Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Zeno's paradox

  1. Jun 17, 2011 #1
    i'm trying to conclude on HOW this would be possible... though its a paradox doesnt it seem very possible?

    in case you dont 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
     
  2. jcsd
  3. Jun 17, 2011 #2

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    Hi ghostman97! :smile:

    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.
     
  4. Jun 17, 2011 #3
    basically an arrow can never reach his goal
     
  5. Jun 17, 2011 #4

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    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

    [tex]\sum_{n=0}^{+\infty}{\frac{1}{2^n}s}=2s[/tex]

    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.
     
  6. Jun 17, 2011 #5
    so what your concluding is that movement would be "impossible"
     
  7. Jun 17, 2011 #6

    Drakkith

    User Avatar

    Staff: Mentor

  8. Jun 18, 2011 #7

    Borek

    User Avatar

    Staff: Mentor

    Have you actually read micromass answer before responding? He clearly stated: "we can". Thats opposite of "impossible".
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook