# Thought-Experimental Principles of Relativity

0. Introduction and Goal
In his considerations concerning simultaneity, Albert Einstein indicated and employed certain very basic abilities of each individual observer, and relations between observers:
* that one may perceive and distinguish various signals,
* that, given one's observations of any two distinct signals, one may judge whether one perceived these two signals together ("coincidently"), or separately ("first" vs. "afterwards"),
* that one may distinguish and consistently recognize others by their signals, which one observed,
* that one's signals may in turn be observable and recognizable to others, and
* that one may recognize a signal as someone else's response ("echo") to an own signal.
These abilities and relations may not be readily exhibited in every practical instance and circumstance. However, being asserted, they may be taken as equally and unambiguously comprehensable. For example (cmp. section (3.)), one cannot even consider the problem of how two observers might come to an agreement on which, if any, of their observations had been "simultaneous" to each other, without thereby already admitting an understanding of the fundamental abilities and relations listed above. The mutual assumption of these observational abilities and experimental relations, even if it presents only an idealization, is consequently also uniquely suited as a starting point towards solving this and related problems.
The descriptions to characterize relations between observers, and first of all, how mutual agreement (measurement) may be reached between those involved, give rise to a great variety of relativistic thought experiments; concerning notably (in historic order)
The goal of this course is to review and motivate the observer abilities which are to be assumed, and strictly on their basis to present the relativistic thought experiments in a systematic development.
As its title indicates, this is a course in experimental physics (evidently concerning its foundational aspects, rather than accounts of specific obtained values). Starting from what any one observer can assert individually, procedures are sought and derived on how several observers may reach mutual agreement on their relations with each other.
Particular attention is naturally given to providing a thought-experimental definition to the notion of "opposite directions"; or more directly concerning observers, and in association with Einstein's usage: to the identification of which one, if any, had constituted a "middle between" certain given observers. The sequence of thought-experimental definitions which are obtained includes further
The student (who can of course be presumed to possess and therefore to understand the indicated fundamental observer abilities as well, at least in principle) will thereby be prepared to encounter the indicated notions where they appear without consideration for a definition in terms that are accessible to observers.
The systematic development of thought-experimental definitions also lends itself to recognizing relations between measured quantities that arise by definition (for instance: the equality of light speed in regions of equal refractive index, the effects of "Time dilation", and "Pericenter advance"), and to distinguish them from relations that are subject to experimental test (such as correspondingly, whether two regions had equal refractive index, whether two twins were aging at equal proper rates, or whether, or to which accuracy, someone moved freely in some particular region and whether, or to which accuracy, observers in this region would find their curvature compatible with the Schwarzschild metric).
In emphasizing these distinctions, and in demonstrating overall that relativity provides definitions for how to measure geometric relations in principle, based on abilities which are unambiguous for everyone involved and which are justified from the outset, this course aims to teach the larger lesson that any measured values which may thereby be obtained are incapable of providing in turn tests (or possibly even falsifications) of these underlying assumptions and definitions.
Outline: