Lorentz Factor Variant: Derivation & Angle Dependence

In summary: But we need you to follow the rules while you’re here, too. In summary, the Lorentz factor depends on the relative speed between two frames of reference, and is always 1/sqrt{1-v^2/c^2}.
  • #1
TheSurfers12
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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?
 
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  • #2
What's ##a##? How did you derive this formula?
 
  • #3
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.
 
  • #4
Ibix said:
What's ##a##? How did you derive this formula?
(Link to bogus source removed by mentors)
 
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  • #5
I'm sorry I asked. Please review the site rules on discussing personal theories.
 
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  • #6
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.
 
  • #7
Thread is now in Moderation pending Mentor review...
 
  • #8
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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  • #9
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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FAQ: Lorentz Factor Variant: Derivation & Angle Dependence

What is the Lorentz Factor Variant?

The Lorentz Factor Variant is a mathematical expression used in special relativity to describe the relationship between an object's velocity and its observed time, length, and mass. It is denoted by the symbol gamma (γ) and is a function of an object's velocity, v.

How is the Lorentz Factor Variant derived?

The Lorentz Factor Variant is derived from the Lorentz transformation equations, which describe how time, length, and mass change for an object in motion. It is calculated by taking the square root of 1 minus the square of an object's velocity divided by the speed of light squared (γ = √(1 - v^2/c^2)).

What is the angle dependence of the Lorentz Factor Variant?

The Lorentz Factor Variant is dependent on the angle between an object's velocity and the observer's frame of reference. As the angle increases, the Lorentz Factor Variant decreases, meaning that the observed time, length, and mass of the object will be less affected by its velocity.

How does the Lorentz Factor Variant relate to time dilation and length contraction?

The Lorentz Factor Variant is directly related to the phenomena of time dilation and length contraction. As an object's velocity increases, its Lorentz Factor Variant also increases, resulting in time appearing to slow down and length appearing to contract from the perspective of an observer in a different frame of reference.

In what situations is the Lorentz Factor Variant most commonly used?

The Lorentz Factor Variant is most commonly used in situations where objects are moving at extremely high speeds, close to the speed of light. It is used in various fields such as particle physics, astrophysics, and engineering, to accurately describe the behavior of objects in motion at these velocities.

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