(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I'm having some trouble understanding the fudge factor (gamma) from Professor Shankar's relativity notes (http://open.yale.edu/courses/physics/fundamentals-of-physics/resources/relativity_notes_2006.pdf). It's at the bottom of the first page and top of the second.

I don't understand why the fudge factor is the same for a stationary [A] and movingobserver (relative to Earth).

2. Relevant equations

To simplify this in my head, I assume there is no time dilation. I do this because Shankar leaves this option open when he writes down his equations. That is t = t' always--there is an absolute time.

3. The attempt at a solution

Now, I make this concrete by fixing's velocity at u = 0.75c to the right. [A] andsynchronize their clocks, and after some time t = t', they watch a photon to their right. To [A], the photon travels with speed c. [A] will think, to, the speed of the photon should be 0.25c. This makes sense from the equation x' = x - ut, because then speed x'/t' = (x - ut)/t' = x/t - u (because t = t') = c - 0.75c = 0.25c. But in this case, becausesees the photon traveling with speed c, the x' [A] calculates must be too small. So, thenwill need to take this x' and increase it by a factor gamma.

This, from what I understand, is the reason for the equation x' = gamma * (x - ut) -- from my reasoning, this gamma > 1

Now, take the opposite case. To, the photon is traveling at speed c. Then,thinks, [A] will see the photon travel at 1.75c. Again, this makes sense from x/t = (x' + ut')/t = x'/t' + u (because t = t') = c + 0.75c = 1.75c. But [A] sees the photon traveling at speed c. In this case, the x reported bymust be greater than what x really is. So [A] must decrease it by some factor.

This, from what I understand, is the reason for the equation x = gamma * (x' + ut') -- from my reasoning, this gamma < 1.

I'm probably missing something simple, because I don't see how the two gamma's are equal. Maybe I'm getting my observers mixed up?

Thanks for any help!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Simple Relativity

**Physics Forums | Science Articles, Homework Help, Discussion**