The most important of these questions are:
If the questions as to whether the world is a chaos or a system and whether the world came into being accidentally or was created according to plan are answered without being preceded with a definition of the form of the world, and do not result from such a definition, these answers lack weight, demand "faith", and fail to satisfy the mind. It is only when the answers to these questions are derived from the definition of the form of the world that they can be sufficiently exact and complete.
It is not difficult to prove that the predominating general philosophies of life of our time are based on such solutions of these three fundamental questions as might have been considered scientific during the 19th century. The discoveries of the 20th century have not as yet affected ordinary thought or have affected it very little.
And it is not difficult to prove that all further questions concerning the world, the development and elaboration of which constitute the object of scientific, philosophical, and religious thought, arise from these three fundamental questions.
In spite of its predominant importance, the question of the form of the world has comparatively seldom arisen independently, being usually included in other problems, cosmogonical, cosmological, astronomical, geometrical, physical, and other. The average man would be greatly surprised if he were told that the world may have a form. For him, the world has no form.
Yet in order to understand the world one must be able to build some model of the Universe, however imperfect. Such a model of the world, such a model of the Universe, cannot be built without a definite conception of the form of the Universe. To make a model of a house one must know the form of the house; to make a model of an apple, one must know the form of an apple.
Therefore, before passing to principles upon which a new model of the Universe can be built, we must examine, though only summarily, the history of the question as to the form of the world, the present state of this question in science, and the "models" which have been built up to the present day.
The ancient and medieval cosmogonical and cosmological conceptions of exoteric systems (which alone became known to science) were never very clear or very interesting. Moreover, the universe they pictured was a very small thing, very much smaller than the modern astronomical world. I shall therefore not speak of them.
By that time the sciences which studied the world of nature had long been divided and stood then in the same relation to one another in which they stand now, or at any rate stood quite recently.
Physics studied phenomena in matter around us. Astronomy studied the 'movements of celestial bodies'. Chemistry endeavoured to penetrate the mystery of the structure and composition of matter.
These three physical sciences based their conceptions of the form of the world entirely upon the geometry of Euclid. Geometrical space was taken as physical space. No difference was distinguished between them, and space was taken apart from matter just as a box and its capacity may be examined independently of its contents.
Space was understood as an 'infinite sphere'. The infinite sphere was geometrically determined only from the centre, that is, from any point, by three radii at right angles to one another, and an infinite sphere was regarded as similar in all its physical properties to a finite sphere.
The question of the non-correspondence of geometrical, that is, of Euclidean three-dimensional space (whether infinite or finite) on the one hand with physical space on the other hand arose only very occasionally, and did not interfere with the development of physics in the directions which were possible to it.
This doubt was aroused, first, by attempts at a revaluation of geometrical values, that is, attempts either to prove the axioms of Euclid or to prove their incorrectness; and second, by the very development of physics, or more exactly of mechanics, that is, the part of physics dealing with motion, for this development led to the conviction that physical space could not be housed in geometrical space and continually reached beyond it. Geometrical space could be taken as physical space only by closing the eyes to the fact that in geometrical space everything is immovable, that it contains no time necessary for motion, and that the calculation of any figure resulting from motion such as a screw, for instance requires four co-ordinates.
Later on, the study of phenomena of light, electricity and magnetism, and also the study of the structure of the atom, necessitated a similar broadening of the concept of space.
The result of purely geometrical speculations concerning the correctness or incorrectness of the axioms of Euclid was twofold. On the one hand, a conviction arose that geometry was a purely speculative science dealing solely with principles and that it was entirely completed: it could neither be added to nor altered. It was also a science which could not be applied to all the facts that are met with and is true only under certain definite conditions, but which, within those conditions, is perfectly reliable and irreplaceable by anything else. On the other hand there arose a certain disappointment in the geometry of Euclid and a desire to remodel it, to rebuild it on a new basis, to broaden it, to make it a physical science which could be applied to all the facts that are met with without the necessity for arranging these facts in an artificial order. This second attitude can be said to have triumphed in science and thus considerably delayed its development. I shall revert to this later.
Kant's ideas of categories of space and time taken as categories of perception and thought have never entered into scientific, i.e. physical, thought, in spite of certain later attempts to introduce them within the compass of physics. Scientific (physical) thought proceeded apart from philosophical and psychological thought and always took time and space as having an objective existence outside us; in virtue of this it was always considered possible to express time and space relations mathematically.
But the development of mechanics and other branches of physics led to the necessity for recognising a fourth co-ordinate of space in addition to the three fundamental co-ordinates of length, breadth, and height. And the idea of the fourth co-ordinate, or the fourth dimension of space, gradually became more and more inevitable, though for a long time it remained a kind of "taboo".
The material for the construction of new hypotheses of space remained in the works of the mathematicians, Gauss, Lobatchevsky, Saccheri, Bolyai, and especially Riemann, who in the fifties of the 19th century was already considering the question of the possibility of a totally new understanding of space. There were no serious attempts at a psychological study of the problem of space and time. The idea of the fourth dimension remained for a long time shelved; it was regarded by specialists as purely mathematical and by non-specialists as mystical or occult.
But if we start from the moment of the appearance of this idea at the beginning of the 19th century and make a brief survey of the developments of scientific thought from that moment up to the present day, it may help us to understand the course which the further development of the idea may take. At the same time we may see what this idea tells us in regard to the fundamental problem of the form of the world.
