[SEQ RERUN] Joint Configurations
Today’s post, Joint Configurations was originally published on 11 April 2008. A summary (taken from the LW wiki):
The laws of physics are inherently over mathematical entities, configurations, that involve multiple particles. A basic, ontologically existent entity, according to our current understanding of quantum mechanics, does not look like a photon—it looks like a configuration of the universe with “A photon here, a photon there.” Amplitude flows between these configurations can cancel or add; this gives us a way to detect which configurations are distinct. It is an experimentally testable fact that “Photon 1 here, photon 2 there” is the same configuration as “Photon 2 here, photon 1 there”.
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This post is part of the Rerunning the Sequences series, where we’ll be going through Eliezer Yudkowsky’s old posts in order so that people who are interested can (re-)read and discuss them. The previous post was http://lesswrong.com/lw/bb7/seq_rerun_configurations_and_amplitude/, and you can use the sequence_reruns tag or rss feed to follow the rest of the series.
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From what I understand of quantum physics, it doesn’t seem that it’s so much that reality doesn’t track photons separately, as that you will always be equally likely to be using photon B and photon C. There’s no way to tell the difference between the two, and they always have exactly the same waveform to begin with.
When you use second quantization (a quantum theory with the ability to create or destroy particles), the notion of particle identity evaporates. Second quantization is a crucial element of the most fundamental theories.
If you’re using a quantum theory without using second quantization, you follow certain rules—symmetrization or antisymmetrization—that make it look like what you said. Symmetrization and antisymmetrization are also a part of theories with second quantization, but they no longer look like that.
They’re just different ways of saying the same math. However, if you represent identical particles as a symmetrized wavefunction, photon emission and absorption becomes a huge pain. It’s sooo much simpler (in a Occam’s razor sort fo sense) to just say that rather than keeping track of photons, the universe keeps track of “photon,” which is a sort of substance (well, it’s a field—the quantum electromagnetic field).
The position of a particle is a dimension in configuration space.
It seems mathematically simpler to do math in a space where the dimensions are distinct. That is, dealing with stuff like (1,0) and (0,1), rather than {0,1}, which is zero in one dimension and one in the other, in no particular order. Thinking about that, it might just be the same. That’s just with bozons though. With fermions Ψ(1,0) = -Ψ(0,1). It has a weird parity thing. That seems easier to work with if it’s a symmetry.
It seems feasible that you know more quantum physics than me, and it will look more like there being only one particle than a symmetry if I learn more. I know how the Schrödinger equation works with entangled particles and all the conceptual stuff on the quantum physics sequence, and that’s about it.
Well, the big trick is that photons really are excitation of the electromagnetic field, just like in classical mechanics. But at low energies the field is quantized, just like a harmonic oscillator. And we associate these quantized chunks of electromagnetic energy with particles. But it turns out that you still have to ask the question “what does the electromagnetic field look like with two photons?” The electromagnetic field is more “real” than the photons.
Isn’t it always quantized?
Is the answer “the same as with one photon, except with six dimensions instead of three”?
I thought those were pretty much the same way of saying the two things.