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Twins Paradox (clock)

  1. Apr 29, 2015 #1
    Dear PF Forum,
    I have a tought experiment here.
    I'm asking about twins paradox, but instead of using twins, I'm using clocks to lock them up in a closed room. Sort of Einstein elevator. (unlike Schrödinger, even in tought experiment, I can't imagine locking human being -- or cat -- in a closed room).
    So, here is the experiment.
    Two clocks are sealed inside a closed room. Clock E on earth, clock R in a rocket.
    Both clock are reset, and the rocket is fired away with acceleration 10 m/s2.
    Clock R practically 'feels' 1 g.
    After 3 billions seconds (about 95 years) the rocket stops and turn around heading toward earth and fired again with acceleration 10 m/s2.
    Of course the speed when it reaches earth would be about zero. The rocket actually deccelerates.


    A. How far away does the rocket travel right before it turns around? Will it reach ½at2 = 45 thousand trillions KM? Actually after 1 year the rocket will travel 1 speed of light, after 10 years = 10 speeds of light?
    I think the energy consumption is very big here. It's Newton's, right?


    B.And this is my question.

    How does the clocks run? Does clock E run faster, in twins paradox it would age faster, than clock R?
    Both clocks are in a closed room. If they were twins, both twins would feel no different with the acceleration.
    Clock E accelerates toward the center of the earth in 1 g, the floor holds it up.
    Clock R accelerates toward the floor of the room in a rocket, again 1 g.


    C. What about the twin who orbits the earth in geostationary orbit.
    Twin E accelerates 1 g, so it actually feels that it moves.
    Twin O, in orbit, doesn't feel acceleration at all tough it travels 11 thousands KM per hour.
    Which one ages faster.
    Supposed both twins are in different rockets in space.
    Twin E accelerates 1 g, and twin O's rocket's machine doesn't run. So twin O actually doesn't feel acceleration at all as in geostationary orbit. Will twin O ages slowlier?

    Thanks for you enlightment.

    Steven
     
  2. jcsd
  3. Apr 29, 2015 #2

    Orodruin

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    With your given setup, the rocket is always travelling away from Earth. It will not come back just when it stops. Furthermore, you say "95 years", this is ambiguous, 95 years as measured by whom?

    A relative velocity will never be faster than the speed of light. You also need to specify who measures the acceleration.

    Time dilation is related to space time intervals, not to acceleration.
     
  4. Apr 30, 2015 #3
    Thanks Orodruin for the answer.
    95 years by clock R, I mean.

    And I think i made some error condition. I have corrected below.


    Correction

    Time R A: (95 years)
    After 3 billions seconds (about 95 years) the rocket stops and turn around. Heading toward earth but not speeding toward earth. Actually it still speeds away from the earth. And the rocket is fired again with acceleration 10 m/s2. But the rocket actually decelerates.

    Time R B: (190 years)
    By around this time the rocket does accelerate toward earth with acceleration 10 m/s2.

    Time R C: (285 years)
    By around this time the engine stops and the rocket turn around again heading away from earth but speeding toward earth. Engine starts again. Now the rocket actually decelerates.

    Time R D: (380 years)
    By around this time the rocket should reach the earth again. Of course the speed when it reaches earth would be about zero. The rocket actually deccelerates.

     
  5. Apr 30, 2015 #4

    Janus

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    You might want to check out this:

    http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html [Broken]
     
    Last edited by a moderator: May 7, 2017
  6. Apr 30, 2015 #5
    The two clocks wont feel a difference in the acceleration. But the clock which has been put in motion will gradually accumulate a large velocity relative to the earth frame - the traveling clock that has been given the energy boost will have been found to run slower when the clocks are ultimately compared - whether they are brought together physically or simply brought to rest in the same earth frame millions of miles apart. All such experiments are disguised versions of a lab experiments where a charged particle in the lab frame is given a boast and its decay time is extended. There is never any doubt which particle gets the long life - i.e., the real "slower clock" In SR Einstein hypothesized that both frames are inertial equivalents and that each clock can be considered at rest, but the reciprocal situation where the high speed clock views the earth clock as running slow does not comport with what is measured when the clocks are brought to rest in the same frame. During any constant velocity phase of the clock experiment (aka the twin paradox), any measurement made by the boosted clock showing the earth clock running slow, is illusory. When the clocks are reduced to the same speed, the boosted clock will have logged a greater time. There is one experimental result that seems to question whether the boosted clock always runs slow, but that teaches away from SR which is not permitted on these forums.
     
