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DanielVarga comments on Ask an experimental physicist - Less Wrong
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Can photon-photon scattering be harnessed to build a computer that consists of nothing but photons as constituent parts? I am only interested in theoretical possibility, not feasibility. If the question is too terse in this form, I am happy to elaborate. In fact, I have a short writeup that tries to make the question a bit more precise, and gives some motivation behind it.
Well, it depends on what you mean by "nothing but". You can obviously (in principle) make a logic gate of photon beams, but I don't see how you can make a stable apparatus of nothing but photons. You have to generate the light somehow.
NB: Sometimes the qualifier "in principle" is stronger than other times. This one is, I feel, quite strong.
What I mean by "in principle" is not that different from what Fredkin and Toffoli mean by it when talking about their billiard ball computer. The intuition is that when you figured out that some physical system can be harnessed for computation in principle, then you can start working on noise tolerance and energy consumption, and usually it turns out that those are not the show-stopper parts. And when I eventually try to link "in principle" to "in practice", I am still not talking about the scale of human engineering. You say you need to generate light for the system, and a strong gravitational field to trap the photons? I say, fine, I'll rearrange these galaxies into laser guns and gravitational photon traps for you.
Fair enough. I'm just saying, the galaxies aren't made purely of light, so you still don't have a computer of "nothing but" photons. But sure, the logic elements could be purely photonic.
It's an intriguing idea, a pure photon-based gate based on elastic scattering of photons, however I don't see how such a system would function, even in principle. Feel free to elaborate. Also, presumably constructing an equivalent electron- or neutron-based gate would be easier.
I have no idea either. All that I have is a flawed analogy: We could in principle build a computer consisting of nothing but billiard balls as constituent parts. This would work even if meeting billiard balls, instead of bouncing off each other, just changed their trajectories slightly, with a very small probability. I'd like to know whether this crude view of photon-photon scattering is A. a simplification that helps focus on the interesting part of the question, or B. a terrible misunderstanding.
Now I'll tell the original motivation behind the question. As an old LW regular, you have probably seen some phrase like "turn our future light cone into computronium" tossed out during some FAI discussion. What I am interested in is how to actually do that optimally, if you are limited by nothing but the laws of physics. In particular, I am interested in whether the optimal solution involves light-speed (or asymptotically light-speed) expansion, or (for entropy or other considerations) does not actually end up eating the whole light cone.
Obviously this is not my home turf, so maybe it is not even true that the scattering question is relevant at all when we try to answer the computronium question. I would appreciate any insights about either of them or their relationship.
The form of the expansion has very little to do with the form of the computronium.
Launch von Neumann probes at c-ε. They can be tiny, so the energy cost to accelerate them is negligible compared to the energy you can harvest from a new star system. When one arrives, it builds a few more probes and launches them at further stars, then turns all the local matter into computers. The computers themselves don't need to move quickly, since the probes do all the long-distance colonization.
You are right. Originally I became interested in purely photon-based computation because I had an even more speculative idea that seemed to require it. If you have a system that terraforms everything in its path and expands with exactly the speed of light, then you are basically unavailable to outside observation. You can probably see where this line of thought leads. I am aware of the obvious counterargument, but as I explained there, it is a bit weaker than it first appears.
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.
I am quite sure that would be impossible without the balls being constrained by some other forces, such as gravity or outside walls.
You can build outside walls out of billiard balls. Eventually, such a system will disintegrate, but this is no different from any other type of computer. The important thing is that for any given computation length you can build such a system. The size of the system will grow with required computation length, but only polynomially.
I would be interested in seeing a metastable gate constructed solely out of billiard balls. Care to come up with a design?
Ah, now I see your point. I had this misconception that if you send a billiard ball into a huge brick-wall of billiard balls, it will bounce back. Okay, I don't have a design.
It sure will, after imparting some momentum to the wall. My point is that I do not know how to construct a gate out of components interacting only through repulsive forces. I am not saying that it is impossible, I just do not see how it can be done.
How much momentum will it lose before it bounces back? If a large enough wall can make this arbitrarily small, then I think the Fredkin and Toffoli billiard gates can be built out of a thick wall of billiard balls. Lucky thing, in this model there is no friction, so gates can be arbitrarily large. Sure, the system might start to misbehave after the walls move by epsilon, but this doesn't seem like a serious problem. In the worst case, we can use throw-away gates that are abandoned after one use. That model is still as strong as Boolean circuits.