The Twin (Earth) Paradox

Discussion in 'Physics & Math' started by conscienta, Mar 23, 2012.

  1. conscienta Registered Member

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    The standard twin paradox has generated considerable controversy. The thought experiment involves the experience of twins – one twin remains on earth while the other twin makes a journey in space at a high rate of speed and upon returning to earth finds that she has aged less than her earthbound twin. If we search the internet for an explanation of this effect, one finds web page after web page after web page of posts purporting to explain how this thought experiment is consistent with the special theory of relativity. An earlier thread in SciForums is a case in point. The question was: Can the Twin Paradox Be Simplified? After 37 pages of sometimes heated exchanges I would say it is still an open question.

    First of all, I would stipulate that the Twin's Paradox is not a paradox and that it should simply be called the Twin’s Effect. To add content to that general statement, let us say for arguments sake that two twins, Twin A and Twin B are twenty years old and it is the year 2000. Twin A remains on Earth while Twin B rockets to a star 8 light years away traveling at 80 percent the speed of light and then returns to Earth at the same speed. In Twin A's reference frame the journey should take 20 years. In Twin B's frame of reference the trip only takes 12 years and upon return to Earth Twin B will agree with Twin A that on earth 20 years have passed and that the year is 2020. According to Twin B’s clock however, only 12 years transpired during Twin B's journey and accordingly she will be only 32 while Twin A will be 40.

    To keep it simple, I will suggest the acceleration/deceleration phases of the journey are instantaneous with the stipulation that a uniform acceleration can be handled within the framework of special relativity at the price, however, of making the mathematics more complicated. I would just say about acceleration that in order to change a clock’s timing rate requires a change of inertial frames which would require a change of velocity which would – by definition - require an acceleration. The acceleration, however, has no affect on the timing rate itself.

    As far as the resolutions to the twin paradox I would suggest they follow a certain progression. In most cases the author will state that although the controversy over the Twin Paradox was resolved 50 years ago, the explanation they are about to provide is definitive and should once and for all resolve the paradox. The author will begin by suggesting that the experiences of the twins are not symmetrical. The stay-at-home twin will not change inertial frames while the traveling twin will accelerate to a high rate of speed then cruise (inertially) for a lengthy period of time, decelerate at her destination, then accelerate again and travel at a high rate of speed (inertially) on her journey homeward and finally decelerate upon arrival back at earth. They will then say that the special theory of relativity applies only to uniform motion and not accelerated motion. Then they will say, however, that it is not the accelerations/decelerations per se that causes the age differential; i.e. that clock rates only depend on the traveling twin’s velocity and not on any derivatives of velocity such as acceleration. And then finally they will apply the equations of special relativity to calculate the time differential between the two twin’s experiences. A convoluted sort of logic but not necessarily inaccurate. If the aforementioned author’s of the numerous explanations of the Twin Paradox on the internet (at least those with PhD’s in physics) were pressed they would probably say that the time dilation is a consequence of changes in the geometry of space and time – whatever that may mean.

    What I would like to propose for consideration in this post is what I call the Twin Earth Paradox. In this variation there is an earth like planet at the star visited by Twin B. The star is exactly the same mass/gravity as our sun, the planet has exactly the same mass/gravity as Earth and has a 24 hour day and is the same distance from the star so it has a 365 day year. We have a relationship with our twin planet and over the years atomic clocks on both planets have been synchronized such that the year 2000 on Earth is the same as the year 2000 on Twin Earth. I would suggest that upon Twin B’s arrival at Twin Earth the year in Twin Earth’s frame of reference will be 2010. However, according to Twin B’s clock only 6 years will have passed and Twin B will be 26 upon his arrival at Twin Earth.

    The proposal seems to short circuit many arguments for the asymmetry between the two perspectives but instead focuses on what “really” happens to Twin B’s clock and more generally what we “really” mean by time. From an outside observer, time in Twin B’s frame of reference is measured to be dilated by 60 percent. However, during the inertial part of Twin B’s journey, Twin B faithfully conducted experiments that indicated the clock in her frame of reference was operating normally; i.e. no evidence of time dilation. Twin B concludes therefore that it was the distance from Earth to Twin Earth that was foreshortened by 60 percent; i.e. the distance was only 4.8 light years.

    Did the distance really contract or was time really dilated? Or is it simply a function of measurement; i.e. the distance/time was measured to be contracted/dilated – motion affects those measurements and hence reality? Or is it as the theory of special relativity seems to imply that we are all moving through time at the speed of light (at rest) and as our motion through space increases our motion through time decreases? At all times, however the total of our motion through time and our motion through space must equal the speed of light. From this perspective Twin B was traveling through time at 60,000 km/sec while she was moving through space at 240,000 km/sec and hence time was dilated by the Lorenz factor. Is this what they mean by changes in the geometry of space and time and if so what does it mean to move through time?
     
