Theoretical Physics and Dialectics of Nature
Theoretical physics in our country has been known all over the world by the brilliant achievements of H. Yukawa.
How could the theory of elementary particles have freely developed in such a society where the feudal system remained for a long time ? J. D. Bernal of London University made the following criticism and prospect of the Japanese science in a book written just before World War II. “It is over-elaborate, pedantic, and without imagination, and unfortunately, in many cases, it is also uncritical and inaccurate.
It is unfair to blame the Japanese scientists for this. In a country where dangerous thoughts are being persecuted with increasing severity, originality in science will hardly be at a premium.
Where science is used more openly and cynically even than in Europe for purposes of war research and for trying to find the absolute minimum of food on which factory workers can exist, it is unlikely to attract the best minds to do the best work. Of recent years there has been a notable though underground reaction against this official and military science. The younger Japanese scientists are beginning to be aware of the social implications of their work, and are thinking for themselves outside the orbit of the imperial and military myth of Shinta, or of its more violent modern forms such as Kõdõ.
If, in the revolutions that threaten East as much as West, the Japanese people should ever acquire any peace of freedom we may expect here also a great improvement in the quality of scientific work”.
Development of the Yukawa theory might certainly be an incident and good fortune. One may assert that in the field of science, such as theoretical physics where contemplative faculty plays a leading role, social conditions do not have much influence. However, it was actually shown by the Nazism in Germany that even the innermost part of modern science could be affected by superstition and barbarism. If there had been no conscious efforts to get rid of the mythological viewpoint of the world and, its narrow-minded method of thinking, the theoretical physics in our country, too, would have followed a miserable path.
In recent years, theoretical physics have experienced a bewilderingly rapid development.
It may certainly be said that the fruits obtained in the last half century surpass to a great extent the development in the passed several centuries. The world of physics by Newton and Maxwell which had been believed to be firm and unshakeable, was overthrown by the advent of the theories of relativity and quantum mechanics. The metaphysical view of matter based on immutable elements and indivisible atoms was radically changed.
While most physicists did not yet fully understand the new theories, the spearhead of physics further invade the interior of atomic nuclei and development began in the theory of elementary particles.
The true character of cosmic ray is to be clarified also. In such an unprecedented revolutionary age, even a scientist who has already accomplished his great work cannot follow the new development.
Planck, who found the clue to quantum theory, and also Einstein, who constructed the theory of relativity, could not correctly understand the foundation of quantum mechanics. Physicists who felt uneasy about the basis of their own beliefs expressed their interests in philosophical problems and began to discuss problems such as “the role of science,,, “the reality of externality” and “the problem of causality.” They are making efforts to get the world view on which they never lose their own confidence even if they are faced with the revolutionary age and to acquire methodology useful for their own studies. But this is not necessarily an easy task.
The reason is that philosophy is a science influenced strongly by social restrictions as it is said to be even a partisan science. It is not only the world of physics that is overtaken by the revolutionary age. In this century all the world was frequently astonished by many great upheavals such as World War I, the Russian Revolution, the financial panic, the rise of fascist’s nations and World War II. Physicists were to a great extent affected directly by these events. Also, these indirect influences were not small ones which were brought about from philosophy reflecting social unrest, philosophy guiding the Russian Revolution, philosophy trying to justify the ideology of fascists, etc.
It was during the period from the end of the 19th century to the beginning of this century, that physicists increased their interest in philosophy at first, while the discoveries of radium, electrons, etc., first shook the foundation of classical theories. As Poincaré stated in Value of Science, a whole of the fundamental laws of old physics such as “Newton’s principles”, “Mayer’s principle”, “Lavoisier’s principle” and “Carnot’s principle” stood on the brinks of their collapse and “crisis of mathematical physics” occurred. Physicists who lost their confidence in the old theories could no longer believe anything other than their own experiences.
Among them such empiricistic and positivistic tendencies were prevalent that science is not any copy of the objective reality, but merely a product of human consciousness, and that the role of science is to faithfully describe experiences and not to explain the essence of nature. Mach, Kirchhoff, Ostwald and Poincaré were representative scientists with these opinions. On the contrary, there appeared scientists such as Boltzmann and Planck who held fast to their viewpoint of realism, and controversies were raised frequently between the two groups of scientists. In the meanwhile, there were tragedies such as the suicides of Boltzmann and Drude. All of the above views of the world, however, were not sufficient to grasp the points of “the crisis of physics.” It was Lenin who correctly analysed these problems, whereas among physicists at that time, only a few knew of his investigation.
