Concepts of space : the History of Theories of Space in Physics. De Max Jammer. Foreword by Albert Einstein. Desde entonces es mi texto favorito en el field. Aquí está: In order to appreciate fully the importance of investigations such as the present work of Dr. Jammer one should consider the following points. The eyes of the scientist are directed upon those phenomena which are accessible to observation, upon their apperception and conceptual formulation. In the attempt to achieve a conceptual formulation of the confusingly immense body of observational data, the scientist makes use of a whole arsenal of concepts which he imbibed practically with his mothers milk; and seldom if ever is he aware of the eternally problematic character of his concepts. He uses this conceptual material, or, speaking more exactly, these conceptual tools of thought, as something obviously, immutably given; something having an objective value of truth which is hardly ever, and in any case not seriously, to be doubted. How could he do otherwise? How would the ascent of a mountain be possible, if the use of hands, legs, and tools had to be sanctioned step by step on the basis of the science of mechanics? And yet in the interests of science it is necessary over and over again to engage in the critique of these fundamental concepts, in order that we may not unconsciously be ruled by them. This becomes evident especially in those situations involving development of ideas in which the consistent use of the traditional fundamental concepts leads us to paradoxes difficult to resolve. Aside from the doubt arising as to the justification for the use of the foreground of our interest, there is a purely historical interest in the origins or the roots of the fundamental concepts. Such investigations, although purely in the field of history of thought, are nevertheless in principle not independent of attempts at a logical and psychological analysis of the basic concepts. But the limitations to the abilities and working capacity of the individual are such that we but rarely find a person who has the philological and historical training required for critical interpretation and comparison of the source material, which is spread over centuries, and who at the same time can evaluate the significance of the concepts under discussion for science as a whole. I have the impression that Dr. Jammer, through his work, has demonstrated that in his case these conditions are in great measure satisfied. In the main he has limited himself -wisely, it seems to me- to the historical investigation of the concept of space. If two different authors use the words red, hard, or disappointed, no one doubts that they mean approximately the same thing, because these words are connected with elementary experiences in a manner which is difficult to misinterpret. But in the case of words such as place or space, whose relation with psychological experience is less direct, there exists a far-reaching uncertainty of interpretation. The historian attempts o overcome such uncertainty by comparison of the texts, and by taking into account the picture, constructs from literature, of the cultural stock of the epoch in question. The scientist of the present, however, is not primarily trained or oriented as a historian; he is not capable of forming nor willing to form his views on the origin of the fundamental concepts in this manner. He is more inclined to allow his views on the manner in which the relevant concepts might have been formed, to arise intuitively from his rudimentary knowledge of the achievements of science in the different epochs of history. He will, however, be grateful to the historian if the latter can convincingly correct such views of purely intuitive origin. Now as to the concept of space, it seems that this was preceded by the psychologically simpler concept of place. Place is first of all a (small) portion of the earths surface identified by a name. The thing whose place is being specified is a material object or body. Simple analysis shows place also to be a group of material objects. Does the word place have a meaning independent of this one, or can one assign such a meaning to it? If one has to give a negative answer to this question, then one is led to the view that space (or place) is a sort of order of material objects and nothing else. If the concept of space is formed and limited in this fashion, then to speak of empty space has no meaning. And because the formation of concepts has always been ruled by instinctive striving for economy, one is led quite naturally to reject the concept of empty space. It is possible, however, to think in a different way. Into a certain box we can place a definite number of grains of rice or of cherries, etc. It is here a question of a property of the material object box, which property must be considered real in the same sense as the box itself. One can call this property the space of the box. There may be other boxes which in this sense have an equally large space. This concept space thus achieves a meaning which is freed from any connection with a particular material object. In this way by a natural extension of box space one can arrive at the concept of an independent (absolute) space, unlimited in extent, in which all material objects are contained. Then a material object not situated in space is simply inconceivable; on the other hand, in the framework of this concept formation it is quite conceivable that an empty space may exist. These two concepts of space may be contrasted as follows: (a) space as a positional quality of the world of material objects; (b) space as container of all material objects. In case (a), space without a material object is inconceivable. In case (b), a material object can only be conceived as existing in space; space then appears as a reality which in a certain sense is superior to the material world. Both space concepts are free creations of the human imagination, means devised for easier comprehension of our sense experience. These schematic considerations concern the nature of space from the geometric and from the kinematic point of view, respectively. They are in a sense reconciled with each other by Descartes introduction of the coördinate system, although this already presupposes the logically more daring space concept (b). The concept of space was enriched and complicated by Galileo and Newton, in that space must be introduced as the independent cause of the inertial behaviour of bodies if one wishes to give the classical principle of inertia (and therewith the classical law of motion) an exact meaning. To have realized this fully and clearly is in my opinion one of Newtons greatest achievements. In contrast with Leibniz and Huygens, it was clear to Newton that the space concept (a) was not sufficient to serve as the foundation for the inertia principle and the law of motion. He came to this decision even though he actively shared the uneasiness which was the cause of the opposition of the other two: space is not only introduced as an independent thing apart from material objects, but also is assigned an absolute role in the whole causal structure of the theory. This role is absolute in the sense that space (as an inertial system) acts on all material objects, while these do not in turn exert any reaction on space. The fruitfulness of Newtons system silenced these scruples for several centuries. Space of type (b) was generally accepted by scientists in the precise form of the inertial system, encompassing time as well. Today one would say about that memorable discussion: Newtons decision was, in the contemporary state of science, the only possible one, and particularly the only fruitful one- But the subsequent development of the problems, proceeding in a roundabout way which no one then could possibly foresee, has shown that the resistance of Leibniz and Huygens, intuitively well founded but supported by inadequate arguments, was actually justified. It required a severe struggle to arrive at the concept of independent and absolute space, indispensable for the development of theory. It has required no less strenuous exertions subsequently to overcome this concept-a process which is probably by no means as yet completed. Dr. Jammers book is greatly concerned with the investigation of the status of the concept of space in ancient times and in the Middle Ages. On the basis of his studies, he is inclined toward the view that the modern concept of space of type (b), that is, space as container of all material objects, was not developed until after the Renaissance. It seems to me that the atomic theory of the ancients, with its atoms existing separately from each other, necessarily presupposed a space of type (b), while the more influential Aristotelian school tried to get along without the concept of independent (absolute) space. Dr. Jammers views concerning theological influences on the development of the concept of space which lie outside the range of my judgment, will certainly arouse the interest of those who are concerned with the problem of space primarily from the historical point of view. The victory over the concept of absolute space or over that of the inertial system became possible only because the concept of the material object was gradually replaced as the fundamental concept of physics by that of the field. Under the influence of the ideas of Faraday and Maxwell the notion developed that the whole of physycal reality could perhaps be represented as a field whose components depend on four space-time parameters. If the laws of this field are in general covariant, that is, are not dependent on a particular choice of coördinate system, then the introduction of an independent (absolute) space is no longer necessary. That which constitutes the spatial character of reality is then simply the four-dimensionality of the field. There is then no empty space, that is, there is no space without a field. Dr. Jammers presentation also deals with the memorable roundabout way in which the difficulties of this problem were overcome, at least to a great extent. Up to the present time no one has found any method of avoiding the inertial system other than by way of the field theory. Princeton, New Jersey. 1953
Posted on: Tue, 27 Jan 2015 13:58:57 +0000
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