johanfprins wrote:Two inertial reference frames Kp and K with clocks at their origins. The clocks are synchronized and the two reference frames move away from one another at a relative speed v.
The Lorentz transformation from Kp to K is given by:
x=gamma*(xp+v*tp) and t=gamma*(tp+(v/c^2)*xp)
The Lorentz transformation from K to Kp is given by:
xp=gamma*(x-v*t) and tp=gamma*(t-(v/c^2)*x)
Clock in Kp remains at position xp=0. When time on this clock is tp, the transformed position x(0) and time t of this clock within K are thus given by:
x(0)=gamma*(v*tp) and t=gamma*(tp): from which it follows that:
x(0)=v*t
Clock in K remains at position x=0. When time on this clock is t, the transformed position xp(0) and time tp of this clock within Kp are thus given by:
xp(0)=gamma*(-v*t) and tp=gamma*(t) from which it follows that:
xp(0)=-v*tp
Now if one of the two clocks are taken on a journey with varying speed v
Stop there!
The previous LT applies only when the frrames stay inertial.
If one frame accelerates then, as a result of the FOR change caused by the acceleration, We have to recompute the relationship between K & Kp.
Physically, remember, we cannot directly measure any relationship between K & Kp until such time as the two frame obsrvers colocate again. So the LT is a mathematical device to make things work out. Now, it is correct as derived if v stays constant.
As soon as v varies we have the problem of reestablishing simultaneity between the new (different v) FOR and the initial FOR.
Nothing in SR, or LT, says what is the answer to this.
Johan here asumes that
no change is needed to account for the change in v. SR says nothing about this, in gfact makes no prediction as soon as v is changed.
In physical reality, the
change in FOR alters the relationship between K and Kp such that all is as expected when the clocks come back together.
Now, I have not proved this, true. After all, it goes beyond the tenets of SR which is what Johan is arguing.
But he, equally, and by definition, cannot disprove it.
so that it eventually returns to meet up and stop within the other clock's reference frame, the distance between the clocks can only have a single value at any instant in time on either clock during this whole journey.
No, the distance between the clocks
relative to (any) given frame can only have a single value at any instant in time on either clock.
This means that for the time tp on the clock in Kp which gives xp(0) =-v*tp, there must be a time t on the clock within K that gives a distance x(0)=v*t so that x(0)=-xp(0).
OK, in Kp there will be such a time tp as measured by its clock. I assume the v here is the initial v between the FORs, not the different v at other points in time. The same spatial separation measured by the observer in K will not have the same distance, because of LF contraction by gamma(v'). Where v' is the instantaneous velocity difference, not equal to v (because of the acceleration).
This demands that after the clocks meet up again, they MUST have that t=tp. If not, it means that the Lorentz transformation is violated and the Special Theory of Relativity is wrong.
No - because above argument incorrect.