forced it into a superposition of two different quantum states, based upon the energy of the atom's outer electrons [why would the wave function "collapse", as soon as those zapping laser photons interacted with the environment ???].

 

*

At absolute zero, an atom would have to be stationary (having zero momentum) and fixed at a precise location. But then we would know both its position & momentum exactly, in violation of the uncertainty principle. Atoms will therefore always have a small amount of energy known as their zero point energy and we can never quite get down to absolute zero.

By itself, this is not very remarkable. Atoms are often in super-positions. What was clever was the fact that the lasers got the different states of the atom quantum entangled with states of its motion, so that it was in a superposition of moving in two directions at once too. The atom would oscillate to and fro, inside its trap, with the two states moving completely out of phase. Their farthest separation would be almost a thousand times the diameter of the atom [[math]1000 \AA[/math] ?]. Note that when I say 'they' I am talking about the two parts of the wave function of a single atom... Each oscillating piece of the wave function has a spread of just one-tenth of the maximum separation between the two pieces [[math]100 \AA[/math] ?]... Here, each piece of the wave function remains localized, and does not spread out in space. When the two pieces are at their farthest separation, there is very little overlap.

 

Jim Al-Khalili. Quantum, pp. 246-247.

 

The genetic coding properties of DNA molecules, in all living cells, are due to the nature of hydrogen bonds between base pairs... Certain natural mutations can occur, due to the random quantum tunneling, of protons, from one site on the DNA, to a nearby one, forming a different chemical bond. This sort of accidental error in the coding of the DNA will occur in one out of a billion sites, but when it does, we get a quantum mutation. So, quantum mechanics certainly has some part to play in evolution...

 

When a strain of E.coli cells, called lac-, that is deficient in an enzyme that allows them to feed on lactose, are provided only with lactose, most are expected to starve. A few, however, should randomly mutate into the strain lac+, which can feed on the lactose and grow, and hence begin to replicate... In each cell, the mutation from lac- to lac+ might be due to the tunneling of a single proton between two adjacent sites. Quantum-mechanically, of course, the proton's wave function is such that it has a certain probability of being found in either site: a super-position of tunneled and not tunneled. And, provided such quantum coherence can be maintained with the cell for long enough, the whole DNA [molecule] should evolve as a super-position of mutated and un-mutated states...

 

 

It has been more than 50 years since Erwin Schrodinger made the startling proposal, that life is based on quantum mechanical principles... Quantum mechanics is likely to be as fundamental to life as water... Protons involved in hydrogen bonding in water are highly de-localized (that is, in a super-position of being in two separated locations). Hydrogen bonding is probably the most fundamental biochemical interaction, involved in DNA base-pairing, enzyme catalysis, protein folding, respiration, & photosynthesis. If quantum de-localization lies at the heart of this phenomenon, then it is central to life.

 

ibid., pp. 232-3,240-1.

Edited September 8, 2010 by Widdekind

[Widdekind]

A compound system is described with its center of inertia variables, say, R, and relative motion variables, say, r. The wave function of relative motion depends on r. It determines the atom size. The center of inertia coordinate R determines the CI position in space. In QM the total wave function factorizes, so the CI wave function may be a plane wave or a wave packet, depending on preparation device. In case of a plane wave you may obtain an interference picture but it does not mean that an atom "balloons".

 

Does that mean, that, for some spatially-extended CI solution (e.g., plane wave), everywhere within that CI solution, that relative-solution must be the same? Or, could you have a spatially extended CI solution, going thru a double-slit experiment, that was "1S" on one side of the envelope, and "2S" on the other ??

 

Crudely conceived, one could consider an atom (e.g., H) [math]1 \AA[/math] across (relative motion solution). Then, that whole system could "ghost out", a little like a deck of (identical) cards, being smeared out across the table. "Quantum copies", of that whole system, spread out through space, in "partial rarified ghosted-out phantom form" (CI solution). Then, it is the spatially extended CI solution, which passes through the double slits.

 

In what way, then, is an individual electron different? The wave function, of the electron orbiting a nucleus (say), or even in free flight, is the "whole system" (being a point particle), which "ghosts out", like a smeared out deck of identical cards, smeared out around the nucleus. Likewise, an individual photon wave function, although now not a point particle but inherently spatially extended object, can, apparently, also "ghost out" (a little like Quaid's illusion-system in the movie Total Recall), so that the "ghosted-out smeared out deck of cards" can be millions of light-years across, large enough to completely engulf a galaxy, and be refracted by the same, per Wheeler's galactic double slit experiment.

 

Thus, in QM, there appears to be a repeating pattern, wherein the "fundamental quantum object" -- matter point particles, or spatially-extended photons -- can "ghost out", into a "phantom state" of "partially present, in many places, at one time". And, if ever two or more fundamental root quantum objects conjoin (e.g., e^- + p⁺ --> H), then they form a "quantum system"... which then, too, can "repeat the process", and "ghost out", into "phantom form", of partially present in multiple places (CI sol'n). (And, if you can make the transition, 'up', from fundamental particles, to atoms... then you could go from atoms to molecules, count the molecule as a 'higher-level system', and make the whole molecule 'ghost out'... and then systems of molecules... in theory, whole macroscopic objects could 'ghost out', at their 'highest level' of large-scale structure, in a strange "spatial many-worlds interpretation-of-QM" kind of way... An 'all-possible-paths' approach looks like an actual physical manifestation, of action-integral-minimization from Classical Physics... "and that's why the Calc. of Variations works" (and, could the whole universe 'ghost out', 'through hyperspace', in an actual physical many-worlds-way) ???)

Edited May 22, 2011 by Widdekind

[Higgs0123]

...refracted by the same, per Wheeler's galactic double slit experiment.

 

Thus, in QM, ... the "fundamental quantum object" ...can "ghost out", into a "phantom state" of "partially present, in many places, at one time".

 

This is really the question of quantum nonlocality. How can the traveling quantum object [e.g. the photon] spread over space and yet remain single and unitary? How can one entangled photon determine the property [spin up or spin down] of its distant twin instantaneously?

Take a look at url deleted and see if it answers any of these questions.

[John Cuthber]

As far as I can see the issue starts here

"If Helium atoms are normally about 1 A across"

They are not. They don't have edges so their size is not defined. There's a small, but non-zero, probability of finding the electron a mile away from the nucleus.

[swansont]

This is really the question of quantum nonlocality. How can the traveling quantum object [e.g. the photon] spread over space and yet remain single and unitary? How can one entangled photon determine the property [spin up or spin down] of its distant twin instantaneously?

Take a look at url deleted and see if it answers any of these questions.

 

!

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