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Manfred 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.