As explained 893 times on this blog, quantum mechanics has replaced, refused, and retired a basic assumption of classical physics, realism, while it has kept the principles of relativity, the Lorentz invariance, and the locality that follows from them.
So we have theories of nearly everything – quantum field theories – and a likely theory of everything – string theory – that predict that the behavior of physics objects in the Minkowski space is perfectly local and Lorentz-invariant but the required correct description cannot be realist. Instead, quantum mechanics is a set of laws of Nature that must be applied on a set of intrinsically subjective observations by an observer – and the precise description of a process generally does depend on whom we consider an observer and what are his observations, on answers that must be given and "inserted" to the quantum mechanical black box before the final calculations of quantum mechanics are made.
Quantum mechanics has been disputed by folks like Einstein, de Broglie, and Schrödinger from the beginning. However, the particular set of facts in the previous two paragraphs began to be obfuscated with the works of John Bell who proved a correct theorem – but started to draw completely incorrect consequences out of it and encouraged many other people to do the same.
The theorem shows that "local realist theories" cannot agree with the observations because those sometimes show greater correlations than the correlations obeying Bell's inequalities, an inevitable consequence of "local realist theories". So far so good. But Bell incorrectly suggested – and many mindless, totally deluded people repeated – that the resolution is that the world is realist but non-local.
As has been known since the very moment when the first papers about quantum mechanics were written in 1925, the correct answer is exactly opposite. (Ignoring quantum gravitational phenomena to be sure,) Nature is local but non-realist. Local realist theories may be ruled out. But many well-defined classes of non-local realist theories may be ruled out, too. It's the realism that is wrong.
This claim – realism is wrong – is something perfectly understood by everyone who has understood at least one legitimate founding paper on quantum mechanics or at least one legitimate textbook or a course on quantum mechanics. It's simply a defining point of quantum mechanics that its description always depends on the choice of an observer and the pre-defined meaning of observations. But it may also be substantiated from the partly theory-independent perspective of those who "haven't learned quantum mechanics correctly" or those "who don't want to depend on the assumptions of that theory" (although it's never possible to do any physics without any assumptions).
In 2007, I described a paper by Zeilinger et al. that had excluded a large number of non-local realist theories.
Now, in Summer 2016, we have another one which was rather meaningfully summarized in Live Science:
But the rest of the article is mostly very reasonable and corrects lots of the myths. For example, a physicist named Pienaar of Vienna is allowed to propose to "retire" Bell's inequalities that many people are irrationally obsessed with. The new paper we're talking about is one by Martin Ringbauer et al. in Science Advances:
I always find the "experimental" character of such papers silly. It's obvious what is gonna be observed in any experiment like that. If simple experiments with several photons were incorrectly predicted by quantum mechanics, we would have surely found out already. So there is no need to do the experiments or their small variations all the time and the controversy is always only about the right interpretation of the theory and its predictions and it's a theorist's job. So the very fact that the title starts with the word "experimental" is weird.
But these experimenters still understand something about quantum mechanics much more correctly than the realist would-be theorists even though they use a somewhat unusual language for some of those things.