The Symmetric Twin Paradox
in [Relativity]
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From: colp on 19 Jun 2010 18:16 On Jun 20, 1:06 am, "Inertial" <relativ...(a)rest.com> wrote: > "train" <gehan.ameresek...(a)gmail.com> wrote in message > > news:8848af8d-c47c-4d28-b572-cfd072537de9(a)s4g2000prh.googlegroups.com... > > Even if the twins both show the same age after te symmetric travel, I > > made the point earlier that twin A has moved relative to twin B and > > twin B has moved relative to twin A. > > Of course they have > > > When realtive motion occurs, time > > dilation occurs. > > Yeup > > > The additional paradox is > > > how can both twins show the same age when relative movement between > > them has occurred? > > Same way as one twin can be younger than the other in the usual twins > paradox. So the usual (assymetric) twin paradox is also a real paradox. > > > Acceleration? > > Yes. . or more exactly .. chagne of rest inertial frame Acceleration does not cause the time compression which is necessary to compensate for the time dilation predicted by SR. > > > put a value a for the time dilation during acceleration, > > and by symmetry in cancels out. > > Yes .. the symmetrical change in frame cancels out the time dilation Not from the point of view of a single twin in the symmetric case it doesn't
From: Daryl McCullough on 19 Jun 2010 18:22 colp says... >It is circular reasoning because you conclude the truth based on >nothing more than a theory. There are two different issues here: (1) What does SR predict? (2) Does that prediction agree with experiments? In trying to answer (1), you *must* understand what SR says (which you don't). -- Daryl McCullough Ithaca, NY
From: Daryl McCullough on 19 Jun 2010 18:27 colp says... > >On Jun 19, 8:12=A0pm, harald <h...(a)swissonline.ch> wrote: >> On Jun 19, 9:59=A0am, colp <c...(a)solder.ath.cx> wrote: >> > In reality the twins age the same as each other, but SR does not >> > predict that result if you examine the experiment from the point of >> > view of either twin. >> >> SR does predict that result; > >Only if you base your observations on what an observer on Earth sees. SR claims that you can use *any* inertial coordinate system, and you'll get the same answer for predictions about the results of experiments. >Relativity says that there is no preferred frame of reference, but you >are clearly favouring one frame of reference over the frames in which >the twins move. That's wrong. SR says that any *inertial* coordinate system is as good as any other. You can't apply what SR says about inertial coordinate systems to a noninertial coordinate system. In the twin paradox, there are three inertial coordinate systems involved: (1) The frame of the Earth. (2) The outgoing frame of the traveling twin. (3) The return frame of the traveling twin. You can use any of those three frames to evaluate the question of how old each twin is when they reunite. You get the same answer for all three frames. -- Daryl McCullough Ithaca, NY
From: Daryl McCullough on 19 Jun 2010 18:31 colp says... > >On Jun 20, 1:06=A0am, "Inertial" <relativ...(a)rest.com> wrote: >> Same way as one twin can be younger than the other in the usual twins >> paradox. > >So the usual (assymetric) twin paradox is also a real paradox. No, there is no paradox in either case. >> > Acceleration? >> >> Yes. . or more exactly .. chagne of rest inertial frame > >Acceleration does not cause the time compression which is necessary to >compensate for the time dilation predicted by SR. If you do as you suggested, and have each twin send out radio signal pulses once per second, you will find that in the twin paradox, the traveling twin sends out fewer pulses than the stay-at-home twin. In the symmetric case, each twin receives the same number of pulses from the other twin. -- Daryl McCullough Ithaca, NY
From: colp on 19 Jun 2010 19:17
On Jun 20, 3:57 am, stevendaryl3...(a)yahoo.com (Dary McCullough) wrote: > colp says... > > >Then what do you think the circumstances are in which SR predicts that > >a twin observes the other to age more quickly, and what mathematical > >relationship quantifies this? > > Sure. Let's assume the following set-up. One twin stays at > home throughout. The other zips away and comes back. You are talking about the classic twin paradox, not the symmetric paradox. However, you haven't introduced acceleration or deceleration, so the issues are the same as in the symmetric case. Also, you have given a worked example, rather than answering my questions directly. A direct answer would be that gamma is always larger than or equal to one, so according to SR, time dilation (or equivalent time if gamma is equal to one) is always observed, and time compression is never observed. Thus the (previously contested) second point of the following argument is true: 1. SR predicts that each twin observes the other twin to age more slowly both on the outgoing leg and the return leg. 2. In no case does SR predict that a twin observes the other to age more quickly. 