I asked a question recently where I wanted to know whether it was physically meaningful to talk about the arrow of time in other universes.
Although many people apparently have an intuitive notion of what is meant by "physically meaningful", the only real context I have found is in terms of "physically meaningful observables" where in a quantum mechanical context we talk about the possible eigenvalues associated with eigenstates of an operator:
$H |\psi\rangle = \lambda|\psi\rangle$
The observables being possible outcomes of experiments or other operations on the state vector. So in the context of the arrow of time, where there are claims of the possibility of a vector time, one would like to think of some possible operation that would produce set of possible values for that time. So the first question one might ask is, "what operation can I perform to observe the vector values of the arrow of time?"
It would seem that there is some difference between defining such an operation and the possibility of it actually being executable. So one might think of a thing being physically meaningful if one can define a set of executable operations (executabality being determined by some set of constraints).
However, I suspect there is a better definition, or a better way to conceptualize what is meant by "physically meaningful", and I would like to read what those are.