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Physics
Special and General Relativity
Deriving Lorentz Factor: An Analysis of Jimmy360's Method
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[QUOTE="DatLemonDoe, post: 6046307, member: 649977"] Hello! 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 [URL='https://physics.stackexchange.com/users/74685/jimmy360']Jimmy360[/URL] is what I followed. [URL]https://physics.stackexchange.com/questions/173268/deriving-the-lorentz-factor-gamma[/URL] 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 [URL='https://physics.stackexchange.com/users/74685/jimmy360']Jimmy360[/URL] 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[SUP]2[/SUP]= l[SUP]2[/SUP]+(vt)[SUP]2[/SUP], I would have expected to see d[SUP]2[/SUP]= l[SUP]2[/SUP]+(vt')[SUP]2[/SUP] 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[SUP]2[/SUP]t'[SUP]2[/SUP]=c[SUP]2[/SUP]t[SUP]2[/SUP]+v[SUP]2[/SUP]t'[SUP]2[/SUP] and then c[SUP]2[/SUP]t[SUP]2[/SUP]=c[SUP]2[/SUP]t'[SUP]2[/SUP]-v[SUP]2[/SUP]t'[SUP]2[/SUP] 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 :) [/QUOTE]
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Deriving Lorentz Factor: An Analysis of Jimmy360's Method
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