The difference I see between photons and your example with billiard balls is that billiard balls have a rest frame. In other words, you can set them up so that they have no preexisting motion relative to you, and any change in their positions is due to your inputs. You can’t do this with photons in a vacuum; they are massless, and must always move at c.
Photon-photon scattering is also a rare process in quantum electrodynamics. If you look at the Feynman diagram:
It has four vertices. Each vertex gives the cross-section of the process another factor of the fine structure constant α, which is a small number, about 1⁄137. A process like electron-electron or electron-positron scattering, on the other hand, has diagrams with only two vertices, so only two factors of α. (Of course, cross-sections also depend on mass, momentum, and so forth, but this gives a very simple heuristic for comparing processes.) The additional factor of α² ~ 0.00005 makes the cross section tiny compared to common QED processes.
If you want to use photons for computing, photonic crystals are your best bet, although the technology is still in early stages of development.
I don’t know much about photon-photon scattering, but I do know that the cross section is very small. I see this as something that does not make a difference from a strictly theoretical point of view, but that might be because I don’t understand the issues. Photonic crystals are not really relevant for my thought experiments, because you definitely can’t build computers out of them that expand with the asymptotic speed of light. Maybe if you can turn regular material into photonic crystal by bombarding it with photons.
If two billiard balls come to occupy an overlapping volume in space at the same time, they will collide with probability (1 - ε) for ε about as small as we can imagine. However, photons will only scatter off each other rarely. Photons are bosons, so the vast majority of the time, they will just pass right through each other. That doesn’t give you a dependable logic gate.
Maybe you are right, but it is not immediately obvious to me that small cross-section is a deadly problem. You shouldn’t look at one isolated photon-photon encounter as a logic gate. Even an ordinary electronic transistor would not work without error correction. Using error correction, you can build complex systems that seem like magic when you attempt to understand them at the level of individual electrons.
The difference I see between photons and your example with billiard balls is that billiard balls have a rest frame. In other words, you can set them up so that they have no preexisting motion relative to you, and any change in their positions is due to your inputs. You can’t do this with photons in a vacuum; they are massless, and must always move at c.
Photon-photon scattering is also a rare process in quantum electrodynamics. If you look at the Feynman diagram:
It has four vertices. Each vertex gives the cross-section of the process another factor of the fine structure constant α, which is a small number, about 1⁄137. A process like electron-electron or electron-positron scattering, on the other hand, has diagrams with only two vertices, so only two factors of α. (Of course, cross-sections also depend on mass, momentum, and so forth, but this gives a very simple heuristic for comparing processes.) The additional factor of α² ~ 0.00005 makes the cross section tiny compared to common QED processes.
If you want to use photons for computing, photonic crystals are your best bet, although the technology is still in early stages of development.
I don’t know much about photon-photon scattering, but I do know that the cross section is very small. I see this as something that does not make a difference from a strictly theoretical point of view, but that might be because I don’t understand the issues. Photonic crystals are not really relevant for my thought experiments, because you definitely can’t build computers out of them that expand with the asymptotic speed of light. Maybe if you can turn regular material into photonic crystal by bombarding it with photons.
If two billiard balls come to occupy an overlapping volume in space at the same time, they will collide with probability (1 - ε) for ε about as small as we can imagine. However, photons will only scatter off each other rarely. Photons are bosons, so the vast majority of the time, they will just pass right through each other. That doesn’t give you a dependable logic gate.
Maybe you are right, but it is not immediately obvious to me that small cross-section is a deadly problem. You shouldn’t look at one isolated photon-photon encounter as a logic gate. Even an ordinary electronic transistor would not work without error correction. Using error correction, you can build complex systems that seem like magic when you attempt to understand them at the level of individual electrons.