rob@osiris.UUCP (Robert St. Amant) (05/30/85)
I've heard the twin paradox, and until recently I thought I had it straight. I thought of something recently, though. When one twin takes off, leaving the other here, why does the one in space age more slowly? Why can't you use a reference frame travelling with him and say that the earth is travelling at a great velocity? Am I missing something? (Obviously I am.) Rob St. Amant
ethan@utastro.UUCP (Ethan Vishniac) (05/31/85)
> I've heard the twin paradox, and until recently I thought I had it > straight. I thought of something recently, though. When one twin > takes off, leaving the other here, why does the one in space age > more slowly? Why can't you use a reference frame travelling with > him and say that the earth is travelling at a great velocity? Am > I missing something? (Obviously I am.) > > Rob St. Amant You can use any reference frame you want. You have a choice of three obvious ones: Earth, astronaut on his way out, and astronaut on his way back. The only requirement of the theory is that when the astronaut returns and compares his age the answer should be consistent with description in any reference frame. We have Earth: Joe consistently aged more slowly than his hidebound brother John who stayed home. Outward bound frame : At first John, sitting on a rapidly moving Earth, was aging more slowly than Joe. However, Joe decided to catch up to the Earth and during this time aged hardly at all. The net effect is that more time passed for John than for Joe. Inward bound frame: At first John and Joe are first moving at high speeds. However Joe is moving much more rapidly than John. After a while he stops moving and John (and the Earth) catches up to him. However, Joe spent very little time standing still and the net effect is still that less time passed for him (because of his earlier high speed motion). -- "Don't argue with a fool. Ethan Vishniac Borrow his money." {charm,ut-sally,ut-ngp,noao}!utastro!ethan Department of Astronomy University of Texas
throopw@rtp47.UUCP (Wayne Throop) (06/01/85)
> I've heard the twin paradox, and until recently I thought I had it > straight. I thought of something recently, though. When one twin > takes off, leaving the other here, why does the one in space age > more slowly? Why can't you use a reference frame travelling with > him and say that the earth is travelling at a great velocity? Am > I missing something? (Obviously I am.) > > Rob St. Amant You may have have heard the twin paradox before, but apparently you just realized why it is a paradox. After all, if one twin simply ages faster than the other, where is the paradox? The paradox is that *each* twin ages faster than the other (depending on your point of reference). To be more specific, imagine two folks of the same age, each traveling at some large fraction of C with respect to the other. Each will find that the other fellow seems to be aging slower. One way to resolve the paradox is to note that, unless one or the other fellow accelerates, they will never meet again, and hence the paradox can never be realized. On the other hand, if they *do* accelerate, that takes it out of the realm of special relativity, and *general* relativity accounts for the situation. (I have heard this hand-wave from several science popularizers, including either Arthur Clarke or Issac Asimov, I can't remember which). As I understand it, the situation *does* key on the acceleration, but the resolution of the paradox doesn't require general relativity. The key to the thing is what is considered "simultaneous" by each person in the situation. Let's tag the people here left-traveling and right-traveling (where "traveling" is simply in relation to the other person). The set of events in space-time considered "simultaneous" by the left-traveling person is *not* the same set of points considered "simultaneous" by the right-traveling person. For example, the left-traveling person considers the event "I've aged 1 year", simultaneous with event "the right-traveler has aged half-a-year". Also, the right-traveling person considers the event "I've aged 1 year", simultaneous with the event "the left-traveler has aged half-a-year". However, these two "facts" don't conflict, since they are derived from different reference frames. Now then, assume that the right-traveler accelerates after having traveled 1 year, and aquires the same velocity as the left-traveler. This acceleration changes the set of events that the right-traveler considers simultaneous. The right-traveler now considers the event "I've aged one year" to be simultaneous with "the left-traveler has aged two years". One way to look at it is that the right-traveler sees the left traveler age one-and-a-half years during the acceleration, and the paradox evaporates in a puff of exhaust gasses. :-) I hope this clarifies things rather than making them worse. It is a little easier to understand with diagrams, but I can't get my space-time charts to look good using simple character graphics. Sigh. -- Wayne Throop at Data General, RTP, NC <the-known-world>!mcnc!rti-sel!rtp47!throopw