Surely whatever constructs support a valid formulation of the laws of physics transportable from one observer’s frame of reference to that of others in different dynamical situations must be embraced as the epitome of a physical theory of relativity. The major initial success of Einstein’s special theory of relativity was its applicability to a covariant formulation of Maxwell’s field equations of electrodynamics. But that theory posited ‘events’ as fixed mathematical points in a four-dimensional manifold, with transportability involving transformation of all spacetime. There are serious inconsistencies with such an agenda involving boosting that presumes what cannot be known of the relative dynamical underpinnings of events.

We need to understand more clearly what is required for the covariant formulation of the laws of physics and how a direct transformation of observations rather than an underlying metaphysical reality satisfies those requirements.

The conceptual framework (almost a ‘philosophy’) of using tensor formulations to leverage independence from an individual observer’s situation has proven of inestimable value. Also key was Einstein’s acknowledgement of the universality of the speed of light in a vacuum and that what we observe in nature are not objects *per se* but fleeting events whose times of occurrence must be used in labeling associated phenomena. Each event is one end or the other of an emission-detection transaction. This focus on events rather than the objects on which they are presumed to occur requires that the observed time of these events be incorporated as a fourth coordinate in the registration of natural phenomena. This complex entanglement of positions and times of occurrence of events is required to coordinate the strangely diverse geometrical aspects of observation and their subsequent assignment to associated objects made by relatively moving observers. This complexity cannot be avoided if the observations made by those in relative motion are to be considered commensurable in any direct way, without which covariance would be impossible. Events are mutual, but their pairing in transactions is not. That is the implication of the universality of the speed of light (in vacuo).

Sophisticated discussions of 3-space typically involve ‘*rotation groups*’ of transformations that preserve length between points on rigid bodies from the vicissitudes of observer-peculiar perspectives. There was certainly reason to believe that directly analogous *groups* would perform the similar function in dynamical situations in four dimensions. The Lorentz transformation equations envisioned by Minkowski and Einstein as a ‘transformation’ constitute such a group. To conjecture by analogy that transactions comprised of separated events and the four-dimensional distance between them can be ‘transformed’ one into the other rather than merely corelated does not make it a fact.

However, if one restricts oneself to a single observed transactions, i.e., single emission and detection events, the Lorentz transformation must be replaced by a somewhat similar observation ‘transformation’ with similar features with regard to ‘transforming’ what is spatially fixed in one frame of reference to where it is located in another.

However, a fully operational ‘spacetime metric’ must be incorporated into the observational relativity paradigm as it eventually would be in Einstein’s general theory. Such a construct avoids attributing obvious observational differences between angles, lengths, and time intervals measured by observers in relative motion to respective metaphysical realities. Counter-factual presumptions of mutual orthogonality of respective frames of reference has given rise to this confusion. Relatively moving observers do NOT share mutually aligned coordinate axes.

The measured geometrical relations of observed transactions between events reported by two relatively moving observers are inevitably incongruent. Some sort of congruency must be established between such reports if there is to be any possibility of achieving covariant formulations of the laws of physics. To realize this there must therefore be a transformation construct to rectify (rather than merely ignore) these geometrical disparities. This has a vestigial counterpart in the special theory; in fact it was key to later use of tensors so essential to extending Einstein’s relativity. But because the special theory presumes mutual orthogonality of coordinate axes, it assigns to this ‘metric’ a role no more significant than a glorified identity matrix. Einstein and Minkowski then chose the *spacetime interval* as an archetype of an invariant entity. That then became a cornerstone in formulating the treatment of mutual scalar invariance.

In subsequent posts we’ll extend and generalize the approach to apply to the observation transformation.

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