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Is motion relative to the size of an object

  1. Jun 27, 2008 #1
    I am not a physicist, but one who is fascinated by the discipline. It has a occured to me that the size of a moving object affects the perception of motion, and perhaps motion itself. I have a thought experiment to illustrate:

    A race is about to take place. In fact, it is the well known tortoise and hare competition, but with two very big differences. The Tortoise is incredibly huge. In fact, it is the size of small mountain, with legs and feet the size of a twenty story building. Each is a full city block at its base. The hare, on the other hand, is equally disproportionate but in the opposite direction. He is the size of a miscroscopic mite. He is so small that he would be just barely visible if he were sitting on your thumb nail right now.

    The race takes place on a straight dirt track exactly one hundred yards long. A starter on the sidelines yells, “Ready…set…” and he fires his pistol.

    Let’s start with the tortoise. He is well aware of his size advantage. Looking down, he sees that the hundred yard space between the Start and Finish line is far below him and it is virtually a rectangular speck -- a thin, short area which he knows he can cover with the slightest forward movement of one huge foot. Positive of his win, when the gun goes off, he simply lifts and moves a single foot in a very leisurely manner from the Start line across the Finish line. This action takes one half second.

    The microscopic hare, on the other hand, has looked at that same hundred yard stretch and he sees what appears to be an infinite distance in front of him. In fact just the Start line is an incredibly wide band of white powder strewn with huge boulders (grains of sand) and tremendous white dunes (the starting line powder). But this microscopic little hare is no pushover. The instant the starting gun is fired, he takes off like a shot.

    Who wins? To everyone’s surprise, the race is a photo finish – an exact tie! And here's where a seeming paradox comes in. According to the clock on the sidelines, the tortoise and the hare moved at exactly the same speed. They both started exactly on the gun shot and crossed the finish line at exactly the same instant. But let's imagine traveling that “same speed" in each of their “worlds.”

    In the tortoise’s immense world, the motion was a slow, easy movement of one foot. He simply lifted it up and slowly moved it forward. In the microscopic world of the mite sized hare, however, in order to get to the finish line at the same time, his motion was lightning fast. To travel that 100 yards in just one half second, he had to blast down the track, virtually like a bullet.

    So the question is: Are these differences in motion only perceptions? Or, is the motion of an object somehow relative to it’s size?
  2. jcsd
  3. Jun 27, 2008 #2


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    They are just perceptions, for example:
    say their eyes were an equal size and equally spaced apart and the tortoise was the same width and length as in your example but was the same height as the hare then the two would perceive exactly the same thing.
    This should tell you that the reason for the difference in perception is because the height of the tortoise makes the angle between the start and finish from his eyes very small, so the distance seems much smaller, but the actual distance his head (and eyes) will travel is the same as the hare.
  4. Jun 27, 2008 #3


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    Welcome to PF!

    Hi diZcomm1! Welcome to PF!! :smile:

    The tortoise and the hare are using different scales (say one is 1000 times the other), but all their units are affected in the same way.

    Distances are 1000 times larger, but so is time, and that makes c (the speed of light) the same, and so v/c is also the same.

    And it's v/c which matters. :smile:
  5. Jun 27, 2008 #4
    Thank you for your reply, jk4. I see -- I think.

    Just for the record, let me state it another way. Imagine two entire worlds, one in which all things, including all men and women are huge (a size relative to the tortoise), and another world in which all things, including all men and women are microscopic (a size relative to the hare).

    Now, if each ran a 100 yard dash in their worlds, the lengths would be different. A hundred yards for the microscopic world would be much shorter than in the huge world. And if they ran the race in this situation, there would be no time difference perception. But if we bring both of them into OUR world, on a track that is correct for neither of their worlds, the perception difference occurs.

    Please forgive me. As I said, I am not a physicist, but it seems that time and motion must pass differently for very small entities than for very large ones.
  6. Jun 27, 2008 #5
    Thanks tiny-tim.

    I have to confess I get a llittle lost. See my answer to jk4.

    Also, I agree that the torsoise and hare are using different scales, but in many of the Einstien relativity illustrations I've read, he talks about different points of view. For instance, a ball bouncing on a train as seen from the point of view of an observer at rest and from the point of view of the person bouncing it on the train. These two individuals would be subject to different criteria as well, right? And this would produce different perceptions. But (I believe) Einstein makes the point that both percetions are valid.
  7. Jun 27, 2008 #6


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    Hi diZcomm1! :smile:

    Yes, both perceptions are valid …

    and they both give the same results because time and distance are scaled in the same proportion. :smile:
  8. Jun 27, 2008 #7
    tiny-tim, Again, thanks!

    Another thought. I guess there are actually 3 points of view or perceptions, right? the tiny world, the huge world and (in between) our world. And if all THREE perceptions are valid, although the results produced may be the same, the experiences are different. Can we interchange the word "experiences" with "realities"? What I keep getting at is the idea that the size of the world you occupy has a direct effect on the speed at which motion happens. You may not realize it from your pespective inside that reality, but from the perspective of an oberver in a different size reality it would seem to be apparent.

    I know you're probalby saying this guy is a little thick headed, and I'm sure you're right!

    Thanks agian.
    Last edited: Jun 27, 2008
  9. Jun 27, 2008 #8


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    diZcomm1, I think you are confusing perception via our senses (eyesight, hearing etc.) with measurement. Our senses evolved with us and are attuned to our size scale whereas measurement has been developed to be objective and independant of scale.

    Take your race for example. To a human judge watching the event the tortoise will appear slow due to its size while the hare will appear very fast. However, when the judge measures the track and times both contestants he'll conclude they both covered the 100 yards in 0.5sec proving they are in fact going the same speed, that is 200yd/sec.

