Station's clock with respect to the train
in [Relativity]
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From: Mike_Fontenot on 1 May 2010 08:42 Here's a brief description of my "CADO" equation: ____________________________________________________ Years ago, I derived a simple equation that relates the current ages of the twins, ACCORDING TO EACH TWIN. Over the years, I have found it to be very useful. To save writing, I write "the current age of a distant object", where the "distant object" is the stay-at-home twin, as the "CADO". The CADO has a value for each age t of the traveling twin, written CADO(t). The traveler and the stay-at-home twin come to DIFFERENT conclusions about CADO(t), at any given age t of the traveler. Denote the traveler's conclusion as CADO_T(t), and the stay-at-home twin's conclusion as CADO_H(t). (And in both cases, remember that CADO(t) is the age of the home twin, and t is the age of the traveler). My simple equation says that CADO_T(t) = CADO_H(t) - L*v/(c*c), where L is their current distance apart, in lightyears, according to the home twin, and v is their current relative speed, in lightyears/year, according to the home twin. v is positive when the twins are moving apart. (Although the dependence is not shown explicitely in the above equation, the quantities L and v are themselves functions of t, the age of the traveler). The factor (c*c) has value 1 for these units, and is needed only to make the dimensionality correct. The equation explicitly shows how the home twin's age will change abruptly (according to the traveler, not the home twin), whenever the relative speed changes abruptly. For example, suppose the home twin believes that she is 40 when the traveler is 20, immediately before he turns around. So CADO_H(20-) = 40. (Denote his age immediately before the turnaround as t = 20-, and immediately after the turnaround as t = 20+.) Suppose they are 30 ly apart (according to the home twin), and that their relative speed is +0.9 ly/y (i.e., 0.9c), when the traveler's age is 20-. Then the traveler will conclude that the home twin is CADO_T(20-) = 40 - 0.9*30 = 13 years old immediately before his turnaround. Immediately after his turnaround (assumed here to occur in zero time), their relative speed is -0.9 ly/y. The home twin concludes that their distance apart doesn't change during the turnaround: it's still 30 ly. And the home twin concludes that neither of them ages during the turnaround, so that CADO_H(20+) is still 40. But according to the traveler, CADO_T(20+) = 40 - (-0.9)*30 = 67, so he concludes that his twin ages 54 years during his instantaneous turnaround. The equation works for arbitrary accelerations, not just the idealized instantaneous speed change assumed above. I've got an example with +-1g accelerations on my web page: http://home.comcast.net/~mlfasf The derivation of the equation is given in my paper "Accelerated Observers in Special Relativity", PHYSICS ESSAYS, December 1999, p629. Mike Fontenot
From: BURT on 1 May 2010 22:33 If the station will have aged more than the fast moving train how when passing the station can the train see the station's clock running slow? Mitch Raemsch
From: John Murphy on 3 May 2010 18:51 On 1 May, 08:26, ben6993 <ben6...(a)hotmail.com> wrote: > On May 1, 5:13 am, John Murphy > <london.accommodation.homest...(a)googlemail.com> wrote: > > On 1 May, 03:08, BURT <macromi...(a)yahoo.com> wrote: > > > > If the train watches the stations clock go slow then when does it have > > > the time to age more? > > > > Mitch Raemsch > > > It never gets a chance to age comparatively, because by definition > > neither 'clock' - nor the train, nor the station knows what the other > > is doing, but it would not help if the train were to visit the station > > in some metrical sense, since that would entail either time gained by > > the train or lost by the station and nor would it work the other way > > around since it would seem to neither 'clock' that they had lost or > > gained. > > > All the same, demons are thought to be able to travel at light speed, > > so could in principle produce a twin-dial clock, available to both > > station and train, although it is unclear how that could be of help to > > anyone other than demons themselves unless they could become an > > interstellar ISP. And if they got a useful role, they might get free > > from messing things up and win a few prizes here and there. > > -- > > Harbinger. > > Is light speed fast enough for the demons to be able to do that job? > Wouldn't they need to travel instantaneously, without any time > elapsing on their own clock or on anyone else's clock, to the station > and back so they could adjust the auxiliary time dial? And they would > need to return very frequently, to keep resetting the time on the > auxiliary dial to the quasi-absolute time. > > If the demons were to pick a speeding clock, with respect to the > station, for use as the quasi-absolute time, then the auxiliary dial > would lag behind the station clock. If the auxiliary clock were to > run very slow then we would need to display milliseconds or > microseconds to see any useful passage of quasi-absolute time. > > Taking more and more decimal places of seconds to be useful for slower > and slower clocks, at the limit of Planck time, assuming time is > quantised, the auxiliary dial might in this limit not be able to show > any passsage of time useful to us. That is because one unit of Planck > time cannot be subdivided on the auxiliary dial. What use is a dial > with only one tick every hundred years, say? Just as well the clocks > will also have the local-time dial. The demons, moving instanteously, would know about the two clocks, but their own 'clock' would be accessible only to them, showing only infinite possibilities. The problem is that they would not be able to communicate their results to any others than they themselves. They might not be of help to Captain Quirk as regards his position because they would not know where he was and where Captain Drake was, but they would not be able to tell him anything useful in relation to either position, even with the help of NASA or MIT. One might think that if they were curving round in opposite directions, they could compare each other's clocks, but they would then need the demons back to inspect the clocks, and the result could only be historical, because listening to the demons would take time. And the demons would then think they had done a good job, but would go away a bit cross,since their NASA invoice was late again! 'It is intirely possible for the station and the train to compare clocks while passing each other is it not? Mitch Raemsch' -- Harbinger.