  7. Apr 30, 2015 #6
    Correction - second to last line of post 5 - the boosted clock will log less time
     
  8. Apr 30, 2015 #7
    When the ship turns around, it is in a new frame of reference in which the earth clock "instantly" gains a lot of time, as the FAQs point out. Just looking at coordinates makes it look as a completely reciprocal situation, but actually only one of the clocks will be in a single inertial frame the whole time. That's the only one where the single set of SR calculations makes sense.
     
  9. Apr 30, 2015 #8
    Response to post 7:

    My take on the proverbial twin thing, aka clock paradox, is to forget about the round trip initially. Ask the question, if a spaceship is accelerated from the earth to a high velocity in a short amount of time and then coast the rest of the way and ether slows to stop on an faraway planet "alpha, or simply reads the time on a clock located on "alpha" then assuming there is no relative motion between the earth and alpha, the time logged by the traveling clock will be less (measured by reference to the earth clock or the alpha clock). Since the earth clock and the alpha clock have been in the same frame during the entire voyage, they will measure same time, and the traveling clock will have measured less as predicted by SR. To figure the round trip time difference, simply double the result for the one way trip

    Einstein actually got into a bit of a problem when he was pushed by a number of critics about the clock paradox. He wrote a paper in 1918 solving the twin paradox using GR - reasoning similar to your resolution ...that the earth clock gains a lot of time when the flying clock turns around - Einstein imposed an artificial G field - Max Born conjured a similar result by reasoning that acceleration field at turn around corresponded to a lot of time passing on the earth clock because the formula for dilation takes into account the distance between the clocks. These solutions give the right numerical value at the expense of fracturing the real physics as to why the passage of time in relatively moving frames is different.
     
  10. May 1, 2015 #9
    You will likely appreciate the Usenet Physics FAQ (they certainly do not mean inertial reaction force but the magical force that appears to pull the children outward):
    "You may be bothered by the Big Coincidence: how come the uniform pseudo-gravitational field happens to spring up just as Stella engages her thrusters? You might as well ask children on a merry-go-round why centrifugal force suddenly appears when the carnival operator cranks up the engine. There's a reason why such forces carry the prefix "pseudo"."
    - http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_gr.html
     
  11. May 1, 2015 #10
    The "feeling of acceleration" should not be understood as physical explanation; texts that use that merely mean (or should mean) that in cases far from gravity it's easy to detect that one is accelerating.
    In the original full "twin paradox" the traveler doesn't feel any acceleration as he is in a slingshot around a star. However, for a sufficiently long travel at sufficiently high velocity the clock slowdown from the Earth's gravity as well as the short-time clock slowdown from the star's gravity become relatively small so that they can be neglected (and perhaps a case can be construed in which those effects exactly compensate each other).
     
    Last edited: May 1, 2015
  12. May 1, 2015 #11
    This video shows a first-person journey for the traveler leaving and returning home. For the purposes of your question, the clock at the upper left shows three simultaneous values: the red one is coordinate time (the time shown on the clock currently just outside a porthole), the green one is the traveler's proper time (the clock in his ship) and the yellow one shows the time actually seen on the home twin's clock by the traveler through a powerful telescope.
    It is easy to see what all three clocks show for the traveler throughout the journey. You will need to view in full HD to see the clock clearly.
    BTW more description is available in the channel notes here.
     
    Last edited: May 1, 2015
  13. May 1, 2015 #12
    Thank you very much, harrylin for you answer.
    But one thing is borthering me. Again.
    At one of those link
    http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_intro.html#standard
    Stella, star, is the one who travel to the star.
    Terence, terra, is the one who stays terresterial on earth.
    "Terence feels nothing", but how can that be?
    Surely Terence "travels" 0 km per hour, but doesn't he feel the earth gravity?

    My questions are:
    A. Does Terence feel acceleration?
    B. Is there a difference between accelerated by a rocket or "feel" accelerated by the gravity?

    Thanks for anyone's attentions


    Steven.
     