Remarkable development of physics in the subsequent period has been attained mainly on the basis of the atomistic viewpoint of matter contrarily to expectation of the positivists.
Studies on the structure of the atom were remarkably increased by invention of “the Geiger counter, which counts the number of particles invisible to the naked eye such as electron and a-particle, and by device of “Wilson’s cloud chamber” which indicates the paths of the particles. In 1911, a model of an atom like the solar system was established by Rutherford. In this case, however, the old theory faced a crisis also. This model, in fact, could not offer any explanation of the stability of the atom and the regularity found in the series of spectrum.
In 1913, Bohr proposed the so-called old-quantum theory by introducing quite a daring hypothesis in which Planck’s concept of quantum was adopted. This theory has an eclectic character which admits, on the one hand, Newton’s and Maxwell’s classical laws and on the other hand, two assumptions being quite incompatible with them. The contradiction of this dualistic character became more serious as the more complicated systems were treated, and then the way to the reconciliation could not be found even by Bohr’s “correspondence principle.”
At that time an astonishing fact was found: Matter as well as light has dual character.
It was clarified that both matter and light were “particles” and “waves” at the same time. This was the problem which could no longer be solved merely by partial modification of classical physics. From many experiences before that time, it had been known that an electron is a particle with a certain amount of electricity and mass and that something like a “fragment” of an electron can never exist.
Nevertheless it was found that an electron is also a wave and it passes simultaneously through two or more lattice points of a crystal and causes a diffraction phenomenon. Since a particle treated by Newtonian mechanics occupies a certain point in space at a certain time and moves along a certain orbit with a certain velocity as a particle of the ordinary concept, it is absolutely incompatible with the concept of wave which spreads over whole space. Obviously such contradictions was quite an intolerable matter for traditional physicists. Lorentz, an aged physicist who had studied the theory of electron and had built the basis of relativity, talked in despair, “Today, people assert just the opposite to what they said yesterday. In such a time, criterion of truth any longer could not be maintained and it is hard to understand what science is. I regret that I did not die five years ago before this contradiction was born”.
Physicists became sceptical again and some of them went into positivism, some into agnosticism and some into mysticism. However, in 1925, a new theory “quantum mechanics” was born brilliantly. Nevertheless, philosophical confusion among physicists still continued concerning the interpretation of quantum mechanics. These confusions were spurred by the fact that pioneers of quantum mechanics often carelessly emphasised their positivistic opinions. For instance, Heisenberg said the following; “physicists are to describe formally, only the relations among perceptions,” “with modern physics we do not treat the reality or the structure of atoms, but only phenomena which we perceive in making observations of atoms” and so on.
Consequently, in its early days quantum mechanics was often expounded from the standpoint of positivism and operationalism of its modern version.
The book by S. Kikuchi, which was published rather early in our country, is a typical example reflecting the above viewpoint. He said for example, “It is possible to consider that generally the law of nature describes in a given experimental operation the relation among indications of meters attached on instruments. It is not such as to grasp the entity behind phenomena through investigation of them”.
However, as my respected friend M. Taketani frequently advises, physics itself should be strictly distinguished from the interpretation given by physicists. In many cases, scientist acts differently from what he says. In his book The Structure of Matter Kikuchi says that the materialistic viewpoint, that the external world exists independently of human consciousness, is a naive standpoint of human beings living in a world of common sense and has no connection with the standpoint of highly advanced science such as quantum mechanics.
Nevertheless, in the same book, he thoroughly returns to that standpoint of naive realism when he explains the diffraction of electron, the scattering of neutron, etc., on which he produced very brilliant achievement.
This proves that in his laboratory he always stands on the viewpoint of naive realism.
The relation between science and view of the world cannot be clarified without historical investigation of the origin and development of science. However, a scientific specialist frequently includes a dogmatic interpretation within his narrow field of vision. Now we part from the theoretical physics for the time being and turn to these problems.
It is concluded that about a million years have passed since the beginning of mankind on the earth.
Presumably tens of thousands of years have elapsed since the appearance of homo sapiens. Meanwhile man produced various materials for life and lived by consuming them. Life of man, unlike that Of an animal, is carried on with a certain program; the characteristic is that he has tried to change the nature that surrounds him so as to adapt it to his own needs. If one may call this practical, then life of mankind is originally practical.
