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The twins paradox

  1. Jan 28, 2005 #1
    the twins paradox

    It is true that the one that traveled is younger, is this a fact or it is a paradox
     
  2. jcsd
  3. Jan 28, 2005 #2
    Einstein's theory of time dilation has been somewhat proven.
    The website: http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.html
    says that:

    In 1971, experimenters from the U.S. Naval Observatory undertook an experiment to test time dilation . They made airline flights around the world in both directions, each circuit taking about three days. They carried with them four cesium beam atomic clocks. When they returned and compared their clocks with the clock of the Observatory in Washington, D.C., they had gained about 0.15 microseconds compared to the ground based clock.
     
  4. Jan 29, 2005 #3

    Fredrik

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    It's a fact, and not a paradox. If you'd like to know more, I suggest you use the search feature to find other threads about the twin paradox. There's about a gazillion of them.
     
  5. Jan 29, 2005 #4

    JesseM

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    It depends what you mean by "the one who travelled". If both travel away from each other at constant velocity, so there's no acceleration involved, each one says the other is younger in his own reference frame, but unless one of them changes velocity they'll just get farther and farther apart, so they won't be able to get together to compare their ages in one spot. If one of them does change velocity so that they eventually meet up again, then the one that changed velocity will be the one who's younger when they meet.
     
  6. Jan 29, 2005 #5
    The word "paradox" is kind of a hang-over from the days of classical physics. In purely classical terms it's a paradox because it was believe that time was absolute and therefore it would be a paradox to conclude that someone could pass through more or less time than someone else.

    However, since that time we've come to realize via experiment that the conclusions of relativity are ontologically correct. In other words, it is possible for someone to pass through more or less time than someone else. This has been precisely verified in countless experiments. In literally billions of experiments actually if we count the experiments that take place in particle accelerators which we most certainly should include. The lifetime of sub-atomic particles is affected for the very same reason that the lifetime of the twins is affected in "The Twin Brothers Paradox" thought-experiment or "gedanken-experiment" as it's called in German.

    The name of this thought-experiment was never changed from it's original name which includes the word paradox. But time dilation is no longer considered to be a paradox. It's now understood to be an actual property of nature. The old Newtonian concept of absolute time is now known to be ontologically incorrect.

    So don't take the word paradox literally in this case. It's really not considered to be a paradox any longer. The word in this context is just a historical hangover.
     
  7. Jan 29, 2005 #6
    didn't they also put one on the space shuttle to test what the effects of gravity on time were? i think i remember hearing it somewhere.
     
  8. Jan 30, 2005 #7
    Yep - a good example of both of these effects can be found in how GPS clocks are preset before launch - There is one correction to account for the velocity of the satellite clocks relative to the non-rotating earth centered reference, and there is a second correction to account for the altitude of the satellite(s) relative to the surface of the earth. The velocity correction is opposite to the height correction - and the latter is much larger. Once in orbit, they keep almost perfect time with the earth stations - small period corrections being required to adjust for the fact the orbits are not perfect.
     
  9. Jan 30, 2005 #8

    JesseM

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    That isn't generally why people call it a "paradox". The reason people call it a paradox is because they mistakenly think that relativity says the laws of nature work the same in *all* reference frames, not just inertial ones, so they imagine that the situation is completely symmetrical, since from the travelling twin's point of view the earth moved away for a while and then turned around and moved back towards him. If the situation was indeed symmetrical, it would seem to be a paradox because each should predict the other ages slower, and both points of view would be equally valid. But since the principle of relativity only applies to inertial frames in SR, it isn't really symmetrical, so there's no paradox in the fact that one has objectively aged less when they meet up.
     
  10. Jan 30, 2005 #9
    But JesseM - they guy who takes off from earth doesn't really have to turn around - he can go to a distant place that is 5 LY away as measured by earth equipment and send a message when he arrives saying: "I am here now and my clock only reads 3 years more than the day I left."
     
  11. Jan 30, 2005 #10

    JesseM

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    Well, it will definitely take more than 10 years for the earth to get this message, as measured by earth-clocks. And if there was a satellite moving in such a way that it was at rest relative to the travelling twin, and 5 LY behind him according to his own measurements, then when this satellite passed by the earth, the earth could send a message saying "the satellite just passed by us and our clock reads only 3 years more than the day you left". Without either one changing velocities the situation must be symmetrical in this way.
     
    Last edited: Jan 30, 2005
  12. Jan 30, 2005 #11

    jtbell

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    For a more recent example of this sort of thing, comparing clocks in airplanes flying around in circles to clocks on the ground, see

    "Timekeeping and Time Dissemination in a Distributed Space-Based Clock Ensemble" (from a conference in 2002)

    http://tycho.usno.navy.mil/ptti/ptti2002/paper20.pdf

    in particular the "Flight Tests" section.
     
