The Twin Paradox

Discussion in 'Physics & Math' started by Space case, May 19, 1999.

  1. Recently I was reading a book called 1001 THINGS EVERYONE SHOULD KNOW ABOUT SCIENCE by JAMES TREFIL when I came across some very intersting information concernig Relativity.
    I wrote some of it below.

    672. The predictions of relativity do not match up with our every day experience. For example, if you stand on a railroad car moving thirty-miles an hour and throw a baseball forward at the speed of twenty miles an hour, you expect that somone on the ground would see the baseball moving at fifty miles an hour-your speed plus that of the railroad car.
    Suppose instead that you were on that same railroad car and sent the beam of a flashlight in the forward direction. You would see the speed as being 186,000 miles per second. Someone one the ground, however,would also have to see the speed of light as 186,000 miles per second-not 186,000 miles per second plus thirty miles an hour-if the principle of relativity is to be right. If the person on the ground saw a different speed from you, then Maxwell's eequations wouldn't be the same for both observers and the principle of relativity would be wrong.
    It is only because relativity is so well verified experimentally that physisicists are now willing to accept this sort of strange proposition.

    674.The twin parodox isn't really a paradox. This paradox arises becuase, according to relativity, if one of two identical twins spent his life in a rocketship traveling near the speed of light, when he comes back to earth, he will be younger than his sibling. Today we know that the twin Paradox is a real effect(see the following). In other words, it shouldn't be called the "twin paradox" but the "twin effect."

    675.The slowing down of moving clocks can be tested experimentally. In the 1960s a group of scientist at the university of Michigan put atomic clocks on airplanes that were flying around the world(it was Pan American flight #1, if you must know). After the clocks completed their journey, they were compared to identical clocks that had been left in the laboratory. The result: the moving clocks had in fact, ticked fewer times than the stationary ones. Of course, these are clocks that can measure time to an accuracy of thirteen decimal places, not your standard wrist watch, but they establish the principle that time is relative.

    I don't know about you but this stuff has got my brains tide in knots. let me know what you think.
     
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  3. Sirius B Guest

    I agree with you! This stuff is enough to cause massive "brain hemorrhaging" for all who dare to study it ~

    Please Register or Log in to view the hidden image!

    -)

    On the other hand, maybe we need to take a closer look at this topic because it just might be the answer we need to conquer the problems of interstellar travel (for human beings anyway!)What do you think?
     
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  5. Athelwulf Rest in peace Kurt... Registered Senior Member

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    This reminds me of the question I asked [Thread=40056]here[/Thread].
     
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  7. Roman Banned Banned

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    Would slower moving planets experience time slower than swifter moving planets?
     
  8. Athelwulf Rest in peace Kurt... Registered Senior Member

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    I think it's vice versa, Roman. Slowly moving planets would experience a faster rate of time than swiftly moving planets, since velocity seems to have a "slowing" effect on time.
     
  9. Roman Banned Banned

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    Oh... right. Silly me.
     
  10. 2inquisitive The Devil is in the details Registered Senior Member

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    Unless, of course, the slowly moving planet had a lot higher g-force of gravity at its
    surface. Clocks run slower under higher gravity. Clocks could even run at the same rate on a 'large and slow' planet as they do on a 'small and swift' planet.
     
  11. LephtShew Registered Senior Member

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    We did questions about "672." in our physics 11 class, the relativity formulas (the simple ones you use for everyday stuff) are not the most accurate. There are actually better formulas which incorporate speeds close to that of light or OF light itself. When you use the smaller (everyday) values in this formula you get answers off by somewhere in the thousandths of decimal places (maybe even further) from the regular formulas, we just use the regular formulas with adding and subtracting because their more efficient and practical.
     
  12. chloris Registered Member

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    This book doesn't seem to go into much detail. The real "paradox" part of the twin paradox has to do with the basic premises of general relativity. Say you're sitting in a stationary car and you see me go past you in another car. Let's say there are no surroundings. Well, what if you looked at things from my point of view? I could very well say that my car isn't moving and you're the one going past me. The physics would be the same.