  14. May 1, 2015 #13
    Firstly, my advice is ignore all talk of acceleration until you understand the basics. It is not irrelevant, but it is unnecessary to describe the effect and will just confuse the hell out of you and everyone else (search past threads if you don't believe me!). Secondly, the younger twin is the one that goes somewhere and returns, the older one is the one who goes nowhere. They each know perfectly well which one they are!
    The easiest source to learn from IMO is the Baez site.
     
  15. May 1, 2015 #14
    Thanks m4r35n357 for your answer.
    But I would like to ask for clarity here.
    What's the different between the red clock and the green clock.
    The green clock is in his ship, what about the red clock? Is it located out side his window, 2 meters away? Where is the red clock located?

    Through a powerful telescope:
    The ship is moving away from the earth, so the yellow clock runs slowler, because the light from the clock must takes time to reach the ship.
    What if the ship is heading toward earth? Does the yellow clock will run faster?
    Supposed, the ship is 10 light year away.
    If the ship compares its clock vs earth clock, there will be 10 year different right? The clock on the earth is 10 years lates. What if the ship is heading toward earth with say... a very slow speed about 1000 km / seconds so it is affected very little relativity effect.. Altough it takes 300 000 years to reach the earth, the yellow clock seems run faster doesn't it such as shown in the video? Because the clocks is rather synchronized.

    Thanks for anyone's attentions.


    Steven
     
  16. May 1, 2015 #15
    Have you read the YouTube channel notes that I linked to? To clarify, the red clock dot is the instantaneously nearest one of an "imaginary" field of clocks in the coordinate frame (the one the traveler is currently passing). All the rotating stuff (including the home station) is showing coordinate time where it is, but there is a visible lag caused by the distance between it and the traveler. You have to look at a clock exactly where you are to read coordinate time.
    The green clock is the traveler's wristwatch.
    As to your other questions, please see the Baez link; he explains it better than I could.
     
    Last edited: May 1, 2015
  17. May 1, 2015 #16
    Ahh, yes, mea culpa. It's the "red clocks", plural.
    Sorry.

    And THANK YOU VERY MUCH.
    This really GIVES ME ENLIGHTMENT!
    The stationary clocks outside the ship!
     
  18. May 1, 2015 #17
    Yes. That is what I was struggling to say (I chose to avoid using the word stationary, perhaps wrongly), but it sounds like you have understood.
     
  19. May 1, 2015 #18

    Janus

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    The red clock represents what a clock just outside the ship's window and stationary with respect to the Earth would read at the instant you pass it. It isn't really a physical clock.
    What you see on the yellow clock is a combination of classic Doppler shift due to the changing distance and Relativity or Relativistic Doppler shift.

    If you are separating you see the yellow clock run slow, if you are coming together, you see it running fast.

    The factor follows the equation

    [tex]\sqrt{\frac{1-\Beta}{1+\Beta}}[/tex]

    Where beta = v/c and is positive when you are separating.

    So in your example of returning at 1000 km/sec from 10 light years, you get a factor of 1.0033389.

    It actually takes 3000 yrs (not 300,000) to travel ten light years at 1000 km/sec, so this works out to you seeing the Earth age by 3010.0167 years during the trip, 10.0167 years more than you do, 10 years of that is due to the decreasing time lag of the light, and the 0.0167 yr (6+ days) will be due to relativistic effects.

    If we beef up the speed to 30,000 km/sec and check the progress of the yellow clock through the telescope for both the outbound and inbound leg we can get the following results.

    Assuming that our ship travels for 10 years by its own clock, it will by its reckoning traveled 1 light year in that ten years. During that time, it will see the yellow clock on Earth run at a rate of ~0.904534 and advance 9.04534 years. On the return leg which takes another 10 years by its clock, it sees the yellow clock run at a rate of 1.105542, and advance another 11.05542 years for a total of 20.1008 years or just a tad or 1/10 of year more than the 20 years it measured by its own clock.
     
  20. May 1, 2015 #19
    Again, my mistake. I hastily calculated. You're right! 3000 years, not 300 000 years.

    Thanks for the correction.
     
  21. May 1, 2015 #20
    Many thanks to Janus for explaining what I had no appetite for!

    I should also point out the trigger for my original post was the part of your original question where you describe sealed clocks. I felt compelled to point out that there is no real paradox here, and no secret concealed magic about time. All the clocks can be made visible to all observers throughout the entire process.
     
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