The Symmetric Twin Paradox
in [Relativity]
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From: Daryl McCullough on 20 Jun 2010 15:00 I wrote: >So signal number 27 was sent 46.4 seconds ago. The Earth >twin ages at half the normal rate, so he has aged 237 seconds >since the signal was sent. I don't know how that got there. What I meant was "he has aged 23.2 seconds since the signal was sent". >So his age at the moment right >before turn-around is about 27 + 23 = 50. So immediately >before turnaround, the traveling twin concludes that the >Earth twin has aged only 50 seconds since the beginning >of the journey, while the traveling twin has aged 100 >seconds. So the traveling twin thinks that he is older. -- Daryl McCullough Ithaca, NY
From: colp on 20 Jun 2010 18:19 On Jun 20, 9:09 pm, "Inertial" <relativ...(a)rest.com> wrote: > "colp" <c...(a)solder.ath.cx> wrote in message > > news:d909afc3-3c9b-4e50-80e2-e1a97793fbad(a)23g2000pre.googlegroups.com... > > > On Jun 19, 8:08 pm, "Inertial" <relativ...(a)rest.com> wrote: > >> "colp" <c...(a)solder.ath.cx> wrote in message > > >>news:97c45dd7-e152-4e3d-8197-42bc43980300(a)y18g2000prn.googlegroups.com.... > > >> > In reality the twins age the same as each other, > > >> As SR predicts > > > ... if you ignore what SR predicts that each twin will individually > > observe throughout the entire experiment. > > you are the one ignoring what SR predict and making up your own nonsense. Now you are contradicting yourself. Later in your post, you agree that SR predicts that an observer observing a non-local clock moving in a inertial frame at a relativistic velocity will observe that clock to be running slow, and that this observation applies both on the outgoing and return legs, and it applies for both twins. > > >> > but SR does not > >> > predict that result > > >> WRONG > > > No, not wrong. > > Yes .. WRONG .. show the math is you think otherwise > > So far nothing from you at all Wrong. The following is an excerpt from an earlier post mine: > t' = gamma (t - vx/c^2) OK. For our example the twins both have x as zero when the experiment starts, so for the outgoing leg: t' = gamma t and since gamma is greater than one, t' > t and the twins both see each other's time to be dilated like I said in my previous post. Let's call the distance between the twins at turnaround x. x = vt, where v is 0.866c and t = 200 seconds per your example. Let's call the velocity for the return leg r. r = -v t' = gamma (t - r.x/c^2) t' = gamma (t + v.vt/c^2) t' = gamma (t + t.v^2/c^2) t' = gamma t(1 + v^2/c^2) Since 1 + v^2/c^2 (and gamma) will always be greater than or equal to 1, the twins both see each other's time to be dilated here as well. There is nothing that occurs at turnaround which compensates for the time dilation of the outgoing and return legs. If you disagree and claim that it is so,then the burden of proof is yours.
From: colp on 20 Jun 2010 18:24 On Jun 20, 9:14 pm, "Inertial" <relativ...(a)rest.com> wrote: > "colp" <c...(a)solder.ath.cx> wrote in message > > What do you think that SR actually says about the symmetric twin > > thought experiment? > > You are the one making claims .. you'd been asked repeatedly to show the > math backing up your claim. you refuse to do so. Until you do, you cannot > be taken seriously I have already shown the math, and I've also reposted it in response to an earlier post of yours. You are the one claiming that turnaround compensates for the observed time dilation of the outgoing and return legs. Using your own standards, you cannot be taken seriously until you show the math with backs up your claim.