    Notice that the objective measurement gives the correct answer regardless of scale. The tortoise, if he's smart enough can do the same calculation and reach the same conclusion. So can the hare.
    Last edited: Jun 27, 2008
  10. Jun 27, 2008 #9
    Hello paw, I do agree with and (I think) understand everything you say. But every point you make is from the point of view of our world. What I'm asking is this: If you WERE that tiny, microscopic hare and you ran that 100 yards in .5 seconds what you would EXPEREINCE as your reality would be a "LIGHTING" fast burst of speed. What the tortoise would expereince on the on the other hand would be a slow easy motion. Yes, the objective measurment from the sidelines would be the same, but the REALITIES of the two expereinces would be completely different, even though the speed and distance were the same. So, are those both of those realities REALLY REAL? And if they are, do they trump the objective measuments as the correct answer?

    The truth is, I'm sure you're right paw. Since I am not a physicist, I have no doubt it's my ignorance that keeps me from seeing this correctly.
  11. Jun 27, 2008 #10


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    I understand what you mean. In fact I've considered this during many a bored moment while at one with nature (:D). A galaxy sized tortoise vs a normal sized hare or a normal sized tortoise and a QM-effect inducing hare and so on.

    Would a galaxy sized object look at us as if we were quantum mechanical particles? Does the uncertainty in a measurement depend on the size/scale of the measuring equipment?

    I think the weird thing is that the tortoise covers 0.00001 of his own body length while the hare covers 100000x his length. Now this is quite strange...

    http://en.wikipedia.org/wiki/Scale_invariance - May be useful.

    Our world is not scale invariant. A human jumps off a 13 storey building and that's the end of their lives, an ant jumps off a 13 storey building and nothing much happens. Of course, that wouldn't hold true in a vacuum but meh...
  12. Jun 27, 2008 #11


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    Not necessarily. If you were that microscopic hare you'd experience what your senses tell you. Maybe your metabolism is so fast you'd feel like it takes a long time to run the race. This is the point I was making. Perception is tied to your biological senses and your biological 'clock'. It has nothing to do with objective measurement.

    Be careful in taking perception to mean the same as real. I used to skydive and I often felt like time had slowed during the jump. That is perception. An observer on the ground with a stopwatch would record the REAL passage of time. So the answer is 'no' those perceptions (what you labeled realities) are not real.

    Yes, objective measurement is the only way to sort perception from reality. That, in some sense, is the heart of the scientific method.
  13. Jun 28, 2008 #12


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    I think you are pretty confused. Especially when you say "the lengths would be different."
    It is important that you realize that is false.
    A meter to the hare is EXACTLY a meter to the tortoise. Although the meter may SEEM larger to the hare and smaller to the tortoise, but that is ONLY due to the relative size of their bodies.

    Another argument I should have put in my first post is that if the hare were to ride on the tortoise' head the hare would perceive the exact same thing as the tortoise.
    another thing that might clear it up is draw a 2D diagram from the side view. Although the tortoise' can easily go across the entire field he still travels the same distance as the hare in the same amount of time so their velocities are the same. Like I said, the perceived difference is due to the angle because the tortoise is so far away from the floor.

    It's like holding a quarter in front of the sun (don't do this, you will probably damage your eyes lol), the sun is enormous but because it is so far away it appears much smaller of a diameter (distance). Now imaging seeing a comet travel across the sun in a few seconds, did the comet only travel a few feet? (that's what you see right?) no.. that is incorrect, that would be a "naive observation" we know we must take into account the distance between us and the event.
  14. Jun 28, 2008 #13


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    ok I made a quick image, I know it's horrible but it might help a little.... maybe

    it's a side view, so the bottom of the image is the ground and the top would be the sky, the red dot is the hares eye, and the green dot is the tortoise' eye.
    You keep imagining things from what the tortoise sees looking down, so 100 meters looks smaller to the tortoise (of course), but you forget that he still travels the same distance horizontally, which is why I said if the tortoise was as short as the hare, regardless of width and length (so it can still cross the same distance with ease but it's eyes are level with the hare) then the tortoise will see the same things as the hare.

    so let me sum it up, what you perceive (in this situation) is based solely on what their eyes see, so in that sense the tortoise is NO different from the hare at all other then the distance he is from the floor, their eyeballs each travel the same distance in the same time interval.

    sorry if I'm over explaining things. It's just that, even after all that, I can see how you may be confused still and I just can't seem to put this one concept in my head into words. I tried my best though, so let us know if you need more explaining.... lol

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    Last edited by a moderator: Jun 28, 2008
  15. Jun 28, 2008 #14


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    There really isn't any physics there - that's just the way our brains perceive things. Yes, what you see is perfectly valid in both cases.

    Have you ever seen a video of a large rocket launch? They look like they take off very slowly, even thought they are accelerating at several g's.
    These perceptions don't disagree with, much less "trump" objective measurements. It's literally all in your head. In the rocket example: you're used to seeing things one way and when you see them another way, your brain has trouble grasping it. That's it.
  16. Jun 28, 2008 #15
    Hello jk4, I've taken up too much of your time already. I want to get my head around your answers and I'm sure this will clear things up for me. Thanks for taking the time to dig in for an explanation. I have to say that I'm not 100% sure that I've been clear as well -- that I've been able to communicate what I am envisioning. I'll take some time with it and if it warrants more questions, I'll post. Thanks!
  17. Jun 30, 2008 #16
    Thanks, Russ for your input!
  18. Jul 2, 2008 #17
    spatzky and mtworkowski: I'm unable to view your posts.
  19. Jul 2, 2008 #18


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    Both posts were deleted (one by the poster, the other was spam). You shouldn't even be able to see that they posted at all.....what do you see?
  20. Jul 3, 2008 #19
    Hello Russ, please see my email response to you. Thanks, Ray
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