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A little paradox in relativity.

  1. Jun 15, 2009 #1

    rpj

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    Einstein once upon a time said that the faster you go the slower time goes.

    Speed is Distance/Time.

    If Time goes slower as a cause of speed, then the Time variable would be smaller and thus the speed greater. This would cause an infinite acceleration as more speed would cause the time to go slower and slower time will cause the object to go faster.

    Here comes the paradox: As Einstein stated, time is relative to space, thus the "slow time effect" caused by the great speed is only present around the moving object. This would mean that the acceleration is only noticed from within this space around the moving object. From a stationary point of view the object would seem to be travelling at a constant speed.

    How can an object accelerate and be at constant speed at the same time?
     
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  3. Jun 15, 2009 #2

    Doc Al

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    One way of putting it is that moving clocks are observed to run slow, and the faster they move the slower they are observed to run.

    OK. Note that when you measure the speed of something, you use your distance and time measurements, not those of some moving clock.

    Your time does not go slower, so this doesn't quite make sense.

    Perhaps you can try again.
     
  4. Jun 15, 2009 #3
    It isn't a paradox.

    Reading this may help, but it may be too dense if you aren't already geeked out by the technical details and mathematics of relativity: http://en.wikipedia.org/wiki/Spacetime_interval

    It isn't a slow time effect, it is slower motion through time.

    You're always moving through time.

    Picture a little arrow moving upwards along an axis marked time, with a horizontal axis marked space.

    The length of that arrow is going to remain the same, this is a simplified description of a spacetime interval.

    If you tilt the arrow over so it is moving along the space axis, you find that it's motion along the time axis is reduced. The closer to a 45 degree angle it gets, the closer to the speed of light through space it is going.
     
    Last edited: Jun 15, 2009
  5. Jun 15, 2009 #4

    A.T.

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    No, "time" in the above formula is "coordinate time" measured by a stationary clock, not a moving one which ticks slower.

    No, it has nothing to do with being in a certain area of space. Every clock which moves relative to the observer goes slower. No matter how close he is to it.

    You don't easily see time dilation directly in a Minkowski diagram with a coordinate time axis. A diagram with a proper time axis is better for this:
    http://www.adamtoons.de/physics/relativity.swf
    But here you tilt to 90 degree for speed of light.
     
    Last edited: Jun 15, 2009
  6. Jun 15, 2009 #5

    rpj

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    Imagine the object moving from a to b to c. From a to b it would take less time measured withing the object than measured outside the movement from a stationary point.

    From b to c it would take even less time measured from within the object and thus it would be accelerating as time goes slower and slower but the distance inbetween a and c remains constant.

    My paradox is how can the object be accelerating if you measure time from withing the object and be at constant speed when time is measured from a stationary point.


    Relativity aproves that they can be multiple places where time goes at different speeds. To divide a certain space into multiple areas each area needs to take up a certain space.

    When the object moves, all around the object time is going slower.
     
  7. Jun 15, 2009 #6

    A.T.

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    There is no accelerattion. You are using the wrong time to define velocity in a recursive way,
    In space time curved by gravity. This is not the case in you example and has nothing to do with movement.
    No. Only for the stuff that moves with the object time goes slower. No matter how close to the object
     
  8. Jun 15, 2009 #7

    rpj

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    Faster you go the slower time goes for the moving object and the faster it goes the slower the time goes. Medition of speed from within the object would read an acceleration. But what speed medition is right? The one taken from within the object or the one of the object relative to the ground?
    Define gravity.


    So you are saying Time is dependant on matter to exist?
     
  9. Jun 15, 2009 #8
    For differences in time due only to velocity, the measurement doesn't depend on where you are in space. It depends on what spacetime coordinate system (reference frame) you're using. Each coordinate system exists throughout space and time. Each coordinate system applies both inside and outside of all the objects being described, regardless of how they're moving relative to each other.

    Consider a reference frame that keeps pace with the object (moves with the object = has the same velocity as the object). We call this the object's rest frame because the object is at rest in such a coordinate system. Measured according to this frame, a certain time passes between the event of the object being at A and the event of the object being at B. But we can't use this time to calculate the velocity of the object, because in the object's rest frame - by definition - it has no velocity: it's standing still.

