The real twin paradox.
in [Relativity]
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From: colp on 26 Nov 2007 14:15 On Nov 27, 4:17 am, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrote: > colp says... > > > > >On Nov 25, 5:50 am, stevendaryl3...(a)yahoo.com (Daryl McCullough) > >wrote: > >> No, you haven't. As I said, you have to look at > >> what relativity *actually* predicts, not your > >> own distorted version of relativity. > > >What do you think the difference is between my version of relativity > >and your version of relativity? > > The biggest single difference is that you seem to believe > that time dilation is a relationship between two *clocks*. It > isn't. It's a relationship between *one* clock and *one* > inertial coordinate system. You CANNOT apply the time dilation > formula to compare distant accelerated clocks. Wrong. Time dilation between two clocks has to be corrected for with GPS sattelites.
From: colp on 26 Nov 2007 14:22 On Nov 27, 5:45 am, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrote: > colp says... > > > > > > >On Nov 25, 5:54 am, stevendaryl3...(a)yahoo.com (Daryl McCullough) > >wrote: > >> colp says... > > >> >The point is that a paradox exists due to the time dilation expected > >> >by SR. > > >> No, there is no paradox in the sense of contradiction. > > >The contradiction between SR prediction ant reality is described > >below: > > >This thought experiment is like the classic twin paradox, but in this > >experiment 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. > > That's correct. And that's exactly what SR predicts. From the frame of reference of the Earth what you say is true. But it isn't true from the frame of reference of a twin. > > >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 > > No, it doesn't say that. Yes it does. In special relativity, clocks that are moving with respect to an inertial system of observation are measured to be running slower. This effect is described precisely by the Lorentz transformation. http://en.wikipedia.org/wiki/Time_dilation > That's what I mean when I say that > you have to look at what SR *actually* says, not your own > parody of it. > > SR does not say that each clock observes the other clock running > slow. What it says is that any *inertial coordinate system* measures > any moving clock to be running slow. Time dilation is *not* a > relationship between two clocks, but is a relationship between *one* > clock and one inertial coordinate system. Time dilation is a relationship between two clocks in the case of GPS sattelites.
From: paparios on 26 Nov 2007 14:36 On 26 nov, 16:15, colp <c...(a)solder.ath.cx> wrote: > On Nov 27, 4:17 am, stevendaryl3...(a)yahoo.com (Daryl McCullough) > wrote: > > > > > colp says... > > > >On Nov 25, 5:50 am, stevendaryl3...(a)yahoo.com (Daryl McCullough) > > >wrote: > > >> No, you haven't. As I said, you have to look at > > >> what relativity *actually* predicts, not your > > >> own distorted version of relativity. > > > >What do you think the difference is between my version of relativity > > >and your version of relativity? > > > The biggest single difference is that you seem to believe > > that time dilation is a relationship between two *clocks*. It > > isn't. It's a relationship between *one* clock and *one* > > inertial coordinate system. You CANNOT apply the time dilation > > formula to compare distant accelerated clocks. > > Wrong. Time dilation between two clocks has to be corrected for with > GPS sattelites. What the Lorentz transformation says is that (t2-t1)=(t2'-t1')/sqrt(1- v^2/c^2), where (t2-t1) is the time interval between two colocal events, as measured by one inertially moving observer A, miving with velocity v, with respect to another inertial observer B, who measures the time interval between the same events as (t2'-t1'). Miguel Rios
From: Sue... on 26 Nov 2007 14:52 On Nov 26, 2:36 pm, "papar...(a)gmail.com" <papar...(a)gmail.com> wrote: [...] > > What the Lorentz transformation says is that (t2-t1)=(t2'-t1')/sqrt(1- > v^2/c^2), where (t2-t1) is the time interval between two colocal > events, as measured by one inertially moving observer A, miving with > velocity v, with respect to another inertial observer B, who measures > the time interval between the same events as (t2'-t1'). Practically speaking: If I fly from London to New York, recording Big Ben's ticks I will have a summation of proper time intervals. Returning, I can similarly record the number of ticks I see on the Times Square clock. If I total the Eastward and Westward ticks from my notes, it will not agree with a count taken by a Beefeater during my absence. It will have no relation to my age. It will have a direct relation to the fuel used by the two aircraft. Is that correct? Sue... > > Miguel Rios- Hide quoted text - > > - Show quoted text -
