Is there even something like true randomness? So a few months ago a research team did the following experiment:
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.118.060401
They shot lasers at certain detectors trying to detect the spin of the photons and to prove that there is an underlying hidden variable that influences all of these properties, for which quantum entanglement exists. The measurement of the spin depends on the orientation of the detector. To each detector is a telescope attached and pointing to a 600ly distant star. And based on the wavelengths of the photons that hit the telescope, the detector is reoriented.
So now my question is, is this really random? I mean yes, the photons from the sun were created even before the laser were set up. But since we live all in the same universe, nothing is really COMPLETELY random, just to a certain degree. Isn't bells theorem even a proof that causality doesn't even exist at a certain degree or that true randomness doesn't exist?
 A: Maxim,
In order to understand the motivation behind this experiment a good understanding of the assumptions on which Bell's theorem stands is required. There are two such assumptions:


*

*Locality (there is no instant communication/influence between the particles'source - S and each detector - D1, D2). In other words S does not instantly influence D1 or D2, D1 does not instantly influence D2 or S and D2 does not instantly influence D1 or S. A theory that denies this assumption is a non-local theory. The de Broglie–Bohm interpretation of QM is an example of such theory.

*Independence (the state of D1 and D2, or D1 and S or D2 and S are not correlated as a result of a past common cause). A theory that denies this assumption is a so-called superdeterministic theory. No such theory is currently available in complete form, but 't Hooft's cellular automaton interpretation of QM is a step in this direction.
The experiment you mention tries to put some limits on superdeterministic theories by pushing the hypothetical common cause 600 years into the past. This is not about randomness per se (S, D1 and D2 could each evolve according to a deterministic process) but about the absence of correlations between the states of these devices.
In my opinion the relevance of such an experiment is minimal. We have experimental proof that such common-cause type correlations apply to the gravitational interaction in the case of galaxies for example (the stars in a galaxy do not move independently - they more or less orbit the galactic center) and there is little reason to assume that the electromagnetic interaction which represents the domain of Bell theorem experiments is more limited in this respect. 
A: There is no scientific experimental way to prove absence of causality. Because that would result into a paradox.
For example, causality is - you do this (in given conditions) and so and so will happen.
Any experimental proof, by definition has to be repeatable. If causality did not exist, we could not rely on any experiment including the experiment that disproves causality. Because how do we know that the results are caused by what we did, or by randomness. 
Science itself would become vague in that case.
There is causality.
Randomness refers to "our inability" to compute the exactness, which becomes impossible at certain levels, specially at quantum levels.
Even in classical case, we can compute how long it will take for a pool of water to evaporate, but we can not compute which day/time, a specific water molecule will evaporate. The process is too random that it is beyond our computational capabilities.
Then, when we go too close to computations, we need to measure things too closely and that process could change our computations. For example, poking an entangled particles, ends its entanglement.
