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vilas
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Bob sets on a voyage with a velocity 0.8c for total 6 years, leaving back Dave on the space station. On return Dave finds him younger by 4 years. Reciprocal results in time measurements in relativity make the theory redundant but here we see application of time dilation equation. This is explained by jumping of Bob’s line of simultaneity at a point where Bob turns around. This is however a basic and correct interpretation of relativity and it has nothing to do with changing frame.
Assume for example, Bob starts at a point P, far away from O. clocks of both are synchronized. Just before starting reading of both the clocks are same and both are on the space axis ox. However when Bob sets in motion instantly, x-axis of Dave is not a line of simultaneity for Bob. It is inclined upwards from the point P. Therefore if zero is the starting time for Bob, it is some positive value for Dave as measured by Bob.
However there is no reason why we should draw lines of simultaneity. Difference in time coordinates occur due to the distance dependent term in the equation. This term is eliminated when we count time duration and not instantaneous value of time. In twin paradox, total duration is counted and so it should not be distance dependent.
So only way we can draw space-time diagram is the usual triangle for Bob’s world line. Now, using scale, we mark 10 dots for 10 years on time axis of Dave and total 6 dots on the world line of Bob. Thus when Bob spends 6 years in his spaceship, Dave has spent 10 years.
In the Bob’s frame, this triangle is the mirror image and now Bob’s 10 years are Dave’s 6 years. No doubt, between the two, they know who is accelerated, but in any of the equations of SR, changes do not depend on history of acceleration.
Assume for example, Bob starts at a point P, far away from O. clocks of both are synchronized. Just before starting reading of both the clocks are same and both are on the space axis ox. However when Bob sets in motion instantly, x-axis of Dave is not a line of simultaneity for Bob. It is inclined upwards from the point P. Therefore if zero is the starting time for Bob, it is some positive value for Dave as measured by Bob.
However there is no reason why we should draw lines of simultaneity. Difference in time coordinates occur due to the distance dependent term in the equation. This term is eliminated when we count time duration and not instantaneous value of time. In twin paradox, total duration is counted and so it should not be distance dependent.
So only way we can draw space-time diagram is the usual triangle for Bob’s world line. Now, using scale, we mark 10 dots for 10 years on time axis of Dave and total 6 dots on the world line of Bob. Thus when Bob spends 6 years in his spaceship, Dave has spent 10 years.
In the Bob’s frame, this triangle is the mirror image and now Bob’s 10 years are Dave’s 6 years. No doubt, between the two, they know who is accelerated, but in any of the equations of SR, changes do not depend on history of acceleration.