What does the path integral randomize in position measurements?

[LarryS]

In all Quantum Physics experiments, the sequence of measurement results is inherently random.

Consider just the position observable.

In the Schrödinger picture of non-relativistic QM, in each measurement-event, nature steps in and randomly selects one of the observable's eigenvalues/vectors to be the measurement result.

In the non-relativistic version of the Path Integral Formulation, what exactly is nature randomizing when a position measurement occurs? The space-time end point of a path? The entire path (beginning point and ending point)?

Thanks in advance.

 

[atyy]

The things that are not random in quantum theory are the averages (and generalizations of the average such as the higher order moments or cumulants).

The path integral computes the averages. So in one sense, there is no randomness in the path integral.

The full probability distribution can be recovered from all moments or all the cumulants. Thus these deterministic quantities fully specify the randomness,

 

[LarryS]

The path integral computes the averages.

By "averages" do you mean the single probability amplitude of the particle transitioning from one space-time point to a future space-time point?