©Fernando Caracena 2019
A previous post on Work and Energy concluded with the following statements.
Even if a force is not conservative, such as friction, the work done by that force represents a transfer of energy from one form to another. In the case of friction, large scale motion is degraded into random motions of atoms and molecules, which constitute heat. And heat is a form of energy. In fact, there are many forms of energy.
So far, physicists cannot find any sources or sinks of energy in the universe. The transfer of energy from one form to another may look like a source of energy, or a sink for energy; but if you look hard enough you can always trace an unbroken chain of energy exchange in a zero sum fashion, the total of which does not change in this universe.
In fact, there is a deep theoretical reason for the conservation laws, such as that of energy and momentum, which comes from Noether's Theorems: wherever there is a symmetry in the laws of physics there is an implied conserved quantity. In the case of energy conservation, it arises from the laws of physics being invariant in time. The laws of physics being the same if the whole laboratory is translated in any direction and any amount implies that momentum is conserved. No matter how the laboratory coordinate axes are oriented, the laws of physics remain the same. In that case, angular momentum becomes the associated, conserved quantity. So there is a deep connection between symmetries and conserved quantities, between dynamically conserved quantities and time and space.
Because energy is conserved, the idea of elastic and inelastic collisions really applies just on the large scale, where ordinary objects are seen to lose their motions in a short time: tops stop spinning; grandfather clocks wind down and have to be rewound to keep going; bouncing balls come to rest. So in some sense, all collisions among everyday sized objects are a certain fraction elastic and the remaining fraction, inelastic; but when the degradation of the motion of macroscopic objects is examined microscopically, all processes are seen as elastic. The degradation of motion on a large scale is seen as the transfer without loss of energy on the large scale to the smaller constituents of the large objects. In this sense, all collisions are elastic. Sometimes to be able to see this we must use all the physics that we know.
One modern subtly is that Einstein's equivalence of mass and energy is at work in high energy collisions of particles in a modern particle accelerator. Two protons moving at energies equal to a plethora of other particle rest masses in undergoing head-on collisions can produce a jet-spray of a bunch other high energy particles not originally there, but created by the transfer of the kinetic energy in collision into the moving masses.
There are several parts to the modern view of energy and momentum. Energy is substance. A particle of matter is made up of energy that is held together in a certain form. This form is not just in time and space, but involves configurations in terms of additional abstract quantities.