    It's only when measured according to a reference frame (spacetime coordinate system) moving relative to the object, that the object has any velocity at all. For example, we could set up a coordinate system in which points A, B and C are at rest. Now it's the object that moves past these points, rather than the points that move past the object.

    From the perspective of the object's rest frame, time goes slow according to the rest frame of the moving points. From the perspective of the points' rest frame, time goes slow according to the rest frame of the moving object. But in each case, it goes slower by the same amount! From this, we see that the velocity of the moving points is the same when measured according to the object's rest frame as the velocity of the moving object when measured according to the points' rest frame. So there is no paradox.

    If the distance from A to B is the same as the distance from B to C, according to a reference frame where the object is moving, such as the rest frame of the points, then it will cover the same distance in the same time - this time being always the time according to the reference frame in which the object's position is changing. We can't use the smaller amount of time that passes according to the object's rest frame, because according to that frame, the object isn't actually moving.

    And it certainly wouldn't make sense to start measuring velocity using the time as measured according to one frame, then switch to using the time according to another frame, then treating the reduced time as if it was the yet to be reduced time, reducing it, and finding the limit as this recursive process is performed infinitely many times.

    Again, for considering only the sort of time differences between coordinate systems due to their movement at a constant velocity relative to each other, the amount of time that passes between two events doesn't depend on where in space you are, only on what spacetime coordinate system you use to locate events. When we say "in a reference frame", we mean "according to a coordinate system", rather than inside an object or within some particular region of space. The coordinate system applies to all of the spacetime under discussion.
     
  10. Jun 15, 2009 #9

    A.T.

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    That is exactly your recursive definition of velocity, which is wrong. You schould use coordinate not the objects proper time The rest is based on it and equally wrong:

    The velocity of the object measured in the frame of the object is always zero. The velocity of the object measured in the "ground frame" is the spatial displacement measured in the "ground frame" divided in by the time as measured in the "ground frame"

    http://en.wikipedia.org/wiki/Gravity#General_relativity

    By "no matter" I meant it is irrelevant.
     
  11. Jun 15, 2009 #10

    rpj

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    Not sure if you are understanding me.

    THIS:

    http://img188.imageshack.us/i/explanation1.png/

    Rocket is moving from A to B at a constant speed if time is measured from the dude's point of view.

    If Time is measured from the rocket's stopwatch then the speed appears to be higher as a cause of the time going slower.

    WHO IS RIGHT? the rocket's clock or the Dude's clock?

    Maybe relativity is wrong after all and the movement is affecting the rocket's clock.

    Who knows? until we develop a non movement dependant clock we will no know if relativity is 100% right.
     
  12. Jun 15, 2009 #11

    Doc Al

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    OK.

    Incorrect. Realize that the rocket observers also measure the distance between A and B to be shorter. The rocket observers measure the dude to be moving past the rocket at the same speed that the dude measures the rocket to be moving past him.

    Both are correct; both measure each other moving at the same relative speed.
     
  13. Jun 15, 2009 #12

    rpj

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    You aren't measuring the speed like that. There is a constant distance inbetween A and B.

    The TIME that takes to go from A to B is different depending if you are the dude or the rocket.

    How is this so?
     
  14. Jun 15, 2009 #13

    Doc Al

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    The distance between A and B is constant (it doesn't vary with time) but it is not invariant. Just like time is measured differently by different observers, so is distance. "The dude" measures a greater distance between A and B than does the rocket.

    True.

    You can't pick and choose the relativistic effects that you like and ignore others. Measurements of both distance and time depend on who is doing the measuring.
     
  15. Jun 15, 2009 #14

    rpj

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    :O So you can compress or dilate space.

    Still makes no sense to me.

    How can a distance be shorter if you are going faster?

    The distance can't be short and long at the same time. How can a distance be shorter and longer at the same time?

    That makes absolutelly no sence.
     
  16. Jun 15, 2009 #15

    Doc Al

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    Yet you seem to have no problem accepting that a time interval can be longer or shorter depending upon who's measuring the time? :wink:
     
  17. Jun 15, 2009 #16

    rpj

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    I personally think relativity is wrong.
     
