I am looking for some help as I am mulling over inertial motion. Taking Aristotle's definition of motion and Newton's account of inertial motion, there seems to be an inherent contradiction.
In analyzing the account of inertial motion, I am struck by Galileo's thought experiment of the sphere rolling down a plane on one side across the floor and up similarly inclined plane on the other. He posited that if this could be done without friction, the sphere would return to the same height on the opposite plane, and so back again, ad infinitum.
I am struck, however, by several questions when I consider this case. First of all, can there be motion without "friction?" I am inclined to think that it is a necessary condition of motion that it be through a medium which at once inhibits and allows for the possibility of motion. This idea is encouraged by the impossibility of a vacuum. Moreover, (and I know that is an area which you have studied Vincentius) is it right to make such an "abstraction" from motion that we see? Indeed, can the idea of inertial motion even be called abstraction? It seems to be a mathematical fiction, useful for calculation. It is hard for me to see that inertial motion is contained virtually in mobile objects the way mathematicals are contained in bodies. A sign of this is that I see nothing in the nature of matter that makes it impossible that there be a perfect sphere or cube. With inertia, on the other hand, there seem to be many impossibilities. One of which is an infinite effect from a finite agent.
Having laid these questions and considerations before you venerable brethren, I eagerly await your comments, questions and guidance.
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This reminds me of a comment one of our tutors ("author" of the Physics,) said concerning motion and inertia. He said something to the effect of, just because with less resistance you can move more freely, does not mean that with no resistance you can move perfectly freely. A bird in a vacuum couldn't fly at all. It seems to me in this respect to be just as you say, a mathematical abstraction which ignores the true terminus of the judgements of a true science of nature: the sensible.
Furthermore, inertial motion seems to give no reality to place, seeing that it holds "space" to be merely the vacuous "place-holder" of what (in the ideal situation) isn't there for the inertially-moving body to run up against. So the idea of inertia really requires the positive existence of absolute space. Which has run into severe difficulties ever since Einstein (at least that's the rumor from the wise that I've receive).
Do you think it's the case that, if every moving bodies requires something else to move it, and if this isn't something immaterial, then something material, that then inertia posits an impossibility, which conception could be repaired by a positing a greater reality of "vacuous interstellar space" than previously conceived? They say that gravitational fields affect the "shape" of the space around attracting objects. Is "space" in a way something real?
Pax, Frater!
At the same time, I agree that motion without any resistance is impossible, as illustrated in Dawnwatchman's example. Further, in the case of the rolling sphere, it could not move down and then up the plane were it's rolling not acting on the plane and similarly being acted on by the plane.
Therefore, I venture the claim that it be not necessary for motion to be through a medium. But that some resistance is necessary for there to be motion.
Let me know what you think.
-Ciao
I will respond to NI first, because his raises a difficulty with the conception of the question put forward.
I would first of all say that when I used the term “medium” I had conceived of it in the most general way possible, such that it would include even the surface on which the sphere is rolling (I am avoiding the Galilean use of plane here because I think of it as a false mathematical abstraction). I will grant that this language is not very accurate. It seems that it is more accurate (though less precise) to say, as you suggested NI, that a mobile requires some resistance to move. I am compelled to agree. However, I would like to note that while air/aether does not need to enter into the account of the sphere moving along the plane, nonetheless, such motion must always take place in air/aether. In conclusion, my response is the following: fair enough.
N.B. I am using aether to name that somewhat indeterminate medium that is “beyond” our atmosphere. I am being intentionally vague, in proportion to my knowledge of the matter.
DW, you have opened up a big can of worms and have guessed precisely the direction in which I was hoping the discussion would go.
I think that it is right that the idea of absolute space has fallen by the wayside. Ever since Einstein posited the Space-Time continuum, no longer could space be conceived of as an empty mathematical locus in which physical phenomena take place. Rather, space-time has become intimately connected with the account of projectile motion. Now, there is much that I do not understand here. I intend to review the arguments for the existence of space-time. If someone has the time or inclination to post on the matter, I would appreciate it. I will try to get on it myself. One concern that immediately comes to mind is that the account of motion, or at least projectile motion, in the theory of relativity usually consists in the idea that the mobile itself is in a “state” of motion, and that what is occurring is that the space-time continuum is what is moving, not the mobile. More on this later...