a cybernetic interpretation of gravity

[happyjack27]

ok, so there is a particle amongst a field ogf particles. its interaction among the others is 1/r^2 for all the forces (because the weighed sum of all possible random walks in an R^3 space creates a 1/r^2 field) thus its change in momentum per unit time is proportional to this distance, per each particle. we call this an "input", its momentum its "state". when one particle alters anothers trajectory("state") this way it is said to be "communicating" and thus the mutual information between the two particles increases.

ok, now take variational look at things. that is, what if the particle was moved just a little bit over, how would that change things? the inputs from the surrounding particles would change in relative magnitude ever so slightly.

the information it is exposed to at position x - call this I(x) vs. position x+dx, call this I(x+dx) would be slightly different. that is, there would be a non-zero kullback leibler divergence between these two points in space. or, rather, there IS a nonzero kl-divergence.

now if you move all of the particles infinitesimally closer to the midpoint between x and x+dx, at a rate relative to 1/r^2, those differences become greater and the kullback liebler divergence between those two points in space thus increases linearly.

this infinitesimal contraction that scales on average with 1/r^2 is of course gravity. so it follows that gravity implies that the kullback liebler divergence between two infinitesimally close points in space increases linearly with time.

but i propose that perhaps the reverse is the case - that the latter is the more neccessary and fundamental and that it implies the former.

[happyjack27]

here's the basic idea:



in any nonlinear and/or open system those flows of information ("variety") MUST exist and be non-zero.

the question is finding the particular rates and relations of the physical space of our own universe, and what the consequences of that are. i would not at all be surprised if some of them turned out to be non-trivial. (though that's certainly not to say i wouldn't be excited!)

EDIT: oh, and "mutual info increase", etc., that's all with respect to time. linearly, in fact. so it should actually say "mutual info increases linearly w/time.", etc.

why linear? well that's just the way information works. sort of by definition it must grow/decay linearly with time. that equates to an exponential divergence in infinitely close trajectories like you see in a chaotic attractor.