Dear Harrison
Again we completely agree that definitions must match a system's actual context.
When you say that the Lorentz transformation does not change a system's ontology, that is tautologically true -- it is impossible to change ontology, which is physical reality. But it does assume a different, incorrect ontology. One cannot 'mix' time and space as Minkowski famously claimed in a (3+1)D ontology. The Lorentz transformation mixes time and space, and this is simple impossible in a universe with local preferred frame and universal simultaneity. Lorentz produces "length contraction" which does not physically occur. People speak as if the MM measurement arms are contracted, but Lorentz doesn't contract material, it contracts "space". Every point in a moving frame is contracted, not just the points in the material arm.
The Lorentz transformation is between two 4D geometries. It has, in my opinion, nothing to do with information, per se. Information involves recording energy-based changes in physical systems and code books for interpreting the record: "one if by land, two if by sea" is meaningless without the context or code book. There are other associated aspects of relativity that, while not actually part of the Lorentz transformation, completely throw away inter-frame kinetic energy, an impossible and rather foolish thing to do.
You say you think my objection is that 'this' leads people to conclude that we can arbitrarily change a system's actual context. I'm not sure what you mean by this. My objection is that special relativity is based on a wrong model of reality. The 4D- 'block universe' is simply not real; reality is 3-space and one universal time. The energy-time theory does yield the gamma(v,c) associated with 'relativistic mass', and consequently does lead to clocks slowing down, as increased mass/inertia resists the acceleration of the oscillator restoring force and hence the oscillator/clock mechanism slows down physically. In my opinion this 'time dilation' is the main reason that people have accepted the many paradoxes of special relativity for over a century. There is now an alternative explanation for time dilation that produces exactly the correct inertia-factor gamma. This is significant, and should be cause for rethinking the paradox-ridden theory. Energy-time theory does not produce length contraction.
I am uncertain of the consequences of your theory, and have not understood it well, but I am quite certain that my statements about Lorentz and the differences in 4D and (3+1)D ontology are correct. I have worked on this theory with quite capable physicists for almost three years, and they have yet to find any math error. Interpretation is in the mind of the observer, and I am sorry to say that after 50 years of dealing with a 'mentally reorganized' world (Smolin), some octogenarian minds have become almost hardwired. Very bright PhD engineers find it much easier to grasp energy-time theory than do physicists. The better one understands relativity, the harder it is to unlearn it. There are all the other psychological factors at work as well, and for academics there are career issues.
You speak of "conserving a system's ontology". Ontology is just a fancy word for physical reality. "Conserving" reality is not an option, or even a meaningful concept. One can misinterpret reality, which is what special relativity does, but reality 'conserves' itself without our help. I do not think that reality is synonymous with "actual physical context", as context to me means 'outside' of the system. Reality is inside, outside, everything. And it is not 4D. Lorentz only operates between 4D geometries, so Lorentz transformation is inappropriate.
Particle physicists are more than enamored by Lorentz. It is built into their Lagrangians at the fundamental level. Why? I believe it is because Lorentz guarantees that relativistic mass is properly taken care of (by the gamma factor) which is paramount in particle physics, whereas the length contraction that erroneously comes with Lorentz is of no significance in particle accelerators.
You say that Lorentz is a transformation of description from one context (inertial framework) to another. My point is that Einstein's inertial frame is a 'cartoon world' that, by introducing multiple time dimensions, destroys universal simultaneity, which is the 1D in (3+1)D, and thus presents the physicist with a false description of reality. I believe the empirical fact of clocks slowing down has caused physicists to accept these cartoon worlds because there seemed to be no other explanation of time dilation. Now there is another explanation. It does not 'disprove' special relativity, but it does provide an alternative theory to be tested against relativity. And it gets rid of the Lorentz-based paradoxes which have bothered so many for so long.
Thanks again for thinking about these issues. It is much easier simply to go with the flow.
Edwin Eugene Klingman