It is wrong to rule out empirical test in judging the validity
of the labour theory of value. It is in principle possible for
the common substance behind value to be something other than
labour. One could hypothesise that some other input that
entered directly or indirectly into the production of all others
was the common substance. Energy would be an obvious candidate,
or more abstractly negative entropy.
If we were to find that the prices of commodities were almost
in exact proportion to their electricity content, but were
uncorrelated with their labour content, then it would be
more reasonable to conclude that energy was the common substance
of value.
Along with Allin Cotterell I have tried this out on the UK
economy and found that alternative value substances - we tried
electricity, oil and steel as alternatives - have little or
no correlation with price whereas labour has a very high
correlation. Thus although alternative value substances are
in principle possible, they are empirically not the basis of
value in this world.
A paper on this is available on a web server if people are
interested. The paper also deals in detail with logical/mathematical
basis of equality relations and the specific form that these
take in commodity space.