To effect the practice, however, we must admit the following: Nature (externality) exists independently of our consciousness and is projected into consciousness through our senses.
This is the point of view always entertained by man in performing his daily rituals, therefore, it has been called naive realism. Philosophically it is the materialistic point of view.
Man’s practice results in success in accordance with the prearranged plan, only when the image of externality made through our senses, namely, our knowledge about nature is not wrong. Through success and failure of man’s performance, he discovers the objective structure and the law of nature to which his desire and volition cannot do anything. Science has advanced as the organisation of knowledge about the objective law that is cognised through the above mentioned practice. Therefore, scientific knowledge guarantees the validity of man’s performance, while the truthfulness of his cognition should always be verified by practice. Considering the intimate relation between science and practice, we find that science should be constructed on the basis of “standpoint of practice,” that is to say, materialism.
Thus we can understand the relation such that the progress in science and the success in practice continuously proves the validity of materialism. In this respect materialism is no longer a naive point of view, but a scientific view of the world which is supported by all the fruits of modern science. Then we may conclude that any standpoint which denies materialism obstructs the progress of science.
It is commonly said that the distinctive character of modern science resides in its positiveness.
This is correct in the sense that it manifests a phase of the above mentioned relation in that the criterion for the truthfulness of scientific cognition lies in “practice.” Natural-scientists, however, emphasise only this positiveness unilaterally and are apt to be oblivious of or to deny intentionally its materialistic premise. This viewpoint is what is implied by the positivism previously mentioned.
This can be regarded as a reflection of the restlessness of scientists who are not able to rely on anything other than their experiences when they are faced with the revolutionary stage.
A positivist says, “Science is to observe nature in itself”, and an operationalist with the new form of the positivism says, “A physical quantity is a symbol of the operation of a certain measurement, and has not any relations with objective reality”. But scientists always stand on “the standpoint of practice” in their laboratory.
This is because “experiment” is one form of “practice.” On the one hand they say, “Physics is to describe formally only the relation among perceptions”, but on the other hand they study the structure of atom which cannot be observed through their direct experience and reveal the property of elementary particles.
The reason why physicists could and did discover atom and reveal its structure is not because they observed nature in itself. But, it is because a man takes “the standpoint of practice,” that a human cognition can go over the limitation of the sense and reveal the essential relation lying behind phenomena although his cognition starts from the direct experience in the beginning.
It is based on the success of human practice forcing atomic energy to he released, that all human beings, now, have been made to recognise the existence of atom.
In spite of the inseparable relation of the natural science to materialism, why do theoretical physicists lean towards positivism and empiricism whenever they are faced with revolutionary ages? The view of the world governing natural-scientists for a long time, until the last century, was the metaphysical materialism (mechanical materialism), in which the world is regarded as being constructed with individual, fixed and invariable objects being observable one by one independently.
This is the viewpoint universalised on the basis of a view of nature obtained from the early development of natural science such as Newtonian mechanics, that is “Nature remained as it was as long as it continued to exist.” The planets and their satellites, once set in motion by the mysterious “first impulse,” circled on and on along their predestined ellipses for all eternity, or at any rate until the end of all things. The stars remained forever fixed and immovable in their places, keeping one another therein by “universal gravitation.” The earth has remained the same without alteration for all eternity or, alternatively, from the first day of its creation. The “five continents” of the present time had always existed, and they had always had the same mountains, valleys, and rivers, the same climate, and the same flora and fauna, except in so far as change or transplantation had taken place at the hand of man.
The species of plants and animals had been established once and for all when they came into existence; “like continually produced like”.
A form of materialism, however, has to change also as science develops. Subsequently remarkable development of science did require a change of the materialism.
After the hypothesis on the formation of the solar system was presented by Kant and Laplace, it became an influential point of view that nature does not just exist, but comes into being and passes away.
There appeared “the evolutionism” in every sphere of science. The thought of Heraclitus was revived that all nature moves in perpetual flow and circulation, and “the dialectic view of nature” was established.
Following the above, materialism had to emerge to dialectic materialism. Physicists, who had believed in the firmness of Newtonian mechanics, were bound to the metaphysical materialism and were thinking in the framework of formal logic. This can be regarded as an evil that modern science falls into this excessive specialisation.
