Help with deriving Lorentz Factor

In summary, the conversation is about trying to derive the Lorentz factor but getting stuck at a certain stage. The person is using a light clock idea and is unsure if they are taking the calculations too far. Assistance is requested in understanding the next step.
  • #1
Joeirvin
4
0

Homework Statement


I am trying to show how the Lorentz factor is derived but i am unsure how to get past a certain stage..
2. Homework Equations / attempt
Let:
c = velocity of light.
v = the velocity as observed from where time t is measured.
D = distance AB.
t = time light occupies to pass from A to B.
t1 = time light occupies to return from B to A.
Firstly we can see that
t= D/(c+v)
And
t1= D/(c-v)
So for the total distance,
t+t1=D/(c+v)+D/(c+v)
Make a common denominator and add the two fractions,
t+t1=(D(c-V)+D(c+v))/((c+v)(c-v))
Expand the brackets,
(Dc+Dv+Dc-Dv)/(c^2+cv-cv-v^2)
Simplify, cancel out where possible,
(2Dc)/(c^2-v^2)
And take out the factor of 2D
t+t1=2D(c/(c^2-v^2)) or 2D(1/(c-(v^2/c))
( I am unsure whether or not taking it that far is right yet..)

Above is where i have arrived and the next step i am supposed to arrive at..
2D (c^2 / (c^2 - v^2)) = 2D (1 + (v^2 / c^2)]

Any help asap please?

thankyou
 
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  • #3
Joeirvin said:
t = time light occupies to pass from A to B.
t1 = time light occupies to return from B to A.
What's A and B? Are they events? Points in space? Wouldn't this make t=t1?

Joeirvin said:
Firstly we can see that
t= D/(c+v)
And
t1= D/(c-v)
I'm not sure what you're doing, but this looks wrong.
 
  • #4
It doesn't matter now, i decided to start over using a light clock idea, and it seemed to work perfectly. Thanks anyway
 

Related to Help with deriving Lorentz Factor

1. What is the Lorentz Factor?

The Lorentz Factor is a term used in special relativity to describe the relationship between an object's velocity and its time dilation and length contraction. It is denoted by the Greek letter gamma (γ) and is calculated as γ = 1/√(1 - v²/c²), where v is the object's velocity and c is the speed of light.

2. Why is the Lorentz Factor important?

The Lorentz Factor is important because it helps us understand the effects of relativistic velocities on an object's perception of time and space. It is a crucial component in many equations in special relativity, including the famous E=mc² equation.

3. How is the Lorentz Factor derived?

The Lorentz Factor is derived from the Lorentz transformation equations, which describe how space and time coordinates change between two reference frames moving at constant velocities relative to each other. By solving these equations, we can obtain the Lorentz Factor and use it in various calculations in special relativity.

4. Can the Lorentz Factor be greater than 1?

Yes, the Lorentz Factor can be greater than 1. This occurs when an object's velocity approaches the speed of light (c), resulting in significant time dilation and length contraction effects. The Lorentz Factor becomes infinite at the speed of light, meaning that an object with a velocity of c experiences an infinite amount of time dilation and length contraction.

5. How does the Lorentz Factor affect our daily lives?

In our daily lives, we typically do not encounter velocities close to the speed of light, so the effects of the Lorentz Factor are not noticeable. However, it plays a crucial role in modern technologies such as GPS, which requires precise time measurements to function accurately. Without taking into account the effects of the Lorentz Factor, GPS systems would be significantly less accurate.

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