Possibly, but I think not. The article states, "... the invariant set is in part characterized by the experiments that humans perform on it, which is to say that experimenters do indeed play a key role in defining states of physical reality."
This is a fancy way of putting the rather common-sense position that actions have consequences. Further, however, it lends a temporal aspect to reality -- "the invariant set" is not static per se, but rather unfolds as "observers" (however defined) interact with the existing invariant set.
The concept of predictability fits nicely into this structure: the fact of my deciding to do a thing, at a particular point in time, closes off other possible actions; the reduced set of actions will fall in the vicinity of a future "path," which gets wider with distance from the decision point.
Of course, none of this is particularly new -- it's been the plot of many a sci-fi novel -- but if Mr. Palmer has managed to formalize it in a useful way, that would indeed be new.
What you describe as arising from fiction was in fact formalized by perhaps the greatest physicist in American History while science fiction was still stuck in its “monsters from Mars” infancy. [Although John Archibald Wheeler fans have a justifiable alternative candidate for the honor.] It is called the Feynman Path Integral Formulation of Quantum Mechanics.
The Feynman Path Integral, by the way, explains why predestination seems to be an ingredient of QM (in fact, the Principle of Least Action, which the FPI is an extension of, says the same thing in classical mechanics.) You can describe physics as the result of a Lagrangian in which the past and future are connected by functionals acting under some constraint. In this view, the end points appear to determine all the paths between them, which indeed they do: under the action of the constraint -- The Principle of Least Action -- this results in a single trajectory through phase space (in classical physics) or a set of trajectories in QM.
Completely equivalent to this is the Hamiltonian formulation of mechanics. In the Hamiltonian perspective, starting points are arrived at by application of the time-evolution operator. As you may know -- but for the benefit of passersby -- it is a first year grad-students' exercise to prove these two formulations are mathematically equivalent (after you struggle through Goldstien.)
So something that seems entirely predestined (Lagrangian mechanics) can arise from something where states move through time purely from one infinitesimal starting point to the next under the influence of the Hamiltonian, and vice versa. The reason two so fundamentally different ways of looking at time evolution appear the same is that the underlying physical principle -- The Principle of Least Action -- governs both.
This is a fancy way of putting the rather common-sense position that actions have consequences. Further, however, it lends a temporal aspect to reality -- "the invariant set" is not static per se, but rather unfolds as "observers" (however defined) interact with the existing invariant set.
The concept of predictability fits nicely into this structure: the fact of my deciding to do a thing, at a particular point in time, closes off other possible actions; the reduced set of actions will fall in the vicinity of a future "path," which gets wider with distance from the decision point.
Of course, none of this is particularly new -- it's been the plot of many a sci-fi novel -- but if Mr. Palmer has managed to formalize it in a useful way, that would indeed be new.
Oh the thing I am falling all over is the name "invariant set" this name should have a meaning and as you have said above, the actual set should recognize that actions have consequences and that the set of possibilities that may yet be expressed in reality is constantly dwindling and thus not be invariant.
Now this may be an aspect of fractal geometry that I just don't get at this moment, such that the fractal is invariant even though the pattern is constrained as it impacts each boundary.
The goo contained in the middle is unmoved by lopping off a slice from the outside, thus the arrow of time more precisely defines the invariant set which is only invariant by the fact that once a chuck is lopped off, it may never be reattached.