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Is the distance between any object infinite?

  1. Jul 16, 2015 #1
    Hi, I just finished grade 11 in high school and I have a question that is there in infinite amount of space in between objects?
    Here is my logic:

    ***First off what is the minimum distance matter can move within the midst of space? I'm thinking there is no minimum.

    On a 2-dimentional graph there is an object at (0,0) and (0,10) (any point would work) objects A (0,0) & B (10,0). Lets say every unit in between them is 1m so ultimately the distance between them is 10m.Let us say object A shoots a bullet at object B, it has to travel through about 10m of space to get there, right? Well the bullet could theoretically .1m , .08m, .002m, .0000000432m through space; so we could keep and keep on putting those zeroes in meaning that the bullet would have in infinite distance to cover to get to object B. Get it? First it needs to move 10m which means it has to cover 5m two times, or 2 meters, 5 times, or 0.00000000000078 x amount of times or 0,0000000000000000000000000000000098969584 m y amount of times and so on?

    So is there an infinite amount of space/distance-to-cover between object A & B?

    Now I've asked many people in school about this and no one knew the answer and would mumble something about asymptotes and one said something about Zola's or Zopha's dilemma (I know I'm getting the Z guys name wrong, sorry), I hope some thing there gets the gears turning.

    ~thanks for your time!
     
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  3. Jul 16, 2015 #2

    jedishrfu

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  4. Jul 16, 2015 #3

    phinds

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    If two objects are X distance apart, X cannot be infinite because there is always X + 1.

    The confusion comes from trying to apply numerical rules to something that is not numerical. It doesn't matter how many zeros you add, you STILL have a number and it is not infinity
     
  5. Jul 16, 2015 #4
    @phinds so say a pixel is traveling across the screen of a computer, it moves from 0,0 to 0,1 to 0,2 and so on. Are you saying that an object moves like that through space? So it does not move smoothly but sorta teleports from 0,0 to 0,1 and so on? i'm sorry i'm not sure how to phrase what I have just asked, I hope it makes sense.
     
  6. Jul 16, 2015 #5

    phinds

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    I understand exactly what you are asking but I have no idea how you inferred that from what I said. I made no comment on the granularity of space-time. I don't think there's any proof one way or the other, but my belief is that it is continuous.
     
  7. Jul 16, 2015 #6
    What is "granularity" of space?
     
  8. Jul 16, 2015 #7
    Guys, I'm thinking that space cannot be gridded, cause there would be minimum movement distances for objects. For example say that an object received 0.0000001N it would not be able to move to the next point on the "grid" of space but if it got 0.0000002N of energy if would move to the next point. I am thinking that this is not what happens on the space fabric, I'm thinking that the bullet mentioned above, moves smoothly from one point on the grid to the next, not suddenly appearing at the second point. Hope that makes sense.
     
  9. Jul 16, 2015 #8

    phinds

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    Granular means "grainy" as in "made up of grains" instead of smooth. My original post made no comment on whether space-time is smooth or not but as I said in my next post, I personally think (without any proof) that it is.
     
  10. Jul 16, 2015 #9
    Hmm, I searched up granularity of space and I've figured out that this topic belongs in the quantum section
     
  11. Jul 16, 2015 #10

    phinds

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    Does it matter, now that your question has been answered?
     
  12. Jul 16, 2015 #11
    It hasn't been answered but that's because nobody knows the answer but thanks for your input, that's the furthers this conversation will probably go.
     
  13. Jul 16, 2015 #12

    russ_watters

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    Your question was answered, it just doesn't seem like you read or understood the answers. The issue you are having is common, ancient and comes from some basic misconceptions about math. I encourage you to reread the above Posts and in particular read the link about Zeno's Paradox.
     
  14. Jul 16, 2015 #13
    Hi Ujellytek

    I think you're putting two different concepts together and maybe getting a bit mixed. Here goes...

    First the infinities. Infinity is a math concept pure and - I was going to say simple, but let's be real - pure and wonderfully complex. However, we don't see infinities in real word space/time - infinities pop up all over the place when trying to model the real world and we've got some fabulous tricks to deal with them (google why 1+2+3+4.. = minus 1/12). But that's just maths and models; there are no specific evidence of any infinite (or infinitesimal) distances, temperatures, densities or the real world - just areas where our models break down. For example, we can't accurately say that black holes have an infinite density, only that the density is tending towards infinity and then who knows... that's when the model breaks down!

    Next Grainy space. You are absolutely spot on that this belongs in the quantum section! Quantum mechanics is possibly the most thoroughly tested and accurate theory we have; as we've been able to measure distances, time, magnetic moments and zillion other things to greater and greater accuracy, QM predictions have been shown to be accurate to within a few parts per many trillions of whatever is being measured. It's all good stuff! And if you extrapolate from the maths to real life (*warning*) then it certainly looks like life isn't continuous at the tiny (plank) scale, but quite digital!

    Why the warning? For similar reasons that you can't take EVERY maths concept and map it to real world (infinity as a case in point), you can't be sure that our interpretation of QM is correct - in fact QM interpretations are akin to religious wars to some! Is life grainy? I've no idea... but spend some time in the QM threads and you'll quickly have a far better understanding than I do :-)

    Regards
    Matt
     
  15. Jul 16, 2015 #14
    This discussion just provoked a thought. General Relativity allows that space and time can be interchanged by motion. This is a continuous function of velocity (itself a continuous variable) as described by the Lorenz transforms. It is this continuity that precludes the 'granularity' of space or time. Both must be continuous variables.
     
  16. Jul 16, 2015 #15

    Drakkith

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    No, the distance between A and B can be divided into an infinite amount of 'pieces', but there is NOT an infinite amount of distance between them because each piece also gets smaller as you divide the distance into more pieces.
     
  17. Jul 16, 2015 #16
    Hey - I got no beef with Einstein! If he say's it's a continuous function then my mortgage is on it being a continuous function!!

    That said (:-) continuous functions are maths concept and no matter how well the maths describes the world, maths and the world are not the same. And even the Duke himself didn't get his relativity and quantum mechanics to stack up at the tiny level.

    There's a fabulous paper written by Eugene Wigner called The Unreasonable Effectiveness of Mathematics in the Natural Sciences and it can make your brain ache and pancake in equal measures; but the underlying message (to me anyway - Wigner was a bit before my time to ask) is as maths as a descriptor of reality, not as an equivalence.
     
  18. Jul 16, 2015 #17

    Drakkith

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    There's no need to get into the details of the granularity of space. The concept is so far over the head of the OP (and most members for that matter) that it serves no purpose. Let's try to keep the discussion at a level appropriate for the OP.
     
  19. Jul 16, 2015 #18
    @Drakkith I see what you mean. But wouldn't it mean that if an object could move less than 0.002 m or less than 0.0000000000000001m or less
    than 0.(lots of zeroes)0001m that an object could theoretically move an infinite amount of times before moving 1m.
    #13
    @mgkii About the 1+2+3... = -1/12: My math teacher told me it is inpossible to add numbers infinitly because infinity is only a concept, not a variable
     
  20. Jul 16, 2015 #19
    @ujellytek you're getting infinity confused here; you can't move an infinite number of times - infinity isn't a number. Have a browse around wiki etc on infinity; the penny will drop.
     
  21. Jul 16, 2015 #20
    mqkii>"you're getting infinity confused here; you can't move an infinite number of times - infinity isn't a number. Have a browse around wiki etc on infinity; the penny will drop. "

    Imean that you could do if forever, always moving lesser and lesser amount and never reaching your destination
     
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