I’m sorry, but this article just adds to my impression that Feynman, Weinberg, and Hawking are right about the usefulness of philosophy in science. So far as I can tell, none of the “theories” discussed in it has any real content.
Right now I have memories which include the memory of not having memories of some “more recent” events and of, within those memories, having memories which include the memory of remembering even fewer events. It turns out that this pattern of successively smaller sets of memories of memories defines a linear ordering of all my memories. I call the direction towards smaller memory sets my past and the direction from any past memory towards the present the future of that past. (I have no actual knowledge of any future now, but my past memories all had futures and I choose to act as if that pattern “will” continue.)
From those observations alone it does not follow that I will find other beings who have similar patterns of memory, but in fact I have done so (along with evidence that similar beings existed “prior” to my own earliest memory) – and none of us have seen any evidence of beings with a similarly defined sense of past direction that differs from my own. (For many centuries of our shared experience it appeared that we all shared a common “present” but more precise observations have established that that is only possible for beings not moving too rapidly relative to one another. However nothing has been observed which is inconsistent with us all seeing the “past” in the same direction.) A number of physical phenomena are observed to behave symmetrically between past and future but others definitely do not, and in those cases there are fairly simple rules which seem to predict which of two physical situations will be seen as “before” the other.
The upshot of all this (and lots more) is that all of the events that I can remember (or have seen reports of) can be consistently associated with points in a 4-dimensional “space-time” in which, at each point, there is a (double) cone of “time-like” directions such that many physical phenomena are consistently asymmetric between the two parts of the cone (ie with respect to any version of a “time” coordinate). This is all we mean when we say that, at least for us and near here and now, “time has a direction”. And it’s true!
And none of the A,B,or C “theories” really adds anything to that.