As a matter of fact, neither of these propositions has any foundation whatever, and the acceptance of them as axioms arrests the progress of thought along the very lines where progress is most necessary. This will be dealt with later.
In our further discussion, of all the physical sciences we shall examine only physics proper. In physics, we shall have to pay most attention at first to mechanics: for since about the middle of the 18th century mechanics has assumed a predominant position in physics so much so that until quite recently it was considered both possible and probable that a means would be found of interpreting physical phenomena as phenomena of motion, asserted that this means had already been found, and that it explained not only physical phenomena but also psychic phenomena and phenomena of life.
At present one often meets with a division of physics into old and new, and in its chief lines this division may be accepted. But it should not be understood too literally.
I will now try to make a brief survey of the fundamental ideas of old physics which led to the necessity for building new physics, which has unexpectedly destroyed old physics; and then I will come to the ideas of new physics which lead to the possibility of building a new model of the Universe which destroys new physics just as new physics destroyed old physics.
Old physics lasted until the discovery of the electron. But even the electron was conceived by old physics as existing in the same artificial world, governed by Aristotelian and Newtonian laws, in which it studied visible phenomena; in other words, the electron was accepted as existing in the same world in which our bodies and other objects commensurable with them exist. Physicists did not understand that the electron belongs to another world.
Old physics was based on certain immovable foundations. The space and time of old physics possessed very definite properties. First of all, they could be examined and calculated separately, i.e. the being of a thing in space in no way affected or touched its being in time. Further, there was one space for all that exists and all that occurred in this space. Time also was one for all that exists and was measured always and for everything by one scale. In other words, it was considered possible to measure with one measure all movements possible in the Universe.
This principle in its modern meaning can be formulated in the following way: in the whole of the Universe and under all possible conditions, the laws of nature must be identical; in other words, a law which has been established at one place in the Universe must hold good at any other place in the Universe. Science, in studying phenomena on Earth and in the Solar System on this basis, assumed the existence of the same phenomena on other planets and in other star systems.
This principle, attributed to Aristotle, in reality was certainly never conceived by him in the form which it acquired in our times. The Universe of Aristotle differed greatly from the Universe as we conceive it. The thinking of the people of Aristotle's time differed greatly from the thinking of the people of our time. Many fundamental principles and many starting-points of thought, which we can accept as already established, had to be proved and established by Aristotle.
Aristotle endeavoured to establish the unity of laws in the sense of a protest against superstitions, against naοve magic, against naοve miracles, and so on. In order to understand the principle of Aristotle it is necessary to realise that he had still to prove that if in general dogs cannot speak in human language, then one particular dog, say, on the island of Crete, also cannot speak; or that if in general trees cannot move of themselves, then one particular tree also cannot move, and so on.
All this has of course been forgotten long ago, and from the principle of Aristotle there follows now the idea of the permanency of all physical concepts, such as motion, velocity, force, energy, etc. This means that what has once been regarded as motion always remains motion; what has once been regarded as velocity always remains velocity, ultimately becoming infinite velocity.
In its first meaning the principle of Aristotle is comprehensible and necessary and is nothing else than the law of the general consecutiveness of phenomena which belongs to logic. But in its modern meaning the principle of Aristotle is entirely wrong.
Even for new physics the concept of infinite velocity, which is exclusively based on the principle of Aristotle, has become impossible, and the principle of Aristotle must be completely abandoned before the planning of a new model of the Universe becomes possible. I shall return to this question later.
Here we are at once faced with the fact that physics operates with undefined and unknown quantities which, for the sake of convenience (or owing to the difficulty of definition) are taken as known quantities and even as quantities requiring no definition.
In physics, a distinction is made between quantities requiring definition and primary quantities, the idea of which is considered to be inherent in all people. Primary quantities do not require definition, for their meaning is clear to everyone. The properties of these quantities are determined by the idea which 'everyone connects with their name, and therefore everyone should look in himself for the indication of their properties'. So writes Prof. Chwolson in his Text-book of Physics.
He further refers to primary quantities:
This profusion of undefined and undefinable quantities is the main characteristic of the old physics. Of course, in a great many cases, it was impossible to avoid operating with unknown magnitudes, and it became the traditional "scientific" method not to recognise anything unknown, and to regard the "quantities" which entirely eluded definition as universally understood quantities, the idea of which was inherent in everyone. The natural result of the vast edifice which had been erected with tremendous labour became artificial and unreal.
In the definition of physics given above we meet with two undefined concepts: space and matter.
I have already dealt with space. As regards matter, Prof. Chwolson writes: 'In objectifying the cause of a sensation, that is, transferring this cause into a definite place in space, we conceive this space as containing something which we call matter or substance.'
Further, he writes: "The use of the term 'matter' was reserved exclusively for matter which is able to affect our organ of touch more or less directly."
Further, matter is divided into organised matter (of which living bodies and plants are composed) and non-organised matter.
This method of division instead of definition is applied in physics whenever definition is difficult or impossible, that is, in relation to all fundamental concepts. Later, we shall often meet with this fact.
The difference between organised matter and non-organised matter is determined only by external characteristics. The origin of organised matter is admitted to be unknown. Although the transition of non-organised matter into organised matter may be observed (feeding, breathing), it is admitted that such a transition takes place only in the presence and through the action of already existing organised matter. The mystery of the first transition remains hidden (Chwolson).
