I Lorentz Factor Variant: Derivation & Angle Dependence

[TheSurfers12]

TL;DR 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?

 

[Ibix]

What's $a$? How did you derive this formula?

 

[PeroK]

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.

 

[TheSurfers12]

What's $a$? How did you derive this formula?

(Link to bogus source removed by mentors)

 

[Ibix]

I'm sorry I asked. Please review the site rules on discussing personal theories.

 

[etotheipi]

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.

 

[berkeman]

Thread is now in Moderation pending Mentor review...

 

[Nugatory]

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.

 

[Nugatory]

I'm sorry I asked. Please review the site rules on discussing personal theories.

Well, we’re glad that you did.