In the case of length and energy, the numerical constants, 2.54 and 4.184,
have no physical content and are only a historical curiosity. Note that one
is dealing only with energy or only with length. On the other hand, the
constant c is the speed of light in vacuum, a measurable quantity. By
defining the value of c to have an exact number, 299792458, one is only
defining the meter in terms of the unit of time, the second. But note that
we are dealing with two different quantities---space and time, albeit,
components of a 4-vector---which have different dimensions. If somewhere in
the universe, the velocity of light is different, then by using our
definition of the second and the meter, they would get a different length
for the meter. The numbers 2.54 and 4.184 are the same anywhere in the universe.
p.s. Perhaps we do need a referee to settle the issue.
>> For the same reason, Planck's E = h f and de Broglie's p =
>> h/ lambda are fundamental features of nature (or our understanding of nature
>> if you like) and not mere conversion factors. These findings of Planck and
>> de Broglie indicate the fundamental particle/wave duality of nature (or our
>> understanding of nature if you like).
> You point out here something that I've puzzled about. Of the 3
>basic constants c, G, & h (which can be combined to give "natural"
>Planck units for length, time, & mass), the first 2 can be seen as
>conversion factors: From special relativity, c converts space units to
>time units, & from general relativity G converts inertial mass units to
>gravitational mass units. But h can't be seen as such a conversion
>factor: Quantum theory (at least in versions I know) doesn't say that
>energy & frequency are really the same thing in different units. Any
> George Murphy