A beautifully told story with colorful characters out of epic tradition, a tight and complex plot, and solid pacing. -- Booklist, starred review of On the Razor's Edge

Great writing, vivid scenarios, and thoughtful commentary ... the stories will linger after the last page is turned. -- Publisher's Weekly, on Captive Dreams

Sunday, January 31, 2010

Against Gravity

The question has been raised in the comm box regarding Aquinas' proof from motion as to how an immaterial First Mover can affect anything material.  This asks for a physical explanation of a metaphysical relation.  The difficulty arises from Cartesianism which, if we may be unfair to Descartes for a moment, holds that life (the "soul" or anima) is a substance in itself.  This led to all sorts of problems now known as the "traditional" problems of philosophy, but are actually the problems of getting Descartes before the horse. 

Recall that "motion" to a pre-Cartesian means any change of form, and not only the form of location, the existence of a First Mover follows for all essentially ordered chains of motion.  An essentially ordered chain is one in which the entities in the chain have no power whatever to move things unless something prior is moving them, right now.  (This is independent of such physical questions of "simultaneity" or of "beginning to be moved.")  For example, imagine a series of gears, with one gear moving the next gear.  Somewhere there must be a first gear moving the lot; otherwise, none of the gears would be moving at all.  Similarly, in a train of rail cars, each car is pulled along by the car in front; but there must be a first car - the locomotive - that imparts the motion to the others.  There cannot be an infinitely long train of cars, because none of the cars itself has an engine. 

Once the First Mover is established, we realize that it must itself be unmoved.  If it were moved by another, it would not be the first mover.  And this leads directly to its immateriality, since anything material is in motion [change], coming into being, growing, changing, passing out of being. 

IOW, the immateriality of the First Mover is a logical consequence if it being the First Mover.  As to how it imparts motion to the physical, who knows?  There are many things that are purely physical that we don't yet understand. 

Which brings us to a question of great gravity; viz., gravity. 

Why Gravity is not a Force
Now, a mass is the very essence of material being.  It is composed of prime matter (which is pure potentiality) realized by some form.  In the sensible world, all matter has form -- i.e., "Every thing is some thing."  In composite beings ("substances") matter and form are inseparable.  You cannot have a triangle without three-sidedness, for example.  We can, however, consider forms independently of their matter.  We can conceive of three-sidedness without having an actual triangle.  We say we have "abstracted" the concept (lit. "pulled out from").  This abstract thinking is the essence of science, here used broadly to include mathematics, theology, and other sciences besides the natural sciences. 

So consider a mass.  It is material

It falls due to something called "gravity." 

But one need only ask of what matter gravity is composed to see that gravity must be immaterial.  (This realization is why "materialists" have rebaptized themselves, put on a new garment, and now call themselves "physicalists."  Gravity, they would say, is physical, but not material.) 

So if gravity acts on a falling apple, it is the immaterial acting on the material, and the mystery is brought as close to us as Newton's noggin.  Newton himself realized that gravity was a metaphysical question.  He wrote in the General Scholium:

Hitherto we have explained the phænomena of the heavens and of our sea by the power of gravity, but have not yet assigned the cause of this power. This is certain, that it must proceed from a cause that penetrates to the very centres of the sun and planets, without suffering the least diminution of its force; that operates not according to the quantity of the surfaces of the particles upon which it acts (as mechanical causes use to do), but according to the quantity of the solid matter which they contain, and propagates its virtue on all sides to immense distances, decreasing always in the duplicate proportion of the distances. ... But hitherto I have not been able to discover the cause of those properties of gravity from phænomena, and I frame no hypotheses; for whatever is not deduced from the phænomena is to be called an hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phænomena, and afterwards rendered general by induction. Thus it was that the impenetrability, the mobility, and the impulsive force of bodies, and the laws of motion and of gravitation, were discovered. And to us it is enough that gravity does really exist, and act according to the laws which we have explained, and abundantly serves to account for all the motions of the celestial bodies, and of our sea.

IOW, he framed no hypothesis over what caused matter to have gravity.  It just does -- and he could study and determine certain behaviors of material bodies from the assumption that there was such a thing. 

