How can a claim about a violation of the
first law be taken seriously?
Prior to Rumford (1797), people thought heat was a conserved
quantity unto itself.
Prior to Einstein (1905), people thought mass was a conserved
quantity unto itself.
Prior to Wu (1956), people thought parity was conserved.
As a practical issue, in my judgement a tabletop experiment is
probably not the optimal approach for persuasively demonstrating
non-conservation of energy. HOWEVER... out of respect for the
scientific process, I insist on keeping open the possibility in
principle.
> I was thinking about a student experiment.
That doesn't change the story. There is no law prohibiting
students from obtaining valid, important, heretical results.
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As an aside, I note with hearty approval that Ludwik considers
"the first law" to be synonymous with "conservation of energy",
nothing more, nothing less. Not everybody does, but they should.
(The alternative is to conflate the first law with various
corollaries involving derivatives, with considerable loss of
generality.)