ladajo wrote:Johan,
Can I simply that to say that you mean that Dilation occurs only in the presence of Acell, Decell, or Gravity? And that your entire point is that during the phase of travel at constant speed, there is no rate difference?
My point is that the Lorentz transformation is only valid for a linear relative speed. The word relative is very important here since it means that this speed is not measured from a third reference frame, but only from one of the two inertial reference frames that are moving relative to one another. Owing to this relativistic symmetry either one of the two inertial refrence frames can be used as the stationary one since the Lorentz transformation gives the same results using either one of the reference frames. If you want to argue that one of the reference frames can be chosen as "different" from the other as tomclarke is arguing you are arguing about physics that is not modelled by the Lorentz transformation and is therefore not part of the Special theory of Relativity.
According to Tom's so-called diagrams he used one inertial reference frame (K) as the stationary one, then argues that the other reference frame (Kp)moves away, stops instantaneously and then moves back; and therefore the twin in Kp is now younger. But since we only have the Lorentz transformation, and since the Lorentz transformation is symmetric BECAUSE the speed v is relative, Tom could just as well have chosen inertial reference frame Kp as stationary and generated an alternative rubbish diagram to show that it is reference frame K that moves away, stops instantaneously, and returns; so that now it is the twin in K that is younger. The Lorentz transformation does not distinguish between these two possibilities, and therefore the one twin cannot be younger than the other when only Special Relativity applies.
In my analysis I went into even more detail, and showed that when the two twins send light pulses to one another when their clocks read the same time on their dials, the clocks must keep the same time rate for the whole journey and thus when at starting off they are synchronised, they must still be synchronized at the end of the journey if the Lorentz transformation is correct.
If this is correct, then could we run an experiment with a centrifuge where we measure the rate of change in the clock rate during spin up, at speed, and spin down? Although my initial take thinks that angular momentum would apply.
Since the Lorentz transformation is only valid for linear motion"
In thinking about the orbiting satellites, that would mean also that incurred SR is merely a component of the angular momentum.
Correct when it comes to linear and rotational motion one has to be very careful. It has happened far to often in modern physics that the two are equated to be the same when they are not. They are never the same! As an aside: It is this same same mistake that Feynman has made with his paths-over-history interepretation of electron waves, and this has led to the wrong interpretation for the Aharanov-Bohm effect, as well as for Josephson tunnelling.
So what we really need is a comparison of a non-orbit clock, like the one on a transiting space craft not in orbit, nor in a course correction cycle?
Correct! But to compare a clock on a linear journey with a clock that stayed behind, the clock that at first moves away must decelerate. Special Relativity says nothing about clock rates during acceleratiion. Einstein's General Relativity assumes that this deceleration acts like gravity and this will time-dilate the clock. In fact, this was also Einstein's explanation why the returning twin will be younger. But if this is the reason, the age difference is caused solely by the deceleration, and NOT by the legs of the journey when there is no acceleration. This is also what I directly derived by applying the Lorentz transformation during thes legs of the journey. Each twin sees a time dilation on the other twin's clock, while in reality the two clocks keep synchronous time all the time.
Although Einstein claimed that normal acceleration (not involving an actual gravity field) is the exact same as gravity, this has never really been experimentally satisfactorily verified. This is why I have proposed the "loom-shuttle" experiment where a shutlle made of a radio-active material is launched to and fro, and after many such inear trips, compared with an identical radio-active shuttle that stayed behind. Since the shuttle is impulse-launched and stopped with each cycle, it will travel most of the time with a constant speed relative to the shuttle that stayed behind. One can then clearly separate the total time spent when accelerating and decelerating and the total time spent travelling with the same constant speed, and calculate the expected time dilations for the two types of linear motion. Note that the field of gravity does not change and you do not have rotational motion.
There will be three possibilities:
1. Time dilation will be measured for both the lineaer motion described by Special Relativity and for acceleration and decelleration as if these stages are equivalent to gravity (as toclarke will probably argue).
2. No time dilation will be measured for the linear motion described by Special Relativity but only for acceleration and decelleration as if these stages are equivalent to gravity (as Einstein has argued).
3. No time dilation will be measured for both the linear motion described by Special Relativity and also not for acceleration and deceleration as if these stages are equivalent to gravity.
I suspect that no. 3 will be correct result.