Previous posts have focused on the relationship between observations of visual images that could be seen by two relatively moving observers in order to check the veracity of claims for unobservable ‘features’ of Einstein’s special theory of relativity. Penrose was first to employ a theoretical approach of visually inspecting images of relatively moving objects to demonstrate that Lorentz contraction can never be directly observed. But he did not extend the approach to the determination of what clock face images would be visible to two such relatively moving observers. What a relatively moving clock would ‘look’ like, whether rotated or not, destroys the ‘appearance’ of time dilation as surely as the test of ‘what it looks like’ destroys the ‘appearance’ of Lorentz contraction. By including the changing time that a clock displays as against a static object that looks essentially the same one moment to the next, we united the ‘appearance’ and ‘reality’ of the associated events that are observed and thereby exposed the lie. Relatively moving observers must acknowledge that much more than mere ‘appearance’ is involved in visual observation. We all exist in the same universe even though there are aspects of ensembles of events that we see differently.
In Einstein’s special theory of relativity uniformly moving observers are assumed to share a common ‘flat’ spacetime metric based on mutually aligned orthogonal axes. But they are not, and cannot be, mutually aligned. In observational relativity this observed ‘non-flatness’ is incorporated into the observation coordination using a more generalized metric similar to what Einstein employed much later in generalizing relativity. Formally what is called the relative metric is employed in both theories to express covariant physical laws in tensor notation. It is what must be employed in the electromagnetic ‘field strength tensor’ in generalizing electrodynamics. It is used in defining a covariant derivative, and to ‘raise’ and ‘lower’ indices as a part of manipulating tensor constructs, etc.
Our insistence on observational aspects of relativity does not force us to reject either covariance or generalization, but merely to address these concepts more formally and at an earlier stage of generalization. In fact this alternative approach embraces relativity in a more direct and legitimate way by employing a non-trivial metric and its inverse for all relative motion.
I will address modifications to, and application of the spacetime interval and modified metrics in subsequent posts.
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