When the discoveries of the new phenomena began to rock Newtonian mechanics to its foundation, they began to notice the brittleness of their views of nature and plunged into confusion.
They could not understand that the narrow-mindedness of their views of the world was not due to its “materialistic character” but its “metaphysical character.” Thus, they erroneously recognised the break-down of some essential principles directly as the negation of a whole of the-objective legitimacy, and threw out the baby with the bath-water.
This is the process that frequently leads physicists to the positivism in revolutionary ages.
It is said that scientists can make themselves understood and co-operate with each other, even if they have different views of the world.
The reason for this is firstly that they usually wear their philosophies only as ornaments and always take “the standpoint of practice” in actual research, and secondly that the content of science is, in a sense, a faithful reflection of the law of nature independent of their interpretations. However, progress in research must be made at quite a different rate, accordingly as they are clearly conscious of “the materialistic dialectics"-the supreme standpoint founded on the whole results of modern science-, or they are tied unconsciously to a standpoint of the naive realism, or an erroneous view of the world.
This can be said about any branch of science. Especially in the theoretical physics, which has been highly developed and deals with fundamental concepts and laws, they are exposed to continual dangers of taking an incorrect turn unless they are on the supreme standpoint and make researches using the logic of high quality. Physicists in the past have relied solely upon the positivistic method, and made their advances by studying the correct directions from nature itself, with the rule of trial and error.
They had blindly believed it to be the only right method. However, now that the great fruits of modern science have proved the validity of “dialectics of nature” and therefore revealed that the cognition of nature is made through the dialectic processes, we must intentionally apply the dialectics of nature as a compass which shows the way of our research.
Recently, the number of scientists who are conscious of the validity of this viewpoint has gradually increased. It should be noted that Russian scientists are studying the dialectics of nature with extraordinary enthusiasm.
In other countries, scientists of the first rank, as J. D. Bernal (British chemico-physicist), J. Needham (British biologist) and P. Langevin (French physicist), have published excellent treatises on the dialectics of nature. Furthermore, I have been told, F. and I. Joliot-Curies, the discoverers of “the artificial radioactivity,” and P. M. S. Blackett, the discoverer of the cosmic-ray shower,” who are the greatest scientists, support it, and moreover R. Oppenheimer,
who is one of the greatest American theoretical physicists and played an important role in the production of “the atomic bomb” is studying it. In our country, M. Taketani, one of my respected friends, has published excellent articles” on the interpretation of quantum mechanics and on the process of the establishment of Newtonian mechanics, where he has developed the new stage (so to speak the quantum-mechanical stage) of the dialectics of nature. Recently, H. Yukawa') said that the course of development of theoretical pliysics is “dialectic” and that its basis is “materialistic.”
Next, let us briefly mention about the fundamental character of the dialectics of nature-"the logic of nature"-extracted from the dialectic view of nature based on the totality of the results of modern science. First, “it is necessary to understand that nature is by no means an accidental collection of objects and phenomena which are mutually separated, isolated and independent, it consists of one thing that is mutually related, dependent, restrictive and connected. The all of nature, from the smallest element to the largest, has its existence in eternal coming into being and passing away, in ceaseless flux, in unresting motion and change.” Secondly, the laws on development and motion of nature have the same form as those found by Hegel as the laws on development of thought. Namely they are: “The law of the transformation of quantity into quality and vice versa; the law of the interpenetration of opposites; the law of the negation of the negation,” etc.
Let us explain these in a slightly concrete way. Current science has found that in nature there exist qualitatively different “levels"-the form of motion — , for example, a series of the levels such as elementary particles — nuclei — atoms — molecules — masses — heavenly bodies — nebulae. These levels form various nodal points which restrict the various qualitative modes of existence of matter in general. And thus they are not merely related in a straightforward manner as described above. The “levels” are also connected in a direction such as molecules — colloids — cells — organs — individuals — societies. Even in the same masses, there exist “levels” of states corresponding to solids-liquids-gases. Metaphorically speaking, these circumstances may he described as having a sort of multi-dimensional structure of the fish net type, or it may be better to say that they have the onion-like structure of successive phases. These levels are by no means mutually isolated and independent, but they are mutually connected, dependent and constantly “transformed” into each other. For example, an atom is constructed from elementary particles and a molecule is constructed from atoms, and conversely the decompositions of a molecule into atoms, an atom into elementary particles can be made. These kinds of transformations occur constantly, with the creation of new quality and the destruction of others in ceaseless changes. Even the elementary particles, which have been regarded as the simplest and the ultimate constituents of matter, no longer have the metaphysical character of eternally invariable “atom” such as postulated by Democritus.
