Algebraic Operations on Energy-Momentum Relationships

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Discussion Overview

The discussion revolves around algebraic operations related to the energy-momentum relationship in physics. Participants are examining calculations and concepts associated with this relationship, focusing on algebraic manipulations and potential errors in reasoning.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant expresses confusion regarding their calculations related to the energy-momentum relationship and questions their understanding of the concept.
  • Another participant points out an error in the calculations, specifically noting that a square root should not be present after raising to the second power.
  • A subsequent reply reiterates the same point about the square root, confirming the previous correction.
  • A different participant presents a simplified version of the energy-momentum equation, suggesting that the expression can be derived directly from the given relationship.

Areas of Agreement / Disagreement

There is no clear consensus on the calculations, as participants identify errors and propose corrections, but the overall understanding of the energy-momentum relationship remains a point of contention.

Contextual Notes

Participants have not fully resolved the underlying assumptions or steps in the calculations, and there may be dependencies on specific definitions of terms used in the energy-momentum relationship.

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.

1654145948091.png

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.
 
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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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