1  Energy is Well Defined – Counterexamples?

Occasionally one hears claims that “energy” is not well defined.

Since reference 1 gives a definition of energy that has, so far, worked well in all practical situations, we have to ask:

Can anybody give a practical counterexample, subject to the following mild restrictions, that shows that energy is not well defined?

Rules of the game:

a)  The goal is to find a specific practical counterexample, such as an experiment that can be readily performed. In particular this excludes Gedankenexperimente on cosmological scales or ultra-subatomic scales where we can’t actually do the experiment. This most explicitly excludes objections to the phrasing of the definition; if a definition is operationally usable, it is good enough for me, regardless of phrasing.

b)  There must be a reasonable way to analyze the experiment in terms of energy.

c)  The analysis must fail to describe some observable outcome of the experiment, and the failure must be due to the lack of a "good" definition of energy. In particular this excludes fussing about gauge independence, since the gauge is unobservable.

d)  We are talking about the physics energy. We are not talking about any nontechnical and/or metaphorical uses of the word. We are not talking about “available” energy, “thermal” energy, or anything other than plain old energy.

I’ve asked this question before, and received a grand total of zero valid counterexamples.

That’s why I continue to believe that for all practical purposes, energy is well defined.

2  References

1.

John Denker, “The Laws of Thermodynamics” www.av8n.com/physics/thermo-laws.htm