I’ve given it some thought, yes. Nanosystems proposes something like what you describe. During its motion, the rod is supposed to be confined to its trajectory by the drive mechanism, which, in response to deviations from the desired trajectory, rapidly applies forces much stronger than the net force accelerating the rod.
But the drive mechanism is also vibrating. That’s why I mentioned the fluctuation-dissipation theorem—very informally, it doesn’t matter what the drive mechanism looks like. You can calculate the noise forces based on the dissipation associated with the positional degree of freedom.
There’s a second fundamental problem in positional uncertainty due to backaction from the drive mechanism. Very informally, if you want your confining potential to put your rod inside a range Δx with some response speed (bandwidth), then the fluctuations in the force obey ΔxΔF≥ℏ/2×bandwidth, from standard uncertainty principle arguments. But those fluctuations themselves impart positional noise. Getting the imprecision safely below the error threshold in the presence of thermal noise puts backaction in the range of thermal forces.
Sorry for the previous comment. I misunderstood your original point.
My original understanding was, that the fluctuation-dissipation relation connects lossy dynamic things (EG, electrical resistance, viscous drag) to related thermal noise (Johnson–Nyquist noise, Brownian force). So Drexler has some figure for viscous damping (essentially) of a rod inside a guide channel and this predicts some thermal W/Hz/(meter of rod) spectral noise power density. That was what I thought initially and led to my first comment. If the rods are moving around then just hold them in position, right?
This is true but incomplete.
But the drive mechanism is also vibrating. That’s why I mentioned the fluctuation-dissipation theorem—very informally, it doesn’t matter what the drive mechanism looks like. You can calculate the noise forces based on the dissipation associated with the positional degree of freedom.
You pointed out that a similar phenomenon exists in *whatever* controls linear position. Springs have associated damping coefficients so the damping coefficient in the spring extension DOF has associated thermal noise. In theory this can be zero but some practical minimum exists represented by EG:”defect-free bulk diamond” which gives some minimum practical noise power per unit force.
Concretely, take a block of diamond and apply the max allowable compressive force. This is the lowest dissipation spring that can provide that much force. Real structures will be much worse.
Going back to the rod logic system, if I “drive” the rod by covalently bonding one end to the structure, will it actually move 0.7 nm? (C-C bond length is ~0.15 nm. linear spring model says bond should break at +0.17nm extension (350kJ/mol, 40n/m stiffness)). That *is* a way to control position … so if you’re right, the rod should break the covalent bond. My intuition is thermal energy doesn’t usually do that.
What are the the numbers you’re using?(bandwidth, stiffness, etc.)?
Does your math suggest that in the static case rods will vibrate out of position? Maybe I’m misunderstanding things.
During its motion, the rod is supposed to be confined to its trajectory by the drive mechanism, which, in response to deviations from the desired trajectory, rapidly applies forces much stronger than the net force accelerating the rod.
(Nanosystems PP344 (fig 12.2)
Having the text in front of me now, the rods supposedly have “alignment knobs” which limit range of motion. The drive springs don’t have to define rod position to within the error threshold during motion.
The knob<-->channel contact could be much more rigid than the spring, depending on interatomic repulsion. That’s a lot closer to the “covalently bond the rod to the structure” hypothetical suggested above. If the dissipation-fluctuation based argument holds, the opposing force and stiffness will be on the order of bond stiffness/strength.
There’s a second fundamental problem in positional uncertainty due to backaction from the drive mechanism. Very informally, if you want your confining potential to put your rod inside a range Δx with some response speed (bandwidth), then the fluctuations in the force obey ΔxΔF≥ℏ/2×bandwidth, from standard uncertainty principle arguments. But those fluctuations themselves impart positional noise. Getting the imprecision safely below the error threshold in the presence of thermal noise puts backaction in the range of thermal forces.
When I plug the hypothetical numbers into that equation (10Ghz, 0.7nm) I get force deviations in the fN range (1.5e-15 N) that’s six orders of magnitude from the nanonewton range forces proposed for actuation. This should Accommodate using the pessimistic “characteristic frequency of rod vibration”(10Thz) along with some narrowing of positional uncertainty.
That aside, these are atoms. De Broglie wavelength for a single carbon atom at room temp is 0.04 nm and we’re dealing with many carbon atoms bonded together. Quantum mechanical effects are still significant?
If you’re right, and if the numbers are conservative with real damping coefficients 3 OOM higher, forces would be 1.5 OOM higher meaning covalent bonds hold things together much less well. This seems wrong. Benzyl groups would seem then to regularly fall off of rigid molecules for example. Perhaps the rods are especially rigid leading to better coupling of thermal noise into the anchoring bond at lower atom counts?
Certainly if drexler’s design is impossible by 3 orders of magnitude rod logic would perform much less well.
No worries, my comment didn’t give much to go on. I did say “a typical thermal displacement of a rod during a cycle is going to be on the order of the 0.7nm error threshold for his proposed design”, which isn’t true if the mechanism works as described. It might have been better to frame it as—you’re in a bad situation when your thermal kinetic energy is on the order of the kinetic energy of the switching motion. There’s no clean win to be had.