On the other hand we see that organised matter easily passes into non-organised matter, losing certain undefinable properties which we call life.
Many attempts have been made to regard organised matter as a particular case of non-organised matter and to explain all the phenomena that take place in organised matter (i.e. phenomena of life) as a combination of physical phenomena. But these attempts, and also attempts at the artificial creation of organised matter from non-organised matter, led to nothing and could neither create nor prove anything. In spite of this they left a very strong impress on general philosophies of life of a scientific kind, from the standpoint of which the "artificial creation of life" is recognised as not only possible but already partly attained. Followers of these philosophies regard the very name of organic chemistry, i.e. chemistry studying organised matter, as having merely a historical meaning, and define it as the "chemistry of hydrocarbons", although at the same time they cannot help admitting the special position of the chemistry of hydrocarbons and its difference from general inorganic chemistry.
Non-organised matter is in its turn divided into simple matter and composite matter (this becomes the province of chemistry). Composite matter consists of a so-called chemical compound of several simple matters. Every matter can be divided into very small parts called "particles". A particle is the smallest quantity of the given matter which is still capable of exhibiting at least the chief properties of this matter. The further divisions of matter molecule, atom, electron are so small that, taken separately, they do not possess any material properties, though this last fact is never sufficiently taken into account.
According to the most recent scientific ideas, non-organised matter consists of 92 elements or simple matters, though not all of them have as yet been discovered. There exists a hypothesis that the atoms of various elements are nothing but a combination of a certain number of atoms of hydrogen which, in this case, is taken as fundamental or primary matter. Several theories exist concerning the possibility of the transition of one element into another, and in some cases such a transition has been established which again contradicts the "principle of Aristotle".
Organised matter, or "hydrocarbons", actually consists of four elements hydrogen, oxygen, carbon, and nitrogen, with a negligible admixture of other elements.
Matter possesses many properties, such as mass, volume, density, etc., which are in most cases definable only relatively one to another.
The temperature of a body is recognised as depending on the motion of molecules. Molecules are considered to be in perpetual motion; as physics defines it, they are constantly colliding and scattering in all directions and returning again. The greater the motion, the greater the shocks when they collide, the higher the temperature (Brownian movement).
If this were possible in reality, it would mean approximately that, for instance, several hundreds of motor-cars, swiftly moving in different directions in a large square of a big city, crash into one another every minute and disperse in various directions while remaining intact.
It is very curious that a quick-motion cinematographic film produces such an illusion. Moving objects lose their individuality and appear to collide and fly off in different directions or pass through one another. [The author once saw a quick-motion cinematograph of the Place de la Concorde with motor-cars rushing from all directions and in all directions. And the impression was exactly as if the cars collided with one another every moment and remained all the time in the square, never leaving it. PDO]
How it can be that material bodies possessing mass, weight, and very complicated structure, moving at great velocity, collide and scatter without being broken up and destroyed, is not explained by physics.
One of the most important conquests of physics was the establishment of the principle of the conservation of matter. This principle consists in the recognition of the fact that matter is never and in no physical or chemical conditions created anew, nor does it disappear. Its total amount remains constant. With the principle of conservation of matter are connected the principles established later, the principle of conservation of energy and the principle of conservation of mass.
But, just as in the case of all other physical concepts, motion is not defined by physics. Physics only establishes the properties of motion duration, speed, and direction in space, without which properties a phenomenon cannot be called motion.
The division, and sometimes the definition, of these properties take the place of the definition of motion itself, and the established characteristics of the properties of motion are referred to motion itself. Thus motion is divided into rectilinear and curvilinear, continuous and non-continuous, accelerating and retarding, uniform and variable.
The establishment of the principle of the relativity of motion led to a whole series of conclusions. The question arose: If the motion of a material point can be determined only by its position in relation to other bodies or points, then how is the motion to be determined if the other bodies or points also move?
This question became especially complicated when it was established, not merely philosophically but fully scientifically with calculations and diagrams, that nothing in the Universe is motionless; that everything without exception moves in one way or another, and that one motion can be established only relatively to another.
But at the same time there were established cases of apparent immobility in motion. Thus it was established that separate component parts of a uniformly moving system of bodies maintain the same position relative to one another as though the system were stationary. Thus, things inside a swiftly moving railway carriage behave in exactly the same way as when the carriage is standing still. And in the case of two trains running on different tracks in the same direction or in different directions, it was established that their relative velocity is equal to the difference between, or the sum of, their respective velocities, according to the direction of movement. Thus two trains approaching one another will approach with a velocity equal to the sum of their respective velocities. For one train overtaking another, the second train will run in a direction opposite to its own with a velocity equal to the difference in velocity of the two trains. What is usually called the velocity of a train is the velocity ascribed to the train observed during its passage between two objects which are stationary for it for instance, between two stations, and so on.
The study of motion in general, and of vibratory and undulatory movements in particular, exercised a tremendous influence on the development of physics. Wave movements began to be regarded as a universal principle, and many attempts were made to reduce all physical phenomena to vibratory movements.
The measurement of quantities was based on certain principles, the most important of which was the principle of homogeneity, namely, that quantities conforming to the same definition and differing from one another only quantitatively were called homogeneous quantities, and it was considered possible to compare them and measure one in relation to another. As to quantities which differed in definition, it was considered impossible to measure them relatively one to another.
Unfortunately, as has already been shown, there were very few definitions of quantities in physics, and therefore definitions were generally replaced by their denominations.
