What is the Flaw in Applying the Lorentz Factor to Time Dilation?

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SUMMARY

The discussion centers on the application of the Lorentz factor in time dilation calculations within the framework of special relativity. The original poster argues that the common reduction of the Lorentz factor, represented as 1 / [(1 - B^2)^1/2] where B = v / c, overlooks critical vector considerations when analyzing time dilation for round trips at relativistic speeds. They demonstrate that using the unreduced formula yields a total relative time difference of zero, while the reduced formula incorrectly suggests a discrepancy in aging. This highlights a potential flaw in the conventional understanding of time dilation.

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  • Understanding of special relativity principles
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  • #31
Antenna Guy said:
It's seems we agree (in an awkward sort of way) that the relativistic form is uni-directional; but the question of "why?" remains. The classical version yields two answers for one velocity (bi-directional result) - the relativistic form yields one answer for one velocity (uni-directional result).
I guess I don't understand what you mean by "two answers for one velocity". Do you mean "speed" rather than "velocity"? In the classical version, two objects which have equal speeds along the axis from the viewer to the object but opposite velocities (i.e. opposite directions, one object coming towards the viewer and one moving away) yield different doppler shifts, and exactly the same thing is true in the relativistic version. I don't understand why you think they're different, except for the magnitude of the shift for a particular velocity.
 

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