Gravity and Darkness

As a trade economist, much of my recent work has involved what we call the "gravity equation" for bilateral trade (it also works for bilateral migration flows and FDI stocks). Originally (1960s) it was inspired by Newton's gravity equation.  Although it seemed to "work" pretty well, it was not respected within our field because models are supposed to be based on assumptions, not analogies. Thankfully, now there are very compelling derivations of bilateral trade equations that bear a strong resemblance to the gravity equation in physics.  

OK, that's the prologue.  The reason I'm actually writing today (other than the usual procrastination motive) is that I was reading my step-father's Physics World magazine and came across the following quote:

there is always a sort of war between those who tend to assume the absolute correctness of the laws of physics that are in use, even when this requires imagining previously unseen entities governed by those laws, and those who instead are inclined to imagine that new laws of physics must be discovered. The conservatives are more frequently right....[but sometimes] the "new laws" hypothesis turns out to be right... (Giovanni Amelino-Camelia, Physics World, July 2009)

The current incarnation of the "new entities" versus "new laws" debate revolves (so to speak) around the questions of dark matter and dark energy. The problem that dark matter solves has to do with the rotation of speed of stars as a function of the distance of the star to the center of the galaxy.

I love this figure because it is the type of figure I have done in my own work so I can almost feel like I understand it (which I don't of course, having only taken 1 semester of university physics and one "physics for poets" course about light). But anyway, the point is you have to postulate the existence of lots of invisible dark matter in order to fit the data using the existing laws.  Similarly (I guess) you have to postulate dark energy to explain why the universe is expanding at an accelerating rate.

The "new laws" types take another approach: they have a more general theory that reverts to standard Newton/Einstein gravity at the scale of the solar system but is capable of explaining the anomalies at the galactic scale. This article explains it all very well and I more or less understood it except the part about tensors. Vectors and scalars, fine. But what the heck's a tensor?

In another article in Physics World, I find the following intriguing idea.

Moffat and Brownstein, however, argue MOG [the theory of modified gravity] can provide a more natural explanation by removing the need to invoke mysterious dark matter. Essentially MOG adds extra terms to Einstein’s theory of gravitation — general relativity — that allow the gravitational constant G to vary across space and time.

So back to my day job: understanding trade. We already know that there is no gravitational constant for bilateral trade.  In addition to distance and country sizes, bilateral trade depends on large set of linkage indicators (shared languages, laws, currencies).  This question of new laws motivates me to revisit questions that came up in earlier work. Do commercial interactions between people decline in proportion to distance at all scales of observation (inside a country, inside a city, inside a building)?  Do the same gravity equation parameters that apply to high-trading country pairs also apply to low-trading country pairs?