Difference between revisions of "Quantum mechanics"

Revision as of 08:05, 1 November 2017

Quantum mechanics is of paramount importance for atomically precise manufacturing. But quantum mechanical treatment isn't necessary for all areas of APM though. Many areas (actually all but the most core ones) can be sufficiently accurate approximated with very "non quantum mechanical" (aka classical) models.

"Nano-..." does not necessarily imply "Quantum-..."

One might be led to believe that everything that is nanoscale behaves deeply quantum mechanically.
This could not be further from the truth.

While there are parts in nanoscale systems that behave very much quantum-mechanically there are other parts that very much don't do so. Prime example of non quantum mechanical (aka classical) behavior in the nanoscale is nanomechanics, which when everything is stiffly anchored and properly restrained, behaves very classical.

If one actually wants to have quantum effects in mechanical nanosystems that are strong and wide ranging it gets quite difficult. To have mechanical mechanisms (or anything else) behave quantum-mechanical three requirements must be met:

• (1) extremely low temperature (extreme cooling)
• (2) very low inertia: "light" structures out of not too many atoms.
  The parts must be very well unconnected that is mechanical decoupled from the housing structure.
• (3) spacial restraints in translation or rotation.
  (Rotation is always restrained to at max 360°. Or maybe 720° for a "fermionic crystolecule")
  (TODO: Does the idea of "fermionic crystolecules" make sense?)

Regarding (1): In most practical products of advanced atomically precise technology there is no cooling necessary. In advanced atomically precise manufacturing systems mechanosynthesis runs better with some moderate level of cooling but mechanosynthesis does not need deep cooling. But even if one goes to extremes with cooling to push efficiency quantum behavior won't appear because of the point following next.

Mechanical decoupling (2) is the antithesis to machine phase. Machine phase systems behave a bit like one single giant (intricately) interconnected mass of axles cogs and gears. Even at ultra low temperatures the quantum matter-wave wavelength which corresponds to this big interconnected mass will still be way below the atomic scale. This is one hallmark of classical behavior. What can happen is that low stiffness structures act in a decoupling way. A long and thin axle e.g. would and could allow a quantum zero point energy torsion oscillation with large amplitude.

At room temperature and pretty far below the "cloudy" uncertainty stemming quantum effects (particle(s) flowing apart) is strongly overpowered and masked by the "noisy" uncertainty stemming from thermal motion. Superficially the two uncertainties are similar thus they often can be treated in a combined way. Even that more severe positional uncertainty stemming from the thermal effect can be sufficiently suppressed in nanomachinery preventing gears from jumping teeth due to thermal fluctuations.

In advanced force applying mechanosynthesis quantum mechanics does play a significant role since quantum chemistry involves massive changes in electronic states which do behave deeply quantum mechanical even at room temperature and far above.

As examples for quantum mechanically behaving mechanical systems one could take:

• A small, strongly cooled, light, long and skinny tuning fork lever that is vibrating (there where experiments conducted)
• A strongly cooled and levitated spinning wheel would do very well.
• A small light crystolecule in a somewhat bigger box. But only in case it can be shaped such that it does not stick to strong to the walls (questionable) or that it at least does not stick to strong to the atomic corrugations of the walls (probably better chances).

These mechanical examples do showcase really strong quantum-mechanical but they are not at all wide in range. The quick growth of mass with the growth of system size (a cube law) makes that impossible. These examples are better described as "simple objects" rather than "complex systems".

A big complex nanosystem, with all its parts strongly coupled together, will actually behave rather non quantum-mechanically. But since we are still bad at stiffly linking stuff together at the nanoscale (state 2017) current research tend to give the impression that all (or the majority of) nanomechanical mechanisms behave quantum mechanically.

Most examples for highly quantum mechanical behaving parts in the nanoscale are of non mechanical nature:

• Electrons: Their quantum behavior gives atom their nature size and shape. In electrically conducting materials the deeply quantum mechanical behavior of electrons gets enormously rich. (Many quasiparticles; interactions with phonons and photons; See: non mechanical technology path).
• Free floating (or freely rotation) molecules (e.g. molecules in gasses or liquids):
  The matter wave function of a single molecule runs apart quantum mechanically. This only happens with a molecule that is not restricted in all of its motion freedoms (translation and rotation)!
• ...

Examples for highly non quantum mechanically behaving parts (classically behaving parts) in the nanoscale are:

• Biology: Water molecules and other molecules do not tunnel through cell membranes (astronomically unlikely).
• Nanotechnology today: The inner nanotubes in multi walled nanotubes do not tunnel out sideways of the outer nanotube layers.
• Atoms in crystals: Unlike free floating molecules, atoms in crystals do not run apart quantum mechanically. They really behave like localized tiny balls. Grossly simplified one could say the bond atoms inherit the macroscopic, localized, non quantum mechanical (aka classical) properties from the macroscopic crystal.
  Several effect are acting together causing this.

