Intertial mass and determining the value of gamma

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SUMMARY

The discussion centers on understanding the derivation of the gamma factor, γ, in the context of relativistic momentum, specifically its form as (1 - u²/c²)^-0.5. The user expresses difficulty in grasping why the variable v² transitions to u² in the derivation process. It is clarified that both v and u represent the relative velocity between two reference frames, emphasizing the importance of consistent terminology in physics derivations.

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  • Understanding of special relativity concepts, particularly Lorentz transformations.
  • Familiarity with the definitions of relativistic momentum and the gamma factor.
  • Knowledge of the relationship between velocity and reference frames in physics.
  • Basic algebraic manipulation skills to handle equations involving square roots and fractions.
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  • Study the derivation of the Lorentz transformation equations in detail.
  • Explore the concept of relativistic momentum and its implications in physics.
  • Learn about the significance of the gamma factor in various relativistic equations.
  • Investigate the differences between classical and relativistic mechanics, focusing on velocity transformations.
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Students of physics, particularly those studying special relativity, educators seeking to clarify concepts of relativistic momentum, and anyone interested in the mathematical foundations of gamma in relativistic equations.

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Homework Statement


This is not a problem I was assigned, I am just trying to figure out how I could prove it to myself.

Basically, I am just wondering WHY the gamma value for relativistic momentum takes the form that it does, namely (1-u^2/c^2)^-.5

I've tried to prove this to myself a few times and I just cannot figure out how to do it. I am not sure if this is above my skill level and that is why I can't do it, as it was not addressed in my book nor was it addressed in my lecture. I tried to follow the same basic argument I used to show myself the value of gamma in the lorentz transformation, I just cannot figure out why the v^2 changes to u^2.

Even a qualitative answer would be helpful here.

Thanks a lot.

Homework Equations





The Attempt at a Solution

 
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I just cannot figure out why the v^2 changes to u^2.
What are v and u in your derivation? That should be the same - the relative velocity between the two reference frames.
 

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