Natural Science Forum / Physics / Research / January 2008

2) sounds very much like pre-relativistic interpretations of the Lorentz
transformations, that movement through the ether shortens rulers and slows
clocks, thereby changing our units of measurement.

Probably the best primary sources (don't have them here to check) would be
Larmor's papers:

Joseph Larmor, A dynamical theory of the electric and luminiferous medium,
Phil. Trans. v. 185, pp. 719-822 (1894), v. 186, pp. 695-743 (1895), v.
190, pp. 205-300 (1897).

or Lorentz's:

H. A. Lorentz, Electromagnetic phenomena in a system moving with any
velocity smaller than that of light, Proceedings of the Koninklijke
Akademie van Wetenschappen te Amsterdam, 6, 809-831 (1904)

or his book, Theory of Electrons.

Note that if it is our units of measurements that are changed by motion,
then there is one special reference frame in which our units are unaltered
(the ether frame in the pre-relativistic theories). Combine this with the
predicted undetectability of said preferred frame, and it's a rather
conspiratorial universe.

Changes in energy of a system due to motion predate special relativity, of
course, since such occurs under Galilei transformations, too. But this is
not a problem, either in special relativity or Galileian relativity, since
it isn't the kinetic energy or potential energy of an object that matters,
but only changes in KE or PE. What is important is conservation of energy,
which is unaffected by the change in total energy due to a change in
choice of reference frame.

In special relativity, we find something interesting: energy is one
component of a 4-vector, the other 3 being the vector components of
momentum. In SR, a 4-vector remains geometrically unchanged by change of
reference frame, but its 4 components can change. In particular, this
means that the magnitude of the 4-vector must be the same, and this gives
us an invariant quantity closely allied to energy. This is the mass (or
"rest mass", if you prefer), which is magnitude of the energy-momentum
4-vector (in appropriate units).

Your 2) gives us the conspiratorial universe noted above, SR gives us 1),
but also provides the proper invariant quantity.

Energy (actually the energy-momentum 4-vector) is conserved,
in all Lorentz frames.
If it weren't, in some Lorentz frame,
that would make that frame special, and distinguishable,
contrary to the relativity principle.

Best,

Jan