## Merely a Shadow The End of Independent Time

On September 21, 1908, the mathematician Hermann Minkowski from Gottingen began his presentation entitled "Raum und Zeit" (Space and Time) at the Assembly of German Natural Scientists and Physicians in Cologne with suggestive words: "Gentlemen! The views of space and time which I wish to lay before you have sprung from the soil of experimental physics. Therein lies their strength. They are radical. Henceforth space by itself, and time by itself are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality."164

These sentences did not fail to impress. In the literature on the theory of relativity, they are frequently quoted, and reference is regularly made to the "Minkowski World." In this four-dimensional world, space and time are thus, each for itself, sentenced to a shadowy existence. They survive only as a unity of four coordinates.

Does this signify the end of time as an autonomous entity? May one speak only of space-time? Does Einstein himself draw such a conclusion? In his presentation of the general theory of relativity, after initial skepticism, Einstein expresses165 his admiration for Minkowski's interpretation of the special theory of relativity: "The generalization of the theory of relativity has been greatly facilitated by the form that was given to the special theory of relativity by Minkowski, the mathematician who first clearly recognized the formal equivalency of the spatial and time coordinates and used it for establishing the theory."166 Without Minkowski, the general theory of relativity would have "perhaps remained stuck in infancy."167

Elsewhere, however, Einstein expressed himself much more cautiously:

From a formal point of view one may characterize the achievement of the special theory of relativity thus: it has shown generally the role which the universal constant c (velocity of light) plays in the laws of nature and has demonstrated that there exists a close connection between the form in which time on the one hand and the spatial coordinates on the other hand enter into the laws of nature.168

He therefore appears to presuppose a difference between space and time despite their arithmetical unification as coordinates of one and the same system. Or is this more an emotional assertion of an elderly man rather than of a scientist? For in "A London Speech," Einstein says when referring to Minkowski: "According to the special theory of relativity the four dimensional continuum formed by the union of space and time retains the absolute character which, according to the earlier theory, belonged to both space and time separately."169 Mathematically, "no statement is more banal than that our familiar world is a four-dimensional time-space continuum,"170 for it can be shown that the laws of nature, which correspond to the requirements of the theory of relativity, "assume mathematical forms in which the time coordinate plays exactly the same role as the three spatial co-ordinates."171

How, then, can this loss of autonomy of time and space be understood?172 Classical physics could allow itself two equally valid interpretations of a space-time continuum, namely, first as a dynamic concept of positions that change in time, and, second, as a static concept of movement as something existing. In the first case, the continuum is broken down into space and time; in the second, it is viewed as a whole. In classical physics, the oscillation between the two concepts presents no problem inasmuch as, according to the idea of absolute time, the time coordinate always remains the same. When relating to another system, only the space coordinates, but not the time coordinates, are transformed. Within the special theory of relativity, on the other hand, a space-time continuum cannot simply be split into a space and a time dimension, since in two different systems, not only the space coordinates, but also the time coordinate, are different. For this reason, in the theory of relativity, the static, continuous conception of space-time is the more useful and objective one. Einstein concedes, "Indeed, we can, if we so desire, continue to work with the dynamic manner of representation also within the framework of the theory of relativity; but then we must always consider that splitting into time and space has no objective significance, since, for us, time is no longer absolute."173 In the "Minkowski World," physics was transformed from an event in three-dimensional space into an existence in this four-dimensional world.174 Because in this four-dimensional continuum there are "no more sections that objectively represent the 'now', the concept of the event and becoming is not completely abolished, but rather, is made more complicated."175 For this reason, Einstein prefers "to think of the physically real as a four-dimensional existence, instead of, as previously, as the becoming of a three-dimensional existence."176

A distinction between space and time that likewise deviates from everyday understanding is linked to the constancy of the speed of light. The speed of light permits causality between two events only when the events lie within the particular area that light, with its finite speed, can reach at a certain time. Graphically, this area corresponds to a cone that, with infinite speed of light, would be opened up to the x level. Events that lie within a light cone are characterized as being situated timelike to one another. Events that lie outside a light cone are characterized as being situated spacelike to one another.

