The real twin paradox.
in [Relativity]
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From: colp on 27 Nov 2007 01:21 On Nov 27, 9:51 am, 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. The original thought experiment that I described in the OP (that Dirk quoted) does talk about inertial coordinate systems. What happend when the twins are accelerating and decellerating doesn't affect the paradox. > > >> >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. The velocity term is squared in the Lorentz factor. That means time dilation is observed on both legs from the frame of reference of either twin. http://en.wikipedia.org/wiki/Time_dilation > > >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. Wrong. The experiment described in the OP is what I am talking about. > > >> 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. GPS clocks have to be corrected for SR (& GR) time dilation. To achieve this level of precision, the clock ticks from the GPS satellites must be known to an accuracy of 20-30 nanoseconds. However, because the satellites are constantly moving relative to observers on the Earth, effects predicted by the Special and General theories of Relativity must be taken into account to achieve the desired 20-30 nanosecond accuracy. Because an observer on the ground sees the satellites in motion relative to them, Special Relativity predicts that we should see their clocks ticking more slowly (see the Special Relativity lecture). Special Relativity predicts that the on-board atomic clocks on the satellites should fall behind clocks on the ground by about 7 microseconds per day because of the slower ticking rate due to the time dilation effect of their relative motion. http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html > > 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. In the real world different clocks do get compared.
From: colp on 27 Nov 2007 01:22 On Nov 27, 9:57 am, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrote: > 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. Because an observer on the ground sees the satellites in motion relative to them, Special Relativity predicts that we should see their clocks ticking more slowly (see the Special Relativity lecture). Special Relativity predicts that the on-board atomic clocks on the satellites should fall behind clocks on the ground by about 7 microseconds per day because of the slower ticking rate due to the time dilation effect of their relative motion. http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html
From: Sue... on 27 Nov 2007 02:19 On Nov 27, 1:22 am, colp <c...(a)solder.ath.cx> wrote: > On Nov 27, 9:57 am, stevendaryl3...(a)yahoo.com (Daryl McCullough) > wrote: > > > > > > > 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. > > Because an observer on the ground sees the satellites in motion > relative to them, Special Relativity predicts that we should see their > clocks ticking more slowly (see the Special Relativity lecture). > Special Relativity predicts that the on-board atomic clocks on the > satellites should fall behind clocks on the ground by about 7 > microseconds per day because of the slower ticking rate due to the > time dilation effect of their relative motion. > > http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html The GPS SVs are at about 20,000 km. If a similar clock was at 35,786 km http://en.wikipedia.org/wiki/Geostationary_orbit ....it would only have to be corrected for the the so-called gravitational redshift. That would add a lot of clarity to that part of the launch preset. 7us per day may be beyond the stability of the clocks used considering the measurement is really just from launch pad to station and the response is difficult to separate from the Sagnac effect. http://relativity.livingreviews.org/Articles/lrr-2003-1/articlese3.html#x6-30003 http://relativity.livingreviews.org/Articles/lrr-2003-1/ I am not aware of any calculations that that involve a real geostationary clock but they could contribute a lot of confidence in the 7us component if they exist. Sue...
From: colp on 27 Nov 2007 03:20 Thanks Sue, I'm thinking about sattelites as well.
From: harry on 27 Nov 2007 03:55
"colp" <colp(a)solder.ath.cx> wrote in message news:3f691012-f547-4146-8a75-b3796fcc60f9(a)s8g2000prg.googlegroups.com... > On Nov 27, 1:05 am, "harry" <harald.vanlintelButNotT...(a)epfl.ch> > wrote: >> One last attempt ... >> >> "colp" <c...(a)solder.ath.cx> wrote in message >> >> news:81a29c49-6048-4f2d-87fd-b59380b5dd98(a)b40g2000prf.googlegroups.com... >> >> >> >> > 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. >> > 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. >> >> Sure. >> >> > 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. >> >> There is no need for that, and this has been explained to you from the >> very >> start. > > What has been explained from the very start? That there is no need for an observation that "shows that the other clock is running fast". And you overlooked the illustration that I prepared specially for you: Suppose you warm up a container with water while in Europe, from room temperature (20 degrees) to 40 degrees and you keep it at that temperature in a thermos flask while you travel to the USA (technically difficult and even more so with the new regulations, but never mind). Then you buy a thermometer and you cool the water down to room temperature - back to its original state. Now you want to verify the temperature. You have read somewhere that EU degrees are dilated compared to US degrees: 1 EU degree = 9/5 US degree. The trip to the USA did not change its temperature. Thus the end reading should be 40 - 9/5*20 = 4 degrees. However, the thermometer indicates 68 degrees. This is a paradox, for you simply cooled it down to its original state; at no time during the trip did you see the temperature rise! Cheers, Harald |