The Lorentz factor gamma and proper time

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Discussion Overview

The discussion revolves around the concept of proper time along light-like curves in the context of special relativity, particularly focusing on the implications of the Lorentz factor, ##\gamma##. Participants explore the nature of proper time, its definition, and its relevance (or lack thereof) when considering light-like trajectories.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • Some participants assert that proper time along a light-like curve is zero, arguing that this does not imply any fundamental issue with proper time itself but rather reflects the structure of ##\gamma##.
  • Others contend that proper time is irrelevant along a null curve, as it is not an affine parameter and does not provide meaningful insights into the physics of light-like paths.
  • A few participants emphasize that while proper time is zero for light-like curves, this leads to complications when trying to parameterize the motion of light, suggesting alternative approaches are necessary.
  • There are corrections regarding the definition of proper time and its relationship to the arc length along timelike versus null curves, with some participants noting that proper time cannot be used to label events along a null curve.
  • Some participants express concern that discussing proper time in the context of light leads to misunderstandings, particularly the notion that "time stops" for a photon, which can result in confusion in calculations.
  • A later reply highlights that the definition of proper time is intentionally constructed to be undefined on null worldlines for the sake of mathematical simplicity and clarity in proofs.

Areas of Agreement / Disagreement

Participants generally agree that proper time along a light-like curve is zero, but there is significant disagreement regarding the implications of this fact and its relevance to physical interpretations. The discussion remains unresolved on the broader implications of these interpretations.

Contextual Notes

Some participants note that the infinities associated with ##\gamma## as ##v \to c## are mathematically problematic and that evaluating ##\gamma## at ##v = c## is outside its defined domain. This raises questions about the proper interpretation of limits and the physical meaning of proper time in this context.

  • #31
Trysse said:
What is the distinction between "not experiencing time" and "experiencing ZERO time"? Does it not amount to the same?
Worrying about that isn't physics.
 
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  • #32
Trysse said:
What is the distinction between "not experiencing time" and "experiencing ZERO time"? Does it not amount to the same?
I don't know. It's a question of semantics, not physics.

The important distinction here is that for anything traveling at speed ##c## the passage of time is not defined. That is very different from saying that the passage of time is zero.

In the parlance of physics you have three types of intervals: timelike, lightlike, and spacelike. The passage of proper time is defined, and makes sense, only for timelike intervals. For a lightlike (as well as a spacelike) interval it is not possible to define the notion of proper time. It is therefore a sloppy use of terminology to say that no time passes for something traveling at light speed. Moreover, that sloppy use of terminology can lead to misconceptions.
 

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