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*To*: starship-design@lists.uoregon.edu*Subject*: starship-design: The "So-called" Twin Paradox*From*: DotarSojat@aol.com*Date*: Sat, 25 Jan 1997 14:52:49 -0500 (EST)*Reply-To*: DotarSojat@aol.com*Sender*: owner-starship-design

Hi all I would like to return to a discussion under way at the end of November, with the idea of stimulating further thought. On 11/29/96, Nick Tosh asked: >Just a quick question: can any one explain to me in relatively >straightforward language, the solution to the twin paradox? [followed by his description of the twin paradox] On 11/29, I responded: >Twin Paradox? There really isn't any. > >All you have to do to dispel the notion that there is a "paradox" >is to ask: What does each twin see when he looks out his window >during the "trip"? The one who sees the UNIVERSE "moving" will >be the younger at the end of the trip. On 11/29, Steve VanDevender added: >However, the Twin non-Paradox would still happen even if one twin >stayed on a fast-moving spaceship while the other took a >relativistic jaunt in the ship's shuttlecraft; the one who left >and came back on the shuttlecraft would be younger. > >The critical issue is acceleration, not apparent motion of the >Universe. The twin in the rocket experiences acceleration, >because in order to make a round trip he must accelerate, turn >around, and accelerate back, and this is the fundamental >asymmetry, because the stay-at-home twin does not experience a >change in acceleration. > >Once can even construct a similar "paradox" where both twins take >round-trips with different accelerations; the twin who >experiences the greater self-measured acceleration will be >younger when they meet again. A typical statement of the "twin paradox" is the one given by Richard Feynman (p. 16-3 in his "Feynman Lectures in Physics," with R.B. Leighton and M. Sands, 1967), as follows: "To continue our discussion of the Lorentz transformation and relativistic effects, we consider a famous so-called 'paradox' of Peter and Paul, who are supposed to be twins, born at the same time. When they are old enough to drive a space ship, Paul flies away at very high speed. Because Peter, who is left on the ground, sees Paul going so fast, all of Paul's clocks appear to go slower, his heartbeats go slower, his thoughts go slower, everything goes slower, from Peter's point of view. Of course, Paul notices nothing unusual, but if he travels around and about for a while and then comes back, he will be younger than Peter, the man on the ground! That is actually right; it is one of the consequences of the theory of relativity which has been clearly demonstrated. Just as the mu-mesons last longer when they are moving, so also will Paul last longer when he is moving. This is called a 'paradox' only by the people that believe that the principle of relativity means that *all motion* is relative; they say, 'Heh, heh, heh, from the point of view of Paul, can't we say that *Peter* was moving and should therefore appear to age more slowly? By symmetry, the only possible result is that both should be the same age when they meet.' But in order for them to come back together and make the comparison, Paul must either stop at the end of the trip and make a comparison of clocks or, more simply, he has to come back, and the one who comes back must be the man who was moving, and he knows this because he had to turn around. When he turned around, all kinds of unusual things happened in his space ship--the rockets went off, things jammed up against one wall, and so on--while Peter felt nothing. "So the way to state the rule is to say that *the man who has felt the accelerations*, who has seen things fall against the walls, and so on, is the one who would be the younger; that is the difference between them in the 'absolute' sense, and it is certainly correct." Professor Feynman says essentially two things here: 1. There can be a paradox only if one believes that the two twins have experienced exactly equivalent conditions, and 2. The conditions differ in the accelerations experienced, so there is no paradox. Suppose, however, that Paul's trip involves 1-g accel/decel periods of 2 years each outbound and the same on return, accumulating 8 years of ship time in a round trip to a far point 5.822 lt-yr away. Peter is waiting in a 1-g gravitational field on Earth. Einstein says (on p.151 of his "Relativity--The Special and the General Theory," Crown, 1920), "Relative to [a system in uniform acceleration]...there exists a state which, at least to a first approximation, cannot be distinguished from a gravitational field." (This was stated by Einstein as the foundation of his General Theory of Relativity.) If you believe that Peter's dilated elapsed time, t, during one of Paul's acceleration periods is given in terms of Paul's time, t', by the relation t = (c/a) * sinh(a * t'/c) (where a = 1 g = 1.0324 lt-yr/yr2 and c = 1 lt-yr/yr), then Peter must live 15.027 years while Paul lives only 8. What difference in their experiences can be used to tell that Paul will be the younger? (We can turn Peter's house upside down at the one-quarter and three-quarter "turnover" times, etc.) If neither looks out the window, how can they explain the difference in their "trip" times? Rex Finke <DotarSojat@aol.com>

**Follow-Ups**:**starship-design: The "So-called" Twin Paradox***From:*Steve VanDevender <stevev@efn.org>

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