As mistakes in the denomination could always occur, and qualitatively different quantities could be named similarly, physical measurements were unreliable all the more so because here again the principle of Aristotle was felt: that is, a quantity once recognised as a quantity of a certain order always remained a quantity of that order. Different forms of energy passed into one another, matter passed from one state into another, but space (or a part of space) always remained space, time always remained time, motion always remained motion, velocity always remained velocity, and so on.
On these grounds it was agreed to regard as incommensurable only those quantities which were qualitatively different. Quantities which differed merely quantitatively were regarded as commensurable.
The artificiality of measures in physics has certainly never been a secret, and for the realisation of this artificiality follow attempts to establish, for instance, the measure of length as a part of the meridian. Naturally, these attempts alter nothing, and parts of the human body, an "ell" or a "foot", taken as units of measure, or a "metre", i.e. part of a meridian, are equally arbitrary. In reality things bear their own measure in themselves, and to find the measure of things is to understand the world. Physicists have dimly guessed this, though they have never succeeded in even approaching these measures.
Prof. Planck in 1900 (this really belongs to new physics) constructed a system of "absolute units", taking as its basis "universal constants", namely:
Planck affirms that these quantities will retain their natural meaning so long as the laws of universal gravitation and of the propagation of light in a vacuum together with the two fundamental principles of thermodynamics remain unchanged; they will always be the same by whatever intelligent beings and by whatever methods they are determined.
But the law of universal gravitation and the law of propagation of light in a vacuum are the two weakest points in physics, because in reality they are not what they are taken to be. And therefore Planck's whole system of measures is very unreliable. What is interesting in it is not the result but only the principle, i.e. the recognition of the necessity for finding natural measures of things. The actual determination of absolute units of measure lies beyond the new model of the Universe.
The scientific formulation is:
There are observed phenomena between two bodies in space which can be described by presuming that two bodies attract one another with a force directly proportional to the product of their masses and inversely proportional to the square of the distance separating them.
The popular formulation is:
Two bodies attract one another with a force directly proportional to the product of their masses and inversely proportional to the square of the distance separating them.
In this second formulation the fact is entirely forgotten that the force of attraction is merely a fictitious quantity accepted only for a convenient description of phenomena. The force of attraction is regarded as really existing both between the Sun and the Earth and between the Earth and a falling stone. [The most recent electromagnetic theory of gravitational fields dogmatises the second view. PDO]
Prof. Chwolson writes in his Text-book of Physics:
'The tremendous development of celestial mechanics, entirely based on the law of universal gravitation taken as a fact, made scientists forget the purely descriptive character of this law and see in it the final formulation of an actually existent physical phenomenon.'
What is important in Newton's law is that it gives a very simple mathematical formulation which can be applied throughout the Universe and on the basis of which it is possible to calculate all movements, in particular the movements of celestial bodies, with astonishing accuracy. Newton certainly never established it as a fact that bodies are actually attracted by one another, nor did he establish why they are attracted or through the mediation of what.
How can the Sun influence the motion of the Earth through the void of space? How in general is it possible to conceive action through empty space? The law of gravitation does not give an answer to this question, and Newton himself was perfectly aware of this fact. Both he and his contemporaries, Huygens and Leibnitz, definitely warned against attempts to see in Newton's law the solution of the problem of action through empty space, and regarded this law merely as a formula for calculation. Nevertheless the tremendous achievements of physics and astronomy attained through the application of Newton's Law caused scientists to forget this warning, and the opinion was gradually established that Newton had discovered the force of attraction.
Prof. Chwolson writes:
'The term "action at a distance" designates one of the most harmful doctrines that ever prevailed in physics and retarded its progress; this doctrine admitted the possibility of immediate action by one object on another object at a certain distance from it, at a distance so great as to make immediate contact between the two impossible.
'In the first half of the 19th century the idea of action at a distance reigned supreme in science. Faraday
'At the present time the conviction that action at a distance should not be admitted in any domain of physical phenomena has obtained universal recognition.'
In the 18th century, phenomena of light were explained by the hypothesis of emission put forward by Newton in 1704. This hypothesis assumed that luminous bodies emit in all directions minute particles of a special light-substance which travel through space with tremendous velocity and, entering the eye, produce in it the impression of light. In this hypothesis Newton developed the ideas of the ancients. In Plato, the expression "light filled my eyes" is often found.
Later, mainly in the 19th century, when the attention of investigators was drawn to those results of the phenomena of light which could not be explained on the hypothesis of emission, another hypothesis obtained wide recognition, namely, the hypothesis of undulatory vibrations in ether. This hypothesis was first advanced by the Dutch physicist Huygens in 1690, but for a long time it was not accepted by science. Later on, investigations of the phenomena of diffraction definitely turned the scale in favour of the hypothesis of light waves as against the hypothesis of emission; and the subsequent work of physicists, mainly on the polarisation of light, for a time gained general recognition for this hypothesis.
In this hypothesis the phenomena of light are explained as analogous to the phenomena of sound. Just as sound results from the vibration of particles of the sonant body and is propagated through the vibration of particles of the air or some other elastic medium so, on this hypothesis, light results from the vibration of molecules of the luminous body and is propagated by means of vibrations in an exceedingly elastic ether which fills both interstellar space and the space between molecules.
