Sorry, I had little time to respond lately but I have read your posts with interest and I appreciate you taking the time to post this. However my question of metrology seems to be mostly about the fundamental assumptions you base your calculation on. So let me explain what I had in mind, when I made my remark. All physical axioms are an abstracted and generalized form of observations/measurements made. Newton’s inertia law you started with is no different. From a pure mathematical point of view it isn’t really a simple axiom but rather comes as one big package including basic assumptions for the vector space (among other) that is needed to even formulate the law. Now the axioms of vector space itself don’t come from nowhere but are too associated with real observations: i assume that they are the properties of the metrology used and each can be experimentally verified to hold true. And even the most basic assumption, that we can describe the world in terms of numeric quantities requires a metrological system which measurements conforms to axioms of mathematical fields and the real numbers. So these most fundamental tools are bound to the metrology. So let’s change to an ancient first day metrology: using a foot of a living person as a measure of length. It abides by axioms of a metric and combined with other geometrical observations will yield a vector space. But It comes with a nasty disadvantage: a field measured to be 100 feet long may become only 98 feet a year later due to the foots owner aging. A pure mathematician would therefore conclude the field has shrunken over the year. While it sounds like a joke from a pure technical point of view it is a valid conclusion since it does not create any formal contradictions. We just wouldn’t ever stick to describing the world in this way because of it immense impracticality. But if it is possible, then for the sake of argument let’s use it for now. Equipped with a metrology we are now able to measure inertia and translate them into mathematical formalism which enables us to check Newtown’s law. And here comes the trouble: all objects will very slowly lose inertia over the years since they move few fractions of a feet less in the same time. The pure mathematician would therefore say that Newton implies the presence of a universal gradient force that shrinks the entire universe thus a rest frame does not really exist (no object can be at rest… apart from the foot itself and other living beings which… ‘have a force of their own to counteract the universal one’). Even if this example metrology is good for nothing else then to make the world look funny I simply don’t see any logical or formal reason which makes it incorrect. Of course it is useless for any practical purpose but an argument of convenience does not invalidate it from a technical point of view. So if you see any formal or logical fault in this line of thought, please point it out. Because if it is not technically wrong it would show that the metrological definitions and choices have much greater and non-trivial implications that just changing units – or at least I don’t think common sense of what units are supposed to be, allows them to make use of all degrees of freedom given by the metrological choice. And this is what I am exploring here.