On Physics (1920-1929)

"It is characteristic of modern physics to represent all processes in terms of mathematical equations. But the close connection between the two sciences must not blur their essential difference." (Hans Reichenbach, "The Theory of Relativity and A Priori Knowledge", 1920)

"Radioactivity is a new primary science owing allegiance neither to physics nor chemistry, as these sciences were understood before its advent, because it is concerned with a knowledge of the elementary atoms themselves of a character so fundamental and intimate that the old laws of physics and chemistry, concerned almost wholly with external relationships, do not suffice." (Frederick Soddy, "Structure of the Atom", 1920)

"[...] the future of thought and therefore of history lies in the hands of physicists, and therefore the future historian must seek his education in the world of mathematical physics." (Henry Adams, "The Degradation of the Democratic Dogma", 1920)

"The most important result of a general character to which the special theory has led is concerned with the conception of mass. Before the advent of relativity, physics recognized two conservation laws of fundamental importance, namely, the law of conservation of energy and the law of the conservation of mass; these two fundamental laws appeared to be quite independent of each other. By means of the theory of relativity they have been united into one law." (Albert Einstein, 1920)

"The physical object cannot be determined by axioms and definitions. It is a thing of the real world, not an object of the logical world of mathematics. Offhand it looks as if the method of representing physical events by mathematical equations is the same as that of mathematics. Physics has developed the method of defining one magnitude in terms of others by relating them to more and more general magnitudes and by ultimately arriving at 'axioms', that is, the fundamental equations of physics. Yet what is obtained in this fashion is just a system of mathematical relations. What is lacking in such system is a statement regarding the significance of physics, the assertion that the system of equations is true for reality." (Hans Reichenbach, "The Theory of Relativity and A Priori Knowledge", 1920)

"The relativity theory of physics reduces everything to relations; that is to say, it is structure, not material, which counts. The structure cannot be built up without material; but the nature of the material is of no importance." (Arthur S Eddington, "Space, Time and Gravitation: An Outline of the General Relativity Theory", 1920)

"In the realm of physics it is perhaps only the theory of relativity which has made it quite clear that the two essences, space and time, entering into our intuition, have no place in the world constructed by mathematical physics. Colours are thus 'really' not even æther-vibrations, but merely a series of values of mathematical functions in which occur four independent parameters corresponding to the three dimensions of space, and the one of time." (Hermann Weyl, "Space, Time, Matter", 1922)

"Results of measurements are the subject-matter of physics; and the moral of the theory of relativity is that we can only comprehend what the physical quantities stand for if we first comprehend what they are." (Arthur S Eddington, "The Mathematical Theory of Relativity", 1923)

"The scene of action of reality is not a three-dimensional Euclidean space but rather a four-dimensional world, in which space and time are linked together indissolubly. However deep the chasm may be that separates the intuitive nature of space from that of time in our experience, nothing of this qualitative difference enters into the objective world which physics endeavors to crystallize out of direct experience. It is a four-dimensional continuum, which is neither 'time' nor 'space'. Only the consciousness that passes on in one portion of this world experiences the detached piece which comes to meet it and passes behind it as history, that is, as a process that is going forward in time and takes place in space." (Hermann Weyl, "Space, Time, Matter", 1922)

"And so in its actual procedure physics studies not these inscrutable qualities, but pointer-readings which we can observe, The readings, it is true, reflect the fluctuations of the world-qualities; but our exact knowledge is of the readings, not of the qualities. The former have as much resemblance to the latter as a telephone number has to a subscriber." (Arthur S Eddington, "The Domain of Physical Science", 1925)

"Scientific laws, when we have reason to think them accurate, are different in form from the common-sense rules which have exceptions: they are always, at least in physics, either differential equations, or statistical averages." (Bertrand A Russell, "The Analysis of Matter", 1927)

