Doesn Heisenbergs Uncertainty Principle forbid the possibility of nanotechnology?
Technical: Assume that we want to place a carbon atom on a specific previously-positioned atom. We need to position it to within roughly a bond length in order to have it bond to the right atom. A typical bond length is around an Angstrom, 0.1 nm or 10^-10 meters. Heisenberg’s uncertainty principle says: sigmaX * sigmaP >~ hbar/2 (eq. 4.12, Nanosystems) Here, sigmaX = 10-10 meters, hbar/2 = 5.3 * 10-35 Joule*seconds (or kg*m2/s) so deltaP >~ 5.3 * 10-25 kg*m/s. Our carbon (12) atom has a mass of 2 * 10-26 kilograms, so the uncertainty in its velocity is 5.3 * 10-25 / 2 * 10-26 = 26.5 m/s. To put it another way, the zero-point energy it must have in order to be confined in this space is roughly sigmaE = ½*m*v2 = ½*2*10-26 kg * (26.5 m/s)2 = 7 * 10-24 J, which is 500 times less than thermal energy, 4 * 10-21 J, at room temperature. So thermal oscillations generate a greater positional uncertainty than quantum uncertainty does. {JS} Less Technical: The uncertainty principle states that pa