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  3. Motor Daddy ☼☼☼☼☼☼☼☼☼☼☼ Valued Senior Member

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    What a tangled web one weaves.

    We are standing on earth. We agree on the distance of a star to be 8 light years distant. We agree that the stay at home person will record the elapsed time of the other person's round trip travel time to the star and back home.

    Ready, GO! The person travels to the star 8 light years distant and returns. The person traveled a total round trip distance of 16 light years, and the stay at home person reports the time...20 years. A little calculation...16/20=.8 means the average speed was .8c.

    Done deal, end of story. There really is nothing to see here folks.
     
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  5. origin Trump is the best argument against a democracy. Valued Senior Member

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    In your twin earth scenario I believe you are saying that the twin earth and the 'normal' earth have identical inertial frames therefore your twin earth scenario is essentially identical to the original twin paradox.

    Am I missing something here?:shrug:
     
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  7. Ophiolite Valued Senior Member

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    Only among people who don't understand it.
     
  8. conscienta Registered Member

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    My point exactly. There is nothing paradoxical about the Twin’s Effect. My broader question was about what is really happening in Twin B’s inertial frame and further what we mean by moving though time.

    Furthermore are you implying (as I suggested) that it is simply a measurement problem?
     
  9. conscienta Registered Member

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    If you look at the planes of simultaneity on a Minkowski Diagram it seems to imply that on the outward leg of the journey that Twin A’s clock is actually lagging behind Twin B’s clock. At the turn around Twin B switches inertial frames and Twin B’s worldline rapidly sweeps to a new plane of simultaneity. This seems seems to imply that the asymmetrical aging occurs during the turnaround phase of the journey. There does not seem to ever be any mention that Twin B changes inertial frames at the start of the journey as well as at the end of the journey.
     
  10. conscienta Registered Member

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    The more I read the less I think we understand the Twin’s Effect.
     
  11. Ophiolite Valued Senior Member

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    I didn't say I understood it, but I am quite comfortable that people of intellect who have studied it do understand it. I should prefer to think about important things like isotope ratios in pre-solar grains.
     
  12. Motor Daddy ☼☼☼☼☼☼☼☼☼☼☼ Valued Senior Member

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    Twin B doesn't have a constant inertial frame for the entire duration of time because he accelerates.

    No, I'm implying that it's an SR problem.

    I can draw a diagram of the situation in the preferred frame and show both twins and the light sphere for any time t, while showing the 4 accelerations (0-.8c, .8c-0, 0-.8c, and .8c-0). I can tell you that if the distance is 20 light years and you include the accelerations, which is reality, that it takes more time than 20 years to travel a round trip distance of 16 light years when the initial velocity and final velocity are 0 m/s, and the maximum velocity is .8c.
     
  13. origin Trump is the best argument against a democracy. Valued Senior Member

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    No, If I am reading you right this is not correct at all! All that is important is the velocity difference; direction is completely unimportant!
     
  14. Janus58 Valued Senior Member

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    Actually, direction is very important when it comes to the Relativity of Simultaneity.

    Example:

    You are traveling from Planet A to Planet B. Clocks on each planet have been synchronized in the Rest frame. For you however, due to the Relativity of Simultaneity the Clock on Planet B reads X years ahead of the Clock on Planet A.

    When you arrive at Planet B, its clock reads Y years and The clock on planet A reads Y-X years. You turn around and head back towards planet A at the same speed you left at. We assume that this turn around is instantaneous so that neither your own or Planet B's clock changes. Thus Clock B still reads Y years. However, since you are now heading from B to A, it is Clock A that is ahead by X years and now reads Y+X years. By your reckoning, Planet A's age "jumps ahead" 2X years when you turn around.
     
  15. origin Trump is the best argument against a democracy. Valued Senior Member

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    Well that's too bad for me. That means I am completely confused about SR and will comment no more on these threads until (if ever) I am educated on SR.:bugeye:
     
  16. conscienta Registered Member

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    I am not sure you are necessarily incorrect about this. I think that in the standard Twin Effect, (not my Twin Earth scenario) unless Twin B turns around to meet up with Twin A back on Earth to compare ages (which is demonstrated by the usual Minkowski Diagram of the effect) the relative differences in their age is a moot point. I guess that is the point of The Twin (Earth) Paradox. In my scenario the year 2000 on Earth is the same as the year 2000 on Twin Earth. There is no turnaround yet there is still asymmetrical aging.
     
  17. conscienta Registered Member

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    I agree. There are four critical changes of velocity (in the standard Twin Effect)– one at the start of the journey, one at the destination, one at the start of the journey home and one upon arrival back at Earth.