    The twin paradox says that one twin, Bob, stays on Earth and another twin, Ann, goes off into space in a spaceship traveling near the speed of light. For stuff going that fast, time dilates, or slows down. So Ann comes back and finds that Bob has aged more than her. But what if we looked at things from Ann's point of view? In her stationary reference frame, Bob was the one moving near the speed of light, so when they meet again she would expect herself to have aged more than Bob. So the two twins would disagree on their ages, but it's got to be one or the other. Hence the paradox.

    The solution has to do with the fact that because Ann has to accelerate and decelerate in order to turn around and come home, we're not dealing with inertial reference frames, so Ann can't say that she's staying still. If ever such an experiment could be carried out, Bob would be older.
     
  13. Persol I am the great and mighty Zo. Registered Senior Member

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    To have the twin paradox you need the twins to meet twice. Once to tell the starting age, once to tell the ending age.

    In order for this to happen one of the twins as to decelerate and change direction to make the pass a second time. This acceleration only happens to one of the twins, and is the reason the problem is not symetrical.
     
  14. marv Just a dumb hillbilly... Registered Senior Member

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    People love puzzles and trying to solve paradoxes. That's the only thing that keeps Einstein's theory alive. Did anybody ever come up with the answer to the number of angels who could dance on the head of a pin?
     
  15. Persol I am the great and mighty Zo. Registered Senior Member

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    That's the only thing that keeps it in the publics mind. It's 'alive' because it provides results, not because people argue about it.
     
  16. Janus58 Valued Senior Member

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    You need to be carefull here. Higher surface gravity does always lead to a slower rate of time in GR. For example, the surface gravity of Earth is actually greater than that of Uranus, but the gravitational time dilation is greater (time would run slower) on the surface of Uranus.
     
  17. 2inquisitive The Devil is in the details Registered Senior Member

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    Of course, Janus58, I worded the sentence poorly. I sometimes say things like 'the
    intensity of the gravitational field where an observer (clock) is located.' But I know
    that is unscientific, ambiguous and not correct according to GR either. But you
    might want to rethink your statement also as it seems contradictory?

    by Janus58:

    "Higher surface gravity does always lead to a slower rate of time in GR. For example, the surface gravity of Earth is actually greater than that of Uranus, but the gravitational time dilation is greater (time would run slower) on the surface of Uranus."
     
  18. Janus58 Valued Senior Member

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    Surface gravity can be calculated by

    A[sub]g[/sub] = GM/r²

    where A[sub]g[/sub] is the acceleration duew to gravity at the surface.

    Gravitational time dilation is calculated by

    T = T[sub]0[/sub]/sqrt(1-(2GM)/(rc²))

    Where T is the time measured from a point well removed from the gravity source.

    Now for Earth, the surface gravity is

    (6.673e-11)(6e24)/(6.378e6)² = 9.842... m/s

    For Uranus it is

    (6.673e-11)(8.68e25)/(2.5559e7)² = 8.866... m/s

    Thus you can see that the surface gravity on Uranus is less than Earth's.

    Now for time dilation.

    One second as measured on the Surface of the Earth would be

    1/sqrt(1-2(6.673e-11)(6e24)/(6.378e6)(3e11)²)) =1.0000000000000006975 sec as measured by our far removed observer. IOW, the Earth clock runs slow by this amount.

    For Uranus:

    1/sqrt(1-2(6.673e-11)(8.68e25)/(2.5559e7)(3e11)²)) =1.000000000000002518 sec as measured by our observer.

    If we compare these two time rates, we find that the Clock on Uranus runs 1.0000000000000018 times slower than the Earth clock, even though the surface gravity on Uranus is less.

    This is because gravitational time dilation is not tied to differences in local field strength but differences in gravitational potential.
     
  19. 2inquisitive The Devil is in the details Registered Senior Member

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    "Higher surface gravity does always lead to a slower rate of time in GR."

    What I was referring to was perhaps you left out a 'not' in your first sentence? Thus
    the contradiction.
     
  20. Janus58 Valued Senior Member

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    Missed that. Even when I re-read it, my mind automatically inserted the 'not' that was omitted, because it was supposed to be there (it got lost somewhere between brain and fingers).
     

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