For instance, a meson produced in the atmosphere by cosmic rays transforms into an electron and a neutrino with such a short life of 2 x 10-6 see.
These types of transformations among different “levels,” the creation of new qualities and their eventual destruction, obey “Hegel’s law.” Some physicists may object to the above statement with the assertion: “The law for the construction of atoms. is quantum mechanics, while the one governing the solar system is Newtonian mechanics”. Quite right, each level is governed by a law inherent to the respective ones. Just for this reason, one needs individual sciences.
It is the “dialectics,” however, that is commonly found as the universal law in “quantum mechanics, Newtonian mechanics, the law of evolution of living organisms, the law of evolution of societies” and even “in the law of development of thought.” Therefore, it may be regarded as “the logic of nature.” In view of this fact, quantum mechanics, Newtonian mechanics, and indeed every science can be understood only by the logic of dialectics. The confusion brought about on the interpretation of quantum mechanics had its main origin in the fact that physicists did not have the logic of dialectics. This point will be discussed again later.
The very law such as “the law of transformation of quantity into quality” is already well accepted in present day natural science.
This law states that “a rapid transformation from one of the levels to another does not happen accidentally, but is based on a law and it occurs as a result of accumulation of gradual quantitative changes.” In physics, every change is the transformations of quantity into quality. For example, in order to create an electron pair, the energy of about 106eV are required and similarly, for meson production, the energy of 108eV is needed. As is well known, recent developments in nuclear physics have been made taking an opportunity of the completion of the high voltage power supply of 8 x 105 volt due to Cookcroft and Walton. And it may be unnecessary to quote an example, to explain that chemistry is a science for the qualitative change of substance caused by the quantitative change of its components. On one occasion, Engels said, in an ironical tone, “And if these gentlemen have for years caused quantity and quality to be transformed into each other, without knowing what they did, then they will have to console themselves with Moliers’s Monsieur Jourdain who had spoken prose all his life without having the slightest inkling of it”.
The second law of dialectics states that every level consists of a unification of “the opposites” and, by the struggle of the opposites, they develop themselves into higher “levels.” Here, let us quote only one example from elementary particle physics. A nucleus is constructed from protons and neutrons. The Yukawa theory clarified the mechanism of how a nucleus is made of these. The essential point of this theory is that a neutron has the property of transforming into a proton and a negative meson.
However, one cannot conclude that, simply because a neutron is transformed into a proton and a negative meson, the former is constructed from the latter two.
For, this relation is of a reciprocal character and thus a proton can be transformed into a neutron and a positive meson. Accordingly, neutron and proton are both “elementary” and at the same time 66 composite,” i.e., they can be said to he the syntheses of both “elementarily” and “compositeness”. Furthermore, this opposition acts as a motive force in the process of constructing a nucleus-"a new quality"-from elementary particles.
In nature, the creation and the destruction of various “levels” occur ceaselessly and they form a history of nature.
Now let us quote part of an excellent description of the evolution of cosmos from a famous work, “The Birth and the Death of the Sun”, by J. Gamov of George Washington University. “The story begins with space uniformly filled with an unbelievably hot and dense gas, in which the processes of the nuclear transformation of the various elements went on as easily as an egg is cooked in boiling water. In this ‘prehistoric’ kitchen of the universe, the proportions of the different chemical elements-the great abundance of iron and oxygen and the rarity of gold and silver-were established. To this early epoch also belongs the formation of the long-lived radioactive elements, which even at the present time have not yet quite decayed.
Under the action of tremendous pressure of this hot compressed gas, the universe began to expand, the density and the temperature of matter slowly declining all the while. At a certain stage of the expansion, the continuous gas broke up into separate irregular clouds of different sizes, which soon took on the regular spherical shapes of individual stars. The stars were still very large, much larger than they are now, and not very hot. But the progressive process of gravitational contraction diminished their diameters and raised their temperatures. The frequent mutual collisions among the members of this primitive stellar family led to the formation of numerous planetary systems and in one of these encounters our earth was born.
While the stars grew hotter and hotter, and their planets-being small and unable to develop the high central temperatures necessary for thermonuclear reactions-covered themselves with solid crusts, the stellar gas’ uniformly filling all space continued to expand, and the distances between the stars began to approach their present values.
