B Algebraic Operations on Energy-Momentum Relationships

AI Thread Summary
The discussion centers on confusion regarding the energy-momentum relationship in basic algebra, specifically the misapplication of square roots in calculations. The participant acknowledges a potential decline in their calculation skills due to age. Corrections are made, indicating that square roots should not be present after squaring terms. A simplified equation is presented, leading to a clearer understanding of the relationship. The conversation concludes with a realization that the expression simplifies effectively, reinforcing the importance of careful algebraic manipulation.
alan123hk
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This is just basic algebra for the energy-momentum relationship, but the calculations confuse me. May I ask what is wrong with my concept or calculation causing the following problem.

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Maybe it's because I'm getting older, my ability to think and calculate has declined...
 
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Second line counting from the bottom - the square root should not be there since you raised it to the second power in the third line from the bottom.
 
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weirdoguy said:
Third line counting from the bottom - the square root should not be there since you raised it to the second power.
My goodness!
got it, thanks.
 
Simpler is
$$E^2 - p^2 c^2 = \gamma^2m^2c^4(1 - \frac{v^2}{c^2})$$And the result follows immediately as the expression in brackets equals ##\frac 1 {\gamma^2}##
 
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