Layman here. It is often said that the pure fundamental theories do not contain any arrow of time, they are fully reversible in time.(adsbygoogle = window.adsbygoogle || []).push({});

But regarding Shrodinger's equation, it describes the evolution of the wavefunction in time. As I understand it, if we consider a static particle after a measurement, let's say event A, its wavefunction will start spreading from that spacetime event location in a spherical shape at the speed of light until it undergoes a new measurement, at which the wavefunction sphere will collapse at some point given probabilistically by the equation.

Is such a sphere expanding at light speed truly spherical, pointing also towards the past as well as to the future? So that there would be a probability of the next measurement finding that particle in a spacetime coordinate which lies in the past of event A, as much as finding it in a spacetime coordinate which lies in the future of event A?

Because if the answer is no, that the wavefunction evolution is not really a sphere, but only a hemisphere from event A towards the future but not towards the past, wouldn't it mean that the very arrow of time is already contained in such a wavefunction evolution equation? Selecting that only coordinates in the future can be canditates to finding the particle from event A, but never coordinates in the past?

Thanks !

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# I Does the wavefunction evolve only to the future?

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