@S1-A.ARPA,@MIT-MC.ARPA:Ghenis.pasa@Xerox.ARPA (06/06/85)
From: Ghenis.pasa@Xerox.ARPA >> The key to the twin paradox is that the travelling twin goes on a ROUND >> TRIP, so his frame of reference is an ACCELERATED FRAME (you cannot >> return to Earth without changing direction, and you cannot change >> direction without acceleration) whereas the stationary twin has an >> INERTIAL FRAME. This is what makes their frames of reference >> non-equivalent, thereby they will experience time differently. > >What if we assume that the universe is closed? Then it would be possible to >return to earth without changing your accelration. What happens then? (You mean without acceleration ...) Interesting thought. This would lead to a paradoxical situation when the twins met again. Since both would have had inertial frames of reference, their ages should be the same (the symmetry of the thought experiment requires this). However, each will expect the other to be younger due to the perceived time dilation (Doppler effect). Summary: The assumption of a closed universe leads to a contradiction. Does this rationale DISPROVE the notion of a closed universe?
@S1-A.ARPA,@MIT-MC.ARPA:Ghenis.pasa@Xerox.ARPA (06/06/85)
From: Ghenis.pasa@Xerox.ARPA >Wrongo. How did the twin leave the earth? How does he return? If >two world-lines become separated, then one or both had to accelerate; hence >one or both spend some time in non-inertial frames. Hence there roles are >asymmetric. > Sigh... I knew I should have been more explicit about the underlying assumptions. Here they are: 1) The thought experiment starts with the travelling twin already possesing an initial velocity v and passing by the stationary twin. Their clocks are synchronized at that moment. The rest of the thought experiment will deal with their delta times. 2) What you are saying is absolutely true in FLAT space-time. This is the domain of special relativity. General relativity goes beyond that, dealing also with CURVED space-time. Without going into details, just think about the fact that free-falling into a gravitational potential (ie. an astronaut floating inside an orbiting space shuttle) is indistinguishable from inertial travel in space (ie. the same astronaut floating inside an interstellar probe with velocity v. If there were no windows he would be unable to tell whether he was still on course or had been trapped into the orbit of some neutron star) The buzzwords CLOSED UNIVERSE (*) refer to the theory that overall, time-space in our universe is curved enough that any trajectory will eventually close. (The curvature coming from the gravitational field of the aggregate mass of everything in the universe), so that the light from a source will return to its point of origin some day. Even if the universe isn't flat it need not be closed, since it can be "hyperbolic" (I'm being a bit loose, but try thinking of the planets' elliptic orbits vs. a hyperbolic orbit that approaches once and leaves, never to return because it has more than the escape velocity for the local gravitational field) (*) Closed universe also refers to whether, within the Big Bang framework, the expansion of the universe will one day stop and contraction will start, giving an eventual "Big Crash", the cycle to be repeated eternally. An open universe would instead expand forever, slowing down but never stopping. If we can determine the total mass of the Universe, knowing the expansion rate we would have the answer to this since it is essentially an escape velocity problem. This certainly seems to be related to the original problem: would a closed universe in the Big Bang sense imply that the curvature of the universe's space-time is closed?