Is Movement Truly Possible Despite the Paradox?

[ghostman97]

i'm trying to conclude on HOW this would be possible... though its a paradox doesn't it seem very possible?

in case you don't know what it is its saying movement is immpossible. Example to get from point a to point b you have to go halfway but before you get from point A to A1/2 you have to get halfway there and so on

 

[micromass]

Hi ghostman97!

Which paradox are you referring to? Zeno has formulated 3 paradoxes (and maybe more).

• Achilles can never catch the turtle.
• An arrow can never reach his goal.
• How can an arrow move if it's standing still at each instance.

 

[ghostman97]

basically an arrow can never reach his goal

 

[micromass]

Hmm, let's see if I can explain this nicely. I'm usually quite bad at such things.

Firstly, the paradox assumes that we can keep dividing the remaining distance. But this is not possible since there is a smallest distance: the Planck length. (but you might want an actual physicist to explain this correct/better).

But let's say that we could keep on dividing, how could the paradox fail? Well, the thing is that the time required to walk all these distance decreases exponentially. When we walk the first part, we might take 1 second, when we walk the second part, we take 0.5 seconds. When we walk the third part we take 0.25 second. In total, it would take us

$$\sum_{n=0}^{+\infty}{\frac{1}{2^n}s}=2s$$

the thing is that this sum converges and thus the number of second to walk the entire distance is finite. So we can complete an infinity of distances in a finite time!

However, if the paradox says: "walk the first distance, then wait for 1s. Walk the second distance, then wait for 1s. Walk the third distance, then wait for 1s..." Then this is indeed not possible to perform, as it would take an infinite amount of time to do so.

 

[ghostman97]

so what your concluding is that movement would be "impossible"

 

[Drakkith]

Other than linking some of the proposed solutions here: http://en.wikipedia.org/wiki/Zeno's_paradoxes#Proposed_solutions
All I can say is that the world shows us that as far as we know time is not divided into steps.

 

[Borek]

So we can complete an infinity of distances in a finite time!

so what your concluding is that movement would be "impossible"

Have you actually read micromass answer before responding? He clearly stated: "we can". Thats opposite of "impossible".