Thursday, December 15, 2011

Quote of the Day: Potency and Potential Energy

"I reply that it must be said that potency as potency is ordered to act so that a potency must be understood in terms of the act to which it is ordered and that there will be a plurality of potencies insofar as there are diverse acts. Acts in turn are distinguished in terms of their object. Every action is of either a passive or active potency and the object of a passive potency relates to its act as an efficient principle or cause: insofar as color moves sight it is the principle of seeing."
Saint Thomas Aquinas, Disputed Question on Truth, Question 2 Article 2
Reprinted in Prof. Ralph McInenry's A first Glance at Thomas Aquinas: A Handbook for Peeping Thomists

We employ similar language--and sometimes similar meanings--in science when discussing such things as energy. An object--let's say it's a ball--of mass m moved to a height of h (h << r_earth) above the surface of the earth is said to have "potential energy," which we express mathematically as V = m g h, g being the gravitational acceleration which object near the earth's surface experience when in free-fall. The object has potential energy: but what is that potential in relationship to? It's tempting to just say that the object has the potential to fall back to the earth, and that is true enough if I am just holding it above the ground: as soon as I release it, it will fall.

But what if I release it and it rolls (or slides) down a ramp? Does the potential energy change? Well, no, though the energy of the ball may be different at the bottom than at the top, not only in quality (it's gravitational potential energy will be reduced, and it will probably gain some kinetic energy), but also in quantity (rolling implies some amount of friction, meaning the object will lose some of its energy in this scenario). Whether the ball is dropped in free-fall or allowed to slide/roll down a ramp, we still say that it has the same potential energy, and it is still expressible as V = m g h.

Rather, we might say that potential energy is (in this example) the potential for gravity to work on the ball, which (again in this example) manifests as the ball's moving [1] from a greater height to a lesser height. What "moves" the ball when it is released? Gravity, of course. Why does gravity do this? Because objects tend to seek the lowest potential energy state available--which in this case means "resting" on the earth's surface.

Of course, this state of "rest" from the fall is a state in which the ball most likely has some amount of kinetic energy--T = 0.5 * m * v^2 < m g h--but as far as the motion of falling is concerned, its potential has been actualized, since the ball was acted upon by gravity, resulting in its fall from the lofty heights to the floor below. And in turn, as it rolls across the floor it begins to slow: friction now work upon the ball: it's kinetic energy is equal to the quantity of work the floor must do on the ball before it comes to a stop. Perhaps we might call this kinetic energy the potency in relationship to the act of friction doing work. I'm not sure what Saint Thomas would think about all of this (he may find it an interesting discussion, or a pointless one): but it certainly makes for an interesting mental picture in solving basic "energy conservation" problems.

As for the ball's actual fall, it seems to me we have and object which is translating from  high point to a low point with a motion described in time by h = 0.5 g t^2 + v_i t, whose motion is affected by gravity, in such a way that it reaches the lowest potential energy state. But of course, we don't rely on Aristotle's causes at all in physics: or so a long line of physicists and philosophers of science--stretching back to Francis Bacon and Rene Descartes--would have us believe.

[1] Moving--This is also defined by Aristotle and Aquinas, though not necessarily in the same way we would define it. We say "it's moving" if an object has a nonzero speed or rotation. But motion is also the middle state between potency and act: the state between having only potential and having that potential actualized. It is the state of falling, but not because the ball has a nonzero speed, but rather because so long as the object is falling, it is in that middle state between potency (potential energy--gravity might yet do some work on the object) and actuality (gravity has done all the work it can on the ball).