From: colp on 20 Jun 2010 18:29 On Jun 21, 4:53 am, Uncle Ben <b...(a)greenba.com> wrote: > On Jun 20, 2:27 am, colp <c...(a)solder.ath.cx> wrote: > > > > > On Jun 20, 11:35 am, "Sue..." <suzysewns...(a)yahoo.com.au> wrote: > > > > On Jun 19, 7:17 pm, colp <c...(a)solder.ath.cx> wrote: > > > > 1. SR predicts that each twin observes the other twin to age more > > > > slowly both on the outgoing leg and the return leg. > > > > No... > > > How does a four dimensional model of spacetime provide for an > > alternative interpretation of the symmetric twin thought experiment? > > > > <<Einstein's 1905 presentation of special relativity was soon > > > supplemented, in 1907, by Hermann Minkowski, who showed that > > > the relations had a very natural interpretation[C 5] in terms > > > of a unified four-dimensional "spacetime" in which absolute > > > intervals are seen to be given by an extension of the > > > Pythagorean theorem.>>http://en.wikipedia.org/wiki/Lorentz_ether_theory#The_shift_to_relati... > > > > << the four-dimensional space-time continuum of the > > > theory of relativity, in its most essential formal > > > properties, shows a pronounced relationship to the > > > three-dimensional continuum of Euclidean geometrical space. > > > In order to give due prominence to this relationship, > > > however, we must replace the usual time co-ordinate t by > > > an imaginary magnitude > > > > sqrt(-1) > > > > ct proportional to it. Under these conditions, the > > > natural laws satisfying the demands of the (special) > > > theory of relativity assume mathematical forms, in which > > > the time co-ordinate plays exactly the same rôle as > > > the three space co-ordinates. >>http://www.bartleby.com/173/17.html > > > > Sue...- Hide quoted text - > > > - Show quoted text - > > See the recent thread addressed to you: "colp, why did Einstein use > the word 'relative'?" in sci.physics.relativity. I'm not interested unless it relates to the symmetric twin paradox. It's up to you to show relevance.
From: Androcles on 20 Jun 2010 18:51
"colp" <colp(a)solder.ath.cx> wrote in message news:1817df86-9c56-4e41-a0a2-db2a8e40c276(a)e34g2000pra.googlegroups.com... On Jun 21, 4:53 am, Uncle Ben <b...(a)greenba.com> wrote: > On Jun 20, 2:27 am, colp <c...(a)solder.ath.cx> wrote: > > > > > On Jun 20, 11:35 am, "Sue..." <suzysewns...(a)yahoo.com.au> wrote: > > > > On Jun 19, 7:17 pm, colp <c...(a)solder.ath.cx> wrote: > > > > 1. SR predicts that each twin observes the other twin to age more > > > > slowly both on the outgoing leg and the return leg. > > > > No... > > > How does a four dimensional model of spacetime provide for an > > alternative interpretation of the symmetric twin thought experiment? > > > > <<Einstein's 1905 presentation of special relativity was soon > > > supplemented, in 1907, by Hermann Minkowski, who showed that > > > the relations had a very natural interpretation[C 5] in terms > > > of a unified four-dimensional "spacetime" in which absolute > > > intervals are seen to be given by an extension of the > > > Pythagorean > > > theorem.>>http://en.wikipedia.org/wiki/Lorentz_ether_theory#The_shift_to_relati... > > > > << the four-dimensional space-time continuum of the > > > theory of relativity, in its most essential formal > > > properties, shows a pronounced relationship to the > > > three-dimensional continuum of Euclidean geometrical space. > > > In order to give due prominence to this relationship, > > > however, we must replace the usual time co-ordinate t by > > > an imaginary magnitude > > > > sqrt(-1) > > > > ct proportional to it. Under these conditions, the > > > natural laws satisfying the demands of the (special) > > > theory of relativity assume mathematical forms, in which > > > the time co-ordinate plays exactly the same r�le as > > > the three space co-ordinates. >>http://www.bartleby.com/173/17.html > > > > Sue...- Hide quoted text - > > > - Show quoted text - > > See the recent thread addressed to you: "colp, why did Einstein use > the word 'relative'?" in sci.physics.relativity. I'm not interested unless it relates to the symmetric twin paradox. It's up to you to show relevance. ============================================= The truth is you are not interested even if it does, all you want is an argument. Which ones are the travelling twins in this gif, the wall and bead, the wall and ruler, the bead and ruler? http://www.androcles01.pwp.blueyonder.co.uk/Wave/bounce.gif No matter which you look at it, the symmetry is undeniably there. |