Lorentz Factor Variant: Derivation & Angle Dependence

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Discussion Overview

The discussion centers around a proposed variant of the Lorentz factor, specifically its derivation and potential dependence on the angle of relative motion between two frames of reference. Participants explore the implications of this variant in the context of special relativity and the relativistic Doppler effect.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant presents a derivation of a modified Lorentz factor, suggesting it is given by 1/(sqrt(1-v^^2*sin(a)/c^^2)+v*cos(a)), and claims that it reduces to the classical Lorentz factor at 90 degrees.
  • Another participant questions the meaning of the angle 'a' and requests clarification on the derivation process.
  • A third participant asserts that the Lorentz factor is always 1/sqrt(1-v^^2/c^^2) and does not depend on the angle of relative motion.
  • One participant references the relativistic Doppler effect and its dependence on the angle between emitted light and the direction of motion.
  • Concerns are raised about the validity of the original derivation, with one participant labeling the source of the derivation as unreliable.
  • Another participant discusses the gamma factor in terms of velocity and its independence from orientation in the unprimed coordinate system.

Areas of Agreement / Disagreement

Participants express disagreement regarding the dependence of the Lorentz factor on the angle of relative motion. Some participants support the idea that it is angle-dependent, while others maintain that it is not, leading to an unresolved discussion.

Contextual Notes

The discussion includes references to personal theories and external sources, which some participants challenge as unreliable. There is also a mention of moderation due to the nature of the claims made.

TheSurfers12
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TL;DR
I saw that lorentz factor could change depending of the angle of the relative movement.
I made a derivation of a general transform of the lorentz factor but i still looking in books that the lorentz factor is 1/sqrt(1-v^^2/c^^2) and my derivation is perfectly correct, my result is 1/(sqrt(1-v^^2*sin(a)/c^^2)+v*cos(a)), if we put here 90 degrees we get the classical lorentz factor. Am i right?
 
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What's ##a##? How did you derive this formula?
 
TheSurfers12 said:
Summary:: I saw that lorentz factor could change depending of the angle of the relative movement.

I made a derivation of a general transform of the lorentz factor but i still looking in books that the lorentz factor is 1/sqrt(1-v^^2/c^^2) and my derivation is perfectly correct, my result is 1/(sqrt(1-v^^2*sin(a)/c^^2)+v*cos(a)), if we put here 90 degrees we get the classical lorentz factor. Am i right?
The Lorentz factor depends on the relative speed between two frames of reference, and is always ##\frac{1}{\sqrt{1-v^2/c^2}}##.

The relativistic Doppler effect depends on the angle between the emitted light and the direction of relative motion and the relevant formula involves this angle.
 
Ibix said:
What's ##a##? How did you derive this formula?
(Link to bogus source removed by mentors)
 
Last edited by a moderator:
I'm sorry I asked. Please review the site rules on discussing personal theories.
 
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I think if ##\vec{\beta} = \frac{1}{c}\vec{v}## is the velocity of the primed frame w.r.t. the unprimed frame, then the gamma factor between the frames is$$\gamma^{-1} = \sqrt{1-\vec{\beta} \cdot \vec{\beta}}$$That is in no way dependent on the orientation of ##\vec{\beta}## as measured in the unprimed coordinate system.
 
Thread is now in Moderation pending Mentor review...
 
TheSurfers12 said:
Summary:: I saw that lorentz factor could change depending of the angle of the relative movement.
That’s because you were looking at a (unfortunately familiar) crackpot website, the one you linked to post #4. That website is garbage, and just about nothing it says about relativity can be trusted.

So the answer to your question (does the Lorentz factor depend on the angle?) is no.

This thread is closed because it has started with a false premise.
 
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Ibix said:
I'm sorry I asked. Please review the site rules on discussing personal theories.
Well, we’re glad that you did.
 
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