  18. Jun 15, 2009 #17
    Believe it or not, most of us went through this in some way at some point or another when first faced with Relativity.

    "How the... but that doesn't... what is this I don't even..."

    Think about what the principle of relativity means, in simple terms, if you're inside a spaceship moving at a uniform velocity and you can perform an experiment which determines you're in motion, that principle breaks down.

    If you set up a light clock (two mirrors spaced a set distance apart where a certain number of trips between the mirrors marks off a certain amount of time) and the speed of light is constant, how can the clock run slow? If the clock doesn't run slow, would you be able to determine you were in motion?

    ____
    `|
    _|__


    .......____
    ......./...\
    ___/_...._\___

    Assume the |'s and /,\'s are the same length, let's say 1/4 a light second.

    At rest you get 1 second per trip up and down, but in motion it's bouncing at an angle between the mirrors, covering a longer distance. Thus it MUST be measuring a longer period of time, say 1.5 seconds per trip up and down.

    If you could simply look at it and see that it was taking longer for each bounce than it should, you could determine you were in motion and have a privileged frame of reference.

    How this is resolved requires your motion through time to vary, so you go slowly enough through time that you observe no change in the period marked by the light pulse bouncing between the mirrors. Even though it's taking 1.5 seconds each trip, in your rest frame it's simply bouncing up and down, and thus appears to take 1 second per trip.
     
  19. Jun 15, 2009 #18

    A.T.

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    Every moving thing is compressed spatially along the movement direction. You can see it as an effect of the orientation in spacetime. The lengths we measure in space are just a projection of an object in 4D spacetime onto 3D space. Depending on the orientation in 4D the projection in 3D can vary in size.

    Look here:
    http://www.adamtoons.de/physics/relativity.swf
    - The length of the rocket in spacetime (yellow line) is always the same but in space (rocket shape) it depends on it's velocity.
    - The rocket's clock ticks slower because the rocket moves more trough space and less trough time.
     
  20. Jun 15, 2009 #19
    Don't worry, from the bits of information you have so far, it really doesn't make sense! It wouldn't make sense to anyone. It's only when you learn all the details of the theory that you can see how they fit together as a logical whole without contradictions. A few important things in relativity are very different from what our common sense tells us: different observers observe different amounts of time passing between the same pair of events, depending on their speed relative to each other. They also measure different distances in space. Even the order in which some events happen can depend on speed. But other quantities are invariant, such as the spacetime interval which measures how far apart events are from each other in time AND space. These are hard things to get your head around because they aren't like anything in everyday life as we experience it. On their own, they each sound paradoxical, but together they eliminate contradictions - not only their own apparent contradictions, but also some of the unspoken contradictions inherent in the more "common sense" view of the world that the theory replaced. It made no sense to me when all I had to go on were garbled bits and pieces from popular science books and TV and stuff. Only when I started looking at actual physics textbooks that explained the mathematical background did I feel like I was beginning to get it. There's still a lot I find hard to understand, but it's not worth racking your brains over till you've seen a proper, coherent explanation.

    Here's an online textbook that I've found helpful; chapter 7 is about relativity.

    http://www.lightandmatter.com/html_books/0sn/ [Broken]

    I think it also helps to read different author's explanations of the same concepts (in fact, the more the better), because some are clearer on some points, other clearer on others.
     
    Last edited by a moderator: May 4, 2017
  21. Jun 15, 2009 #20

    rpj

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    Relativity is wrong because it doesn't apply to quantum scale.

    If movement where composed by small near to 0 teletransportations then the arrow paradox would make sense and quantum teletransportaions would too.

    Movement is an illusion. In films you have an illusion of movement when you reach 25 frames/second. In real life it would be X teletransportations/second.


    ARROW PARADOX:

    You shoot an arrow. Before it gets to the bullseye in needs to go past a half way point. Before it get's to that halfway point it needs to get to a half way point inbetween the the starting point and the half way point, but before it needs to get to another half way point. To infinite thus the arrow can't move.


    Time for me is constant and unvariable. Nothing can exist without it because the term existance needs time to have a meaning. You can't exist for 0 seconds.

    At the beggining of all, time was created. Obviously.
     
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