3. Points 1 &2 mean that SR predicts that each twin will younger than the other at the end of the experiment. > Each twin sends out a radio pulse once per second (as > measured by his own clock). > > From the point of view of the stay-at-home twin, the traveling twin > travels away at 0.866 c for 200 seconds, turns around rapidly, > and comes back at 0.866 c for 200 seconds. The traveling twin > experiences time dilation of a factor of two, so the trip takes > 400 seconds, as measured by the stay-at-home twin, and only > 200 seconds, as measured by the traveling twin. According to > the stay-at-home twin, the traveling twin sends out pulses at > the rate of one pulse every two seconds. > > What about the pulses? The stay-at-home twin will receive signals > from the traveling twin at the rate of one signal every 3.73 seconds > for the first 373 seconds (for a total of 100 pulses). Then, the > stay-at-home twin will receive signals at the rate of one signal > every 0.27 seconds for the next 27 seconds, for a total of 100 more > pulses. > > Why these numbers? On the way out, each successive pulse from > the traveling twin is sent from farther and farther away. Since > the traveling twin travels 1.732 light seconds between sending > any pulses. That means that the second pulse takes an additional > 1.732 seconds to travel back to Earth. Since it is sent 2 seconds > later, that means it will arrive at Earth 3.732 seconds later. > > When the traveling twin is on his way back, each pulse is sent > from a closer and closer distance. One pulse is sent. Then the > next pulse is sent 2 seconds later. But since it is sent from > closer in, it takes 1.732 seconds *less* time to travel the > distance back to Earth. So the second pulse arrives only > 2 - 1.732 = 0.268 seconds later. A rate faster than the rest rate of pulse reception should not be confused with observed time compression, since the decreasing signal transit time results in the pulse rate increase. > > So the stay-at-home twin sees pulses arrive at rate once per > 3.732 seconds for part of the time, and sees pulses arrive at > the rate of once per 0.268 seconds for the rest of the time. > When does the changeover happen? Well, it happens when the > last pulse from the traveling twin's outward journey is sent. > Since the traveling twin travels outward for 200 seconds, he > is 200*0.866 = 173.2 light-seconds away. So it takes another > 173.2 seconds for that pulse to reach the Earth. So the > earth only gets that pulse at time 200 + 173.2 = 373.2 seconds. > > So the earth receives at the rate of one per 3.732 seconds for > 373.2 seconds, for a total of 100 pulses, and then receives at > the rate of one per 0.268 seconds for the next 26.8 seconds, > for a total of 100 more pulses. So the Earth twin receives > 200 pulses from the traveling twin. > > Now, let's look at the situation from the point of view > of the traveling twin: > > The two rates are the same (by relativity): The traveling > twin receives pulses from the Earth twin at the rate of one > pulse per 3.732 seconds during his outward trip, which lasts > 100 seconds (according to his clock) for a total of about 27 > pulses received. In his return trip, he receives pulses from the > Earth at the rate of one pulse per 0.268 seconds for the > next 100 seconds, for a total of 373 more pulses. So altogether, > the traveling twin receives 373 + 27 = 400 pulses. > > So the traveling twin receives 400 pulses from the stay-at-home > twin, while the stay-at-home twin receives only 200 pulses from > the traveling twin. By counting pulses, they both agree that > the traveling twin is younger. The standard explanation for the classic twin paradox requires the consideration of the role of acceleration and deceleration in the experiment. Since you haven't considered this, your example is at odds with that explanation in terms of resolving the paradox. We can treat your example exactly the same as the symmetric case because acceleration and deceleration are not an issue in showing the paradox, only relative velocity. In other words, we can say that there is no significant difference between the motion of the two twins in your example. Thus the paradox can be expressed similarly to the classic case - looked at one way, one twin receives half as many pulses as the other, but looked at in another way the situation is reversed, which is clearly paradoxical. |