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Twin paradox 
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#1
Jan1808, 05:10 PM

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As we all probably know, the twin paradox states that a twin goes off in a spaceship at c and returns, aging less than the twin on Earth because he traveled at c relative to Earth. However, relative to the spaceship, Earth is travelling away from it at c also, so technically, if I were on that spaceship, I'd think I'm stationary and Earth is moving, causing me to think the twin on Earth would age less since he's travelling at c relative to the spaceship. Why does the twin in the spaceship age less nevertheless?



#2
Jan1808, 05:38 PM

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Hi Fred2028,
No spaceship will ever be able to go at c, whatever frame of reference you're in, so let's keep its velocity (relative to the earth ) at v which will always be less than c. The difference between the twins is that the spaceship passenger has to be accelerated by rocket motors on the outward trip and then decelerated before begining the return trip. So the situation is not symmetric, and the accelerated twin ages less. There are many threads on this subject, just scroll down the list of previous threads. 


#3
Jan1808, 07:01 PM

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Mentz explained why they don't have to age the same, but not why it's the astronaut twin that ages less. If you want to understand the twin "paradox" fully, you first have to understand spacetime diagrams and how simultaneity works in SR.
This diagram explains everything that's relevant about the twin paradox: (Why doesn't the "img" tag work here?) I'm calling the twin on Earth "A" and the twin in the rocket "B". Blue lines: Events that are simultaneous in the rocket's frame when it's moving away from Earth. Red lines: Events that are simultaneous in the rocket's frame when it's moving back towards Earth. Cyan (light blue) lines: Events that are simultaneous in Earth's frame. Dotted lines: World lines of light rays. Vertical line in the upper half: The world line of the position (in Earth's frame) where the rocket turns around. Green curves in the lower half: Curves of constant t^2+x^2. Points on the two world lines that touch the same green curve have experienced the same time since the rocket left Earth. Green curves in the upper half: Curves of constant (t20)^2+(x16)^2. Points on the two world lines that touch the same green curve have experienced the same time since the rocket turned around. From A's point of view B is aging at 60% of A's aging rate. From B's point of view A is aging at 60% of B's aging rate. The reason this isn't a paradox is that the moment before B turns around, he's in a frame where A has aged 7.2 years, and the moment after he's turned around, he's in a frame where B has aged 32.8 years. 


#4
Jan1908, 12:38 AM

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Twin paradox
Whether Special Relativity really explains the age difference is a subject of much debate what is not in question is the fact that two clocks in relative motion will not accumulate the same amount of time during the same spacetime interval.



#5
Jan1908, 04:33 AM

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That's not true at all. There's no debate about this.



#6
Jan2008, 02:16 AM

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Read the books by Sciama, Lederman, Born, Atkins etc etc for one view Read the books by Wheeler, Rindler, Resnick etc for another view. Then Read the papers of Selleri, Hatch and others for a third view. If there is no debate, why so many different assertions.
Einstein himself waited 13 years before attempting to explain the time difference between relativly moving inertial frames in terms of a general relativity arguement. 


#7
Jan2008, 03:07 AM

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#8
Jan2008, 07:48 PM

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Jesse  we have already been over this in several threads  recall "Space, Time and Mass" and "Confusion in basic SR" Here is quote from Atkins (Physics, Universie of Pennsylvannia ) at p 509: "The problem cannot therefore be satisfactorily discussed in terms of the special theory. It is necessary to apply the general theory."
I have already in past discussions given you citations to Born's view and direct quotes from his book. The fact that some people do not see a conflict does not mean that others do not. I don't have at this location, most of my library, so I cannot oblige you with what you asked. If I recall it was you that changed your argument as to the reality of the time difference that i cited in Part 4 of the 1905 paper  I think you began by saying that the example involving the relative motion of one of two synced clocks brought together cant mean "a real object time difference" ...that led to a lot of posts between us, and each being convinced the other was misunderstanding what Einstein was saying. For the purpose of my post  I really don't care what camp you are in  but there is nonetheless a disagreement as to whether SR explains the cause or simply rationalizes the result "What counts in the end is experimental predictions. If you set up an experiment where one twin travels at a high velocity, accelerates and turns around, and then returns to a twin that has stayed in a single inertial frame, everyone agrees that the twin who has remained inertial has the longer elapsed time. In a similar vein, one can say with definiteness that when one compares two clocks, one on a mountain top, and another in a valley, that the clock on the mountaintop will tick appear to tick faster when compared by light signals that have a constant propagation time. One can even have two clocks start out in a valley, carry one up to the mountain (via slow clock transport), let it sit for a while, then carry it back, and one will find that the clock that remained in the valley has less elapsed time. Now there are a number of ways to explain this all philosphically, as long as one can get to the same conclusions in the end, one can take several different philosphical positions about what is "real" and what is "not real". So my advice is not to worry too much when the phiolsophical parts of the answers differ. Focus on some experimental results (even thought experiments)  those are what must agree." 


#9
Jan2008, 08:20 PM

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#10
Jan2008, 09:09 PM

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Isn't there a forum rule against repeatedly posting crackpot claims?
The claim that some of the "paradoxes" of SR can't be resolved within SR itself, but need GR, is a common misconception (even among people who are intelligent and have studied SR), but that doesn't mean it isn't absurd. Really absurd. It's right up there with "I believe there's life on all planets but perhaps not in our dimension" and "I believe that when the Maya calender ends in 2012, humans will stop living in 3 dimensions and start living in 5". (Those two claims were made in a Swedish forum about paranormal stuff). If it had been true, just about all of mathematics would fall with it. Even the integers would have to be thrown out the window. SR is just the set [itex]\mathbb{R}^4[/itex] and some functions. Those functions can't introduce a contradiction into the theory, so any inconsistency would have to be present in the real numbers, but the reals are constructed from the rationals, the rationals from the integers, and the integers from the ZF axioms of set theory, so we'd have to dismiss the integers and everything else constructed from the ZF axioms. 


