Speculations 2: Absolute simultaneity, the occurrences of events on different reference bodies at the same timepoint, would require absolute time clocks (ATCs, ITICs, non-distortable clocks) which are "independent of the state of motion of [their bodies] of reference" [Einstein, Relativity, 1961 edition, p. 27] for the identical timepoint needed for determining absolute simultaneity.

ATCs/ITICs/non-distortable clocks are realities.

Among the ATCs/ITICs/non-distortable clocks are the adjustable clocks which are the radio clocks which are used by the US NIST, USNO and French Bureau of Weights and Measures to generate the standard second and therefore the standard time used for scientific experiments and the radio clocks of the GPS nav system, whose master clock is synched with the USNO standard clock and whose satellite slave clocks are NOT measuring satellite local time because they are in fact 'independent of the state of motion of [their bodies] of reference' and thereby fit Einstein's requirements/standards for clocks which measure absolute time and whose timepoints can be used for determining absolute simultaneity.

We can note that the standard time generated by the adjustable clocks of the USNO are being used for the recent OPERA experiments wherein the USNO standard time is transmitted via the GPS nav system satellites as controlled by the GPS master clock.

Real scientists really are using the 'outputs' of adjustable clocks for the time/standard time/standard second/etc. for real scientific experiments, therefore the dispute inre whether or not adjustable clocks 'output' time is over, and therefore my theory of time, which describes the reality of time being categorized as local time when distortable clocks are used for temporal measurement and as absolute time when adjustable/non-distortable clocks are used for temporal measurement, is correct. And note that relativity does NOT describe the possibility and/or reality of adjustable/non-distortable clocks and absolute simultaneity and absolute time, b/c, in fact, inre pp. 25-27 of Relativity, 1961 edition, Einstein denied the reality of absolute simultaneity/absolute time.

Therefore, ATCs/ITCs are realities. They can be used to measure absolute time and to determine absolute simultaneity.

Q: If ... T-1 <- T0 -> T+1 ... is not a continuum, whatizzit?
A: _____ (?)

A set of 'categorically different states'?

The dimension of time is continuous—one moment is contiguous with another, the timepoints being only arbitrary marks separated by a chosen duration/time-interval upon the timeline which is the continuum of time.

The continuum of time is continuous with respect to its infinite/unbounded/limitless existence/duration/endurance.

The universal m/e system is a single system whose sum total does not change b/c it is a closed/isolated system b/c there are no other m/e systems with which it could exchange m/e, therefore, it undergoes changes of its configuration without a change of its sum total and therefore it has a continuous existence/duration/endurance and, inre its continuous existence/etc., and its continuous sum total, the universal m/e system can be considered to be a physical continuum in contrast to a temporal or spatial continuum.

Any changes of the universal m/e system configuration occur during the continuous endurance/duration of the system itself, observable by the flow of the motions of entities comprised of m/e from one position to another.

Space, as a volume of infinite size, with no shape and therefore no surface and therefore no boundaries, is itself a continuum in two respects: (1) the continuity of the infinite size of its volume and (2) the continuity of its infinite existence/duration/endurance inre time.