If the positional uncertainty was close to the error limit, can we just bump up the logic element size(2x, 3x, 10x)? I’d assume scaling things up by some factor would reduce the relative effects of thermal noise and uncertainty.
That’s correct, although it increases power requirements and introduces low-frequency resonances to the logic elements.
Also, the expression ( ΔxΔF≥ℏ/2×bandwidth ) suggests the second concern might be clock rate?
In this design, the bandwidth requirement is set by how quickly a blocked rod will pass if the blocker fluctuates out of the way. If slowing the clock rate 10x includes reducing all forces by a factor of 100 to slow everything down proportionally, then yes, this lets you average away backaction noise like √10 while permitting more thermal motion. If you keep making everything both larger and slower, it will eventually work, yes. Will it be competitive with field-effect transistors? Practically, I doubt it, but it’s harder to find in-principle arguments at that level.
That noted, in this design, (I think) a blocked rod is tensioned with ~10x the switching drive force, so you’d want the response time of the restoring force to be ~10 ps. If your Δx is the same as the error threshold, then you’re admitting error rates of 10−1. Using (100 GHz, 0.07 nm [Drexler seems to claim 0.02nm in 12.3.7b]), the quantum-limited force noise spectral density is a few times less than the thermal force noise related to the claimed drag on the 1GHz cycle.
What I’m saying isn’t that the numbers in Nanosystems don’t keep the rod in place. These noise forces are connected with displacement noise by the stiffness of the mechanism, as you observe. What I’m saying is that these numbers are so close to quantum limits that they can’t be right, or even within a couple of orders of magnitude of right. As you say, quantum effects shouldn’t be relevant. By the same token, noise and dissipation should be far above quantum limits.
Yeah, transistor based designs also look promising. Insulation on the order of 2-3 nm suffices to prevent tunneling leakage and speeds are faster. Promises of quasi-reversibility, low power and the absurdly low element size made rod logic appealing if feasible. I’ll settle for clock speeds a factor of 100 higher even if you can’t fit a microcontroller in a microbe.
My instinct is to look for low hanging design optimizations to salvage performance (EG: drive system changes to make forces on rods at end of travel and blocked rods equal reducing speed of errors and removing most of that 10x penalty.) Maybe enough of those can cut the required scale-up to the point where it’s competitive in some areas with transistors.
But we won’t know any of this for sure unless it’s built. If thermal noise is 3OOM worse than Drexler’s figures it’s all pointless anyways.
I remain skeptical the system will move significant fractions of a bond length if a rod is held by a potential well formed by inter-atomic repulsion on one of the “alignment knobs” and mostly constant drive spring force. Stiffness and max force should be perhaps half that of a C-C bond and energy required to move the rod out of position would be 2-3x that to break a C-C bond since the spring can keep applying force over the error threshold distance. Alternatively the system *is* that aggressively built such that thermal noise is enough to break things in normal operation which is a big point against.
I’ve given it some thought, yes. Nanosystems proposes something like what you describe. During its motion, the rod is supposed to be confined to its trajectory by the drive mechanism, which, in response to deviations from the desired trajectory, rapidly applies forces much stronger than the net force accelerating the rod.
But the drive mechanism is also vibrating. That’s why I mentioned the fluctuation-dissipation theorem—very informally, it doesn’t matter what the drive mechanism looks like. You can calculate the noise forces based on the dissipation associated with the positional degree of freedom.
There’s a second fundamental problem in positional uncertainty due to backaction from the drive mechanism. Very informally, if you want your confining potential to put your rod inside a range Δx with some response speed (bandwidth), then the fluctuations in the force obey ΔxΔF≥ℏ/2×bandwidth, from standard uncertainty principle arguments. But those fluctuations themselves impart positional noise. Getting the imprecision safely below the error threshold in the presence of thermal noise puts backaction in the range of thermal forces.
Sorry for the previous comment. I misunderstood your original point.
My original understanding was, that the fluctuation-dissipation relation connects lossy dynamic things (EG, electrical resistance, viscous drag) to related thermal noise (Johnson–Nyquist noise, Brownian force). So Drexler has some figure for viscous damping (essentially) of a rod inside a guide channel and this predicts some thermal W/Hz/(meter of rod) spectral noise power density. That was what I thought initially and led to my first comment. If the rods are moving around then just hold them in position, right?
This is true but incomplete.
You pointed out that a similar phenomenon exists in *whatever* controls linear position. Springs have associated damping coefficients so the damping coefficient in the spring extension DOF has associated thermal noise. In theory this can be zero but some practical minimum exists represented by EG:”defect-free bulk diamond” which gives some minimum practical noise power per unit force.
Concretely, take a block of diamond and apply the max allowable compressive force. This is the lowest dissipation spring that can provide that much force. Real structures will be much worse.
