I understand the second part of this comment to be saying that Jacob & I can reconcile based on the fact that the electron mean free path in metal wires is actually much larger than 1 nm. If that’s what you’re saying, then I disagree.
If the lowest possible interconnect loss is a small multiple of kT/(electron mean free path in the wire), then I claim it’s a coincidence. (I don’t think that premise is true anyway; I think they are off by like 4 OOM or something. I think there is like 6 OOM room for improvement in interconnect loss compared to Jacob’s model, so replacing 1 nm with copper mean free path = 40 nm in Jacob’s model is insufficient to get reconciliation.)
I think that, if there were two metal wires A & B, and wire A had 10× higher density of mobile electrons than B, each with 10× lower effective mass than B, but the electrons in A have 100× lower mean free path than B, then the resistivities of A & B would be the same, and in fact we would not be able to tell them apart at all, and in particular, their energy dissipation upon transmitting information would be the same.
One point of evidence, I claim, is that if I give you a metal wire, and don’t tell you what it’s made of, you will not be able to use normal electrical equipment to measure the electron mean free path for that wire. Whereas if the electron mean free path was intimately connected to electronic noise or binary data transmission or whatever, one might expect that such a measurement would be straightforward.
Oh, no. I just meant to highlight that it was a physically incorrect picture. Metallic conduction doesn’t remotely resemble the “electronic cellular automata” picture, any version of which would get the right answer only accidentally, I agree. A calculation based on information theory would only care about the length scale of signal attenuation.
Even for the purposes of the cellular model, the mean free path is about as unrelated to the positional extent of an electron wavefunction as is the de Broglie wavelength.
I understand the second part of this comment to be saying that Jacob & I can reconcile based on the fact that the electron mean free path in metal wires is actually much larger than 1 nm. If that’s what you’re saying, then I disagree.
If the lowest possible interconnect loss is a small multiple of kT/(electron mean free path in the wire), then I claim it’s a coincidence. (I don’t think that premise is true anyway; I think they are off by like 4 OOM or something. I think there is like 6 OOM room for improvement in interconnect loss compared to Jacob’s model, so replacing 1 nm with copper mean free path = 40 nm in Jacob’s model is insufficient to get reconciliation.)
I think that, if there were two metal wires A & B, and wire A had 10× higher density of mobile electrons than B, each with 10× lower effective mass than B, but the electrons in A have 100× lower mean free path than B, then the resistivities of A & B would be the same, and in fact we would not be able to tell them apart at all, and in particular, their energy dissipation upon transmitting information would be the same.
One point of evidence, I claim, is that if I give you a metal wire, and don’t tell you what it’s made of, you will not be able to use normal electrical equipment to measure the electron mean free path for that wire. Whereas if the electron mean free path was intimately connected to electronic noise or binary data transmission or whatever, one might expect that such a measurement would be straightforward.
Oh, no. I just meant to highlight that it was a physically incorrect picture. Metallic conduction doesn’t remotely resemble the “electronic cellular automata” picture, any version of which would get the right answer only accidentally, I agree. A calculation based on information theory would only care about the length scale of signal attenuation.
Even for the purposes of the cellular model, the mean free path is about as unrelated to the positional extent of an electron wavefunction as is the de Broglie wavelength.