During the 19th century the theory of vibrations gradually became the basis of the whole of physics. Electricity, magnetism, heat, light, even life and thought (purely dialectically, it is true) were explained by the theory of vibrations. And it cannot be denied that in the case of the phenomena of light and electromagnetics the theory of vibrations gave remarkably convenient and simple formulas for calculation. A whole series of remarkable discoveries and inventions was made on the basis of the theory of vibrations.
But the theory of vibrations required ether. Ether as a hypothesis was created for the explanation of very heterogeneous phenomena, and it was therefore endowed with strange and contradictory properties. It is omnipresent, it fills the whole Universe, pervades all its points, all atoms, and all interatomic space. It is continuous, and possesses perfect elasticity. Yet ether is so rarefied, thin, and permeable that all earthly and heavenly bodies pass through it without meeting with perceptible resistance to their movement. Its rarety is so great that if ether were to be condensed into a liquid, the whole of its mass within the limits of the system of the Milky Way could be contained in one cubic centimetre.
At the same time Sir Oliver Lodge considers the density of ether to be approximately a billion times greater than the density of water. From the latter point of view the world proves to be composed of a solid substance "aether" which is millions of times denser than a diamond; and matter, even the densest matter we know, is merely empty space, a bubble in the mass of aether.
Many attempts have been made to prove the existence of ether or to discover facts confirming its existence. Thus it was recognised that the existence of ether would be established if it were once proved that a ray of light moving faster than another ray of light changes its character in a certain way.
It is a known fact that the pitch of a sound rises or falls as the hearer approaches or retreats from it (Doppler's Principle). Theoretically this principle was considered applicable to light. This would have meant that a swiftly approaching or retreating object should change its colour (as the sound of an engine-whistle changes its pitch as it approaches or retreats). But owing to the structure of the eye and the speed of its perception it was impossible to expect that the eye would notice the change of colour even if such a change actually took place.
In order to establish the fact of the change of colour it was necessary to have recourse to the spectroscope, that is, to decompose a ray of light and observe the displacement of the lines of the spectrum.
The apparatus was mounted on a stone slab fixed upon a wooden float in a tank filled with mercury, and made one full revolution in six minutes. A ray of light from a special lamp fell on mirrors attached to the revolving float and partly passed through them and partly was reflected, one half going in the direction of the movement of the Earth and the other at right angles to it. This should have given a noticeable displacement of the interference fringes consequent upon the change of the velocity of light plus the velocity of the Earth while the other moved without this additional velocity. Both halves of the ray the half that was reflected and the half that was allowed to pass were caught by a system of mirrors and reflected back to a mirror which united the two halves and thus made it possible to observe whether or not displacement had occurred.
Observations were made at all times of the day and night, but no alteration in the interference fringes was observed. This fact was taken as an unexpected proof that there exists no relative movement between the earth and the ether and as confirmation of Fizeau's experiment, which had shown the impossibility of increasing the velocity of light by means of movement in the medium in which it is propagated.
From the standpoint of the original problem it was necessary to recognise that the experiment failed. But it disclosed another phenomenon, possibly much more significant than that which it attempted to establish. This was the fact that the speed of a ray of light cannot be increased. The ray of light moving with the Earth differed in no way from the ray of light moving at right angles to the direction of the movement of the earth in its orbit.
It was necessary to recognise as a law that the velocity of a ray of light is a constant and limiting quantity which cannot be increased. And this, in turn, explained why Doppler's principle was inapplicable to phenomena of light. At the same time it established the fact that the general law of the composition of velocities, which was the basis of mechanics, could not be applied to the velocity of light.
This would mean that if, for instance, we imagine a train moving at the rate of 30 kilometres a second, i.e. with the velocity of the movement of the Earth, and a ray of light overtaking or meeting it, then the composition of velocities will in this case be impossible. The velocity of light will not be increased by the addition to it of the velocity of the train and will not be decreased by the subtraction from it of the velocity of the train. In other words, the ray of light will light up the first and last carriages simultaneously independently of whether the train is retreating from the source of light or standing still, or is moving towards it.
At the same time it was established that no existing instruments or means of observation can intercept a moving ray. In other words, it is never possible to catch the end of a ray which has not yet reached its destination. In theory we may speak of rays which have not yet reached a certain point, but in practice we are unable to observe such rays. Consequently, for us, with our means of observation, the propagation of light is virtually instantaneous.
At the same time the physicists who analysed the results of the Michelson-Morley experiment explained its failure by the presence of new and unknown phenomena resulting from great velocities.
The first attempts to solve this question were made by Lorentz and Fitzgerald . The experiment could not succeed, was Lorentz's formulation of his propositions, for every body moving in ether itself undergoes deformation, namely, for an observer at rest, it contracts in the direction of motion. Basing his reasoning on the fundamental laws of mechanics and physics, he showed by means of a series of mathematical constructions that the Michelson-Morley installation necessarily suffered a contraction and that the amount of the contraction was exactly such as to counterbalance the displacement of the light waves consequent upon their direction in space, and thus to annul the results of the difference in velocity of the two rays.
Lorentz's conclusions as to the presumed contraction of a moving body gave rise in their turn to many explanations, and one of these explanations was put forward from the point of view of Prof. Einstein's special principle of relativity. But this relates to the new physics.
The new theory, says Prof. Chwolson, appears to be a return to the Newtonian emission theory although considerably altered. This new teaching is far from being completed, and its most important part, the quantum itself, still remains undefined. What a quantum is cannot be defined by new physics.
