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.
John Denker, “The Laws of Thermodynamics”