Going back to the rod logic system, if I “drive” the rod by covalently bonding one end to the structure, will it actually move 0.7 nm? (C-C bond length is ~0.15 nm. linear spring model says bond should break at +0.17nm extension (350kJ/mol, 40n/m stiffness)). That *is* a way to control position … so if you’re right, the rod should break the covalent bond. My intuition is thermal energy doesn’t usually do that.
What are the the numbers you’re using?(bandwidth, stiffness, etc.)?
Does your math suggest that in the static case rods will vibrate out of position? Maybe I’m misunderstanding things.
Having the text in front of me now, the rods supposedly have “alignment knobs” which limit range of motion. The drive springs don’t have to define rod position to within the error threshold during motion.
The knob<-->channel contact could be much more rigid than the spring, depending on interatomic repulsion. That’s a lot closer to the “covalently bond the rod to the structure” hypothetical suggested above. If the dissipation-fluctuation based argument holds, the opposing force and stiffness will be on the order of bond stiffness/strength.
When I plug the hypothetical numbers into that equation (10Ghz, 0.7nm) I get force deviations in the fN range (1.5e-15 N) that’s six orders of magnitude from the nanonewton range forces proposed for actuation. This should Accommodate using the pessimistic “characteristic frequency of rod vibration”(10Thz) along with some narrowing of positional uncertainty.
That aside, these are atoms. De Broglie wavelength for a single carbon atom at room temp is 0.04 nm and we’re dealing with many carbon atoms bonded together. Quantum mechanical effects are still significant?
If you’re right, and if the numbers are conservative with real damping coefficients 3 OOM higher, forces would be 1.5 OOM higher meaning covalent bonds hold things together much less well. This seems wrong. Benzyl groups would seem then to regularly fall off of rigid molecules for example. Perhaps the rods are especially rigid leading to better coupling of thermal noise into the anchoring bond at lower atom counts?
Certainly if drexler’s design is impossible by 3 orders of magnitude rod logic would perform much less well.
No worries, my comment didn’t give much to go on. I did say “a typical thermal displacement of a rod during a cycle is going to be on the order of the 0.7nm error threshold for his proposed design”, which isn’t true if the mechanism works as described. It might have been better to frame it as—you’re in a bad situation when your thermal kinetic energy is on the order of the kinetic energy of the switching motion. There’s no clean win to be had.
That’s correct, although it increases power requirements and introduces low-frequency resonances to the logic elements.
In this design, the bandwidth requirement is set by how quickly a blocked rod will pass if the blocker fluctuates out of the way. If slowing the clock rate 10x includes reducing all forces by a factor of 100 to slow everything down proportionally, then yes, this lets you average away backaction noise like √10 while permitting more thermal motion. If you keep making everything both larger and slower, it will eventually work, yes. Will it be competitive with field-effect transistors? Practically, I doubt it, but it’s harder to find in-principle arguments at that level.
That noted, in this design, (I think) a blocked rod is tensioned with ~10x the switching drive force, so you’d want the response time of the restoring force to be ~10 ps. If your Δx is the same as the error threshold, then you’re admitting error rates of 10−1. Using (100 GHz, 0.07 nm [Drexler seems to claim 0.02nm in 12.3.7b]), the quantum-limited force noise spectral density is a few times less than the thermal force noise related to the claimed drag on the 1GHz cycle.
What I’m saying isn’t that the numbers in Nanosystems don’t keep the rod in place. These noise forces are connected with displacement noise by the stiffness of the mechanism, as you observe. What I’m saying is that these numbers are so close to quantum limits that they can’t be right, or even within a couple of orders of magnitude of right. As you say, quantum effects shouldn’t be relevant. By the same token, noise and dissipation should be far above quantum limits.
Yeah, transistor based designs also look promising. Insulation on the order of 2-3 nm suffices to prevent tunneling leakage and speeds are faster. Promises of quasi-reversibility, low power and the absurdly low element size made rod logic appealing if feasible. I’ll settle for clock speeds a factor of 100 higher even if you can’t fit a microcontroller in a microbe.
My instinct is to look for low hanging design optimizations to salvage performance (EG: drive system changes to make forces on rods at end of travel and blocked rods equal reducing speed of errors and removing most of that 10x penalty.) Maybe enough of those can cut the required scale-up to the point where it’s competitive in some areas with transistors.
But we won’t know any of this for sure unless it’s built. If thermal noise is 3OOM worse than Drexler’s figures it’s all pointless anyways.
I remain skeptical the system will move significant fractions of a bond length if a rod is held by a potential well formed by inter-atomic repulsion on one of the “alignment knobs” and mostly constant drive spring force. Stiffness and max force should be perhaps half that of a C-C bond and energy required to move the rod out of position would be 2-3x that to break a C-C bond since the spring can keep applying force over the error threshold distance. Alternatively the system *is* that aggressively built such that thermal noise is enough to break things in normal operation which is a big point against.
Just to follow up, I spell out an argument for a lower bound on dissipation that’s 2-3 OOM higher in Appendix C here.