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Stupider Twins Question

  1. Jun 2, 2008 #1
    Say we have the twins plus an observer at a space station(at rest with earth) 8 ly from earth. v = 0.8c. All clocks read 0 when the ship leaves earth (already at 0.8c). When the ship's twin is observed to reach the space station, all observers stop their clocks. Ship's clock should read 6 yrs, Space station clock should read 10 years, Earth clock should read 18 yrs, but the earth twin knows to subtract 8 yrs due to signal delay. Everyone agrees that when the ship reached the space station(a single event observed locally from each frame), the ship's twin was 4 yrs younger than the earth twin.

    Nobody accelerated.
    Nobody changed frames.


    Whether or not the twins ever meet again will not change the fact that the ship's twin aged less during this trip.

    Of course this trip is not symmetrical, but acceleration and changing of reference frames are both irrelevant, because they never happened.

    Comments? Please feel free to tell me how I botched this up. Besides the fact that I left out the novelty of the ship's twin getting to sneer at his brother in person for being older.

    Thanks,
    Al
     
    Last edited: Jun 2, 2008
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  3. Jun 2, 2008 #2

    Fredrik

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    You didn't botch it. That's the way it is. While the twin on the ship was moving at 0.8c, his brother was aging slower than him in the ship's frame. The moment before he stopped he was simultaneous in his own rest frame with t=3.6 years on Earth, but as soon as he stopped, he became simultaneous in his own rest frame (which is now another frame) with t=10 years on Earth.

    That's right, he can't stop the ship without having his brother age 6.4 years.
     
  4. Jun 2, 2008 #3
    In my example, the ship didn't stop. Just compared clocks. The ship's clock read 6 yrs, and the space station clock read 10 yrs. Although there is a lack of simultaneity, the ship's twin can see that the earth twin ages more during the trip by just looking at the space station clock which is at rest with earth. He doesn't have to actually stop because he can compare clocks locally with the space station. This point was the reason for my post.

    Yes, I realize that the earth clock and space station clock were not started simultaneously in the ship's frame, but the ship's twin, being a smart guy, realizes that they started simultaneously in their own rest frame, and that his brother is at rest in that frame, and that the space station clock shows the elapsed time on earth, in earth's frame, since the ship left earth.

    Thanks,
    Al
     
    Last edited: Jun 2, 2008
  5. Jun 2, 2008 #4

    Fredrik

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    OK. In that case, this statement is wrong: "the ship's twin can see that the earth twin ages more during the trip by just looking at the space station clock".

    Yes, he can read the time on that clock, but the correct conclusion isn't that his brother is ten years older at that event. His brother isn't at that event. What he can do is say how old his brother is at events that are simultaneous with that event, and to do that he must specify what frame he's talking about. In his own rest frame, the event where he reads the clock is simultaneous with the event where the clock on Earth shows t=3.6 years. In the space station's frame, the clock-reading event is simultaneous with the event where the clock on Earth shows t=10 years.
     
  6. Jun 2, 2008 #5
    I guess I should revise that statement to read:

    "the ship's twin can see that the earth twin ages more during the trip (as measured in his own rest frame) than the ship's twin does (as measured in his own rest frame) by just looking at the space station clock".

    Why would the ship's twin judge how much his brother aged by calculating what earth's clock should read in the ship's frame? The earth twin is not at rest in the ship's frame.

    The earth twin aged 10 yrs between the events as measured by a clock at rest with him.
    The ship's twin aged 6 yrs between events as measured by a clock at rest with him.
    This is the asymmetry that was my point. And with no acceleration or change of frames by anyone.

    In other words, if each twin took a picture of himself simultaneously with the ship reaching the space station (each in his own respective rest frame), the earth twin will have more grey hair when and if the photos are compared.

    Thanks,
    Al
     
    Last edited: Jun 2, 2008
  7. Jun 2, 2008 #6
    Which events? As far as I can see there are no events in your scenario. A spaceship "leaving" Earth which is already traveling at 0.8c and "arriving" at the spacestation by passing it with a whopping 0.8c are not events.
     
  8. Jun 2, 2008 #7
    Well, since I defined them as events, and they are easily observed and distinguished in time and space, I would call them events. But they are not acceleration events, which was my whole point.

    If it would help, we can say that there were light flashes involved, but I wanted to keep it simple.

    Thanks,
    Al
     
  9. Jun 2, 2008 #8

    Fredrik

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    This statement doesn't make sense. A person's age can't be specified by specifying a frame. You have to specify an event. You can do that either by specifying that event explicitly (e.g. "at the space station, when its clock shows t=10 years"), or by specifying a time in that frame (e.g. "t=6 years in the ship's frame"), in which case the event is implicitly specified as the intersection of the person's world line with the line that has the specified time coordinate in the specified frame.

    It seems that what you had in mind is that the Earth twin's age at the event where the Earth clock shows t=10 years is greater than the ship twin's age at the event where the ship's clock shows t=6 years. This statement is correct in both SR and prerelativistic physics. What you don't seem to realize is that this is a very different claim from "everyone agrees the Earth twin is older". What the ship twin really thinks when he passes the space station is this: "My brother will have aged 10 years, 10 years and 8 months from now". He's not thinking "My brother has aged 10 years now".