"We wish to obtain a representation of phenomena and form an image of them in our minds. Till now, we have always attempted to form these images by means of the ordinary notions of time and space. These notions are perhaps innate; in any case they have been developed by our daily observations. For me, these notions are clear, and I confess that I am unable to gain any idea of physics without them. […] I would like to retain this ideal of other days and describe everything that occurs in this world in terms of clear pictures." (Hendrik A Lorentz, [Fifth Solvay Conference] 1927)

"It seems to be the impression among students that mathematical physics consists in deriving a large number of partial differential equations and then solving them, individually, by an assortment of special mutually unrelated devices. It has not been made clear that there is any underlying unity of method and one has often been left entirely in the dark as to what first suggested a particular device to the mind of its inventor." (Arthur G Webster, "Partial Differential Equations of Mathematical Physics", 1927)

"Physics has progressed because, in the first place, she accepted the uniformity of nature; because, in the next place, she early discovered the value of exact measurements; because, in the third place, she concentrated her attention on the regularities that underlie the complexities of phenomena as they appear to us; and lastly, and not the least significant, because she emphasized the importance of the experimental method of research. An ideal or crucial experiment is a study of an event, controlled so as to give a definite and measurable answer to a question - an answer in terms of specific theoretical ideas, or better still an answer in terms of better understood relations." (Thomas H Morgan, "The Relation of Biology to Physics", Science Vol. LXV (1679),  1927)

"Physics is mathematical not because we know so much about the physical world, but because we know so little: it is only its mathematical properties that we can discover." (Bertrand Russell, "An Outline of Philosophy", 1927)

"Euclidean geometry can be easily visualized; this is the argument adduced for the unique position of Euclidean geometry in mathematics. It has been argued that mathematics is not only a science of implications but that it has to establish preference for one particular axiomatic system. Whereas physics bases this choice on observation and experimentation, i. e., on applicability to reality, mathematics bases it on visualization, the analogue to perception in a theoretical science. Accordingly, mathematicians may work with the non-Euclidean geometries, but in contrast to Euclidean geometry, which is said to be "intuitively understood," these systems consist of nothing but 'logical relations' or 'artificial manifolds'. They belong to the field of analytic geometry, the study of manifolds and equations between variables, but not to geometry in the real sense which has a visual significance." (Hans Reichenbach, "The Philosophy of Space and Time", 1928)

"It is unreasonable to expect science to produce a system of ethics - ethics are a kind of highway code for traffic among mankind - and the fact that in physics atoms which were yesterday assumed to be square are now assumed to be round is exploited with unjustified tendentiousness by all who are hungry for faith; so long as physics extends our dominion over nature, these changes ought to be a matter of complete indifference to you." (Sigmund Freud, [Letter to Oskar Pfister] 1928)

"So far as physics is concerned, time's arrow is a property of entropy alone." (Arthur S Eddington, "The Nature of the Physical World", 1928)

"If to-day you ask a physicist what he has finally made out the æther or the electron to be, the answer will not be a description in terms of billiard balls or fly-wheels or anything concrete; he will point instead to a number of symbols and a set of mathematical equations which they satisfy. What do the symbols stand for? The mysterious reply is given that physics is indifferent to that; it has no means of probing beneath the symbolism. To understand the phenomena of the physical world it is necessary to know the equations which the symbols obey but not the nature of that which is being symbolised [...]" (Arthur S Eddington, "Science and the Unseen World", 1929)

"What had already been done for music by the end of the eighteenth century has at last been begun for the pictorial arts. Mathematics and physics furnished the means in the form of rules to be followed and to be broken. In the beginning it is wholesome to be concerned with the functions and to disregard the finished form. Studies in algebra, in geometry, in mechanics characterize teaching directed towards the essential and the functional, in contrast to apparent. One learns to look behind the façade, to grasp the root of things. One learns to recognize the undercurrents, the antecedents of the visible. One learns to dig down, to uncover, to find the cause, to analyze." (Paul Klee, "Bauhaus prospectus", 1929)