The theory of the atomic structure of light and electricity entirely altered the view on electrical and light phenomena. Science has ceased to see the fundamental cause of electrical phenomena in special states of ether and has returned to the old doctrine which admitted electricity to be a kind of substance which has real existence.
The same thing has happened with light. According to modern theories, light is a stream of minute particles rushing through space at the rate of 300,000 kilometres a second. It is not the corpuscles of Newton, but a special kind of matter-energy formed by electromagnetic vortices.
The materiality of the light stream was established by the experiments of Prof. Lebedeff of Moscow. Prof. Lebedeff proves that light has weight, that is to say, that when falling on bodies light produces a mechanical pressure on them. It is characteristic that at the beginning of his experiments to determine the weight of light, Lebedeff based them on the theory of the vibrations of the ether. This shows how the old physics confuted itself.
Lebedeff's discovery was very important for astronomy; for instance it explained certain phenomena which had been observed at the passing of the tail of a comet near the Sun. But it was chiefly important for physics, as it supplied a further confirmation of the unity of the structure of radiant energy.
The impossibility of proving the existence of the ether, the establishment of the limiting and constant velocity of light and, above all, the study of the structure of the atom, indicated the most interesting lines of the development of the new physics.
Thus it is presumed that the success or unsuccess of the conclusions of mathematical physics might depend upon three factors:
There was a time when the importance of mathematical physics was greatly exaggerated.
It was expected that it was precisely mathematical physics which should have served the principal course of development of physics as a science. This, however, is quite erroneous. In the deductions of mathematical physics there are a great number of essential defects. In the first place, in almost every case it is only in the first rough approximation that they correspond with the results of direct observation. This is caused by the fact that the premises of mathematical physics can be considered sufficiently exact only within the narrowest limits; moreover these premises generally disregard a whole series of collateral circumstances, the influence of which outside these narrow limits cannot be neglected. Therefore, the deductions of mathematical physics correspond to ideal cases which cannot be practically realised and are often far removed from actuality.
And further:
It should be added that the methods of mathematical physics make it possible to solve special problems in hardly any but the simplest cases, especially so far as the form of the body is concerned. But practical physics cannot limit itself to these cases and is continually faced with problems which mathematical physics is incapable of solving. Moreover, the results of the deductions of mathematical physics are often so complicated that their practical application proves to be impossible.
In addition to this should be mentioned yet another very characteristic property of mathematical physics, namely, that as a rule its deductions cannot be formulated otherwise than mathematically, and lose all their meaning and importance if an attempt is made to interpret them in the language of facts.
The new physics which developed from mathematical physics possesses many of the properties of the latter.
There exists an enormous literature devoted to the exposition, explanation, popularisation, criticism, and elaboration of the principles of Einstein but, owing to the close relationship between the theory of relativity and mathematical physics, deductions from this theory are difficult to formulate logically. And the fact must be accepted that neither Prof. Einstein himself nor any of his numerous followers and interpreters has succeeded in explaining the meaning and essence of his theories in a clear and comprehensible way.
One of the first reasons for this fact is pointed out by Mr Bertrand Russell in his popular book, The A B C of Relativity. He writes that the name "the theory of relativity" misleads people, and that a tendency to prove that everything is relative is generally ascribed to Prof. Einstein, while in reality he endeavours to discover and establish that which is not relative. And it would be still more exact to say that Prof. Einstein endeavours to establish the relation between what is relative and what is not relative.
Further, Prof. Chwolson writes of the theory of relativity:
The foremost place in Einstein's theory of relativity is occupied by a perfectly new and, at first glance, incomprehensibly strange conception of time. Much effort and prolonged work on oneself are needed to become used to it. But it is infinitely more difficult to accept the numerous consequences which follow from the principle of relativity and affect all branches of physics without exception. Many of these consequences obviously contradict what is usually, though often without adequate motive, called "common sense". Some of these may be called the paradoxes of the new doctrine.
Einstein's ideas about time may be formulated as follows:
Each of two systems moving relatively to each other has in fact its own time, perceived and measured by an observer moving with the particular system.
The concept of simultaneity in the general sense does not exist. Two events which occur at different places may appear simultaneous to an observer at one point, whereas for an observer at another point they may occur at different times. It is possible that for the first observer the same phenomenon may occur earlier, and for the second, later (Chwolson).
Further, of the ideas of Prof. Einstein, Prof. Chwolson singles out the following:
In making use exclusively of Lorentz's transformations, Einstein affirms that a rigid rod moving in the direction of its length is shorter than the same rod when it is in a state of rest, and the more quickly such a rod moves, the shorter it becomes. A rod moving with the velocity of light would lose its third dimension. It would become a cross-section of itself.
Lorentz himself affirmed that an electron actually disappeared when moving with the velocity of light.
These affirmations cannot be proved, since the contractions, even if they really occur, are too negligible with all possible practical velocities. A body moving with the velocity of the Earth, i.e. 30 kilometres a second, must, according to the calculations of Lorentz and Einstein, undergo contraction by 1/200,000 of its length; that is, a body 200 metres long would contract by 1 millimetre.
Further, it is interesting to note that the supposition as to the contraction of a moving body radically contradicts the principle established by new physics, of the increment of energy and mass in the moving body. This latter principle is perfectly correct, although it has remained unelaborated.
As will be seen later, this principle, in its full meaning, which has not yet been revealed in new physics, is one of the foundations of the new model of the Universe.
