This is what wikipedia says about it: "the Planck length is, in principle, within a factor of 10, the shortest measurable length – and no theoretically known improvement in measurement instruments could change that."
And "In some forms of quantum gravity, the Planck length is the length scale at which the structure of spacetime becomes dominated by quantum effects, and it is impossible to determine the difference between two locations less than one Planck length apart." - https://en.wikipedia.org/wiki/Planck_length
So, taken together, and if right (maybe not), then there is a smallest unit, and no movement within that unit can be determined, as the whole deal counts as a single location. — Wosret
As I said before, this reasoning begs the question by assuming from the start that it takes a finite time amount of time to travel a certain distance, and then considers the infinite divisibility of that finite time. In using an infinite series of fractions you've assumed your conclusion. — Michael
If you take that approach, your paradox also begs the question; it becomes "if it takes an infinite time to travel from one point to anther, then motion is impossible".
Indeed. — Banno
But measurable in principle, not just in practice, as it says that this isn't a problem of technology, or measuring ability. — Wosret
The argument is "if space is infinitely divisible and if no distance can be travelled instantaneously then it takes an infinite amount of time to travel from one point to another". — Michael
An infinite number of non-instantaneous movements to get from A to B makes it impossible to get from A to B. — Michael
This is akin to saying that counting each half division of a segment (of an infinite series) takes half the time as counting the whole segment, and that the sum of those times adds up, not to an infinite magnitude, but to the total time it takes to count the whole series. — Michael
So the case rests with you: why is it impossible to get from A to B? — Banno
Traversing each half division of a segment takes half the time as traversing the whole segment did, and the sum of those times adds up, not to an infinite magnitude, but to the total time it takes to traverse the whole line. — John
For the same reason that it's impossible to sequentially count the rational numbers from 1 to 2. — Michael
But you can sum them. Which is what is asked in the supposed paradox. — Banno
It takes a non-zero amount of time to travel any distance, and so given the infinite divisibility of space it should take an infinite amount of time to travel from any arbitrary point to the other. — Michael
The paradox is about moving from one point to another, which is analogous to counting from one number to another. — Michael
I can count from 1 to 2 in a finite time (see, I just did it); there is no need to count every rational number in between. — aletheist
Likewise, I can move from point A to point B in a finite time; there is no need to "touch" every point in between. — aletheist
Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.