Finally, we shall come back to the questions raised at the beginning of this chapter concerning the experiences leading to new space and time concepts, and address them on the basis of the cases discussed. One of the most striking novel features of relativity theory is the emergence of the concept of spacetime connecting space and time into one entity. Within relativity, time and space can only be separated depending on the state of motion of a particular observer.
This particular relation between space and time can only be articulated within a specific theoretical framework. More generally speaking, however, space and time are connected in many ways within other layers of knowledge.
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In particular, as cognitive structures space and time have their origin in the experience of motion and change. In sensorimotor experience, spatial, temporal, material, and causal aspects are not differentiated from the beginning. The specific characteristic of these models will depend on historically specific experiences and the possibilities to establish relations among them, for instance in societies that develop elaborate metrologies.
In the course of history, experiential spaces have expanded considerably, including the development of instrument-based measurement operations. Only when spatial and temporal experiences and their linguistic representations become the subject of explicit reflections, general concepts of space and time can be constructed that are no longer confined to specific experiential domains, as is, e. At the same time, it must be possible to relate these general concepts somehow to the existing experiences, thus rendering these general concept operationable to some extent.
Space and Time in Contemporary Physics an Introduction to the Theory of Relativity and Gravitation
This does not imply that these general concepts are connected to instrument-based measurement operations, as they underlie, e. While the emergence of instrument-based measurement operations is a common phenomenon in complex societies such as the early civilizations of Mesopotamia , Egypt , and China , the independent emergence of explicit reflections on linguistic representations of spatial experiences have been a rather rare phenomenon.
In all theoretical traditions prior to relativity theory, however, space and time largely occur as separate concepts. This is all the more astonishing as the individual concepts of space and time vary significantly among different theoretical traditions.
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This separation is therefore probably inherited from intuitive thinking. In particular, the elementary identification of stable entities such as objects and places implies a distinction from the aspect of change, the latter eventually giving rise to the concept of time. Temporal change, moreover, covers a much wider experiential field of which spatial change, i. This does not preclude, however, close connections between spatial and temporal aspects within thinking, in theoretical as well as in practical and specifically in metrological contexts. The way in which elementary spatial and temporal experiences are processed depends on the available means of representations, first and foremost language.
Such symbolic representations may vary among cultures but nevertheless typically display or generate a number of structural parallels between spatial and temporal categories. One instance of such parallels is the use of spatial linguistic markers in representing time which may leave its mark in theoretical reflections on space and time.
Another instance is the use spatial properties in the metrology of time. This symbolic connection between space is not yet present in intuitive concepts of time which merely presuppose the correlation of different processes. Clocks make use of this in a practical way by selecting a process to which other processes can then be related, thus establishing a symbolic representation of the passage of time that can be shared.
An immediate representation of points in time and of time intervals by spatial magnitudes is then established by the fact that for most clocks the process in question is a change of spatial position. Theoretical reflections may either start from such practical experiences or from the linguistic representations and the parallels of spatial and temporal experiences embodied by them.
As soon as spatial concepts and magnitudes are represented by the means of geometry, they could also be used for representing other magnitudes including as is evident from the above time. Another matter is a combined geometric representation of space and time. A first extensive use of geometric techniques for representing non-spatial magnitudes is found in the work of Nicole Oresme from the fourteenth century.
Oresme developed diagrams that depicted the variation of a quality, such as heat, whiteness, or grace, over an extension, which could represent either temporal or spatial dimensions. The extension is typically represented by a line. The intensity of the quality in each point of the extension is represented by a vertical line of a given length.
The extensive use, exploration, and ensuing transformation of such diagrams in the study of motion eventually led to a fundamental re-interpretation, in early modern times, of this geometrical technique in terms of a space-time-diagram for motion. While motion is naturally described in terms of space and time, it is also intimately connected to the notion of causation.
However, the borderline between a descriptive space-time kinematics and an explanatory causal dynamics is subject to fundamental historical change. The main reason is that the causes of motion may themselves be connected to the structure of space and time.
An extremely influential theoretical model of space and motion is Aristotelian natural philosophy , which originated in Greek antiquity and was the prevalent philosophical framework in Europe well into early modern times. Aristotelian space is anisotropic , because it privileges directions, e. Space or place , more precisely participates in the causation of motion, since all bodies strive to reach their natural place.
Motions towards natural places happen by themselves and are classified as natural motions, whereas motions caused by extrinsic forces are classified as violent motions. The eternal motions of celestial bodies are a class of their own and are supposed to proceed along circles. Extensive exploration of this explanatory model — focused on planetary motion on the one hand and mechanical motion on the other — highlighted its problematic aspects and led to its transformation. The establishment of a new model of planetary motion given by the Copernican system constituted a major challenge, because the neat distinction between celestial and terrestrial physics in the Aristotelian model became questionable.