At another stage of the expansion, corresponding to the average concentration still to be found within individual galaxies, the ‘stellar gas’ broke up into separate giant clouds of stars. While these stellar islands were still close to one another, their mutual gravitational interaction led in many cases to the formation of the odd-looking spiral arms and supplied them with a certain amount of rotational momentum.
By that time most of the stars that made up these receding stellar islands had become sufficiently hot in their interior regions to start off various thermonuclear reactions between hydrogen and other light elements. First deuterium, then lithium, beryllium, and, finally, boron were turned into ‘ashes’ (nuclear ‘ash’ being the well-known gas helium); and, passing through these different phases of ‘red giant’ development, the stars approached the main and longest part of their evolution. When no other light elements were left, the stars began to transform their hydrogen into helium through the catalytic action of the phoenix-like elements, carbon and nitrogen.
Our Sun is in this stage now”. And furthermore, J. Gamov mentions the fate of our sun.
The earth, which was born in a certain stage of the evolution of the cosmos, was gradually cooled down and its surface was covered with the atmosphere and the hydrosphere.
During the evolution of the earth in several hundreds or thousands million years, the organic matters with simple structure was first synthesised from various elements such as carbon, hydrogen, oxygen and nitrogen. In the next stage, the protein and the other substances were composed, which are required to construct living organisms. Then they formed the coacervate with more complex organism, and at last the protista was generated. On these matters a Russian biochemist, I. A. Operlin has given full details of them in his work Origin of Life, and they will increasingly be clarified with the further development of biochemistry, geochemistry, etc. The evolution of life from the protista to mankind was revealed by C. Darwin in his work The Doctrine of Evolution, and with this very stage of the appearance of human being, it runs into the genuine domain of history.
The above description is a brief sketch of the dialectic view of nature which has been clarified by modern science.
Although the contents of the dialectics of nature as mentioned above are supplemented by the remarkable progress of individual sciences, they are not essentially different from those stated by Engels at the end of the last century. The contents of the dialectics of nature must be enriched constantly in the future by the development of science, but the essential features such as discussed previously, will never be lost through all ages. Because, it is “the logic of nature.”
Let us again return to theoretical physics. Newtonian mechanics was the law which governs objects of a visible size, that is, “macroscopic world.” Therefore it is no wonder that, when the object of physics turned on the 4 6 microscopic world” of atoms and electrons, which are quite distinct quantitatively from the “macroscopic objects,” a “new law” being qualitatively different from “Newtonian mechanics” was discovered.
This may be nothing more but again to prove “the law of transformation of quantity into quality.” And one needs not become desperate of the fact that an electron is a “wave” and at the same time can be a “corpuscule.” For this predicts only that there would be discovered, behind those phenomena, a more fundamental relationship which unifies opposites; “corpuscular character” and “wave character.” In fact, there had been two different currents of development in the establishment of quantum mechanics; one was “matrix mechanics” developed by the Göttingen school, Heisenberg was its leader, the other “wave mechanics” developed by de Broglie and Schrödinger.
Although these two were considerably different in their appearances, they have later been proved to be mathematically equivalent to each other and unified into a rational theory as it is presently formulated. C)n the interpretation of quantum mechanics, after much meandering all scientists have arrived at almost the same view'), except for the problem such as the observation problem which is closely connected with their own philosophies. Then the so-called “Copenhagen spirit” that contains Bohr’s “correspondence principle” as its main content constantly played a leading role, and also a confrontation between the realistic trend of the wave mechanics school and the positivistic trend dominating the Gbttingen school was a remarkable feature.
The Göttingen school, which employed as a guide the principle of positivism, i.e., physics should be constructed on directly observable quantities only, avoided the introduction of quantities such as orbit and velocity of electron in an atom and attempted to describe atomic phenomena in terms of only frequency and intensity of light emitted from an atom. People of the school built up the matrix mechanics on the basis of this view and of Bohr’s correspondence principle.
At one time, Schrödinger, independently of such an epistemology of positivism, established the wave mechanics by introducing “wave equation” on the analogy of mechanics with optics following de Broglie’s idea of “material wave.” He first considered the “material wave” as a real matter which should take the place of “particle picture” of the old mechanics to satisfy the demand of immediacy, but it had become clear that such a naive interpretation should not be acceptable. For, even if electron is a real wave such as water wave and propagates into the whole space according to the Schrödinger wave equation, the electron must be necessarily found at a space point due to its particle nature when one observes the position of the electron. This means that the wave suddenly contracts into a point by an observation and furthermore that this contraction arises discontinuously and non-causally.
