The real twin paradox.
in [Relativity]
|
From: colp on 29 Nov 2007 20:55 On Nov 30, 3:41 am, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrote: > colp says... > > > > >On Nov 29, 1:36 pm, stevendaryl3...(a)yahoo.com (Daryl McCullough) > >wrote: > >> If you calculate elapsed times using only *inertial* coordinates, > >> then you don't get any contradictions. So you are completely > >> wrong. > > >The contradiction is as follows (the following points ar made with > >respect to the first twin's frame of reference): > > There is no such thing as "the first twin's frame of reference"! O.K. I should have said: "with respect to the observations made by the first twin"
From: Dono on 29 Nov 2007 20:58 On Nov 29, 5:55 pm, colp <c...(a)solder.ath.cx> wrote: http://img83.exs.cx/img83/8330/retard6xj.gif
From: colp on 29 Nov 2007 21:21 Daryl McCullough wrote: > colp says... > > > >On Nov 29, 1:32 pm, stevendaryl3...(a)yahoo.com (Daryl McCullough) > >wrote: > > >> If you want to show that that formula is applicable, > >> then *derive* it from the postulates of Special Relativity. > > > >You are making the claim. The burden of proof is yours, not mine. > > What? You snipped the context, not me. delta t = gamma delta t0 is relativistic mathematics, despite your denial. You claimed that I was applying this formula in a "*different* circumstance" to when delta t and delta t0 are from intertial frames of reference. Yet you haven't shown where I did this. The formula says that a twin travelling in an inertial FOR observes time dilation of the other twin when the other twin is getting further away. The formula also says that a twin travelling in an inertial FOR observes time dilation of the other twin when the other twin is approaching. This is because gamma is greater than one in both cases. For the twins to have the same time at the end of the experiment they must see time compression of the other twin. When does that happen?
From: colp on 29 Nov 2007 22:51 On Nov 21, 11:40 pm, "Dirk Van de moortel" <dirkvandemoor...(a)ThankS-NO- SperM.hotmail.com> wrote: > "colp" <c...(a)solder.ath.cx> wrote in messagenews:06b84031-18aa-4644-bfb7-43f49f46ae6a(a)i37g2000hsd.googlegroups.com... > > This thought experiment is like the classic twin paradox, but in this > > expirement both twins leave earth and travel symmetric return trips in > > opposite directions. > > > Since the paths taken by the twins in this experiment are symmetric, > > they must be the same age when they meet on their return to earth. > > > In this experiment the twins maintain constant observation of each > > other's clocks, from when they depart until they return and find that > > their clocks tell the same time. > > > Special relativity says that each twin must observe that the other's > > clock is running slow, and at no time does special relativity allow > > for an observation which shows that the other clock is running fast. > > No, special relativity says much more precise than that > "moving clocks" are running slow. Is it more precise than delta t = gamma delta t0, when gamma is greater than one regardless of whether the other frame is approaching or going away? Delta t0 is the time interval between two colocal events (i.e. happening at the same place) for an observer in some inertial frame (e.g. ticks on his clock). Delta t is the time interval between those same events, as measured by another observer, inertially moving with velocity v with respect to the former observer. http://en.wikipedia.org/wiki/Time_dilation > > It says something about intertial observers who measure > times between ticks on remote, moving clocks. > > When your two clocks fly apart, each clock will measure > this time to be longer and conclude that the other clock > is "running slower". > While clock A is coasting, according to clock A, each > tick on clock A is simultaneous with some tick on clock B > with a smaller time value. > While clock B is coasting, according to clock B, each > tick on clock B is simultaneous with some tick on clock A > with a smaller time value. > > After clock A has made its turnaround, it has shifted to > another inertial frame, in which according to clock A, each > tick on clock A is simultaneous with some tick on clock B > with a larger time value. > After clock B has made its turnaround, it has shifted to > another inertial frame, in which according to clock B, each > tick on clock B is simultaneous with some tick on clock A > with a larger time value. Consider a third observer in this experiment, called the inspector. The inspector travels constantly in an inertial frame such that after twin A has made his turnaround and accelerated to coasting speed, the inspector's ship is travelling close and parallel to ship A. The inspector observes ship B and notes that it has completed it's turnaround and that time appears to have slowed for ship B as it approaches. The inspector's ship docks with twin A's ship and the inspector changes ships and talks to twin A about their observations of the time dilation of ship B. Do they both observe time dilation of ship B or not?
From: Bryan Olson on 30 Nov 2007 00:27
Sue... wrote: > Daryl McCullough wrote: >> Sue... says... >>> Daryl McCullough wrote: >>>> Sue... says... >>>>> The page shows a young twin beside an old twin after >>>>> one twin has traveled. >>>>> Does one of the twins have a medical disorder or is the page >>>>> it offering argument against the principle of relativity? >>>> One twin looks older because he is *older*. He has lived longer. >>>> The "time" that is important for physical processes is not >>>> coordinate time, but *proper* time. >>> Proper time is the appearace of a distant clock. >> It's hard to imagine a more incorrect answer than that. >> No, that's completely wrong. Proper time is the time >> shown on a *local* clock. Look at your watch. Note >> the time. Now walk a couple of blocks and look at >> your watch again. The difference in the two times is >> the proper time for the path that you just took. >> >> It doesn't have anything to do with distant clocks. > > << A clock in a moving frame will be seen to be > running slow, or "dilated" according to the Lorentz > transformation. The time will always be shortest as > measured in its rest frame. The time measured in the > frame in which the clock is at rest is called the > "proper time". >> > http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/tdil.html > > It's a good job my temper isn't as short as your > memory. Sue, that quote that shows you had it wrong. -- --Bryan |