Derivation of Minkowski norm of the four-momentum

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SUMMARY

The discussion focuses on the derivation of the Minkowski norm of the four-momentum, specifically the transition from the expression -E²/c² + p² to -m²c². Participants emphasize that this relationship is more of a definition than a derivation, as the term "mass" is defined in relation to the four-momentum norm. The conversation also touches on the interconnectedness of physical quantities and their relationship to time, highlighting the foundational concepts necessary for understanding momentum and force in physics.

PREREQUISITES
  • Understanding of Minkowski spacetime and four-momentum
  • Familiarity with the concepts of energy (E), momentum (p), and mass (m)
  • Basic knowledge of classical mechanics, including Newton's laws
  • Grasp of the relationship between physical quantities and time
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  • Study the derivation of the Minkowski norm in detail
  • Explore the implications of four-momentum in special relativity
  • Learn about the relationship between mass, energy, and momentum in physics
  • Investigate the role of time in defining physical quantities
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High school students, physics enthusiasts, and anyone seeking to understand the fundamentals of relativity and the relationships between mass, energy, and momentum.

TheCanadian
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I have attached a derivation of the Minkowski norm of the four-momentum but just don't quite see how the writer arrived at ## -m^2 c^2 ## from what was given. How exactly does this quantity follow from ## -\frac {E^2}{c^2} + p^2##? I feel like it might be very obvious, so any explanation would be great!
 

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I would say that it is a definition rather than a derivation. We use the norm of the four momentum often enough that it deserves a name, so we define the name "mass" to refer to it.
 
Guys ...is it so that every physical quantity is related to time?
like ...acceleration is rate of change in the velocity of an object over time...similar is for velocity n power...but what abt other...

cuz simply p=mv ...i don't get it...but ...by equating ...p=mv n F=ma...we can get F=p/t...n can't get this as well...

please sombody helppppp...m a 11th class student n can't go further if i can't get the basics clearly...pleasezz
 

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