Cartesian – Will Johncock

Mario Castagnino and Rafael Ferraro explain the differentiation between curved space-time, and the measurement of it by a clock. Whilst the physical parameters recorded by the clock are recorded as natural time, there is said to exist an infinite number of such parameters, all of which are defined as observer-dependent.

It is well known that there is a small confusion between a physical observer’s system and a geometrical coordinate system (or chart) in several papers. Of course they are two different concepts, e.g., in classical physics, an observer’s system is a rigid frame and a clock, where we can use all kinds of charts, for instance, Cartesian or polar coordinates. In curved space-time we cannot use a rigid frame and the natural generalization of the observer’s system will be a timelike fluid of observers, each one endowed with a clock, i.e., a set of timelike paths, each one with a different parameter, the “time” measured by the clock. This time is not necessarily the proper time; it is only an arbitrary continuous function of space-time. Of course we can describe this fluid of observers with any chart we like. We will find that physics is, in fact, observer dependent, but it is of course, chart independent. We shall restrict ourselves to irrotational fluid; thus we can define a set of orthogonal timelike hypersurfaces to the fluid paths, and we can define a parameter T, on each surface, such that the equations T = const would define the orthogonal hypersurfaces. We shall call this parameter a “natural time.” Of course, there exists an infinite set of natural times. We can pass from one to another via a continuous function T -> T’ = T'( T). We shall see that physics is independent of the natural time we use; it is only dependent on the chosen observer’s fluid. Of course, in general, natural time is different from proper time. We can label each fluid world line by three real parameters x1, x2 , x3 ,* and we can call x0 to the natural time T induced by the fluid of observers. Then x0, x1, x2, x3 is a chart and every event of space-time has its coordinates x0, x1, x2, x3 – namely, the space coordinates of the fluid world line, where the event happens, plus the natural time measured by the clock of this world line when the event happens. We shall call this chart an adapted chart (Castagnino and Ferraro 1988, 52-53).

Castagnino, Mario, and Ferraro, Rafael. 1988. “Toward a complete theory for unconventional vacua,” In Claudio Teitelboim (ed.) Quantum mechanics of fundamental systems 1, 51-62. New York: Springer Science+Business Media.

Eduardo Mendieta observes an historical differentiation between natural time, historical time, and social time. These differences are said to be reducing, however, as the rate at which historical events develop is accelerated. Furthermore, despite an opposition between natural and social constitutions, social time is regulating shorter temporalities for naturally occurring rhythms.

The symbolic deconstruction of time, partly a result of the information revolution discussed above, has lead to a rethinking of the differences among natural, historical, and social time. Social time is the time in which and at which societies experience their lifeworld. Or rather, just as Henri Lefebvre spoke of the “social production of space,” we must also speak of the “social production of time.” This socially produced time is social time; it is the time that punctuates the rhythms of social existence. This is the time that ticks at the sounds of seconds, minutes, hours, days, months. This is the time that keeps track of workdays, academic calendars, and leisure time. This time, however, is timed by clocks and timetables that have been arranged in terms of assumptions, beliefs, and ideologies about how much time constitutes a workday, a work week, how long should persons work in their lifetime, and so on. Like maps, clocks clock only what they have been arranged to clock. The rhythms of social existence, however, intersect with historical and natural time. Historical time has to do with the time in which historical events, forces, processes, and transformations take place. Historical time is the time in which societies and civilizations live and mark their transformations. Historical time, one may say, is punctuated by political revolutions, wars, elections, and technological revolutions that may have accelerated the rhythms of social time. Finally, natural time is the time of nature, of tectonic plates, of seas, of weather patterns, of draughts and floods, of freezing or melting polar ice caps, and other such forces that are punctuated in millennia, in cycles whose regularity or patterns are not discernable because their time span is beyond human time.

What is distinctive about the global condition, at the phenomenological level, is that these three times have began to merge, or seem to have collapsed into each other. Social time has accelerated to such an extent that it has caught up with historical time. Revolutions are lived within decades. Major social transformations occur where entire societies are uprooted and restructured in the blink of the eye. What took centuries, now takes decades, and sometimes a score of years. History is being televised at any given moment, even as its revisionism is aired and posted that same evening. By the same token, historical time seems to have caught up to natural time: The El Niño weather pattern is now part of pedestrian speak. The greenhouse effect is melting the ice caps, and sea levels are rising, regions are turning into desserts, while desserts are turning into irrigated gardens. The cumulative effect is that time has to be symbolically reconstituted. The self-assurance of Cartesian and Newtonian thought that operated on the dependability and seeming immutability of natural and world historical time have to be traded for a type of thinking that will set out from the social productivity of temporality (Mendieta 2007, 21-22).

Mendieta, Eduardo. 2007. Global fragments: Latinamericans, globalizations, and critical theory. Albany: State University of New York Press.