Physics, Astronomy & Cosmology / Re: What is Important About Instantaneous Age Changes in the Twin "paradox"?« on: 05/09/2018 16:06:23 »
My reasoning may be wide of the mark, here, so I would value comments.You are forgetting the relativity of simultaneity. While time dilation and length contraction are only dependent on the speed difference between two frames, the relativity of simultaneity is dependent on the velocity difference, which involves direction.
Acceleration involves a change in speed, direction or both, thus, the “turn-around” constitutes acceleration.
The “twins paradox” comes about as a result of time dilation and length contraction.
The Lorentz equations, which gave mathematical veracity to time dilation and length contraction, feature only time, length, velocity and the speed of light. There is no mention of acceleration.
Einstein incorporated time dilation and length contraction into SR, and SR is concerned only with uniform motion. There seems to be no need to venture into general relativity. So why do we have to use acceleration to solve this particular paradox?
For example, if you are traveling between two clocks A and C while passing a third clock B, and assuming that A, B, and C are synchronized in their own rest frame, then:
If you are traveling from A to C, then clock C will be, according to you, ahead of clock A in respect to what time it reads and if you are traveling from clock C to A then according to you, clock A will be ahead of clock B.
A numerical example:
You're traveling at 0.6c relative to the three clocks, for which the proper distance between the clocks is 1 light hour.
You pass clock B while it reads 12:00, while traveling towards A, At that moment, according to you, Clock A reads 12:36 and Clock B reads 11:24
On the other hand, if you pass B at the same speed while going from A to C, then Clock A reads 11:24 and Clock C reads 12:36 at that moment.*
If you were to suddenly reverse direction as you pass B, while initially traveling from A to B, then clock A will "jump" from reading 11:24 to 12:36*
Acceleration comes into play with time dilation and length contraction when it involves a change speed, as changing speed changes the magnitude of these two effects. Acceleration additionally effects the relativity of simultaneity when it involves a change of direction.
*Keep in mind that this is the time it "is" at these clocks and not the time you would "visually see" on these clocks. In all these examples, when you are next to clock B when it reads 12:00, both you and an observer sitting by clock B would be visually seeing images of Both Clocks A and C reading 11:00.
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