Does this theorem falsify macrorealism?

Aug 2017
Good evening!

Recently I have found this article:

It tells about a no-go theorem which is considered to rule out several forms of macrorealism. The description of the theorem is on the page 9. As authors say, it implies contradiction between macrorealism and predictions of quantum mechanics.

I had some troubles in understanding of mathematical sense of this theorem. However, I don't ask for explaining the steps of it formulation. But it would be great if someone told me whether this theorem is sufficient to falsify macrorealism or it just provides some conditions where macroscopic objects cannot be considered as classical objects?

My question appeared because I thought that we can rule out macrorealism only empirically, for example, by violating Leggett-Garg inequalities. Also we can put the parallel to Bell's inequalities and their violation ruling out local hidden variables. But the authors of this paper seem to tell that macrorealism is already falsified only by their theoretical assumptions. That is why I was confused. I am sure that I missed something in this theorem, that is why I make wrong conclusions.

So, rephrasing my initial question metaphorically:"Does this theorem really prove that, for example, the moon or the table have not macroscopically definable state while one is not observing them?"

I should mention that the question is not about decoherence or measurement problem – it is about implications of concrete theorem.

Thank you in advance!
Jun 2016
I have not read the paper you link to beyond the Abstract,
however I would just like to fire in my own take on this concept.

The state of any object may be defined by a probability function,
I would guess that a normal probability distribution should not be too far from a sensible description of the shape of the function.

I suggest that anything much beyond 5 sigma in such a probability distribution is essentially non-existent.

For a microscopic object 5 sigma represents a vast variation relative to the dimensions of the object.
For a macroscopic object 5 sigma lies well within the noise of the variability of the size of the object (due to random thermal stresses etc, etc).