From: colp on 26 Nov 2007 14:53
On Nov 27, 5:00 am, bz <bz+...(a)ch100-5.chem.lsu.edu> wrote: > colp <c...(a)solder.ath.cx> wrote in news:a99bf3bb-6f11-4a6a-bfbd- > 4c285e3b2...(a)s19g2000prg.googlegroups.com: > > > One could argue that switching reference frames half way through the > > experiment is another form of misdirection. > > You have multiple reference frames in the problem as originally stated. > If you want to use one reference frame through the experiment, you would do > better to stick with the point of origin of both ships [the earth]. There would be no paradox from that frame of reference. The frame of reference which shows the paradox is that of one of the ships. > > That is because both ships accelerate several times during the experiment. > That means that neither of them stays in the same inertial frame of > reference(iFoR). > This is because each CHANGE in velocity is also a change of iFoR. 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. > > That means that SR will not tell us how things look from the viewpoint of > one of the ships during acceleration. Linear relative acceleration maps to an increase in observed time dilation. > > We can look at what happens inside the ships from the earths iFoR [ignoring > the earths motions through space and considering it to be an iFoR. > We can look at things from the viewpoint of a ship as long as it is > 'coasting'. > But if you want to use SR, You need to find a way to treat the ship as if > it is inertial. > One way to do that is to assume it instantly goes to the velocity, coasts > all the way to the turn around point, then drifts home and stops instantly. > That way each ship is in one iFoR for the entire outbound trip. > > At turn around you can assume it instantly reverse direction of travel. > It is NOW in another iFoR. > > There is no cheating done. This is one way to approach the problem. > > Hint: All approaches that are consistent with SR should give similar final > results, ie both travelers end up with the same number of ticks. The number of ticks that are sent is greater than the number of ticks that are expected to be received by either ship, hence the paradox. > > The way I worked it, with the Doppler shifts and 1 second signal pulses > works AND there is nothing 'odd' happening. That is because you ignored the relativistic time dilation in your example. > > The way Dirk explained it ALSO works but things are a bit odder because of > non inertial frames of reference involved. Wrong. Dirk's description of the return leg disagrees with SR. > > It is much easier to understand if you do make all your clock observations > from the Earth's iFoR. Yes, the paradox does not occur from that FOR. > > From earths iFoR, it is clear that both clocks are 'in sync' through out > the trip, but the clocks are NOT in sync with the earthbound clock. Right. > > If you insist on looking at things from the iFoR of a ship, you MUST keep > in mind that the ship changes iFoR at turn around. That does not change the number of ticks sent or expected. > When you do calculations of 'current' time on the other ship, just before > turn around and again just after turn around, there are large changes in in > the time on the other ship. That is a hint that the situation is paradoxical. > Your time also changes in going from iFoR_outbound to iFoR_inbound, or it > would if you looked from one of those iFoRs the instant before turnaround > at the iFoR just after turn around. You mean the observed time of the other ship? How is that going to affect the number of ticks that are sent? > Of course, as you are using the ship's iFoR for your standard, when you > look at the outside world, YOU see no change in your clock. > All the changes that WOULD show up as changes in your clock get put onto > the clocks of others. Yes, that is a consequence of time dilation. > > As I said before, it is much simpler to look at things from the earths iFoR > and to look at the signals from the other ship as I did. Yes, but the paradox involves look at things from the FOR of one of the ships. > > In any case, there is no actual paradox as long as you remember what pocket > you are putting your ticks into and why. Reality isn't paradoxical. But SR does not describe reality in all frames of reference, hence the paradox. |