John Cramer and transactional interpretation for by far the most prominent example. Wheeler-Feynman absorber theory was the historical precursor; also see “Feynman checkerboard”. Mark Hadley I mentioned. Aharonov-Vaidman for the “two state vector” version of QM, which is in the same territory. Costa de Beauregard was another physicist with ideas in this direction.
This paper is just one place where a potentially significant fact is mentioned, namely that quantum field theory with an imaginary time coordinate (also called “Euclidean field theory” because the metric thereby becomes Euclidean rather than Riemannian) resembles the statistical mechanics of a classical field theory in one higher dimension. See the remark about how “the quantum mechanical amplitude” takes on “the form of a Boltzmann probability weight”. A number of calculations in quantum field theory and quantum gravity actually use Euclideanized metrics, but just because the integrals are easier to solve there; then you do an analytic continuation back to Minkowski space and real-valued time. The holy grail for this interpretation, as far as I am concerned, would be to start with Boltzmann and derive quantum amplitudes, because it would mean that you really had justified quantum mechanics as an odd specialization of standard probability theory. But this hasn’t been done and perhaps it can’t be done.
I think that you mean Euclidean rather than Minkowskian. Euclidean vs Riemannian has to do with whether spacetime is curved (Euclidean no, Riemannian yes), while Euclidean vs Minkowskian has to do with whether the metric treats the time coordinate differently (Euclidean no, Minkowskian yes). (And then the spacetime of classical general relativity, which answers both questions yes, is Lorentzian.)
That is an excellent book even if one ignores the QM part. (In fact, I found that part the weakest, although perhaps I would understand it better now.)
Could you give a couple of keywords/entry points/references for the zig-zag thingie?
John Cramer and transactional interpretation for by far the most prominent example. Wheeler-Feynman absorber theory was the historical precursor; also see “Feynman checkerboard”. Mark Hadley I mentioned. Aharonov-Vaidman for the “two state vector” version of QM, which is in the same territory. Costa de Beauregard was another physicist with ideas in this direction.
This paper is just one place where a potentially significant fact is mentioned, namely that quantum field theory with an imaginary time coordinate (also called “Euclidean field theory” because the metric thereby becomes Euclidean rather than Riemannian) resembles the statistical mechanics of a classical field theory in one higher dimension. See the remark about how “the quantum mechanical amplitude” takes on “the form of a Boltzmann probability weight”. A number of calculations in quantum field theory and quantum gravity actually use Euclideanized metrics, but just because the integrals are easier to solve there; then you do an analytic continuation back to Minkowski space and real-valued time. The holy grail for this interpretation, as far as I am concerned, would be to start with Boltzmann and derive quantum amplitudes, because it would mean that you really had justified quantum mechanics as an odd specialization of standard probability theory. But this hasn’t been done and perhaps it can’t be done.
I think that you mean Euclidean rather than Minkowskian. Euclidean vs Riemannian has to do with whether spacetime is curved (Euclidean no, Riemannian yes), while Euclidean vs Minkowskian has to do with whether the metric treats the time coordinate differently (Euclidean no, Minkowskian yes). (And then the spacetime of classical general relativity, which answers both questions yes, is Lorentzian.)
Also, the book by Huw Price.
That is an excellent book even if one ignores the QM part. (In fact, I found that part the weakest, although perhaps I would understand it better now.)