If you could move infinitely fast, would you occupy all points along your trajectory at the same time?

Answer 1

Yes, according to quantum theory (not relativity). The Heisenberg Uncertainty Principle states that the product of the uncertainty in an object's position and it's uncertainty in momentum is a constant. If the speed, and therefore the momentum, is infinite, then it's uncertainty in location would be infinite; it would have a wave function such that it would be equally likely to be at all points in the universe simultaneoulsly.

Answer 2

Photons, which normally travels at the speed of light, are taking all possible paths to get from A to B. That means possibly all over the universe. Sometimes going faster or slower than the speed of light. What we observe is the resultant amplitude.
What's this go to do with your question? Well we can never predict anything for sure. Everything and anything happening is a probability. As long as it's a non-zero possibility the matter that makes up you can be else where.
therefore you can be anywhere and everywhere even if you're just standing still.

Answer 3

If you could move infinitely fast, would there even BE a trajectory? (Looking at it from the point of view of Discrete Mathematics, trajectory is an onto mapping involving space and time.)

OR

Would there just be a starting position and an ending position (both occupied at the same time)?
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Answer 4

There's that concept again, "infinitely."

I would suggest that if an object were traveling infinitely fast, it would occupy no points on its trajectory at the same time or any time. It would simply transverse the entire trajectory in no time.

Answer 5

According to Einstien, it is only possible to travel as fast as the speed of light. So the scenario of travelling at an infinite speed would not arise.

Also, i don' think there is such a thing as "infinitie speed". There could be infinite distance, but speed is presumably defined as "distance travelled" divided by "time taken to travel that distance". I am not sure that it is mathematically feasible to say that something travels an infinitie distance in zero seconds ? Perhaps someone else can confirm this.

Answer 6

Moving infinitely fast is the equivalent of moving at the speed of light, since time slows to zero at that speed. This is only possible for massless particles (if there are any) and photons. From a photon's point of view it isn't moving at all - it is simply everywhere at once (so maybe there's only one photon in the entire universe!).

Answer 7

Yes, you would be able to be omnipresent