Light Cone and Ordering of Past, Present, and Future

Events having a spacelike position can have no interaction with one another at all. The boundary of the cone is termed an event horizon. Events that are situated spacelike and timelike can thus be distinguished from one another by the clearly defined boundary of the event horizon. On the one hand, this use of "spacelike" or "timelike" points to the change in meaning of the colloquial concepts of "space" and "time" within relativistic physics; on the other hand, it gives the impression that time and space are still strictly distinguishable variables. Furthermore, the descriptive model of the light cone enables a special definition of past, future, and present. For an event E, the past consists of all events that can have causally influenced E. The future consists of all events that can be influenced by E. The present then consists of all events that neither influence E nor are influenced by E. Conceptually, these definitions completely agree with the framework of classical physics. Mathematically, however, interesting differences result, especially for the description of the present. In relativistic physics, the lower portion of the light cone corresponds to the past, and the upper part, to the future. In classical physics, only the event points lying on the x-axis belong to the present, while in relativistic physics, all spacelike points must be thought of as belonging to the present.177

The question of autonomy, however, concerns not only the relationship of time to space and vice versa. In the general theory of relativity, an even more radical loss of autonomy takes place. If space (or space-time) had an autonomous existence vis-à-vis matter or field in classical mechanics and also according to the special theory of relativity, then, in the general theory of relativity, the "separate existence" of space disappears vis-à-vis that which "fills space"; there is no space without field.178

In summary, Einstein says: "The process of development here sketched [toward the general theory of relativity] strips the space-time coordinates of all independent reality. The metrically real is now only given through the combination of the space-time co-ordinates with the mathematical quantities which describe the gravitational field."179 Thus, the requirements of the general theory of relativity take "from space and from time the last trace of physical concreteness."180

On the whole, from these considerations, it should be noted that according to Einstein, time and space are still distinguishable and that each by itself has significance, but not an objective significance. In terms of conception, both appear to be much less concrete than in classical physics. Nevertheless, they obtain an operational character, for it became clear that the definitions of physical concepts require the specification of measurement procedures. In this regard, the question "What is time?" receives the answer: "That which is measured with clocks." Both the special and the general the ory of relativity allow the assumption of timelessness under certain physical conditions, but they do not allow its realization.

The assertion that time has been degraded to a function of space is inappropriate. Why speak of a spatialization of time when one can just as easily speak of a dynamization of space?181 If the need for the transformation of spatial coordinates was already expressed in the Galilean Transformation, then with the theory of relativity, time has approached space in the sense that now its necessity for transformation also becomes clear. Time and space emerge together as entities tied to movement. Thus, they find themselves equally relativized, but not identified with each other: "Relativity has broken down the isolation of time and space but not their distinction."182 It has thus become clear "that already within the framework of physics, time, space, and matter have a deep internal structural connection."183 It is not autonomy in the sense of qualitative distinction that has thereby disappeared, but rather autonomy in the quantitative sense. Instead of a four-dimensional continuum, it would be better to speak "of a (3 + i)-dimen-sional continuum,"184 since one is dealing with differences within a framework of relatedness—not with absoluteness, but rather with relationality.185

The dualism between absolute space or absolute time and relative space or relative time, as well as between space and time, has become superfluous.186 If there is something in the theory of relativity that is to be characterized as absolute, then it is the principle of the constancy of the vacuum speed of light. Light sets the "boundary and dimension" of space and time; as the basic variable of nature, it attains a unique metaphysical, though finite, status.187 For this reason, it is not surprising that theologians using this interpretation have tried to see links here to the discussion of God's infinite light and that they look for connections, for example, to the Johannine symbolism of light.188

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