tomclarke wrote: Johan,
The issue here is you do not distinguish between an inertial frame (no acceleration) which is what we have been talking about, and what SR applies to, and a frame which is accelerating.
No it is
you who believe that you can apply the Lorentz transformation and time dilation formula to accelerating frames, while the latter concepts ONLY apply to non-accelerating frames.
You did agree that if the motion is “symmetric” as I have described where both twins accelerate, decelerate and coast identically, they will not age at different rates. Correct?
This can only mean that during the whole journey the clocks of the two twins must have kept synchronous time, or else the age of the twins would have had to be different.. And this synchronous time-keeping also happened during the time that both twins coasted relative to one another, even though according to special relativity there is now a time dilation when observing each clock from its opposite inertial reference frame: For some wondrous reason, this time dilation, according to you, does not “bite” when the motion is “symmetric” but only when the motion is “not symmetric” to include acceleration of one of the reference frames.
Consider again the two twins with their identical space ships and, to please you, only one of them accelerates away for two days until he reaches his top speed v relative to his “stay-home” brother. He then coasts at that speed for 10 years, spend four days to turn around and coasts back for another 10 years, then decelerates for two days and stops next to his brother. Thus the trip took 20 years and eight days. How do you interpret the relative ages of the twins solely in terms of the Special Theory of Relativity?
Firstly, in contrast to what you are claiming, the Special Theory of Relativity tells us
nothing about what happens to clocks during acceleration. The Lorentz equations are
only valid for symmetric unidirectional motion with a single relative speed v. Furthermore, in the thought experiment I have just given, the twins are for twenty years coasting
symmetrically relative to one another. Thus, since this twenty years of coasting is symmetric, the twins should, by your own reasoning, not age relative to one another during this time: The only possibility is that, if there is an age difference, this must be solely caused by the 8 days of acceleration and deceleration of the one twin.
This age difference can obviously NOT be explained in terms of the Special Theory of Relativity. The effect of acceleration was only considered by Einstein many years (about 10?) later. By that time there had already been many arguments about the twin paradox. These arguments were clearly premature, since the Lorentz transformation only applies to a symmetrical situation where the reference frames move unidirectional relative to one another. And as we have already agreed above, this must mean that clocks within both reference frames (which move relative to one another) must then keep synchronous time when the time is measured within their own inertial reference frames respectively: i.e. if the “stay-home” clock shows that 8 years have passed during coasting, the “travelling clock” will also show that 8 years have passed during coasting. There is no time dilation between these clocks when there is no acceleration, AND I even doubt that there will be a time-dilation when only one clock accelerates. But what stands out like a sore thumb, is that the Lorentz transformation cannot model
any return trip and that it is thus ludicrous to claim that in terms of the Lorentz transformation one twin will age more than the other.
It is thus also ludicrous for Kip Thorne to write about a future space trip to the centre of our Galaxy that:
“The entire trip of 30,100 light years distance will require 30,102 years as measured on Earth; but as measured on the starship it will require only 20 years. In accordance with Einstein’s laws of special relativity, your ship’s high speed will cause time, as measured on the ship, to “dilate” and this time-dilation (or time warp) in effect, will make the starship behave like a time machine, projecting you far into the Earth’s future while you age only a modest amount.” The motion is obviously symmetric so that the time on the spaceship DOES NOT dilate relative to the time on a clock on earth when ignoring earth’s gravity.
You state that the case of two twins, one stationary relative to an inertial frame, the other moving outwards and then inwards is entirely symmetric.
The Special Theory of Relativity can only model the situation when the outgoing twin is not accelerating but moving with a constant speed relative to the other twin. I thus state that during coasting away and coasting back, the situation is symmetric and the clocks must keep then synchronous times. If the twins do differ in age after such a trip, this cannot be a result of the time-dilation formula of the Special Theory of Relativity: And Special relativity cannot be used to explain this time difference if it is really there.
That is only true if non-inertial frames are identical to inertial ones. Clearly they are not, for example the laws of physics are different in non-inertial frames.
Thanks for this admission: So you must agree that clocks within two inertial reference frames moving with a speed v relative to one another (no acceleration) must according to the Lorentz transformation keep synchronous times. You must then also agree that if there is in the end an age difference between the twins this difference can only be ascribed to acceleration, and can thus not be explained in terms of the Lorentz transformation and the time-dilation formula of the Special Theory of Relativity.
Either way you cannot claim that acceleration without gravity is equivalent to no acceleration without gravity.
I should not have brought in GR concepts since they are not relevant to this conversation which should be based solely on the Special Theory of Relativity; which obviously cannot be used to reach conclusions when there is acceleration.