Are "timed" measurements actually revealing error-distributions of the measurement apparati? A thought experiment:
Given some object moving (swinging) from left to right and back with constant velocity, imagine a camera set up to take a picture of the scene at a fixed interval so that we can expect the object to be in the center.
Now "the perfect"/expected scenario would be: in every picture taken the object is found at the same place.
In reality what we probably get is a distribution: in some pictures the object more or less slightly left or right of the center even though in most pictures the object is really centered.
That's quite resembling to the position measurements we do at small levels which come up with "distributions" and "probabilities" for positional (and other) information of atoms or electrons for example.
Now, why are those distributions believed to be properties of the measured entities? Why can't they "simply" be explained by inexact timing of the camera triggers in the example above? The results would be the same, right?
Or would they? I'm a layman so most probably I missed something profound and would like to know what ;)
Thanks in advance
Cheers
 A: See this, if by probability you mean quantum mechanical expectation value.
If you're referring to classical probability distributions, for example in statistical physics, then the answer is that we can actually observe the the fluctuating states with high precision in certain circumstances.  If you use a high-speed camera then you can actually see for example, Brownian motion. The particles are very clearly moving in a stochastic fashion; you can view them with respect to a fixed reference if you wish. It's not as if you just have a few snapshots and you can't tell if it's the camera or the particle that's responsible.
That being said, it is certainly true that measurement error is convoluted with the intrinsic variability in a problem; the fluctuations that you observe are a due to the sum (in quadrature) of the measurement error and the system's real, physical, fluctuations. So, if you want to measure the fluctuations in a physical observable, then you need higher precision experiments than you would need if you only want to measure the mean of that observable.