Passing to Einstein's own exposition of his fundamental theory, we see that it consists of two "principles of relativity", the "special principle" and the "general principle".
The "general principle of relativity" is introduced where it becomes necessary to make the idea of the infinity of space-time agree with the laws of the density of matter and the laws of gravitation in the space accessible to observation.
To put it briefly, the "special" and the "general" principles of relativity are necessary for agreement between contradictory theories on the borderline of old and new physics.
The fundamental tendency of Einstein is to regard mathematics, geometry, and physics as one whole.
The principle is certainly quite correct: the three ought to constitute one. But "ought to constitute" does not mean that they do constitute.
The confusion of these two concepts is the chief defect of the theories of relativity.
In his book The Theory of Relativity Prof. Einstein writes:
Space is a three-dimensional continuum.... Similarly the world of physical phenomena which was briefly called "world" by Minkovsky is naturally four-dimensional in the space-time sense. For it is composed of individual events, each of which is described by four numbers, namely three space co-ordinates and a time co-ordinate....
That we have not been accustomed to regard the world in this sense as a four-dimensional continuum is due to the fact that in physics, before the advent of the theory of relativity, time played a different and more independent rτle as compared with the space-time co-ordinates. It is for this reason that we have been in the habit of treating time as an independent continuum. As a matter of fact, according to classical mechanics, time is absolute, i.e., it is independent of the position and the condition of the system of co-ordinates....
The four-dimensional mode of consideration of the "world" is natural on the theory of relativity, since according to this theory time is robbed of its independence....
But the discovery of Minkovsky, which was of importance for the formal development of the theory of relativity, does not lie here. It is found rather in the fact of his recognition that the four-dimensional space-time continuum of the theory of relativity, in its most essential formal properties, shows a pronounced relationship to the three-dimensional continuum of Euclidean geometrical space. In order to give due prominence to this relationship, however, we must replace the usual time co-ordinate t by an imaginary magnitude i.ct proportional to it
The formula i.ct means that the time of every event is taken not simply by itself, but as an imaginary quantity in relation to the velocity of light, i.e. that a purely physical concept is introduced into the presumed "meta-geometrical" expression.
The time-duration t is multiplied by the velocity of light, c, and by the square root of -1 which, without changing its magnitude, makes it an imaginary quantity.
This is quite clear. But what is necessary to note in relation to the passage quoted above is that Einstein regards Minkovsky's "world" as a development of the theory of relativity, whereas in reality the special principle of relativity is built on the theory of Minkovsky. If we suppose that the theory of Minkovsky is derived from the principle of relativity, then again, just as in the case of the theory of Fitzgerald and Lorentz relating to the lengthwise contraction of moving bodies, it remains incomprehensible on what basis the principle of relativity is actually built.
In any case, the building of the principle of relativity requires specially prepared material.
In the very beginning of his book, Prof. Einstein writes that in order to make certain deductions from the observation of physical phenomena agree with one another, it is necessary to revise certain geometrical concepts. He writes: "Geometry" means "land-measuring". Both mathematics and geometry owe their origin to the need to know something of the properties of real things.
On the basis of this, Prof. Einstein considers it possible to "supplement geometry", that is, for instance, to replace the concept of straight lines by the concept of rigid rods. Rigid rods are subject to changes under the influence of temperature, pressure, etc.; they can expand and contract. All this must, of course, greatly alter "geometry".
Einstein writes:
Geometry which has been supplemented in this way is obviously a natural science, and is to be treated as a branch of physics.
I attach special importance to the view on geometry expounded here because, without it, it would have been impossible to construct the theory of relativity.
And again: Euclidean geometry must be abandoned.
The next important point in Einstein's theory is his justification of the mathematical method that he applies:
Experience has led to the conviction that, on the one hand, the principle of relativity (in the restricted sense) [i.e. the principle of the relativity of velocities in classical mechanics. PDO] holds true, and that on the other hand the velocity of the transmission of light in vacuo has to be considered to be a constant.
According to Einstein, the combination of these two propositions supplies the law of transformations for the four co-ordinates determining the place and the time of an event:
Every general law of nature must be so constituted that it is transformed into a law of exactly the same form when, instead of the space-time variables of the original co-ordinate system, we introduce new space-time variables of another co-ordinate system. In this connection the mathematical relation between the magnitudes of the first order and the magnitudes of the second order is given by the Lorentz transformation. Or, in brief: General laws of nature are co-variant with respect to Lorentz transformations.
Einstein's assertion that the laws of nature are co-variant with Lorentz's transformations is the clearest illustration of his position. Starting from this point he considers it possible to ascribe to phenomena the changes which he finds in the transformations. This is precisely the method of mathematical physics which was condemned long ago and which is mentioned by Prof. Chwolson in the passage quoted above.
In The Theory of Relativity, there is a chapter under the title Experience and the Special Theory of Relativity:
To what extent is the special theory of relativity supported by experience? This question is not easily answered.
The special theory of relativity has crystallised out from the Maxwell-Lorentz theory of electromagnetic phenomena. Thus all facts of experience which support the electromagnetic theory also support the theory of relativity.
Prof. Einstein feels very acutely the necessity of facts for establishing his theories on firm ground. But he succeeds in finding these facts only in respect of invisible quantities electrons and ions. He writes:
Classical mechanics required to be modified before it could come into line with the demands of the special theory of relativity. For the main part, however, this modification affects only the laws for rapid motions, in which the velocities of matter are not very small as compared with the velocity of light. We have experience of such rapid motions only in the case of electrons and ions; for other motions the variations from the laws of classical mechanics are too small to make themselves evident in practice.
