Here's my question;
If we have a line of connected cogs, arranged in such a way that for any one cog to move each other cog would necessarily have to move also, and that line of cogs were of an arbitrarily large distance, would we be able to induce motion in the first cog at one end of the line immediately, thus acting upon the farthest cog faster than $c$, or would the line of cogs become an immovable object for a period of time due to constraints regarding the speed at which information can propagate?
To help with answering the question assume these things to be true;
- The cogs can not be made to go out of alignment.
- The energy needed to move every cog is arbitrarily small.
- The cogs can maintain their physical integrity even when subject to arbitrarily large amounts of force.
Thank you all for any time you take to answer my question.
The speed of sound i think may not be a problem here, because the moment a force is applied on one side of the first cog and reaches the first point of the second cog, the balance of the second cog would change. Since the second cog is put off balance, gravity would begin to act on that second cog inducing motion on its farthest point at the speed of sound, but faster than the information would travel from the closest point of the first cog to the farthest point of the second. Its the instantaneous action upon the farthest most points of each cog created by gravity or another constant force that happens at the moment that force is applied to the closest most points of those cogs, that overcomes the speed of sound barrier, as the information telling each cog to move in a certain way is communicated to every point in the cog either by the force itself or by the nearest most points which contain that information, those points being nearer to the center most points of the cogs than the closests most points are. The distance that any informatjon has to travel is less than the distance which light has to travel, and therefore as the length of the line of cogs increases, the distance information has to travel to move each cog within the line, relative to the distance light has to travel to cross the same distance, approaches zero.
This is the sort of fun thing we could get into, if people didnt just assume this question is the same as the rigid pole question.
This question is substantially different from the pole question for numerous reasons, and the differences make the appropriate discussion about this different from that had concerning the rigid pole.
For instance, each cog is individually bound by the EM force, where as the pole is a single object bound by the EM force, this makes a couple things different but one simple thing is that while pushing a long pole would compromise the integrity of the pole itself, stopping one cog does not compromise the integrity of the others because they are individually bound and therefore the EM force which binds the farthest cog together is not compromised when a force is applied to the first cog, that difference is hugely substantial. The motion of each cog is dependent on the cogs next to it, whereas the motion of one end of the rigid pole is dependent on action at the other end, this difference is also substantial. in these ways and others the cog question is substantially different from the pole question, even though rigidity is a factor the way rigidity is discussed would neccessarily be substantially different, and even though the EM force should be mentioned it does not play the same role as it does with the pole. This question and the pole question are fundementally different and they should be treated as such, even though the difference may be subtle, they are fundemental non-the-less.
I used postulates specifically so i wouldnt get answers that are mostly irrelevant to the given context, and they were largely ignored for their intended purpose, and it seems mainly considered only so much as it allowed for my question to be answered as something else.
The cogs cant go out of allignment, is like saying the pole cant bend, because were talking about cogs not a pole and the physics are different.
The cogs can maintain their physical integrity, is like saying the pole cant break, if each cog on its own can withstand a substantial amount of force without breaking than infinitesimal differences between the motion of one cog will not cause the structure of the surrondings cogs to be functionally compromised
I can not stress enough, that im grateful for any effort that people have given, and will give, im just a little bummed out is all.
Could somebody delete this question.