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Revised Twin Paradox

  1. Aug 13, 2008 #1
    Thought experiment / story:

    Albert the Alien sits atop a non-accelerating comet traveling 0.5c. He approaches earth, barely missing it, and passes on by. After he has passed Earth, he looks back toward it with his ultra-sensitive telescope and sees the face of Hyphy the Human. Hyphy the Human watches from her condo balcony with her ultra-sensitive telescope and sees the face of Albert the Alien. Suppose at this moment they are exactly the same age. It is love at first sight. One problem though. To Albert, earth is moving away at 0.5c so time is slowing down for Hyphy, making her appear younger and younger relavitve him. To Hyphy, the comet is moving away at 0.5c so time is slowing down for Albert, making him appear younger and younger relative to her. After staring deeply into each other's eyes for a long time, both give up hope because they feel like the other is too good for them.

    Question: What is wrong with this picture? Obviously time isn't slowing down for both. Also, notice that the original Twin paradox is resolved because the twin on the space ship eventually accelerates, comes to a stop, and accelerates back up to a constant v and returns to earth. This does not occur here.
     
    Last edited: Aug 13, 2008
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  3. Aug 13, 2008 #2

    Janus

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    Nothing is wrong with the picture. According to each, the other is aging more slowly. It is a consequence of time being relative.
     
  4. Aug 13, 2008 #3

    paw

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    Nothing wrong with this picture at all. That's exactly what SR is telling us. As long as they are both moving inertially neither one can make any special claim to be the one who is at rest. They need to share a spacetime event in order to compare ages in an objective fashion. Therefore your analysis is correct.

    Now that's not to say that Albert can't calculate what would happen if he got into a rocket and travelled back to meet Hyphy. Albert would calculate that he would have to accelerate to do that and after he got back to Hyphy he would have aged less than she.

    Similarly, if Hyphy got in a rocket and caught up with Albert she will have aged less than he.

    And if they both got in rockets and set off after each other..... well someone will probably write a country & western tune about it! ;^}
     
    Last edited: Aug 13, 2008
  5. Aug 13, 2008 #4
    Enough information is what is missing.
    Without a turn around it needs a stationary string of Earth synchronized clocks strung out for light years along the path of the 0.5 c Comet(s) clocks. Plus a mini Comets on the same speed and path ahead of and behind Albert’s Comet each with a Comet synchronized clocks.
    Now the observer on Earth or the Comet can directly watch time in the passing reference frame like numbers changing as you riff through a deck of cards.

    NOW what does each observers know?

    1) They can use their ultra-sensitive telescope and by accounting for the time delay of light traveling distances to confirm that all clocks in their frame of reference are synchronized to read the same time all the time; simultaneously.

    2) They can directly observe from the passing clocks that Time in the other frame of reference is running FAST!

    3) But they can also confirm by tracking any one single clock in the other frame of reference by using their ultra-sensitive telescope and by accounting for the time delay of light to confirm that one clock is running SLOW!

    4) Thus each observer can conclude from 2 & 3 that the in the other reference frame None of the other clocks are simultaneously reading the same time as any other clock in that other frame at any simultaneously point in time; ever.

    The two observers insist that 5:00 happens simultaneously on every other clock in their own reference frame and they both consider the others frame of reference has clocks horribly out of synchronization. And between the two of them, they will not be able to agree on a standard for simultaneity; at least when there is any real distance between any two events they my wish to consider might happen at the same time.

    Lack of simultaneity is the real lesson of SR and the twins.
     
  6. Aug 13, 2008 #5
    Thanks for the help RandallB, Janus, paw. I understand my thought experiment now. Sorry for the elementary SR question but one last quick layman clarification:

    In Albert's RF, he is aging faster. Let's say some time t passes where he is gazing into Hyphy's eyes. He finally takes a break from his telescope and calculates 10 years have passed. To Hyphy though, Albert is only 5 years older. Am I correct in concluding that both Albert and Hyphy's calculations are right?
     
  7. Aug 13, 2008 #6

    Janus

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    According to Albert, at the moment he calculates the time he has aged 10 years and Hyphy has aged 5.
    According to Hyphy, at the moment Albert calculates the time he has aged 10yrs and she has aged 20 yrs.
     
  8. Aug 14, 2008 #7
    Albert on the comet does not need to calculate how much time has passed he can see both times locally. He can read his clock directly as 5 years and see the clock passing by simultaneously reading 10 years. What he needs to calculate is how long he must wait to view through his telescope the event on earth that occurred when clock reading 10 years in the earth frame was recording his clock as running slow showing only 5 years and sending a report about it back to earth.

    Note: based on the time dilations you have here I can see the Comet is traveling at 0.8 c wrt earth not 0.5c

    And when he eventually make that observation he can confirm by direct observation of the clock in his own reference frame that is passing next to earth and reading 5 years he is looking at events that happened simultaneous with the event of his locally observing 5 years and 10 years on the two clocks years ago. He knows this because all the clocks in his frame have been carefully synchronized.
    However he can also see that in fact the earth clock is running slow only reading 2.5 years.

    Obviously the earth frame cannot be trusted to judge when things happen simultaneously!
    But earth has made the same judgment about the comet frame.

    So NO they cannot both be viewed as “Correct” only that they are different.
    More important under these conditions SR has no means to prove one as correct (preferred) over the other!
    The point is inhabitants of both frames can see that as true.
    Meaning we must doubt own frame of reference as being a correct judge of simultaneity.
     
