gill1109 wrote:Physics does not say that past and future both contain particles and waves. That is your interpretation of mathematics which the physicists have found useful. The fact is that we human beings experience time going in a rather definite direction, and moreover, in the lab, we see an electron choosing one of the two possible paths out of the Stern-Gerlach device. QM tells us the probability it will go each way.

Complex analysis is a wonderful tool. I think you are wrong to think that the pictures we can draw in complex analysis are pictures of what is actually going on in the real world. We do not live in complex Hilbert space. We live in houses and we work in laboratories. We experience a "real" world in which random things happen. Fortunately we have found out how to compute the probability of those random events, and moreover to harness the possibilities which QM offers for exciting applications (technologies).

In all scales we use e.g. time/CPT symmetric Lagrangian mechanics: from QFT to GR - what means that past and future are conceptually the same, not completely different: one particles, second waves. Wave-particle duality also says they are both. If you want to use some made up asymmetries, please at least give any argument.

Imagine general relativity: we live in spacetime satisfying Einstein's equation for intrinsic curvature.

Particles are their trajectories there - what happens with them when passing "present moment"?

Where exactly is this "present moment"? Remember that, starting with special relativity, hyperplane of constant time is no longer objective - depends on velocity of observer.

Regarding complex analysis, I also see it only as a tool - e.g. to represent periodic processes, or vector fields in 2D. Here I meant the latter.

We know that charge is quantized in nature, Gauss law "counts" charge inside a region - it should only return integer values.

However, standard Gauss law allows for any real charge instead - we need to repair it, and it can be done analogously to the argument principle: by using topological charge and Gauss-Bonnet theorem - saying that integrating curvature of vector field over a closed surface we get topological charge inside - which has to be integer.