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- Newsgroups: sci.physics
- Path: sparky!uunet!stanford.edu!CSD-NewsHost.Stanford.EDU!CSD-NewsHost!jmc
- From: jmc@SAIL.Stanford.EDU (John McCarthy)
- Subject: Re: twin paradox
- In-Reply-To: phillies@wpi.WPI.EDU's message of 26 Jul 92 18:45:39 GMT
- Message-ID: <JMC.92Jul26135152@SAIL.Stanford.EDU>
- Sender: news@CSD-NewsHost.Stanford.EDU
- Reply-To: jmc@cs.Stanford.EDU
- Organization: Computer Science Department, Stanford University
- References: <1992Jul26.184539.16856@wpi.WPI.EDU>
- Date: 26 Jul 92 13:51:52
- Lines: 51
-
- There is no twin paradox in special relativity, as I suppose most
- of the posters have said. Here's an approach to understanding
- the phenomenon and explaining it to students.
-
- Suppose on twin travels to Alpha Centauri, 4 light years away
- at half the speed of light and immediately returns at the same
- speed. Consider the event of his arriving At Alpha Centauri.
-
- What event on earth is simultaneous with it? According to
- special relativity, this depends on the co-ordinate system.
- There are three relevant co-ordinate systems, that of the
- stay-at-home twin, one moving at half the speed of light
- from earth in the direction of Alpha Centauri, and one moving
- at half the speed of light in the opposite direction.
-
- 1. In the stay-at-home system, the traveler's arrival at Alpha Centauri is
- eight years after his departure from earth.
-
- 2. In the going-out system, the arrival is 4 sqrt(3) years have
- elapsed, because in that system, Alpha Centauri wasn't 4 light years
- from earth but only 2 sqrt(3) light years. The stay-at-home twin
- has aged only that amount of time in that co-ordinate system.
-
- 3. In the coming-back system, the clock at home reads 16 - 4 sqrt(3)
- years when the traveller turns around at Alpha Centauri.
-
- In this approximation we imagine the traveller to turn around
- instantaneously, i.e. to switch from going at half light speed
- towards alpha centauri to going at half light speed back towards
- Earth. Taking into account a finite acceleration would make the
- problem somewhat more complicated but change the numbers only
- a small amount if the acceleration was high enough. If you don't
- like high accelerations, consider a longer journey in which the
- time for reversal of direction would be smaller in comparison
- with the time spent going at constant speed.
-
- To get the aging of the traveller, not that he spent 4 sqrt(3)
- years going out by his own watch and the same time coming back,
- so he is 8 sqrt(3) years older when he arrrives at Earth. His
- twin is 16 years older.
-
- The apparent symmetry between the twins, which has misled many people
- into believing there is a paradox, is broken by the fact that
- the travelling twin is involved with two co-ordinate systems,
- which differ in what Earth event is simultaneous with the
- turn-around at Alpha Centauri.
- --
- John McCarthy, Computer Science Department, Stanford, CA 94305
- *
- He who refuses to do arithmetic is doomed to talk nonsense.
-
-