Thus, it is by any means impossible to interpret classically, the quantum phenomena as a continuous and causal change by assuming the matter wave as to be realistic.
On the other hand, the methodology of the Göttingen school which attempted to construct the theory only in terms of the directly observable quantities, also could not help disclosing their narrow-mindedness. In fact, in the present theory there are again contained the position and the velocity of the electron which the school thought to have been excluded from the theory, and it has been clarified that the central problem is not on the point of whether these quantities are “directly” observable, but whether these quantities can be observed “simultaneously.” What Heisenberg’s “uncertainty relation” has told us is that the position and the velocity of electron are “complementary” quantities which cannot he measured simultaneously. The characteristic feature in quantum mechanics is in the point that one recognised the existence of such complementary quantities.
Consequently it becomes impossible to describe the state of the particle, as in the case of Newtonian mechanics, in terms of the values of its position and velocity at a moment, so that it is necessary to introduce a new concept of the state which is represented by a vector (wave function) in the Hilbert space.
The reason that an electron exhibits a contradictory character of corpuscule and wave is due to the fact that behind these phenomenological forms exists a fundamental relationship understood in terms of the quantum-mechanical state. Furthermore, it should he stated here that the wave function with such a significant meaning is a quantity which can neither be observed “directly,” of course, nor “in principle,” and this implies that the present quantum mechanics has been developed by getting over the epistemology of the positivism.
Sometimes the development of quantum mechanics has been related as if it implies a success of the methodology of Machism.
However, the positive role, in its true sense, played by the methodology of the Göttingen school is found in the point that it forbid- the application of “the concepts of daily life” to the microscopic region without criticism. And this point can be understood by the dialectics of nature, in which the law of transformation of quantity to quality is realised, more properly than by the positivistic epistemology. The discovery of the dual nature of the electron has enlightened us that the various concepts of Newtonian mechanics, which were taken from the macroscopic experiences, cannot strictly be applied to the microscopic region. However, the macroscopic and the microscopic regions should “not mutually be separated, isolated or independent,” but should “be correlated to, dependent on and restricted within each other.” Therefore one can never construct a new theory by merely being forbidden to apply all the ordinary concepts.
It may be said that Bohr’s “correspondence principle,” which demands that, New theory should always coincide with the classical theory asymptotically in the boundary region”, puts this point into its consciousness. Heisenberg, too, eliminated at last the positivism and stated, “Even if one attempts to purify all the unclear concepts before all the science, one can do nothing but to resort to the ‘compulsion of experience’ since there is no standard to judge which concept is in doubt.
To make the concepts clear beforehand is equivalent to prearranging the future development of science by means of a logical analysis of language”, and further “Since the law of classical physics holds in the limit of the action quantum being zero, the classical concepts corresponding to these quantum laws should be indispensable elements of the natural science”. The reason why the correspondence principle, as a guide in searching for an unknown law, has always played a leading role during the entire development of quantum mechanics from the stage of old-quantum theory, is due to the fact that it reflects in part the dialectics of nature.
And though the Göttingen school was led by this misleading philosophy, it has well succeeded in establishing the matrix mechanics mainly due to the help of the correspondence principle.
If, however, theoretical physicists had been conscious of the dialectics of nature and learned the logic of high quality, they would have taken a more straightforward way to establish quantum mechanics. And it is no doubt that they would have arrived more quickly at the methodology, which Bohr and Heisenberg acquired at last through their excellent intuitions and their many years of struggles with nature, and would have given more adequate expressions for it.
The methodology of Bohr and Heisenberg, though it worked well as an active weapon in constructing quantum mechanics, has frequently worked negatively in the recent development of theories of atomic nuclei and of elementary particles. This is due to the fact that the methodology consists of only a partial consciousness of the dialectics of nature.” Indeed, a misleading methodology, if one applies it extensively as a creed, is always transferred into the opposition, according to the well-known law of dialectics.
