Published claimed falsifications of objective collapse theories

My main source of information about objective collapse theories is this review article by Bassi et al. There seem to be some problems with the theory that its practitioners readily admit to, such as being incompatible with relativity and not having exact conservation of energy. However, it does seem interesting because it evades Gisin’s and Kapustin’s no-go theorems for nonlinear quantum mechanics, and it can be used as a test theory for designing and interpreting experimental tests of quantum mechanics, such as TEQ.

Poking around on the internet led me to some blog posts by Lubos Motl in which he claims to have two simple arguments that trivially falsify objective collapse theories. I don’t want to provide a link, because these posts use vituperative language, and I don’t think that should be encouraged by driving traffic to his blog or increasing his google page rank. I also don’t think his arguments seem sufficiently detailed to be compelling. What I’m interested in is whether there are any published papers developing such arguments.

One of the arguments seems to be that the existence of collective states in condensed matter physics falsifies the theory. Bassi’s review paper explicitly discusses this on p. 24, but without giving any reference and without indicating that anyone actually considers this a falsification of the theory.

The other argument is that all realist theories, including objective collapse theories, predict the wrong heat capacities for matter. The argument seems to me like a reasonable one if the theory we want to disprove is some kind of 1900 classical theory of the planetary atom, but the leap to a claimed disproof of objective collapse — or even all realist theories — seems insufficiently developed to be convincing.

Are there any actual published papers expressing similar opinions that objective collapse is already falsified?