🚀 go-pugleaf

Consider the following scenario: we wish to construct an object massing
1 kg from molecular building blocks.  During construction, we must
examine the work in progress after each step to be certain that it is
correct.  This requires a vast number of measurements, and, as we know,
measurements require the expenditure of free energy.  Is the energy
cost of such a procedure prohibitive?  To get a handle on this, I ran
the following calculation through a spreadsheet.  You can argue with
some of the assumptions, but I don't think the "real" answer can be
more than a factor of 1,000 away from what I get here.

I would like feedback in the form of alternate assumptions or critiques of
the existing ones.

	     1000 grams (object)
	/      89 grams/mole (for alanine, a simple amino acid building block)
	  -------
	    11.23 moles
	* 6.0E+23 molecules/mole (Avogadro's number)
	  -------
	  6.8E+24 molecules
	*       1 photon/molecule (perfect efficiency - must be too low)
	  -------
	  6.8E+24 photons
	* 3.6E-12 ergs/photon (yellow-green light, 5560 Angstroms)
	  -------
	  2.4E+13 ergs
	/ 1.0E+07 ergs/joule
	  -------
	  2.4E+06 joules (= watt-seconds)
	/    3600 seconds/hour
	  -------
	      669 Watt-hours
	/    1000 Watts/kW
	  -------
	    0.669 kW-hours
	*   0.138 dollars/kW-hour (from my last PG&E bill)
	  -------
	    0.092 dollars

Assumptions:

Building block size of alanine.  I think this is conservative for most real
nanotech, which will assemble larger chunks.  However, for Merkle-style
atom-at-a-time construction of diamond with abstraction of hydrogens in
intermediate steps, the effective molecular weight could be 12 or less.

Observing with light. There may be other (more or less efficient) ways to
observe.  Propose some.  I chose 5560 angstroms since that is the wavelength
to which the human eye is most sensitive.  Some people have argued that such
a photon can't measure anything smaller than its own wavelength (thus we need
X-rays instead), but I don't buy that.  Fluorescein is smaller than the
wavelength of the light it so efficiently emits, to say nothing of the sodium
D-line.  Once you decide on a wavelength, you get energy by dividing into the
speed of light to get frequency, and multiplying by Planck's constant.

Likewise, the perfect quantum efficiency assumed may seem unrealistic
but the real question is free energy per measurement anyway.  Consider a
mechanism in which a hinged lever is pressed against the workpiece, and the
far-end deflection is a (magnified) measure of whether the desired reaction
took place.  This pressing may be done slowly and nearly reversibly.  Can we
thus reduce the required photon energy, by bouncing it off the lever instead
of the workpiece?  Also, a small angular deflection (of, say, a mirror) can be
turned into a large positional difference (of a photon bounced off that mirror).
Consider sticking a mirror on the lever ...

A lower bound on the energy cost can be had by considering the equivalence
of information and a change in entropy, and assuming room temperature.  I
haven't run through this one yet.  Clearly, at least one bit of information
is required (good or bad?).

The only other assumption is the cost of electricity (and the implicit one
that it can be converted to photons efficiently).  This is probably pretty
good.  Especially if nanotech makes electricity "too cheap to meter". :-)
And gives us really good molecular "LEDs".

	Howard A. Landman
	landman@hal.com

[Given the existence of nano-scale robot arms for construction, using
 a similar arm as a nano-AFM (or indeed, just another tool on the same
 arm) seems reasonable.  If you build the arm to ask the question right,
 (i.e. with one-bit answer), you can get away with kT ln 2 J per 
 question; the total energy is in the kilojoules rather than the 
 megajoules.  However, this represents a theoretical lower limit,
 and I wouldn't be too surprized if in actual applications Howard's
 figures were closer to the truth.
 --JoSH]