Why relativistic momentum equals the following?

AI Thread Summary
The discussion centers on the derivation of relativistic momentum, specifically how to express momentum in terms of energy and mass. It highlights the equation P = √(γ² - 1) * mc, derived from the relationship between momentum and the Lorentz factor γ. Participants note that while using p = γmv is valid, eliminating velocity from the equations can lead to the same result. However, it is suggested that using the energy-momentum relation E² - p²c² = m²c⁴ is a more straightforward method to solve for momentum. The conversation emphasizes the importance of understanding these fundamental equations in relativistic physics.
Foruer
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In a solution to a problem we were given, it is written that a positron momentum with energy of 2mc2
(where γ=2) is √(γ2-1)*mc = √(4-1)*mc = √3*mc

How did they get that P=√(γ2-1)*mc?
 
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You are familiar with p = ϒmv right?
And also with ϒ = 1/√(1-(v/c)2) right?

Eliminate v from the two equations and what do you get?
 
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What I get is the answer ?:) thank you :wink:
 
While it gives you the right answer, it is much simpler to use the energy-momentum relation ##E^2 - p^2 c^2 = m^2 c^4## and just solve for ##p##.
 
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