Financial momentum

The following is derived from watching some Khan Academy videos on macroeconomics and reading Piketty's book.

From the discussion, the financial health of a country is significantly impacted by the 'velocity' of money within its economy. The videos indicate that the quantity moving is important as well as the speed. This is, of course, basic economic theory arising from Keynes and others.

I am not an economist although I have been trying to build up some knowledge of the principles. However, I am a physicist (or was) and the key factor in the study of motion is 'momentum' or mass times velocity. Which raises the question about the equivalent metric in economics - what does it mean to refer to financial momentum.

This does not mean to say that the analogy is valid but it does prompt the thought experiment to see how far it can be pushed. For instance: is there a economic equivalent of conservation of momentum? Is the net flow of money (wealth?) within a system is constant?

First: the more common important quantity in the physics of motion is the rate of change of momentum or force: F = ma according to Newton. Economics, as with natural language, usually less precise terminology, but forces could be interpreted as changes in the flow of money.

But perhaps 'money' is not the correct entity to use as a measure of an amount of substance in economics. It is representative of a deeper underlying concept - wealth perhaps? "Capital", especially in Piketty's case, refers to something more specific, but it may be meaningful to refer to the flow of wealth or value, with money being the unit of measure. The concept of what exactly is flowing may require more thought.

More basic is that the distinction *must* be made between velocity and speed. The two are NOT the same and the distinction is critical in understanding movement. Speed is a single value and can be added and subtracted simply as a number. Velocity, on the other hand, depends on direction and changes when the direction changes even if the measured speed is the same. And a force is required to change the direction even if the quantity doesn't change. Velocities (or momenta) add as vector quantities and only cancel out if they are in opposite directions. 

The economic equivalent would be the exchange of items of equal value between two entities which would lead to a zero net flow of wealth. Also the net force driving further motion, after the exchange is complete, would be zero so the impact on the larger system can be disregarded. I don't think this is the same in economics - but it should be a point of further investigation. [As a side-note, there is some relativistic influence here since the value of the items will differ for each entity else they would not be exchanging them; another break-down of the analogy or can it be extended into electromagnetism?]

But when there are more than two bodies the direction of flow is not directly opposing and so the net forces do not necessarily cancel out. In physics, the mathematics for a multi-body system can be *very* complicated and there is no general solution to the equations; they must be calculated on a case by case basis and the computation may be difficult.

Hence it is not the flow of wealth that matters, but the circulation which requires a sort of centripetal (or centifugal?) force to maintain. Which is another interesting concept: what does the push of wealth away from the centre, as would happen with high velocities, mean for an economy?

One other point on this collection of ideas before I take it away for more incubation. Wealth at rest, like mass at rest, has inertia holding it in place. It is ballast which requires larger forces to move. According to Piketty it also accumulates (at least within our economic model) which gives it gravitational attributes - the larger the body the faster is gathers more substance to itself and the greater the influence on (particularly moving) entities around itself.

Maybe the analogy is not entirely far-fetched?