Tom,
""Your example making use of mass, energy, and force uses these properties after they have been usurped by theoretical speculation.""
"No, James. My example shows that the theoretical prediction is identical to the experimental (empirical) result. The terms match. If they did not, one would expect that mass-energy is not conserved, and therefore Noether's theorem is wrong."
The terms do match because they are designed to match. Whether they are defined properly or not, they will match whether one choses three indefinable fundamental properties or two indefinable fundamental properties. Predictions will follow so long as the form of the equations accurately models the patterns observed in empirical evidence. The difference is not the numbers. The difference is learning what physics looks like when invented properties are disallowed.
Mass is a real property but its definition is artificial. It is made up. It is arbitarily made to be an indefinable property. There is no justification for this act. It was done only because theorists did not see how to pursue defining all properties in the same terms as the empirical evidence. That connection was broken without justification. The penalty paid ever since is disunity.
"I can live with "Bell's theorem" being wrong, based on a wrong choice of topology (the hidden variable); I can't live with Noether's theorem being wrong -- for that would imply that the same laws of physics are not uniform in time. (It would also contradict your own assertion that Newtonian time is the true measure of time.)"
Getting the definition of mass correct does not lead to contradiction in the operation of the universe. It can't. What it does do is establish the existence of unity right from the beginning of analyses.
"Your assumption that there is an absolute rest mass (at rest relative to what?) is, I acknowledge, a deep question -- it goes back to Lemaitre's unasked question of whether the universe as a whole was ever at rest. We would never know that answer *in principle* by empirical methods, because empirical evidence reveals to us only relative motion. We can soundly reason Noether's generalized symmetry of universal dynamics from this empirical fact."
I do not have an assumption that there is an absolute rest mass. Mass is always varying. Even with all other things being equal and constant, mass is still a variable. It varies with distance. With all other things being not equal and not constant, mass is varying both with and without distance.
""Mass must have units that are formed from some combination of meters and seconds only.""
"It does. One need not assume that the hammer has mass until it is translated to motion in spacetime resulting in force. Meters are measures of space (rods); seconds are measures of time (clocks)."
Kilograms remains an indefinable unit. My point of making it a definable unit has nothing to do with needing relativity theory or any other theory for justification. It has to do with getting f=ma right at the beginning. Newton's f=ma must have mass and force defined in terms of length and duration. Both properties must begin their role in f=-ma with units that consist only of combinations of meters and seconds. Both force and mass must be and are definable using only the terms of empirical evidence.
"Force then also receives units that are formed from some combination of meters and seconds. That is how those two properties are expressed in the same terms as is the empirical evidence from which their existence was inferred."
"The empirical evidence tells us that the existence of force follows the existence of mass -- just as you claim -- though we do not find it necessary to make your assumption of the prior existence of mass in an absolute rest state, which is a metaphysical assumption incorporated neither into the physical (empirical) result nor the theory (kinetic theory of matter)."
I don't have an absolute rest mass. I have an explanation for what mass is. That explanation comes from maintaining a direct conenection between empirical evidence. The manner in which that connection is maintained is to define mass and force in the terms of their empirical evidence.
""Once mass is established as a defined property, all other properties in mechanics follow suit.""
"True. Your definition is not a definition, however; it is a metaphysical assumption. It is entirely equivalent to Aristotle's Unmoved Mover."
This is a strange conclusion considering that my definition is solidly empirically based. I chose to not invent the definition of mass as an indefinable property. Mass is currently undefined. It doesn't have a definition. It isn't defined in terms of force because force is defined using an indefinable mass. It can't be defined in terms of energy. Having a relationship between mass and energy does not tell us what either one is unless we first know what one of them really is. I define mass. I define it right from its start of use in f=ma. Force and energy are then definable based upon an understanding of what mass is right from the start. Right from the beginning of Newton's f=ma.
Tom