Language and Reality in Modern Physics

Throughout the history of science new discoveries and new ideas have always caused scientific disputes, have led to polemical publications criticizing the new ideas, and such criticism has often been helpful in their development; but these controversies have never before reached that degree of violence which they attained after the discovery of the theory of relativity and in a lesser degree after quantum theory. In both cases the scientific problems have finally become connected with political issues, and some scientists have taken recourse to political methods to carry their views through.

This violent reaction on the recent development of modern physics can only be understood when one realizes that here the foundations of physics have started moving; and that this motion has caused the feeling that the ground would be cut from science. At the same time it probably means that one has not yet found the correct language with which to speak about the new situation and that the incorrect statements published here and there in the enthusiasm about the new discoveries have caused all kinds of misunderstanding.

This is a fundamental problem.

The improved experimental technique of our time brings into the scope of science new aspects of nature which cannot be described in terms of the common concepts. But in what language, then, should they be described? The first language that emerges from the process of scientific clarification is in theoretical physics usually a mathematical language, the mathematical scheme, which allows one to predict the results of experiments. The physicist may be satisfied when he has the mathematical scheme and knows how to use it for the interpretation of the experiments.

But he has to speak about his results also to nonphysicists who will not be satisfied unless some explanation is given in plain language, understandable to anybody. Even for the physicist the description in plain language will be a criterion of the degree of understanding that has been reached. To what extent is such a description at all possible? Can one speak about the atom itself? This is a problem of language as much as of physics, and therefore some remarks are necessary concerning language in general and scientific language specifically.

Language was formed during the prehistoric age among the human race as a means for communication and as a basis for thinking. We know little about the various steps in its formation; but language now contains a great number of concepts which are a suitable tool for more or less unambiguous communication about events in daily life.

These concepts are acquired gradually without critical analysis by using the language, and after having used a word sufficiently often we think that we more or less know what it means. It is of course a well-known fact that the words are not so clearly defined as they seem to be at first sight and that they have only a limited range of applicability. For instance, we can speak about a piece of iron or a piece of wood, but we cannot speak about a piece of water.

The word ‘piece’ does not apply to liquid substances. Or, to mention another example: In discussions about the limitations of concepts, Bohr likes to tell the following story: ‘A little boy goes into a grocer’s shop with a penny in his hand and asks: “Could I have a penny’s worth of mixed sweets? " The grocer takes two sweets and hands them to the boy saying: “Here you have two sweets. You can do the mixing yourself.”’’ A more serious example of the problematic relation between words and concepts is the fact that the words ‘red’ and ‘green’ are used even by people who are colorblind, though the ranges of applicability of these terms must be quite different for them from what they are for other people.

This intrinsic uncertainty of the meaning of words was of course recognized very early and has brought about the need for definitions, or – as the word `definition’ says – for the setting of boundaries that determine where the word is to be used and where not. But definitions can be given only with the help of other concepts, and so one will finally have to rely on some concepts that are taken as they are, unanalyzed and undefined.

In Greek philosophy the problem of the concepts in language has been a major theme since Socrates, whose life was – if we can follow Plato’s artistic representation in his dialogues – a continuous discussion about the content of the concepts in language and about the limitations in modes of expression. In order to obtain a solid basis for scientific thinking, Aristotle in his logic started to analyze the forms of language, the formal structure of conclusions and deductions independent of their content. In this way he reached a degree of abstraction and precision that had been unknown up to that time in Greek philosophy and he thereby contributed immensely to the clarification, to the establishment of order in our methods of thought. He actually created the basis for the scientific language.

On the other hand, this logical analysis of language again involves the danger of an oversimplification. In logic the attention is drawn to very special structures, unambiguous connections between premises and deductions, simple patterns of reasoning, and all the other structures of language are neglected. These other structures may arise from associations between certain meanings of words; for instance, a secondary meaning of a word which passes only vaguely through the mind when the word is heard may contribute essentially to the content of a sentence. The fact that every word may cause many only half-conscious movements in our mind can be used to represent some part of reality in the language much more clearly than by the use of the logical patterns. Therefore, the poets have often objected to this emphasis in language and in thinking on the logical pattern, which – if I interpret their opinions correctly – can make language less suitable for its purpose. We may recall for instance the words in Goethe’s Faust which Mephistopheles speaks to the young student (quoted from the translation by Anna Swanwick): Waste not your time, so fast it flies; Method will teach you time to win; Hence, my young friend, I would advise, With college logic to begin.

Then will your mind be so well brac’d, In Spanish boots so tightly lac’d,

That on ’twill circumspectly creep, Thought’s beaten track securely keep, Nor will it, ignis-fatuus like, Into the path of error strike. Then many a day they’ll teach you how The mind’s spontaneous acts, till now As eating and as drinking free,

Require a process; — one, two, three! In truth the subtle web of thought Is like the weaver’s fabric wrought, One treadle moves a thousand lines, Swift dart the shuttles to and fro, Unseen the threads unnumber’d flow, A thousand knots one stroke combines. Then forward steps your sage to show, And prove to you it must be so; The first being so, and so the second. The third and fourth deduc’d we see; And if there were no first and second, Nor third nor fourth would ever be. This, scholars of all countries prize, Yet ‘mong themselves no weavers rise. Who would describe and study aught alive, Seeks first the living spirit thence to drive: Then are the lifeless fragments in his hand, There only fails, alas! — the spirit-band. This passage contains an admirable description of the structure of language and of the narrowness of the simple logical patterns.

On the other hand, science must be based upon language as the only means of communication and there, where the problem of unambiguity is of greatest importance, the logical patterns must play their role. The characteristic difficulty at this point may be described in the following way. In natural science we try to derive the particular from the general, to understand the particular phenomenon as caused by simple general laws. The general laws when formulated in the 117 language can contain only a few simple concepts — else the law would not be simple and general. From these concepts are derived an infinite variety of possible phenomena, not only qualitatively but with complete precision with respect to every detail. It is obvious that the concepts of ordinary language, inaccurate and only vaguely defined as they are, could never allow such derivations. When a chain of conclusions follows from given premises, the number of possible links in the chain depends on the precision of the premises. Therefore, the concepts of the general laws must in natural science be defined with complete precision, and this can be achieved only by means of mathematical abstraction. In other sciences the situation may be somewhat similar in so far as rather precise definitions are also required; for instance, in law. But here the number of links in the chain of conclusions need not be very great, complete precision is not needed, and rather precise definitions in terms of ordinary language are sufficient. In theoretical physics we try to understand groups of phenomena by introducing mathematical symbols that can be correlated with facts, namely, with the results of measurements. For the symbols we use names that visualize their correlation with the measurement.

Thus the symbols are attached to the language. Then the symbols are interconnected by a rigorous system of definitions and axioms, and finally the natural laws are expressed as equations between the symbols. The infinite variety of solutions of these equations then corresponds to the infinite variety of particular phenomena that are possible in this part of nature. In this way the mathematical scheme represents the group of phenomena so far as the correlation between the symbols and the measurements goes. It is this correlation which permits the expression of natural laws in the terms of common language, since our experiments consisting of actions and observations can always be described in ordinary language.

Still, in the process of expansion of scientific knowledge the language also expands; new terms are introduced and the old ones are applied in a wider field or differently from ordinary language. Terms such as `energy,“electricity,“entropy’ are obvious examples. In this way we develop a scientific language which may be called a natural extension of ordinary language adapted to the added fields of scientific knowledge.