  9. Aug 14, 2008 #8
    Is there a quick solution you can post to show how you calculate this? Thanks. If not that's cool. Just curious.

    So they both can't be viewed as "Correct", but they also cannot both be view as "Incorrect"? I'm guessing this was the point of Einsteins own thought experiment where Lightening hit two ends of train simultaneously to the observer on the ground (in earths RF) but not to the observer in the train's RF.
     
  10. Aug 14, 2008 #9
    All the observer can claim with validity is that he received (light) signals from both events at the same time. That is something entirely different from saying that both events happened at the same time.

    In spacetime there is no objective measure as to what event happens before another event. I think the significance of that is far more important than thinking in frame of references.
     
  11. Aug 14, 2008 #10
    Hello MeJennifer.

    Quote:-

    -----In spacetime there is no objective measure as to what event happens before another event.------

    Perhaps i do not totaaly understand your point. If two events are caually related can we not infer that one event happened before or after another. Of course we may not observe it the same order in terms of light signal reception at our location.

    I do understand that saying that two events are simultaneous is frame dependent and so practically meaningless, but sometimes helpful to me in trying to get a picture of things, although i could probably do without it.

    Matheinste.
     
  12. Aug 15, 2008 #11
    In the man on earth's RF, the lightening hit the two ends of the train at same time t, lets call it tc. If event A is the lightening hitting the front of the train and event B is lightening hitting the back of the train, and again both events happened at tc how can we not say that the events happened at the same time? Remember we are only talking about the man on earth's RF.
     
  13. Aug 15, 2008 #12
    What is wrong with the more accurate and less confusing assertion that the observer received signals from two separate events at the same time? To properly understand relativity I think it unwise to insist on Galilean reference frames that "have" the same time everywhere in that frame.
     
  14. Aug 15, 2008 #13
    It just seems like the next logical step (after asserting that the observer received signals from two separate events at the same time) is concluding that these events happened both at a particular time, tc,in our case,and that therefore in their RF the events were simultaneous.
     
  15. Aug 15, 2008 #14
    from what you have learned and now know you can no longer make statement like that and need to be more careful about making a false at worst or misleading assertions. The one you are most likely to confuse is yourself as I believe you are here causing you to take “your eye of the ball”.
    For two event separated by a distance in a common Ref Frame; you cannot say “therefore in their RF the events were simultaneous” since SR has shown you must idoubt your own frame of reference as being a correct judge of simultaneity the best you can say is “the events Appear To Be simultaneous”.

    So the real question is can you establish, with any certainty and agreement between other frames if two separate events are actually occurring simultaneously. Said another way; can you establish a preferred frame of reference to use as a standard over your own Ref Frame.

    Resolving an understanding of simultaneity is the real issue of SR & the Twins.
     
  16. Aug 15, 2008 #15


    I never said my reference frame was the "correct" judge of simultaneity. All I meant was that in my RF, standing beside the railroad track and not on the train, the two events occured at exactly the same time, tc. That fact is not debatable. Because to me the two events occurred at the exactly the same time, why can't I tell myself that the events occurred simultaneously? To you on the train, I understand they did not. But to me, they did so wouldn't I be lying to myself if I said they did not occur at the same time? Again this isn't saying that I am correct, it's only stating what I observed.
     
  17. Aug 15, 2008 #16

    Fredrik

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    "To me the two events occurred at the exactly the same time" means "In the inertial frame that everyone associates with my world line, the two events have the same time coordinate". It's a statement that's objectively true. The statement "In the inertial frame that everyone associates with the train's world line, the two events don't have the same time coordinate" is also objectively true. The statement "The events occurred simultaneously" is neither true nor false. It's nonsense, since it doesn't specify in which inertial frame the time coordinates of the events are equal.

    Just make sure you always specify what frame you're talking about.
     
  18. Aug 15, 2008 #17
    I think that is what I've been trying to say all along. I just don't see what is wrong with the statement "The events occurred simultaneously in my RF" (assuming I am the person standing beside the train). How is that nonsense? How would I better describe the event? Should I say "Event A (Lightening hitting the front of the train) occurred at tc and Event B (Lightening hitting the back of the train) occurred at tc"? In my RF, what is the difference between these two statements?
     
  19. Aug 15, 2008 #18

    Fredrik

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    There's nothing wrong with it.
     
  20. Aug 15, 2008 #19
    Ok cool. One last thought...

    Suppose my friend is standing directly behind me. Remember we have established in my RF Event A and Event B were simultaneous and occurred at time, tc. My friend directly behind me (he plays in the NBA and is a foot taller) has a clear view of event A and event B. He too concludes the two events were simultaneous, but at a slightly later time, td because he is slightly further away. We both conclude that the same event was simultaneous in our respective RF's.

    So can two observer's viewing the same event both conclude that in their RF's the same event occurred simultaneously?
     
  21. Aug 16, 2008 #20

    Fredrik

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    That's not how it works. Since you guys are moving at the same velocity, you will always agree about which events are simultaneous.

    If on the other hand your friend's velocity in your frame is v, then the slope of his world line in a spacetime diagram representing your frame is 1/v, and the slope of his simultaneity lines is v. (Otherwise the speed of light wouldn't be the same in his frame). As you described it, v=0, and his simultaneity lines are the same as yours.
     
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