Conservation of energy predict invariance of elastic collisions?

[wumple]

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?

 

[bcrowell]

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.

 

[starthaus]

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