    I don't know how to explain that. It seems obvious to me that since he's trying to answer the question "how old is my brother now?", he must use his own "now" rather than someone else's. And in his own "now" (as he passes the space station) his brother has only aged 3.6 years.

    If you don't see that, you probably haven't fully understood how simultaneity works in SR.
     
    Last edited: Jun 2, 2008
  10. Jun 2, 2008 #9
    But he's not asking "how old is my brother now?", he's asking "How much does my brother age between these two events?" This point is totally different. And I do understand that there is a loss of simultaneity between frames. I do understand that in the ship's frame, the space station clock and the earth clock did not start simultaneously.

    I'm referring to the time that passes in each respective frame between the two events. That's what I meant by "during the trip". Everyone will agree that 10 yrs passed in earth's frame between the two events, and 6 yrs passed in the ship's frame between the same two events.

    Or, in other words, these two events are separated in time by 10 years in earth's frame, the same two events are separated in time by 6 yrs in the ship's frame. Is this statement true?

    I'm not asking if it's relevant, just if it's true.

    Thank's
    Al
     
    Last edited: Jun 2, 2008
  11. Jun 2, 2008 #10

    Fredrik

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    This is the part you keep getting wrong. There are three events:

    Event A: Ship leaving Earth
    Event B: Ship reaching space station
    Event C: Earth at t=10 years

    The statement doesn't make sense, since there are 3 events, not 2.
     
    Last edited: Jun 2, 2008
  12. Jun 2, 2008 #11
    True, but only in SR is the event of earth's clock showing 10 yrs simultaneous (in earth's frame) with an event (ship at space station) which is simultaneous (in the ship's frame) with the event of the ship's clock showing 6 yrs.

    Thanks,
    Al
     
  13. Jun 2, 2008 #12
    There is the problem. Space ship and earth are separated by 8 ly. How are all clocks going to read zero simultaneously? Simultaneously in which frame?
     
  14. Jun 2, 2008 #13
    You may call them so but with all respect if you want to learn about relativity it would be better to understand why something zooming at 0.8c past something else is not the same event, their respective worldlines are are not even close in spacetime.
     
  15. Jun 2, 2008 #14
    How about Event D: Ship at t=6 yrs.

    Ah, but since events B and C are simultaneous in earth's frame, 10 yrs passed between event A and event B/C in earth's frame.
    And since events B and D are simultaneous in the ship's frame, 6 yrs passed between event A and event B/D in the ship's frame.

    Obviously more than two events exist, but my statement only referred to the two.

    Thanks,
    Al
     
  16. Jun 2, 2008 #15
    This part is wrong. When the travelling twin paases the spacestation and looks back towards the clock on the Earth he sees the other twin as 2 years old. This is because light leaving the Earth twin when he is 2 years old takes 8 years to travel the distance and arrives at the spacestation after 10 years Earth time just as the travelling twin is passing.

    The travelling twin might argue that that since the spacestation clock is synchronised with the Earth clock, then if the spacestation clock reads 10 years then the Earth twin must be 10 years old too. Open and shut case? No! If the travelling twin was at the front of a rocket that happened to have a proper length of 13.333 light years long, then due to length contraction the tail of the ship will be level with the Earth when the travelling twin arrives at the spacestation. Now if the clocks are synchronised on the ship as they probably would be if it was always travelling at 0.8c then the clock at the tail of the ship passing Earth will be reading 16.666 years. The Earth twin then argues that since the clocks on the rocket are synchronised, the travelling twin MUST also be be 16.666 years old while he is only 10 years old.

    Each has a valid argument that they are 60% of the age of the other twin.
     
    Last edited: Jun 2, 2008
  17. Jun 2, 2008 #16
    Issue already addressed:
    They don't all read zero simultaneously. The space station clock is synched with earth's clock in their rest frame.

    Thanks,
    Al
     
  18. Jun 2, 2008 #17

    Fredrik

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    B and D are not just simultaneous in the ship's frame. They are by definition the same event.

    In Earth's frame, B and C are both 10 years later than A.
    In the ship's frame, B is 6 years later than A.
     
  19. Jun 2, 2008 #18

    Fredrik

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    In other words, this statement is correct if the two events are A and B:

    But your original statement isn't:
    If everyone agrees, it includes the twin on the ship, and he was 2.4 years older than his brother at this time in his rest frame.
     
  20. Jun 2, 2008 #19
    Yeah, you're right, that second statement isn't worded right. I hereby retract it. :smile:

    This one:
    is my point. Isn't this asymmetrical?

    Thanks,
    Al
     
  21. Jun 2, 2008 #20
    I agree with Fredrik,

    The interval between the events (Ship leaving Earth) and (Ship reaching space station) is measured as 10 years by the Earth frame observers and as 6 years by the travelling twin. That conclusion in no way implies that the event (travelling twin celebrates 6th birthaday) is universally simultaneous with (Earth twin celebrates 10th birthday) according to any observer. It is true to observers in the Earth frame but to observers in the travelling twins frame the events (travelling twin celebrates 6th birthaday) is simultaneous with (Earth twin is 3.6 years old).
     
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