Dear Elliot,
As promised, I will reply here for the sake of readability.
Having experienced bad things due to a „heroic thinking leader of a nation", I do not share the widespread desire to idolize people. On the contrary, I suspected Minkowski was not as sure as he pretended to be about his two symmetrical cones.
I agree that the laws of physics will certainly be valid for future time as they obviously were for past time too, at least as far we can judge from all experience available to us. However, the naked laws alone do not yet represent the world. At least equally important are the so called influences, coefficients, and some restrictions that went astray when the originally integral relationships were reduced to differential equations. There are no influences from future, and we have to exclude unphysical mathematical solution, in particular advanced ones.
While Schwarzschild himself did not interpret his odd solutions as anti-worlds, I see so called Rosen-bridge marking the broken border between serious work and slippery fiction.
What about manipulations including time reversal, this is only possible for abstract time:
Differential equations like L d^2 i(t)/dt^2+ R di(t)/dt + 1/C i(t) = 0 have two solutions. One is the reasonable retarded one. The other one increases with growing time and must therefore be excluded. For R=0 both solutions coincide, i.e., i(t)=i(-t).
In reality, future will rarely exactly mirror the past. Perfect T-symmetry rather indicates the unavoidable redundancy within a complex time-domain.
Those who are still reluctant to swallow that there is a natural origin zero of elapsed time not just in the real world but also in any anticipated future might get aware that t in any calculated function f(t) is never larger than t.
Your baeztime-quote mentioned Zeh who right now and here takes issue against putatively superluminal tunneling.
Why are you not ready to accept that complex numbers are mathematical tools rather than something with a particular meaning in reality? They do not suddenly pop out. Except for heuristics, one should know what one does. Well, x+iy denotes a possible complex plane. However, do you need the imaginary unit in order to express the orthogonality between x and y or between x and z or between y and z? Incidentally, the functions sin(wt) and sin(3wt) also fulfill the condition for orthogonality.
You repeatedly quoted Einstein: "One has to keep in mind that the fourth coordinate u is always purely imaginary". Isn't this rather a matter of taste? Does a builder need the imaginary unit as to measure (3 m)^2 + (4 m)^2 = (5 m)^2?
Again, I cannot confirm that ict is based on a transform into either complex time domain or complex frequency domain. While omega and t constitute a Fourier transform pair as well as a cosine transform pair, c is constant.
Nonetheless, I expect the unilateral imaginary fourth coordinate of possibly connected location to be similar to some extent to imaginary resistance, which cannot be transformed back into reality but has a non-fundamental physical meaning among other mutually related quantities. The different signs of imaginary resistance correspond to contrary physical phenomena.
Regards,
Eckard