It is geometrically obvious that as a "quantity" of gravity proceeds outward from a source, it must intersect spheres at progressively farther radii in projected circles that grow progressively larger.  Thus the "density" of the gravitational "substance" -- whether waves or flocks of graviton particles -- must grow progressively less, proportionately to the square of the radius of the sphere.  So, gravitational attraction, like light or electrical charge, diminishes in inverse squares from the source. 

Now, here is a mystery.  Once you get to this point, you have 1/r^2 which is 1/meters^2.  And you have the mass of the body in kg.  But where the heck do you get newtons (N) from (kg*m/s^2), because you don't have any seconds in your input.  Newton's Law of Universal Gravitation is F = GMm/r^2. That's established experimentally. The units of Mm/r^2 are kg^2/m^2, and the units of G are Nm^2/kg^2. But why does G have these dimensions?  Just so we get the proper units in our answer? 

[I once saw a set of calculations which, IIRC, reduced capacitance (in farads) to pure length (in meters), so maybe there is something Platonic in dimensional analysis.] 

But Newton is old-fashioned!  Gravity is "really" a warp in space-time.  But this does not salvage the immateriality of gravity, since according to general relativity, space and time do not exist as material entities, either.  Einstein called them metaphysical intrusions into empirical science.  If all matter were to disappear, he said, space and time would vanish with it.  (This is weirdly consonant with the Aristotelian-Thomistic understanding of space and time: space is the consequence of extension of material bodies and time is the measure of motion in changeable (material) bodies.  In addressing the question of what was before Creation, Aquinas famously said that "With the motions of creatures, time began.  How can there be time before time?" 

Or is Newton not old-fashioned enough? 

Gravity is not a force in the usual sense. 
A force affects the closer parts of a body before the farther parts.  (Imagine being hit by a truck.  The proximate side of your body would be compressed by the force before the force propagates to the far side.  But gravity famously affects the entire body all at once.)  Unlike electromagnetism, which is (in Aristotelian terms) "unnatural", gravity has only one "charge."  Gravity only attracts.  It has no opposite charge to neutralize its influence, which is why you cannot "shield" matter from gravity the way you can insulate it from electromagnetic forces.  If you were acted upon only by gravity, you would feel no force ("free fall").

Then what is it?  In Book 8 of the Physics, Aristotle defines natural motions as those that "that bring to actuality the proper activities that [material bodies] potentially possess."  Also, nature, from natus [birth], is a source of motion originating within the thing itself  (On the heavens, Book 3).  Because the natural motion moves the body to actualize its own potentials, we say that it perfects the body.  Furthermore, natural motions are accelerating motions.  Aquinas wrote:
"And insofar as anything is closer to its perfection, it is proportionately more powerful and more intense  Hence, it follows that the motion by which rest is generated becomes proportionately faster as it approaches nearer the state of rest.  This is quite clear in natural motions."  -- Commentary on the Physics, Lect. 10. 
(The contractions of childbirth are another example of accelerating motion as they approach their natural end.)

Gravity thus conforms to the notion of natural motion.  It originates within matter itself, that is, it is a natural property of matter.  It works to unite matter through matter itself.  And because the more matter is already united the stronger the gravity, the Aristotelian formulation applied: matter has the inherent tendency to seek further unity to the degree that it already possesses unity.  Further, the attraction is stronger and the acceleration faster as two bodies draw closer. 

So, gravity is not a force [violent motion] but a natural motion, inherent to the stuff it moves.  It is not destructive, but perfective, and it accelerates as it moves bodies closer to this perfection.  It makes no more sense to ask "how" an immaterial substance called gravity can affect a material substance called matter than it does to ask how three-sidedness can cause a plane figure to become a triangle.  Three-sidedness is simply a form of a triangle; and gravity is simply a form of matter. 

So, why is the universe expanding? 

Because there are other motions in the world besides gravity. 

Aristotle.  On the Heavens
----------    The Physics
Aquinas, Thomas of.  Commentary on the Physics
Keck, John W.  "The Natural Motion of Matter in Newtonian and Post-Newtonian Physics," (The Thomist, 71 (2007), pp. 529-554.

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