Quantum mechanics

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 properly anchored and restrained (stiff - machine phase), behaves very classical. Side-note: In some respects thermal motion has similar effects to the quantum effect of wave packet dispersion (partilce(s) flowing apart) but at room temperature the thermal effect is much more severe. Even that more severe part can be sufficiently suppressed in nanomachinery.

Examples for highly quantum mechanical behaving parts in the nanoscale are:

• 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: 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) Within the atoms potential box (the lattice location) the atom is fully delocalized and in ground state. It can not run apart any further. (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.

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. Thefe are animations on the web (TODO: (maybe) find and link electron state transition animation)
• Going even deeper: "second quantization"

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

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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?)