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

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The discussion centers on the application of the Lorentz factor in time dilation, questioning its validity when reduced to a simplified form. The original poster argues that this reduction ignores vector directionality, leading to potentially incorrect conclusions about time experienced during round trips at relativistic speeds. They illustrate this with a hypothetical scenario, suggesting that the simplified formula results in a discrepancy in perceived aging compared to the full equation. Other participants clarify that the Lorentz factor and time dilation calculations do not depend on direction, emphasizing that the velocities involved are treated as absolute values. The conversation highlights the complexities of relativity and the importance of maintaining mathematical rigor in its application.
  • #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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