This undermined the Aristotelian concept of spherically structured space , favoring a homogeneous and isotropic conception of space. The establishment of insights such as the parabolic shape of the projectile trajectory similarly constituted a challenge, because the neat distinction between natural and violent motion made it difficult to explain how this shape comes about. Instead it turned out to be more plausible to explain this on the basis of a uniform inertial motion and an accelerated motion of fall caused by a force.
The adaptation of the Aristotelian explanatory scheme to these challenges eventually led to the establishment of Newtonian mechanics and its explanation of celestial and terrestrial motions. Newtonian space is homogeneous and isotropic. Uniform motions i. Only accelerated motions need a causal explanation. The cause is either a force independent of the structure of space, or the inertial force caused by space in reaction to such an independent force.
In Newtonian physics , space offers an absolute frame of reference , which cannot be detected, since rest and uniform motion with respect to it are physically equivalent. This non-observability of the absolute standard of rest led to a reformulation introducing a privileged class of reference systems, called inertial systems. The space of classical mechanics is highly counter-intuitive, because space no longer offers landmarks with respect to which all motion can be described, and only allows for the identification of accelerated but not of uniform motions.
The introduction of the inertial system concept was only possible after classical mechanics had been consolidated to an extent that such abstractions could be made, which, while being counter-intuitive, were uniquely suited to the formal structure of the theory. What are the implications of Newtonian physics for the relation between space and time? Newtonian physics relates space and time by distinguishing one particular kind of motion: uniform motion in a straight line.
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No spacetime metric and not even an affine connection is required for this. A projective structure is sufficient. Uniform motion in a straight line is distinguished in Newtonian physics by not being in need of a causal explanation. Only deviations from the straight lines in four-dimensional projective space are in need of a causal explanation, namely by forces. This suggests a separation between space and time on one hand and physical processes in space and time on the other: spacetime with its inertial structure serves as an unchanging stage for physical processes that require causal explanation.
Newtonian physics thus separates inertia and gravitation : inertia is part of the space-time structure and gravitation is part of the material structure of the universe. The resulting projective structure of Newtonian spacetime is universal and trivial. If gravitation is itself considered part of the spacetime framework, this framework becomes non-trivial, namely locally variable and dynamic.
Obviously, to integrate gravitation with the description of inertial motion, one is in need of the principle of equivalence. A weak form of this principle is already an ingredient of Newtonian physics , although not a fundamental one. We shall later come back to the question of why Newton and his contemporaries did not formulate a strong principle of equivalence.
Here we only note that the non-trivial geodesics resulting from it may have spoken for a four-dimensional formulation of physics. But still there would have been no four-metric in Newtonian spacetime. Historically, the four-metric entered mechanics through the back door of optics and electrodynamics. This will be discussed in the following section. Since the notion of space of classical mechanics had been developed on the basis of mechanical experiences only, new perspectives on space emerged when experience from other branches of physics, in particular optics, was taken into account.
As such the concept of a stationary ether presents a modification of the concept of space of classical mechanics defined by the relativity of inertial motions. Indeed, historically, the further elaboration of ether-based physics led to substantial modifications of the concept of space, not by introducing a standard of rest, however, but rather by reasserting the principle of relativity for all of physics.
Initially, the absence of internal motion in the ether was strongly suggested by the phenomenon of stellar aberration , because it was possible to consistently define relative motion of a source and an observer as the difference between two absolute motions with respect to the ether. It could thus seem even plausible that the laws of refraction might be used to establish absolute motion. In particular, the direction of light that determined the magnitude of the angle of refraction was expected to be the direction of light with respect to the ether at absolute rest. From the perspective of an ether theory, it was in need of an explanation.
Such an explanation was provided by Augustin Fresnel who assumed that the medium slightly drags along the ether in dependence on its refractive index , thereby effectively compensating any explicit effect of absolute motion relative to the ether. The Michelson-Morley experiment was designed to probe the motion of the Earth with regard to the ether.
To this end, the travel times of light rays in different directions with regard to the motion of the Earth were compared by the means of observing phase differences of light revealed by displacements of interference patterns. Early attempts at formulating such a theory by Hertz and Heaviside assumed that the ether was fully dragged along inside matter, and could thus explain why the motion of the Earth did not have to be taken into account in the explanation of any terrestrial electric or magnetic phenomena.
Whereas a slightly dragged-along ether seemed to be the most simple explanation for the unobservability of the motion of the Earth with regard to the ether in optics — with the exception of the Michelson-Morley experiment —, a totally dragged-along ether seemed the simple-most assumption to explain the unobservability of the motion of the Earth in the realm of electric and magnetic phenomena.
Through the Michelson-Morley experiment, however, this merely formal hypothesis gained physical plausibility, clashing as it does with the optical evidence in favor of an essentially stationary ether. With a further elaboration of electromagnetic theory it became possible to explain effects that had formerly been explained mechanically, such as ether dragging, by electromagnetic interactions.
Related Space and Time in Contemporary Physics: An Introduction to the Theory of Relativity and Gravitation
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