Prof. Muni Mahendra Kumar
Some other scientists have interpreted the theory of relativity in a different way. Though they do not differ in the interpretation of physical aspect of the four-dimensional continuum of space and time, they do not accept the view that space and time exist only subjectively. Hans Reichenbach, who, in his critical work 'The Philosophy of Space and Time', has discussed both the philosophical and physical aspects of the theory of relativity, stands prominent amongst these scientists.
First of all, Reichenbach distinguishes between the mathematical space and physical space. He explains the distinction thus: "Mathematics shows a variety of possible forms of relations among which physics selects the real one by means of observations and experiments. Mathematics, for instance, teaches how the planets would move if the force of attraction of the sun should decrease with the second or third power of the distance; physics decides that the second power holds in the real world Mathematics reveals the possible space; physics decides which among them corresponds to physical space. In contrast to all earlier conceptions, in particular to the philosophy of Kant, it becomes now a task of physics to determine the geometry of physical space, just as physics determines the shape of the earth or the motions of the planets, by means of observations and experiments."[1] Thus, Reichenbach has clearly accepted the objective existence of physical space.
Further, refuting the view of conventionalists (such as Poincare) who contended that it depended wholly upon our convention which structure is attributed to space, Reichenbach states: "From conventionalism the consequence was derived that it is impossible to make an objective statement about the geometry of physical space, and, that we are dealing with subjective arbitrariness only; the concept of geometry of real space was called meaningless. This is a misunderstanding. Although the statement about the geometry is based, upon certain arbitrary definitions, the statement itself does not become arbitrary: once the definitions have been formulated, it is determined through objective reality alone which is the actual geometry. Let us use our previous example: although we can define the scale of temperature arbitrarily, the indication of the temperature of a physical object does not become a subjective matter. By selecting a certain scale we can stipulate a certain arbitrary number of degrees of heat for the respective body, but this indication has an objective meaning as soon as the coordinative of the scale is added. On the contrary, it is the significance of coordinative definitions to lend an objective meaning to physical measurements."[2] It means: whether we regard the temperature of a certain body to be 15°C. or 59°F. depends upon our choice of measuring system, but it does not mean that the temperature of a substance is in itself dependent upon our choice; temperature remains an objective property of matter. In the same way, whatever system of geometry we choose, the objective characteristics of space remain unchanged. Reichenbach has considered that the formulation of spatial visualization as a developmental adaptation is itself already based on an epistemological assertion, which it merely tends to emphasize, namely, the assertion that there exists a real space independent of those spaces represented by mathematics, that it is a scientifically meaningful question to ask which of the mathematically possible types of spaces corresponds to physical space, and that the "harmony" of nature and reason does not depend on an inner priority of Euclidean space, but that, on the contrary, the priority depends on this "harmony".[3]
Refuting the wrong belief of some scientists regarding the concept of time, Reichenbach writes: "Whereas the conception of space and time as a four-dimensional manifold has been very fruitful for mathematical physics, its effect in the field of epistemology has been only to confuse the issue. Calling time the fourth dimension gives it an air of mystery."[4] Reichenbach believes that just as we determine any colour by the three basic colours, viz., red, green and blue, by stating how much it contains of each of these three components, so also the meaning of combining space and time in four dimensions is only that we can describe any event by means of four co-ordinates-three of space and one of time. He, therefore, says: "Our schematization of time as a fourth dimension, therefore does not imply any changes in the conception of time."[5]
He, further states: "We may, therefore, retain the perceptual difference between space and time without fear of contradicting the mathematical representation....The properties of time which the theory of relativity has discovered have nothing to do with its treatment as fourth dimension".[6]
Reichenbach is of the view that the statement of Minkowski that "from now on the ideas of space and time as independent concepts shall disappear and only a union of the two shall be retained as an independent concept", has unfortunately caused the erroneous impression that all visualizations of time as time and of space as space must disappear.[7]
Reichenbach has also pondered over the number of dimensions of space. Some scientists and mathematicians have conceived of space consisting of n dimensions where n may be greater than three, but Reichenbach has believed that objectively space can have only three dimensions. He states: "The number three of dimensions represents primarily a fact concerning the objective world.... We consider the parameter space merely by a mathematical tool with no objective reference, whereas we regard the three-dimensional space as the real space."[8] Again, he positively asserts. "The statement that physical space has three dimensions, has, therefore, the same objective character as, for instance, the statement that there are three physical states of matter, the solid, liquid, and gaseous state; it describes a fundamental fact of the objective world."[9]
Thus, although Reichenbach has accepted the theory of relativity, he has maintained that the absolute space and time have objective existence. In the concluding chapter of his work on space and time, he observes: "We may, therefore, regard the following statement as the most general assertion about space-time order: everywhere and at all times there exists a space-time coordinate system.
"This result implies the topological distinguishability of space and time. In a space-time coordinate system one of the dimensions is to be considered as time and the three others as space."[10]
Further, after having discussed the difference between subjectivity and objectivity, and their relation with space and time, in conclusion Reichenbach states: "The fact that an ordering of all events is possible within the three dimensions of space and the one dimension of time is the most fundamental aspect of the physical theory of space and time.
"The most important result of these considerations is the objectivity of the properties of space. The reality of space and time turns out to be the irrefutable consequence of our epistemological analyses, which have led us through many important individual problems.
"Philosophers have thus far considered an idealistic interpretation of space and time as the only possible epistemological position, because they overlooked the twofold nature of the mathematical and the physical problems of space. Mathematical space is a conceptual structure, and as such ideal. Physics has the task of coordinating one of these mathematical structures to reality. In fulfilling this task, physics makes statements about reality, and it has been our aim to free the objective core of these assertions from the subjective additions introduced through the arbitrariness in the description."[11]
Thus the gist of Reichenbach's view is that he accepts the theory of relativity, and at same time he considers the assertion of objectivity of space and time the inevitable consequence of the theory of relativity.
