Conservation of energy predict invariance of elastic collisions?

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SUMMARY

The discussion centers on the principle of conservation of energy and its implications for elastic collisions across different inertial reference frames. It establishes that if one observer measures a collision as elastic, all observers in inertial frames will also measure it as elastic, aligning with the overarching principle that physical laws are invariant across frames. While Newtonian mechanics supports this through conservation of momentum, special relativity complicates the matter, as conservation of energy is not universally applicable in general relativity. The conversation emphasizes the need to understand these principles in the context of both Newtonian and relativistic physics.

PREREQUISITES
  • Understanding of Newtonian mechanics and Galilean relativity
  • Familiarity with special and general relativity concepts
  • Knowledge of conservation laws in physics, specifically conservation of energy and momentum
  • Ability to interpret physical laws across different inertial reference frames
NEXT STEPS
  • Study the implications of conservation of momentum in elastic collisions
  • Explore the differences between special relativity and general relativity regarding conservation laws
  • Examine practical applications of conservation of energy in various inertial frames
  • Review the provided attachment "Collision.pdf" for detailed examples and explanations
USEFUL FOR

Physicists, students of physics, and anyone interested in the foundational principles of mechanics and relativity, particularly those studying the behavior of elastic collisions in different reference frames.

wumple
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If one observer in an inertial reference measures a collision to be elastic, then all observers in an inertial reference frame will measure the collision to be elastic - can this be explained with the conservation of energy? What exactly does the conservation of energy principle say in regards to different inertial reference frames?
 
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wumple said:
If one observer in an inertial reference measures a collision to be elastic, then all observers in an inertial reference frame will measure the collision to be elastic - can this be explained with the conservation of energy? What exactly does the conservation of energy principle say in regards to different inertial reference frames?

The law of conservation of energy doesn't explicitly say anything about different frames of reference. However, we have an overarching principle in all of physics that the laws of physics are supposed to be valid regardless of the frame of reference.

In Newtonian mechanics, which operates according to Galilean relativity, the valid frames of reference are Newtonian inertial frames. In this context, if you combine conservation of energy with frame-independence, you end up requiring conservation of momentum: http://www.lightandmatter.com/html_books/0sn/ch03/ch03.html#Section3.1

In relativity, things become more complicated. Special relativity has conservation of energy, but general relativity doesn't, except locally or in special cases.
 
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wumple said:
If one observer in an inertial reference measures a collision to be elastic, then all observers in an inertial reference frame will measure the collision to be elastic - can this be explained with the conservation of energy? What exactly does the conservation of energy principle say in regards to different inertial reference frames?

Look up the attachment "Collision.pdf" https://www.physicsforums.com/blog.php?b=1857
 
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