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This is my first post on this forum, so make sure to tell me if I am doing something wrong :)

I was trying to derive the Lorentz factor today, and I used the following page as a guide. The top answer by Jimmy360 is what I followed.

https://physics.stackexchange.com/questions/173268/deriving-the-lorentz-factor-gamma

I was unable to solve for t' as they did, and it occurred to me that there was perhaps an issue with the derivation. Now I am in no way knowledgeable nor talented in derivations so I wanted to have someone look at my thought process. I have a hard time imagining that the derivation I linked is wrong, but then again I made it work for me with a small change that seems to make sense.

I realize that I am most likely wrong but I can't figure out why. That's why I need your help. If I'm misunderstanding something I want to find what that something is.

So, it seems that Jimmy360 set t' to be the coordinate time, and t to be the proper time.

Hence l=ct (that's an observation made by an observer in the reference frame of the rods), and d=ct' (that's an observation made by an observer in the other reference frame, which doesn't follow the rods)

Now when they find that d

^{2}= l

^{2}+(vt)

^{2}, I would have expected to see d

^{2}= l

^{2}+(vt')

^{2}instead. The distance that the rods travel in the x-axis is not measured at all by an observer in the rods' reference frame, is it? That's why I expected d to be expressed in terms of f' rather than f

After that change is made we get

c

^{2}t'

^{2}=c

^{2}t

^{2}+v

^{2}t'

^{2}

and then

c

^{2}t

^{2}=c

^{2}t'

^{2}-v

^{2}t'

^{2}

From there I am able to solve for t and in doing so find the Lorentz factor.

Is my thought process correct? If not, can you guide me towards what I don't understand?

Thank you very much for your time, I appreciate it :)