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New Theories / Re: How does Hamdani explain the twins paradox?
« Last post by Halc on Today at 17:05:36 »Your numbers in both posts are good except for that bit about 120/4 being 15.Not sure where 120/4 comes from. The 4 was from the perpendicular case, but the case being discussed was not the perpendicular one.
For an inertial object (like Earth) and an instantaneous frame change, t' = Lv
where t' is the inertial clock's time jump, v is the velocity component change towards the inertial thing as measured in the inertial object's frame, and L is the distance component between the two as measured by the inertial thing. Velocity component is negative if the accelerating thing accelerates away.
Things get more complicated (and require calculus) if the acceleration is smooth and not abrupt.
How are those numbers calculated?The numbers come from integrating the interval of the remote worldline between the event where it is simultaneous with the acceleration event in the first frame, and the the event where it is simultaneous with the acceleration event in the second frame. This is pretty easy for an inertial object, but your traveling clock is not inertial, so it is best done in two pieces.
For an inertial object (like Earth) and an instantaneous frame change, t' = Lv
where t' is the inertial clock's time jump, v is the velocity component change towards the inertial thing as measured in the inertial object's frame, and L is the distance component between the two as measured by the inertial thing. Velocity component is negative if the accelerating thing accelerates away.
Things get more complicated (and require calculus) if the acceleration is smooth and not abrupt.
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They should depend on the distance and change of velocity.Yes, Einstein called it 'moment of acceleration', kind of like moment of inertia which is zero for mass at the axis, and increases proportionally with the distance of the mass from the axis.
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The other travelling clock is further than the earth clock during the turn around. But somehow it undergoes less time jump. Where did I miss?You missed the fact that the Earth clock is inertial between the two events of the 'jump' and the traveling clock is not, so its worldline is half the temporal length that it would have had had it been inertial between its two events.