APPENDIX B MOTION WITHIN MASS AREAS AND THE AETHER
If we consider the established notion of impenetrability the result occurs, that either:
1. Impact is not possible or,
2. Motion transfer is instantaneous
As to the question of having two motions in the same instant, Jammer describes Boscovich’s words: “…it would amount to saying that the body would be bound to have 12 degrees of velocity and 9 at one and the same instant”.1
Boscovich therefore concluded that impact was illogical and proceeded to use forces to describe changes in motion (impulse). Others accepted the notion of instantaneous transfer motion2.
I concur with the later as having two velocities to a body at the same instant only follows from what the concept of an instant is, that is (analogous to mathematical points and area) it is not an interval of time but the separation point of time intervals. So the first velocity occurs up until that instant (of contact) and the second velocity occurs after that instant.
Therefore there is no reason to suppose instantaneous transfer of motion is not possible.
For rod contact as described in chapter 2, here the contact between two rods have an area = zero. This point of contact on the two rods, or any point of contact of two areas or lines, is the same point (Principle I-1, See Appendix I). This seems odd as the two rods have a outer "point" for each, but when they come together it becomes the same point. But this is so, as that point is just a defining measure, what was the separation of mass area with non-mass area (unoccupied space), becomes, as the gap is closed, the separation point of the two masses.
So, the quality of motion (momentum) must “pass through” a point of zero area. So, if only for an instant, momentum must move in one dimension. As mass is decreased the velocity becomes infinite, however, in my opinion, the quality/quantity, even at infinite velocity remains as the original v x m factor. So that when motion is given back from a mathematical point to a mass area the proportion is v x m : v1 x m1 again.But the idea remains that motion has been accounted the property of traveling through a mathematical point (if the proposition of motion rod to rod is accepted). Furthermore if 2 rods are brought to contact along their lengths we have a line of contact with no area and momentum must be transferred instantly along this one dimensional line also. And since mathematical points and lines separate areas of mass that are in contact anywhere in a mass area, then momentum can be transferred from any part of a mass area to another instantly. So I consider motion is transferred instantly within a rod or between two rods in contact.
Most people considering an aether have thought of it as a continuous medium, but this cannot be in my opinion, arguments against it are along the lines expressed in Appendix K: The incorrectness of point forces and Appendix B Motion within mass areas. Or I will describe it directly, simply put in any continuous medium a particle cannot move, for to do so it pulls apart the medium! Else the medium is in name only offering no resistance, but if it does resist, then impact is necessary and the particle leaves its place to impact the medium, leaving a rip in the medium. Or if it is embedded in the medium it must push it to move, the medium then must fill in where it moved from, and those forces cancel, so no force is left to move any other particles by the medium, and it all must have been instantaneous over this fill back distance, or not motion could have occurred over any instant. Others have described this better in the past than I have, I think.
Let me try to explain it again. For any continuous medium, or discontinuous also if action of one part immediately effects all other parts, if particle A moves and deforms the medium, one could say there is a rate of deformation, but is there? It deforms, but not instantaneously it is said, why? One says because its takes time, at a certain rate. But the instant A moves it must deform the medium if you have a responsive medium. Say it deforms 10 square feet per second. It has to do some rate to be proportional to the force of motion. But if one part deforms, the rest its deforming into must deform right away, else deforming is not occurring. So its instantaneous or not at all. So, for it not to deform it must be a time it was not deforming, but that time it was not deforming A must also be not moving. That’s is only when is deforming that you can have a rate of deformation. That is unless there is a space, void, to travel though it must be pressing on something that requires deformation, which would then have to deform all at once if so connected! Thereby proving that matter or mediums are absolute solids, and transfer of motion at impact is instantaneous. Also proving then that any “ether” is radically discontinuous. And no medium beyond the void of space exists except discreate absolute solids.
Instead there is indeed a VERY large volume of absolute voids between matter. The true aether, call it another term if you like, is discontinuous in my opinion. It is the atomistic atoms, the primary particles, that are a continuous medium within their boundaries. Within the particle motion is instantaneous, by needs on the “laws” of continuity.
Time itself is only possible in relation to matter and motion in a discontinuous aether. For it is the motion though the void that takes time, in a continuous medium it would be instantaneous.
Scott, Wilson L., The Conflict Between Atomism and
Conservation Theory 1644 to 1860, Elsevier/MacDonald, 1970.General in book.