The real twin paradox.
in [Relativity]
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From: bz on 26 Nov 2007 13:23 colp <colp(a)solder.ath.cx> wrote in news:70c0e3b2-fddd-4048-be43- 1f651123ffc4(a)s6g2000prc.googlegroups.com: > If the change of frame is excluded the paradox becomes clear. > If the change of frame is excluded, the twins each continue away from each other forever. No 'paradox' is involved. The best way to study the problem you set forth without changing frames is from the earth's iFOR. You CAN also study it from A's initial frame of reference, which continues to move away from earth AFTER A has turned around. You can also study it from B's initial frame of reference, which continues to move away from earth After B has turned around. You can also study it from A's second frame of reference. If A travels 1 LY and turns around, you will have to start 2 LY from earth at the same time A leaves earth and 'Join with A' as s/he turns around. likewise with B's second frame of reference. If you do ALL your calculations from any of those iFoRs and stick in that frame, you will see that there is no paradox. -- bz please pardon my infinite ignorance, the set-of-things-I-do-not-know is an infinite set. bz+spr(a)ch100-5.chem.lsu.edu remove ch100-5 to avoid spam trap
From: colp on 26 Nov 2007 15:20 On Nov 27, 7:49 am, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrote: > colp says... > > >SR describes time dilation. SR does not describe time compression. > > That's incorrect. According to your gamma equation. > The Lorentz transform for time > has two factors: > > t' = gamma (t - vx/c^2) > > t' can be greater than t or less than t, > depending on the value of x. According to Wikipedia the equation is: gamma = 1 / (sqrt (1 - v^2/ c^2)) http://en.wikipedia.org/wiki/Time_dilation This means that time dilation occurs regardless of x and regardless of whether v is positive or negative.
From: bz on 26 Nov 2007 14:19 stevendaryl3016(a)yahoo.com (Daryl McCullough) wrote in news:fif4gk01kds(a)drn.newsguy.com: > colp says... > >>SR describes time dilation. SR does not describe time compression. > > That's incorrect. The Lorentz transform for time > has two factors: > > t' = gamma (t - vx/c^2) > > t' can be greater than t or less than t, > depending on the value of x. Or of v (velocity) which is a vector. And THAT is what colp's missing. The direction of the time shift is dependent on the direction of travel. -- bz please pardon my infinite ignorance, the set-of-things-I-do-not-know is an infinite set. bz+spr(a)ch100-5.chem.lsu.edu remove ch100-5 to avoid spam trap
From: Daryl McCullough on 26 Nov 2007 15:43 colp says... > >On Nov 27, 7:49 am, stevendaryl3...(a)yahoo.com (Daryl McCullough) >wrote: >> colp says... >> >> >SR describes time dilation. SR does not describe time compression. >> >> That's incorrect. > >According to your gamma equation. > >> The Lorentz transform for time >> has two factors: >> >> t' = gamma (t - vx/c^2) >> >> t' can be greater than t or less than t, >> depending on the value of x. > >According to Wikipedia the equation is: gamma = 1 / (sqrt (1 - v^2/ >c^2)) >http://en.wikipedia.org/wiki/Time_dilation > >This means that time dilation occurs regardless of x and regardless of >whether v is positive or negative. Did you notice that gamma is always greater than or equal to 1? So the combination gamma (t - vx/c^2) is sometimes greater than t, and is sometimes less than t. Let's take some specific examples. Let t = 1 second. Let x = 0. Let v = 4/5 c. Then gamma = 1/square-root(1-(4/5)^2) = 1/square-root(9/25) = 5/3. Plugging everything into the equation gives: t' = 5/3 (1 second - 0) = 5/3 second So in this case, t' > t. Try different numbers. Instead of x = 0, let's try x = 1 light-second. t' = 5/3 (1 second - 4/5 second) = 5/3 (1/5 second) = 1/3 second So, in this case, t' < t. So whether t' is greater than or less than t depends on the choice of x, as I said. -- Daryl McCullough Ithaca, NY
From: Daryl McCullough on 26 Nov 2007 15:45
colp says... >That is true, but it does not change the fact that according to SR >time dilation is observed when the ships accelerate and when the >travel at constant velocity. Time tilation is observed on both the >outgoing leg and the inbound leg. Don't say "according to SR". That isn't what SR predicts. Do the derivation from the postulates of SR, if you claim that SR predicts something. -- Daryl McCullough Ithaca, NY |