Causality means that an effect cannot occur from a cause that is not within the back (past) light cone of that event.
We assume that quantum mechanics respects causality.
However, some physicists and mathematicians claim that in some SE solutions the effect may precede the cause, which nature disapproves of.
This can only be one way to solve the SE, while it's easier to go back and look for a solution.
This is exactly what happens even when solving the 1D, 2D and 3D Schrödinger equation via B-matrix statistical chains, while it is better to first assume the potential landscape before solve.
We recall here the revolutionary discovery of the Planck constant h.
The great Max Planck knew in advance the experimental value of h and went backwards from the erroneous formulas of Wiens and Rayleigh to his exact law of Planck's radiation.
The Schrödinger equation doesn't have anything to do with causality. The Schrödinger equation describes the evolution of the states of a system in phase space, where causality doesn't make sense. Causality makes sense in spacetime.
In the non-relativistic approximation, the halfspaces t0 define the past and future respectively, whether in classical, or quantum, mechanics. The only difference is that the space of states is much bigger in quantum mechanics, than in its classical limit.
Considering causality as a linear propagation, from cause to effect, would continue to be accurate even in the solutions in which cause preceded effect if we consider the relativistic nature of reality. In a given scenario within a physical system, there remains a frame of reference. While effect could appear to precede cause from an observer, the linear nature of causality is retained within the reference frame of the object. The solutions in which effect precedes cause, in my understanding, are solutions in which the frame of reference is removed. Thus becoming an observer frame instead of an integrated reference coordinate.
* Observer being defined as any external position outside of the reference frame object being considered
I admire the discussion. Yet, I think that there is another important question which contibututes to the entire picture: how to discriminate between causality and randomness? More precisely, the question is twofold: (i) how to discriminate between causal correlataions and provisional ones. (ii) whether and how the same process gives rise to both causal and random-like events?! In this line I still wonder how and why the fluctuations of any matter are specific to that matter regardless to the fact that all current theories of randomness do not prescribe any specificity. As an example my question is why the fluctuations of water are water?!
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