  13. Jan 30, 2005 #12
    I don't understand this, I always thought it in this way:
    there is one clock in S and another in S' if we measure the time from S to the clock at S' we get time contraction, but if we are sitting in S' and measure the time at the clock there there is not time contraction. Therefore I always thought that the twin that made the trip is equal biologically old to the one that stayed in earth because the aging occur in the the frame you are. Of course if you try to measure the time at S' from S there is time contraction.

    thanks in advance :confused:
     
  14. Jan 30, 2005 #13

    russ_watters

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    He has to stop when he gets there though.
     
  15. Jan 30, 2005 #14

    JesseM

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    That's not relevant, he could just send a message the moment he passes next to the planet (if you idealize both the planet and the traveller as point-sized, there can be a moment when his position exactly coincides with the planet).
     
  16. Jan 30, 2005 #15

    JesseM

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    S will see the clock at S' slowed down, but likewise S' will see the clock at S slowed down. The key thing to understand is that different frames define simultaneity differently, so S may say his clock read 10:00 "at the same time" that the clock at S' reads 8:00, while S' may say his clock reads 8:00 "at the same time" that the clock at S reads 5:00. And when the travelling twin switches from heading away from the earth to heading back towards it, his definition of simultaneity changes too, so he will go from thinking the earth clock is way behind his own to thinking it is way ahead of his own. As he returns to earth, he will still say the earth-clock is running slower than his own, but since it started out far ahead of his own when he turned around and began to return, it will still be ahead of his own when he reaches earth. So, even though the earth-clock was running slow from his point of view during both the outbound leg of the trip and the inbound leg, he will still agree with the earth-twin's prediction that his clock will be behind the earth-clock when he returns, because his plane of simultaneity swung around this way when he turned around.

    This page has a diagram which may be helpful, with the verticle line representing the worldine of the earth-twin A, the bent line representing the outbound and inbound legs of the travelling twin B's worldline, and the red lines representing B's definition of simultaneity at different moments on his trip.
     
    Last edited: Jan 30, 2005
  17. Jan 30, 2005 #16
    Russ and Jessie - Quite right Jessie - the traveler doesn't have to slow down - he can send the message on the fly - and when it is received 5 years later by the stay at home on earth, he will be older of course by 5 years plus the time it took the traveler to make the journey as measured in the earth frame - but all that is irrelevant to the discussion - what is of consequence is that we can make a comparison of the time accumulated in the frame of the traveler with the time accumulated in the frame of the stay at home w/o having to postulate acceleration, or changing frames. It is a direct consequence of the invariance of the interval. It is the high speed particle experiment - the one why twin excursion - whatever you want to call it.
     
  18. Jan 31, 2005 #17

    JesseM

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    Time accumulated between what two events? The two frames will disagree about simultaneity, so if neither changes frames, both will say the other twin aged less over a given time interval.
     
  19. Jan 31, 2005 #18
    Jessie--There are two events - the starting point which is an event measured by twin 1 and twin 2 each in their own frame, and the ending point which is an event measured by twin 1 and twin 2 each in their own frame -- since each twin only measures time and distance in their own frame (the stay at home measures proper time and proper distance in the earth frame and the traveler measures proper time using the clock which accompanies him) - the spacetime interval according to SR must be the same (invariant). There is never any need for either twin to make any measurement in the other twins frame therefore there is no simultaneity confusion
     
  20. Jan 31, 2005 #19

    JesseM

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    Whose "ending point"? Each twin sees himself at rest and the other in motion, so it makes just as much sense to define the ending point as the moment the travelling twin passes a planet which is at rest relative to the earth as it does to define it as the moment the earth twin passes a satellite which is at rest relative to the travelling twin.
    Yes, of course it's true that if you just want to measure the spacetime interval/proper time between two events, there will be no disagreement between observers on this. But the travelling twin's proper time between departing the earth and passing the planet is the same as the earth twin's proper time between departing the travelling twin and passing the satellite (assuming, as I did before, that the distance to the planet in the earth's rest frame is equal to the distance to the satellite in the travelling twin's rest frame). And whichever twin you pick to measure the proper time between two points on his worldline, the other twin will say this time is less than his own coordinate time between those two points. So do you agree that if neither twin changes velocity, the situation is completely symmetrical in every way?
     
  21. Jan 31, 2005 #20
    Jessie - It is true, that if you introduce a satellite that is spaced 5LY away in the traveling twins frame, there is symmetry by definition because neither frame can tell which is in motion - but what is of moment in the present proposition is the relationship between the proper time logged by two clocks in relative motion where one clock does not have a spatial component in its interval and the other one does - Let us simply say that at a time that both twins agree upon, the traveler takes off at 0.8c and heads toward a planet 5 LY away as measured in the earth frame. When the traveler arrives at the planet, he sends a message to his earth twin telling him how much time has passed on his pocket watch which he carried with him. What will he transmit?
     
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