Does space know proper place and movement real rest? The answer depends, as with all answers to all theoretical scientific questions, on convictions already pre-logically accepted and stubbornly adhered to. Or to say it otherwise: the answer depends on “facts” we consider to be self-evident, since from our tenderest years we are told and taught them so often that we have lost even the capability to doubt their truth.
The present paper endeavours to come to grips with one of the most important of such “facts”. And the first step this enterprise compels us to take is that we have to decide which of the three methods available for approaching the matter of celestial motions we shall use. Do we prefer to think in terms of mechanical and kinematical analogy or in those of mathematical formalism? Or do we want to halt between those two approaches, switching from the first to the second whenever logical reasoning, leaning on the available data, obliges us to accept a conclusion that we a priori judge to be unacceptable?
The first method is the classical one. The second cannot be used in a simon-pure form, for it has still to reckon with immutable givens in rock-bound reality. The third possibility is our century’s escape route from the morass of anomalies clustered around the notions of definable cosmic movement and rest, a morass in which at the turn of the century the practitioners of three hundred years of astronomical “New Science” found themselves bogged down. Now, such a hybrid approach may not necessarily produce misleading cosmological models, but it surely can and does make room for inconsistent argumentation. Applying mathematics as part of a process of elucidating matter-bound observations is not the same as using these observations for the purpose of justifying matter-free mathematics. Newly discovered phenomena may compel scientists to change their theories, but no thinkable theory is able to change the “raw” phenomena. Furthermore, to accept anything as “proven” is not the same as actually having proved it. “Proof” and “disproof” in the commonly accepted sense of giving absolute truth may even be argued to be chimerical, since only omniscience would not have to reckon with the possibility of unexpected input, always again spoiling our mortal certainties.
The discussion will in this paper be strictly confined to a kinematical inquiry, that is, to the question whether we do or do not have, or can find, a firm and absolutely coordinated hold on the space in which we observe motions relative to ourselves, a space to the modern mind only conceivable as infinite and nowadays characterized as “unbounded”. Only when such is
unavoidable will theoretical deliberations about attributes, content, and extent of this space be touched upon, since the chosen line of access presupposes adherence to the common-sense spatiality of workaday kinematics, that is, the spatiality – a circumstance often conveniently overlooked! – beyond which theorists can only offer ingenious mathematical derivations that supersede our perceptible and perceived reality. For nolens volens theorists can do no more then analogically explain these derivations and the hypotheses extracted from them by means of “flat space” models, ironbound as they are to the three dimensions and the untouchable, not to be manipulated by time, in which their minds are created and constrained to operate.
Many will claim the method used here to be outmoded for any other than low-level workaday operations. Maybe so, but we should not forget why, now almost a century ago, the flight into a fourth dimension, a so-called “space-time continuum”, was urged to be theoretically necessary. In the closing of the eighteen hundreds, experimental evidence and the ruling Newtonian world view had become increasingly difficult to reconcile. The Earth seemed at rest in the stellar domain, and this being “unthinkable”(2) in Newtonian terms, a way had to be found and a device adopted that logically forever would banish such an “impossible” state of affairs. Yet, however “unthinkable” and “impossible”, this geocentric abomination is not “impossible” after the manner of a square circle. From our earthly perspective we experience it all the days of our lives. Hence unless and until it logically leads to antinomies, there are no valid reasons to prohibit and condemn the use of “flat-space” kinematics. For procedures, theories and hypotheses may rise and fall – the logic employed in their construction is not subject to human whims, while on the other hand Einsteinian demonstrations by means of analogies are never strictly compelling. They may elucidate difficult postulates but do not “prove” them.