(1) An atom in a crystal is enclosed by the nearest neighbors the atom binds to (if not on the surface non bonding enclosure suffices) These barriers form a potential box and restrict the lattice location of the atom (side-note: not considering thermal motion here). Within this box the atom is fully delocalized and in ground state. It can not run apart any further. Note that this is not about the potential box created by the nucleus restraining the electrons, this is about the surroundings restraining the atom as a whole. (2) With growing size of the surrounding crystal the mass of atom-plus-crystal goes up, the matter wavelength goes down, and the dispersion speed consequently shrinks. Long before a macroscopic crystal size is reached dispersion speed becomes too small to be noticeable/measurable. A matter wave with extremely short wavelength (e.g. near or even below the plank length) may not even make physical sense anymore (model breakdown). (3) With growing size of the surrounding crystal there are more and more interactions with the surrounding environment (collisions with gas molecules). This causes the wave function of atom-plus-crystal to collapse from the perspective of the surrounding practical system. The fancy name for this is "decoherence".

• ...

Aspects of APM where exact quantum mechanical treatment really matters are e.g.

• The quantum chemistry of mechanosynthesis.
• Crude estimation of friction levels
• Some aspects in early APM systems
• ...

Aspects of APM where classical approximations suffice:

• Simulation of crystolecule machinery: Classical mass and spring simulations (tech term: molecular dynamic simulations) suffice. The errors are not small but since the safety margins are are still much larger than the errors this is A-OK. Note though that the "big errors" are no way as big as one might suspect when one is used to the superficially similar problem of natural protein folding. In the problem of natural protein folding slightly different initial conditions (slightly different initial placement of atoms) can lead to vastly different results (a chaotic system). Crystolecule machinery keeps small errors small (a strongly nonchaotic system). So errors (while they may not be small) do not exponentially grow to catastrophic levels.
• Higher level system design: This behaves pretty much by definition classical, since this is an abstraction over lower level implementation details. (Except one is designing quantum computers. This though is a completely different topic mostly unrelated to gem-gum factories).
• ...

"Quantum-..." does not imply "Magic-..."

Quantum mechanics is often thought of something utterly mysterious that fundamentally can't be understood.
This too could not be further from the truth (at least in the sense of its practical predictions).

It is true that there is no consensus on a philosophical interpretation of quantum mechanics, but that does not mean that it fundamentally can't be made sense of. It just mean that this is still an interesting field of investigation in this regard.

Its also a matter of getting used to. When we (as humans) are born into this world it (as a whole) is something utterly mysterious. We just quickly get used to and blind to the miracles we are permanently immersed in. Very few people are deeply immersed in quantum mechanics and no one is immersed in it as much as in the directly experienceable world that surrounds us everyday. A problem is that there aren't many visualizations yet that help build some kind of intuition for quantum behavior (a "for-quantum intuition" – Note: the shorter term "quantum intuition" would very likely be interpreted the wrong way). There might be a big potential for such visualizations (held back by general software issues). Perhaps even much more potential than people knowledgeable about quantum-mechanics may think.

Potential wells

• TODO ...

Interpretations of quantum mechanics

Warning! you are moving into more speculative areas.

• TODO: discuss Copenhagen, Multi-World, Pilot Wave, ...

Quantum computers are fundamentally not as powerful as full parallelism of the same scale (if it could be implemented which it can't). With quantum computers only a quadric speedup is achievable on a general class of problems (grover algorithm). This is albeit with every additional q-bit the quantum parallelism doubles. The number of "parallel worlds" double.

If the degree of "realness"/"existence" of these "parallel quantum worlds" is judged by their degree they can be practically used then one could say they are in somewhat of a limbo in-between. Neither as useful as a "real" parallel world nor as useless as a non existent ghost world.

Notes (APM off-topic)

• Energy quantization of photons is not fixed it depends on the wavelength or equivalently frequency of the light which can vary continuously.
• On very short timescales the transition between the quantized energy states of electrons in atoms become continuous. There are animations on the web (TODO: (maybe) find and link electron state transition animation)
• Going even deeper: "second quantization"
• (TODO: Maybe discuss the usual suspects (particle wave duality, entanglement) in somewhat in context of APM ...)

The quasiparticle zoo

Main article: Quasiparticles

Related

• The nature and shape of atoms
• Trapped free particle
• Nanomechanics is barely mechanical quantummechanics

External Links

Wikipedia

• Wave function
• Wave packet
• Quantum & Quantum_mechanics
• Mathematical_formulation_of_quantum_mechanics

Warning! you are moving into more speculative areas.

• Interpretations_of_quantum_mechanics
• Copenhagen_interpretation_of_quantum_mechanics (mainstream)
• Many-worlds_interpretation
• De Broglie–Bohm theory (global hidden variables ...)
• Quantum_logic
• Von Neumann–Wigner interpretation (links wave collapse with conciousness - generally frowned upon since not necessary, quantum eraser experiment and quantum computers show relativity of wave collapse ... - relation to anthropic principle?)
• Ghirardi–Rimini–Weber theory (Does this propose a limit to scale of quantum system? If true might this limit the potential of quantum computers?)