The discussion centers on the Klein-Gordon (KG) equation and its implications for relativistic causality, particularly concerning superluminal phase velocities. Participants argue that while signals cannot travel at phase velocity, they can influence spacelike-separated events through group velocities. The conversation highlights the necessity of proving that contributions from various wave components cancel out at spacelike intervals, referencing the Green function's properties. The mathematical framework includes the massless KG equation and the role of Fourier transforms in analyzing wave behavior.
PREREQUISITESPhysicists, mathematicians, and students studying quantum field theory, particularly those interested in the implications of the Klein-Gordon equation on wave propagation and causality.
It would be nice if you could present details of an example were the Sommerfeld's argument can be applied.vanhees71 said:Here Sommerfeld's argument cannot be applied ...
I'm not sure what exactly is the Sommerfeld's argument, but there is a very general proof inAvodyne said:I continue to claim that the inapplicability of Sommerfeld's argument is due to the form of the KG dispersion relation (with branch points on the real axis), and not due to the singular initial condition.
Argh, I've not seen this posting. It's indeed identical. Sorry for that.Demystifier said:@vanhees71, have you noticed that your proof in #28 is almost identical to my proof in #21?