Stephen Hawking brilliantly observed that entropy increases with time because we measure time in the direction in which entropy increases. We simply adopt the entropy increasing direction as our temporal reference direction, and so we do not usually notice the orthogonal components of time. Entropy (or increasing disorder) defines our forward direction in time, so order propagates backward through time; thus we can see why the theory of causality works so well in reverse but not so well forward. We can always find a reason for something that has happened but we can rarely predict precisely what will happen. Things often happen for insufficient causes in forward mode, but afterward we often construct sufficient causes and reasons.
I suspect that the orthogonal components of time correspond to net entropy changes no larger than those that could slip through at the quantum level. We could write an equation with entropy and orthogonal time as another pair of complementary terms in a Heisenberg style uncertainty/indeterminacy relationship thusly:
DST Dti ~ h
Where D(delta) ST means entropy change (at a particular absolute temperature),
D(delta) ti means imaginary (orthogonal) time, and h means Planck's constant (an exceedingly small number)
This provides a key to understanding three-dimensional time and the association of quantum weirdness with exceedingly small energy differences. It means that you can have as much orthogonal a process as you like, so long as entropy changes remain minimal; but I digress.
Most magical descriptions of reality still require some nebulous extra component to the universe beyond the matter and energy that science can measure. Spirit, spirits, astral planes, occult energies, morphic fields, and disembodied thoughts or information have, at various times, all filled this role.
If the HD8 interpretation of physical phenomena remains unfalsified then it remains as a valid, if highly eccentric, description of fundamental physical behavior that could form part of the metadynamic. The problem then reduces to one of describing the phenomena of magic using only the extra degrees of temporal freedom afforded by three-dimensional transactional time, and avoiding the traditional spooky immaterial explanations.
A General Metadynamic including magic would have to offer an explanation of only divination and enchantment, for these lie at the root of all magical phenomena.
Divination presents the simplest case. If at some point in the future the diviner can know the answer to a question, then that answer can feed back from the future to the present. However because the universe behaves with a degree of randomness and chaos, several different futures can feed back to the diviner's present to give mixed results. In some cases the diviner's choice of one particular item of feedback could even act to increase the likelihood of that future becoming more probable. Thus divination can work as enchantment by self-fulfilling prophecy.
Pure divination works best in pursuit of a fixed but concealed future. As a simple example consider the case of a well-shaken dice. If you slam the dice cup upside down over it without looking and then try to guess the number showing, the number remains a fixed element of your future (except to an extreme quantum solipsist). If however you try to guess the number that will appear before even shaking the dice, then all six futures exist at the time of divination and only enchantment offers any hope of obtaining a non chance result. In practice, the former type of divination works far better than the latter.
Dowsing provides a classic example of how divination actually works. The dowser basically divines what effect digging a hole in a certain place will have on his future perceptions. It plainly does not depend on mysterious geomantic energies emanating from water or minerals because experts can dowse from mere maps of the terrain.
Note that in this metadynamic of divination we do not require anything immaterial to pass between the diviner and the target. The diviner functions as a collection of superposed states entangled with the superposed states of his past and future. As the ‘particles' of the diviner move forward through time they simultaneously move backward through time as well (because they actually consist of particle/reversed-particle pairs), however we do not normally notice this.
The metadynamic of enchantment (making things happen by magic) has symmetries with that of divination but it also demands something else.
The collapse of quantum superpositions and entanglements remains officially indeterminate and random, but macroscopic phenomena often behave with deterministic chaos according to general scientific consensus.
‘Deterministic chaos' means that the behavior of a complicated system like the weather exhibits extreme sensitivity to its initial conditions. Change the airflow or the temperature just a tiny bit and you may change tomorrow's weather quite a lot; this in turn could change next week's weather totally. This gives rise to the rather poetically named ‘Butterfly Effect,' in which a butterfly changing course over Belgium could result in a hurricane devastating Cuba, or not devastating Cuba, sometime later. In another age we recognized this as the horseshoe nail effect: for want of a horseshoe nail, the horseshoe was lost, and hence the horse, the messenger, the message, the battle, and the whole empire became lost, for the want of that horseshoe nail.