The real twin paradox.
in [Relativity]
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From: Daryl McCullough on 26 Nov 2007 15:51 colp says... > >On Nov 27, 5:45 am, stevendaryl3...(a)yahoo.com (Daryl McCullough) >wrote: >> >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. SR doesn't say *anything* about the frame of reference of an accelerated twin. It only talks about how things work within a single inertial coordinate system. If the twins are accelerating, then they are not in an inertial coordinate system. >> >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. You don't know what you are talking about. >In special relativity, clocks that are moving with respect to an >inertial system of observation are measured to be running slower. Yes, but in the case you are talking about, *neither* twin is in an inertial coordinate system. >> 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. No, it is not. You don't know what you are talking about. Relativity tells you how much proper time a clock experiences for a given path through spacetime. That's an invariant. It's not a comparison of two different clocks. -- Daryl McCullough Ithaca, NY
From: Daryl McCullough on 26 Nov 2007 15:57 colp says... > >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. No, that's wrong. You don't know what you are talking about. For GPS calculations, what's important is not special relativity, but General Relativity. The prediction of general relativity is this: If a clock travels a path given by the quantities x(t) y(t) z(t) in some coordinate system, then the proper time on the clock will be given by: tau = Integral of square-root(sum over u and v of g_uv dx^u/dt dx^v/dt) dt where g_uv is the metric tensor, which GR tells how to calculate. The equation relates tau, the time on the clock, to the coordinates x,y,z,t used to describe the path of the clock. It does *not* relate two different clocks. In the case of slowly moving clocks near the Earth, this integral is approximately given by: tau = Integral of (1 - GM/(c^2 r) - 1/2 (v/c)^2) dt where r is the distance from the center of the Earth, and v is the velocity of the clock. It's not a comparison of two clocks. -- Daryl McCullough Ithaca, NY
From: Sue... on 26 Nov 2007 16:10 On Nov 26, 3:51 pm, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrote: > colp says... > > > > >On Nov 27, 5:45 am, stevendaryl3...(a)yahoo.com (Daryl McCullough) > >wrote: > >> >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. > > SR doesn't say *anything* about the frame of reference of an > accelerated twin. It only talks about how things work within > a single inertial coordinate system. If the twins are accelerating, > then they are not in an inertial coordinate system. > > >> >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. > > You don't know what you are talking about. > > >In special relativity, clocks that are moving with respect to an > >inertial system of observation are measured to be running slower. > > Yes, but in the case you are talking about, *neither* twin > is in an inertial coordinate system. > > >> 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. > > No, it is not. You don't know what you are talking about. > > Relativity tells you how much proper time a clock experiences > for a given path through spacetime. That's an invariant. It's > not a comparison of two different clocks. For a clock to *experience* something wouldn't it have to be real? << Note: if you know about complex numbers you will notice that the space part enters as if it were imaginary R2 = (ct)2 + (ix)2 + (iy)2 + (iz)2 = (ct)2 + (ir)2 where i^2 = -1 as usual. This turns out to be the essence of the fabric (or metric) of spacetime geometry - that space enters in with the imaginary factor i relative to time. >> http://www.nrao.edu/~smyers/courses/astro12/speedoflight.html http://www.quackwatch.org/01QuackeryRelatedTopics/pseudo.html Sue... > > -- > Daryl McCullough > Ithaca, NY
From: Daryl McCullough on 26 Nov 2007 16:13 Sue... says... > >On Nov 26, 1:47 pm, stevendaryl3...(a)yahoo.com (Daryl McCullough) >wrote: > >> >> What SR says is that, from the point of view of any >> *inertial* coordinate system, > >No... the inertial modifier does not appear. Not on that page, but on previous ones it does: "If K is a Galileian co-ordinate system, then every other co-ordinate system K' is a Galileian one, when, in relation to K, it is in a condition of uniform motion of translation. Relative to K' the mechanical laws of Galilei-Newton hold good exactly as they do with respect to K." http://www.bartleby.com/173/5.html He's clearly talking about the relativity between two coordinate systems that are in *uniform* motion relative to one another. -- Daryl McCullough Ithaca, NY
From: Daryl McCullough on 26 Nov 2007 16:22
Sue... says... >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. Practically speaking, the effect of time dilation is negligible for speeds of normal jets. However, a precise enough clock (atomic clock, for instance) would notice a difference. If you left one atomic clock at Big Ben, and carried the other one with you to New York, then when you get back to Big Ben, there will be differences in the elapsed times on the two atomic clocks. -- Daryl McCullough Ithaca, NY |