From: BURT on 4 May 2010 00:01 On May 3, 3:51 pm, John Murphy <london.accommodation.homest...(a)googlemail.com> wrote: > On 1 May, 08:26, ben6993 <ben6...(a)hotmail.com> wrote: > > > > > > > On May 1, 5:13 am, John Murphy > > <london.accommodation.homest...(a)googlemail.com> wrote: > > > On 1 May, 03:08, BURT <macromi...(a)yahoo.com> wrote: > > > > > If the train watches the stations clock go slow then when does it have > > > > the time to age more? > > > > > Mitch Raemsch > > > > It never gets a chance to age comparatively, because by definition > > > neither 'clock' - nor the train, nor the station knows what the other > > > is doing, but it would not help if the train were to visit the station > > > in some metrical sense, since that would entail either time gained by > > > the train or lost by the station and nor would it work the other way > > > around since it would seem to neither 'clock' that they had lost or > > > gained. > > > > All the same, demons are thought to be able to travel at light speed, > > > so could in principle produce a twin-dial clock, available to both > > > station and train, although it is unclear how that could be of help to > > > anyone other than demons themselves unless they could become an > > > interstellar ISP. And if they got a useful role, they might get free > > > from messing things up and win a few prizes here and there. > > > -- > > > Harbinger. > > > Is light speed fast enough for the demons to be able to do that job? > > Wouldn't they need to travel instantaneously, without any time > > elapsing on their own clock or on anyone else's clock, to the station > > and back so they could adjust the auxiliary time dial? And they would > > need to return very frequently, to keep resetting the time on the > > auxiliary dial to the quasi-absolute time. > > > If the demons were to pick a speeding clock, with respect to the > > station, for use as the quasi-absolute time, then the auxiliary dial > > would lag behind the station clock. If the auxiliary clock were to > > run very slow then we would need to display milliseconds or > > microseconds to see any useful passage of quasi-absolute time. > > > Taking more and more decimal places of seconds to be useful for slower > > and slower clocks, at the limit of Planck time, assuming time is > > quantised, the auxiliary dial might in this limit not be able to show > > any passsage of time useful to us. That is because one unit of Planck > > time cannot be subdivided on the auxiliary dial. What use is a dial > > with only one tick every hundred years, say? Just as well the clocks > > will also have the local-time dial. > > The demons, moving instanteously, would know about the two clocks, but > their own 'clock' would be accessible only to them, showing only > infinite possibilities. The problem is that they would not be able to > communicate their results to any others than they themselves. They > might not be of help to Captain Quirk as regards his position because > they would not know where he was and where Captain Drake was, but they > would not be able to tell him anything useful in relation to either > position, even with the help of NASA or MIT. > > One might think that if they were curving round in opposite > directions, they could compare each other's clocks, but they would > then need the demons back to inspect the clocks, and the result could > only be historical, because listening to the demons would take time. > And the demons would then think they had done a good job, but would go > away a bit cross,since their NASA invoice was late again! > > 'It is intirely possible for the station and the train to compare > clocks while passing each other is it not? > > Mitch Raemsch' > -- > Harbinger.- Hide quoted text - > > - Show quoted text - 'It is intirely possible for the station and the train to compare clocks while passing each other is it not? If the train sees the station's clock running slow while passing when does the station get to age more? Mitch Raemsch
From: artful on 4 May 2010 08:23
On Apr 1, 6:11 am, BURT <macromi...(a)yahoo.com> wrote: > When the train is passing the station at high speed and it looks at > its clock SR says it will be running slow. The train observer can't tell if the station clock is running fast or slow by just looking at that instant. It has to 'look' at the time on that clock at different times and see how much time has elapsed on the station clock compared to its own > But for how long can the > station clock be running slow Forever > if it is aging faster? It (the station clock) isn't aging faster; it is aging slower > This is the fundamental clock time contradiction in SR. There is no contradiction |