In the interpretation of quantum mechanics, it was the so-called “observation problem” that most numerous misunderstandings were spread, in connection with philosophy. In quantum mechanics, “state” of a microscopic system such as an atom, is expressed by “wave function” and develops continuously every moment according to Schrödinger’s wave equation. This is a causal change described in terms of the differential equation, and does not differ in quality from the change of state of macroscopic system. The characteristic feature of quantum mechanics, however, arises in the observation of such microscopic system; a measurement of the same physical quantity in the same state, does not always yield a definite result and we can only predict statistically a probability for getting a specific result. Moreover, the state of system or the wave function changes discontinuously and non-causally through the measurement, thus which state the system changes to depends on the measured result of the physical quantity.
An example is the aforementioned “contraction of wave.”
The essential point of “the observation problem,” is to clarify the relation of these two changes, i.e., a continuous and causal change of the state of a closed system and a discontinuous and non-causal one which arises in the measurement of the system. Now consider the characteristic feature of the measuring process. An observation is an action on “an object” with the “measuring apparatus” to measure quantities concerning the former by, for example, reading a change of the scale appearing in the latter.
Then, in quantum mechanics even if a combined system of two is as a whole in a pure quantum mechanical state, it can be proved that as for the sub-system, it is generally no longer in a pure state, but consists of a statistical mixture of a number of quantum-mechanical states.” This is a characteristic of quantum mechanics and indicates the dialectical relationship between the part and the whole and between the contingency and the necessity, which can never be understood by a formal logic.
The discontinuous and non-causal change which arises in the measuring process, contrarily to the continuous and causal change of the state of the closed system, is a consequence of such an objective “quantum mechanical law of combination” between “object” and “measuring apparatus,” and has nothing to do with the so-called “action of the subject on the object.” The statement, which has hitherto frequently been made that quantum mechanics “rejects” the “objective reality of externality,” is based on a wrong understanding of the observation problem. This has been already pointed out by Taketani.
However, to sweep away such a misunderstanding it would be necessary to take note of another characteristic point of the quantum-mechanical measuring process. It is the fact that, while the object of measurement is microscopic, the main part of the measuring apparatus must necessarily be macroscopic. In other words, while the object is governed by the quantum-mechanical law, the measuring apparatus must be a device which amplifies a microscopic process arising within the apparatus into a macroscopic process.
Therefore the microscopic portion within the apparatus has a close connection with the object, so that it may be difficult to determine to what part the observed object is extended and what part the measuring apparatus is. However, as Neumann has proved, using the above mentioned “law” of combination, quantum mechanics always gives the same result independent of the position of the cut-plane between the object and the measuring apparatus. This means that quantum mechanics is constructed quite ingeniously.
Neumann stated, in the excess of emphasising the arbitrariness of the position of this cut-plane, that the object could he enlarged gradually to the limit that only the “abstract ego” remained as a cognisant subject; this is obviously going too far.
For, the characteristic feature of the measuring apparatus is to contain the device which amplifies the microscopic process to the macroscopic one, thus we cannot push it into the side of the object.
Moreover as the procedure that an observer reads a change of the scale, appearing in the apparatus produces no effect on the result of measurement, it is meaningless to involve the cognisant subject as well into the measuring apparatus. From the consideration of these points it will become very clear that the statistical nature arising in the quantum-mechanical measurement is a consequence of a “material interrelation” between the “object” and the “measuring apparatus”; both of which are of the “objective existence” and that the statistical nature is not due to the action of the subject on the object.
Though it has sometimes been argued that in the quantum mechanics “causality” should not be denied, the correct way to resolve this problem is found in the analysis of the measuring process as mentioned above. In quantum mechanics the concept of state is of essential importance and the state obeys the strict law of causality. On the other hand, the statistical law governs the phenomenal world which is concerned with the correlation among the observed values of physical quantities.
However, as mentioned above, this statistical nature never denies the causality, but it is the “statistical nature” of the “portion” which is founded on the “causal nature” of the “whole system”. This relationship can be grasped only by the logic of dialectics which unifies the confrontations between the phenomenon and the essence, between the part and the whole, between the contingency and the necessity, and so on. And, much confusion which has been raised concerning the problem of the causality is due to the understanding of structural composition of quantum mechanics by means of a plane formal logic.”
From the standpoint of the dialectics of nature, M. Taketani has analysed in detail the logical structure and the process of the establishment of quantum mechanics and has developed a powerful methodology-three-stage theory-for the theoretical physics. How his methodology has played a great role in the development of the elementary particle physics in our country will be mentioned in another place.