#11
Jan2008, 09:36 PM

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hehe I remember in the old physics forum, I made a post asking about the twin paradox, and I wondered why it was even a paradox, and the thread ended up being one of the top 10 most replied or something . I didn't even post after the initial post.



#12
Jan2108, 04:37 PM

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Fredrick  what gives you the right to decide who is crackpot  I suppose now I will have to hunt down Born's book and find Lederman's quote  who are you compared to these Nobel winners.
Jesse: Your last scathing criticism is not of my ideas, that was a direct quote copied from one of pervects post  gotcha Also, jesse, to clarify, the quote from Atkins was in Chapter 256 entitled the Twin Paradox I just happened to have looked up something and came across that chapter and was surprised to realize Atkins was aligned with the Lederman, Born, Sciama crowd. Here is the rest of it: "The problem cannot therefore be satisfactorily discussed in terms of the special theory. It is necessary to apply the general theory. It can then be proved that the combined effects of B's velocities and accelerations are that, when he lands back on earth, his clocks have indeed registered a shorter period of time than A's clocks" Finally, I am not saying that it is necessary to use GR  I am not expressing a personal opinion. Einstein seemed to think something was needed by way of explanation  otherwise why would have taken the time to write the 1918 article If Einstein considered the problem totally resolved by SR, the 1918 article is redundant. My opinion is not in issue  all that was said is that its debated as to whether SR explains the Twin Paradox  that statement still stands  I don't care whether its resolved in the mind of any particular poster or not  it is not resolved in the minds of some real bright people falc39  that is almost always the case with the Clock paradox  everyone jumps in to condemn the paradox  but in different ways  so many solutions, so many authorities, very little humility 


#13
Jan2108, 04:48 PM

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#14
Jan2108, 05:06 PM

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Followup Jesse:
From Einstein's Theory of Relativity by Max Born At page 356: "Thus the clock paradox is due to a false application of the special theory of relativity, namely, to a case in which the methods of the general theory should be applied." I am not going to go through the whole development  since you don't believe anything I say  buy the book and see for yourself 


#15
Jan2108, 05:12 PM

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As it happens, much of the book is available online, and looking at p. 261 confirms my assumption that Born sees no problem in resolving the twin paradox in SR by pointing out that the time dilation formula is only supposed to work in inertial frames, although he points out that you can analyze things in a noninertial frame if you invoke GR: 


#16
Jan2108, 05:37 PM

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That is the very issue  see the last two lines of the page (261) and p 355 .."when the system of reference is altered, definite gravitational fields must be introduced during the times of acceleration"
I think he is saying "we can't explain why one twin ages less using SR alone" contrary to your interpretation. I call that a debateable point  My assertion still stands. We seem to always be interpreting words differently  for me the meaning is clear  the development of Born is based upon the need to explain the aging in terms of a pseudo gravitational field  of course, as you pointed out earlier, we don't really explain things in physics I will get you a citation of the 1918 paper 


#17
Jan2108, 06:05 PM

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1. "The apparent paradox comes from falsely trying to apply SR's time dilation formula to the noninertial frame of twin B; that formula is only supposed to work in inertial frames. As long as we stick to inertial frames, we will correctly predict that B ages less than A." 2. "The apparent paradox comes from falsely trying to apply SR's time dilation formula to the noninertial frame of twin B; that formula is only supposed to work in inertial frames. If we want to analyze things from the perspective of B's noninertial frame, we must use GR, not SR." You see physicists making statements of type #2, and you "read between the lines" to infer that they're saying that the twin paradox itself can not be adequately resolved by SR. But in fact there is absolutely no inconsistency between #2 and #1; someone who agrees with #2 (like me) can also agree with #1, and both would certainly be correct under the standard understanding of relativity. I'm sure everyone on this forum who agrees that SR can resolve the twin paradox would basically agree with #2 (with the caveat that some would say that a 'uniform gravitational field' on flat spacetime is not really an application of GR since there's no spacetime curvature...I'm sure everyone would at least agree that in order to analyze things from the perspective of a noninertial frame, one must go beyond the standard algebraic equations of introductory SR like the time dilation equation [tex]\Delta t' = \Delta t / \sqrt{1  v^2/c^2}[/tex]). So it seems fairly perverse for you to interpret physicists who say things along the lines of #2 as somehow denying #1; unless you can find a mainstream physicist specifically denying that SR alone is sufficient to tell us how much each twin ages, I think this is just a case of you misinterpreting their words. 


#18
Jan2108, 09:55 PM

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But I suppose we could define a "weirdoMinkowski" space as the set [itex]\mathbb{R}^4[/itex] with the standard topology and the same metric tensor as Minkowski space, but with an atlas of coordinate systems that only includes the Poincaré group transformations, instead of a maximal atlas (including all [itex]C^\infty[/itex]related coordinate systems). Then we can define an alternative theory, "weirdoSR", as the claim that space and time can be represented mathematically by "weirdoMinkowski" space. If these authors define "SR" the way I defined "weirdoSR", then it's technically correct to say that "SR" (really meaning "weirdoSR") doesn't include the accelerating twin's point of view. It would however still be incorrect to say that we need GR. What we need is a version of SR that isn't crippled by its definition. And as you (unlike Yogi) already understand, there's no actual paradox in "weirdoSR" either. The twin "paradox" would arise from an incorrect application of that theory, exactly the same way as it arises as an incorrect application of "real" SR. 


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