My amateur reading of QED: The Strange Theory of Light and Matter left me with the impression that the universe we live in has self-consistent time travel. Summing over histories involves summing over histories in which particles go back in time.
For example, on page 97, the caption to Figure 63 says
The example in (c) shows a strange but real possibility: the electron emits a photon, rushes backwards in time to absorb a photon, and then continues forwards in time.
Over the page
This phenomenon is general. Every particle in Nature has an amplitude to move backwards in time, and therefore has an anti-particle.
I vaguely assumed that the reason we don’t observe macroscopic time travel drops out of the principle of stationary phase. All the lumps of high amplitude arise from paths such that minor deviations don’t really change the phase, allowing a bunch of similar paths to add coherently. But try to travel back in time and you create a loop. Pull the loop a little tighter and the phase changes a lot. Loops never have stationary phase and the amplitudes of similar paths fail to add coherently, averaging out to pretty well zero.
Several mathematicians I know (and, I would guess, a sizable population of physicists as well) regard Feynman sums-over-histories as mathematical abstractions only. From this perspective they don’t describe processes that are actually happening out-there-in-the-world, they’re just mathematically convenient and maybe also intuitively useful. (I haven’t thought about whether or how this position can be reconciled with what I think is the standard LW position on many-worlds.)
My limited impression of physics is that there is a tendency for mathematically convenient but “not real” descriptions to turn out to be either subtly inaccurate, or to actually correspond to something real. For example, negative frequency photons seem to have some element of reality to them, along with the quantum wave function and virtual particles. I assign some non-trivial probability weight to “either sums over histories are inaccurate descriptions of what happens, or they correspond to something that acts a lot like a real thing”, even when knowledgeable physicists say they aren’t a real thing.
Me too, but almost all of it would be concentrated at “sums over histories are inaccurate descriptions of what happens.” Sums-over-histories are conceptually unsatisfying to me in that they use the classical concept of a history in order to describe quantum phenomena. My vague intuition is that a truer theory of physics would be more “inherently quantum.”
My amateur reading of QED: The Strange Theory of Light and Matter left me with the impression that the universe we live in has self-consistent time travel. Summing over histories involves summing over histories in which particles go back in time.
For example, on page 97, the caption to Figure 63 says
Over the page
I vaguely assumed that the reason we don’t observe macroscopic time travel drops out of the principle of stationary phase. All the lumps of high amplitude arise from paths such that minor deviations don’t really change the phase, allowing a bunch of similar paths to add coherently. But try to travel back in time and you create a loop. Pull the loop a little tighter and the phase changes a lot. Loops never have stationary phase and the amplitudes of similar paths fail to add coherently, averaging out to pretty well zero.
Several mathematicians I know (and, I would guess, a sizable population of physicists as well) regard Feynman sums-over-histories as mathematical abstractions only. From this perspective they don’t describe processes that are actually happening out-there-in-the-world, they’re just mathematically convenient and maybe also intuitively useful. (I haven’t thought about whether or how this position can be reconciled with what I think is the standard LW position on many-worlds.)
My limited impression of physics is that there is a tendency for mathematically convenient but “not real” descriptions to turn out to be either subtly inaccurate, or to actually correspond to something real. For example, negative frequency photons seem to have some element of reality to them, along with the quantum wave function and virtual particles. I assign some non-trivial probability weight to “either sums over histories are inaccurate descriptions of what happens, or they correspond to something that acts a lot like a real thing”, even when knowledgeable physicists say they aren’t a real thing.
Me too, but almost all of it would be concentrated at “sums over histories are inaccurate descriptions of what happens.” Sums-over-histories are conceptually unsatisfying to me in that they use the classical concept of a history in order to describe quantum phenomena. My vague intuition is that a truer theory of physics would be more “inherently quantum.”