    I also agree that it is an SR problem.

    Are you, however, saying that (in the standard Twin Effect) Twin A travels through time at c a distance of twenty light years while Twin B travels through space at .8 c a distance of 16 light years?

    The issue of measurement is in Twin B’s frame of reference. It is one of the basic tenets of SR that time in Twin B’ frame of reference is unaffected. From Twin B’s perspective the distance to Twin Earth has contracted to a distance of 4.8 light years. The question is whether this is the actual distance traversed (space contracts) or whether the distance is just measured to be different (and time is somehow affected or some combination of space and time).
     
  18. conscienta Registered Member

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    I do not even think those with PhD’s really understand the effect otherwise I would think they would be able to agree on one cogent explanation for its consequences. I still think it is an important open question.
     
  19. Janus58 Valued Senior Member

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    Unless Twin B comes to a stop at Twin Earth he will not agree that he aged less than his Earth Twin. He will agree that it is the Year 2010 at Twin Earth when he arrives, but will conclude that it is only 2003 and some months back on Earth. IOW, by his reckoning, Earth has aged less than him during the trip. If he now comes to rest with respect to the two Earth's, He has to change inertial frames, and this change will cause a shift forward for Earth's clock just like for the turn around.

    Unless you bring all clocks back into the same frame, you cannot unequivocally say which one aged less.

    For example, let's assume that twin B is already moving at 0.8c when he passes the Earth and notes the that time year on the Earth is 2000. 6 years later, by his clock, he flies past Twin Earth without stopping and notes that the time there is the year 2010.

    Now even though it is the year 2000 at Earth and Twin Earth when Twin B passes the Earth in the rest frame of the Earth, this is not true according to Twin B. According to him, it is already the year 2006 at Twin Earth when he passes the Earth and Twin Earth ages 3.6 years for his 6 during the Trip so that it is 2010 at Twin Earth when he arrives. And as I mentioned above, the Earth ages 3.6 years and it is 2003 on the Earth when he passes twin Earth.

    Of course, according to the Earth/Twin Earth frame, Ten years pass while Twin B ages 6 years.

    The thing is they are both right. This is what I think confuses people the most about Relativity; They can't wrap their head around how both viewpoints can be right. They want to believe that that there is one unequivocal answer as to who really aged slower during the trip.
     
  20. James R Just this guy, you know? Staff Member

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    Motor Daddy:

    It is clear that you don't understand the basics of the twin paradox, since you're missing half the story. The reason is the usual one with you: you recognise the existence of only one frame of reference, and have a wilful blindness to the existence of all others.

    The current thread is NOT the place to educate you on the basics of relativity (again). If you wish to discuss your misunderstandings further, please start a new thread. Further posts from you seeking to divert the current thread into nonsense based on your misunderstandings of the basics will result in deletion of your posts from this thread (as off-topic).
     
  21. conscienta Registered Member

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    I assumed that Twin B would stop at Twin Earth and not return. I do realize there is Twin A’s time and Twin B’s time and they happen to be different.

    I guess the question I posed at the start of this thread was what was really happening in Twin B’s frame of reference. If the answer is time dilation I would agree. But my original question was about what most physicists would say is the true source of the time differential (time dilation) - changes in the geometry of space and time. The other question I posed was about what it means to move through time if indeed this is what changes in the geometry of space and time implies.

    I guess maybe what I am asking is too existential a question but that is the question I am asking.
     
  22. OnlyMe Valued Senior Member

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    Just a note to clarify the discussion. The classical twin paradox is a special relativity SR thought experiment that assumes a flat space time and the abscence of the conditions which would be present if general relativity GR were included.

    While as per SR time is dilated or slows down proportional to an object's velocity, within the context of GR as an object move out of a gravity well time speeds up. Case on point is the GPS satellites were the satellite clocks run fast as per GR and slow as per SR effects. The GR effects being the greater influence in the case of satellites in orbit.

    Trying to work out the GR time dilation effects would require accounting for all involved gravity wells, affecting the geometry of space.

    It would seem that if you assume relativistic velocities, as in the classical twin paradox and assume that the traveling twin never leaves the local galaxy, the SR effect would exceed the GR effect. The result being somewhat more aging for the traveling twin, than is projected in the classical paradox, but still less aging that would be expected for the stay at home twin. The approximate amount of time dilation is almost impossible to determine without clearly defining the gravitational masses which would be involved during the trip.

    I hope I have not side tracked the discussion too much. This issue was touched on briefly in an earlier thread, but even there only briefly. It becomes overly complex very quickly.

    The existential aspects become even more complex and phylosphical.
     
  23. the_epic_retard Registered Member

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    that is just strange.
     

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