The classical principle of relativity, relating to three-dimensional space with the co-ordinate of time t (a real quantity) is violated by the fact of the constant velocity of light.
But the fact of the constant velocity of light is violated by the curvature of a ray of light in gravitational fields. This requires a new theory of relativity and a space, determined by Gaussian co-ordinates, applicable to non-Euclidean continua.
Gaussian co-ordinates differ from Cartesian by the fact that they can be applied to any kind of space, independently of the properties of that space. They adapt themselves automatically to any space, whereas the Cartesian co-ordinates require a space of special definite properties, i.e. geometrical space.
In continuing the comparison of the special and the general theories of relativity, Einstein writes:
The special theory of relativity has reference to domains in which no gravitational field exists. In this connection a rigid body in the state of motion serves as a body of reference, i.e. a rigid body the state of motion of which is so chosen that the proposition of the uniform rectilinear motion of "isolated" material points holds relatively to it.
In order to make clear the principles of the general theory of relativity, Einstein takes the space-time domain as a disc uniformly rotating around its centre on its own plane. An observer situated on this disc regards the disc as being "at rest". He regards the force acting upon him, and generally upon all bodies which are at rest in relation to the disc, as the action of the gravitational field:
The observer performs experiments on his circular disc with clocks and measuring rods. In doing so, it is his intention to arrive at exact definitions for the signification of time and space data with reference to the circular disc.
To start with, he places one of two identically constructed clocks at the centre of the disc, and the other on the edge of the disc, so that they are at rest relative to it....
Thus on our circular disc, or, to make the case more general, in every gravitational field, a clock will go more or less quickly according to the position in which the clock is situated (at rest). For this reason it is not possible to obtain a reasonable definition of time with the aid of clocks which are arranged at rest with respect to the body of reference. A similar difficulty presents itself when we attempt to apply our earlier definition in such a case....
The definition of the space co-ordinates also presents insurmountable difficulties. If the observer (moving with the disc) applies his standard measuring-rod (a rod which is short as compared with the radius of the disc) tangentially to the edge of the disc, then, ... the length of this rod will be less since moving bodies suffer a shortening in the direction of the motion. On the other hand, the measuring-rod will not experience a shortening in length if it is applied to the disc in the direction of the radius....
For this reason non-rigid (elastic) reference-bodies are used, which are as a whole not only moving in any way whatsoever, but which also suffer alterations in form ad. lib. during their motion. Clocks, for which the law of motion is of any kind, however irregular, serve for the definition of time. We have to imagine each of these clocks fixed at a point on the non-rigid (elastic) reference-body. These clocks satisfy only the one condition, that the "readings" which are observed simultaneously on adjacent clocks (in space) differ from each other by an infinitely small amount. This non-rigid (elastic) reference-body which might appropriately be termed a "reference-mollusc", is in the main equivalent to a Gaussian four-dimensional co-ordinate system chosen arbitrarily. That which gives the "mollusc" a certain comprehensibleness as compared with the Gauss co-ordinate system is the (really unjustified) formal retention of the separate existence of the space co-ordinates as opposed to the time co-ordinate. Every point of the "mollusc" is treated as a space-point, and every material point which is at rest relatively to it is at rest so long as the "mollusc" is considered as reference-body. The general principle of relativity requires that all these "molluscs" can be used as reference-bodies with equal right and equal success in the formulation of the general laws of nature; the laws themselves must be quite independent of the choice of mollusc.
In respect of the fundamental question as to the form of the world, Einstein writes:
If we ponder over the question as to how the Universe, considered as a whole, is to be regarded, the first answer that suggests itself is surely this: As regards space (and time) the Universe is infinite. There are stars everywhere, so that the density of matter, although very variable in detail, is nevertheless on the average everywhere the same. In other words: However far we might travel through space, we should find everywhere an attenuated swarm of fixed stars of approximately the same kind and density.
This view is not in harmony with the theory of Newton. The latter theory rather requires that the Universe should have a kind of centre in which the density of the stars is a maximum, and that as we proceed outwards from this centre the group-density of the stars should diminish until finally, at great distances, it is succeeded by an infinite region of emptiness. The stellar Universe ought to be a finite island in the infinite ocean of space.
The reason why an unbounded Universe is impossible is that, according to the theory of Newton, the intensity of the gravitational field at the surface of a sphere filled with matter, even if this matter is of very small density, would increase with increasing radius of the sphere, and would ultimately become infinite, which is impossible....
The development of non-Euclidean geometry led to the recognition of the fact that we can cast doubt on the infiniteness of our space without coming into conflict with the laws of thought or with experience.
Admitting the possibility of similar conclusions, Einstein describes the world of two-dimensional beings on a spherical surface.
In contrast to ours, the Universe of these beings is two-dimensional; but, like ours, it extends to infinity.
This surface of the world of two-dimensional beings would constitute "space" for them. This space would possess very strange properties. If the spherical-surface beings were to draw circles in their "space", that is, on the surface of their sphere, these circles would increase up to a certain limit, and would then begin to decrease:
The Universe of these beings is finite and yet has no limits.
Einstein comes to the conclusion that the spherical-surface beings would be able to determine that they are living on a sphere and might even find the radius of this sphere if they were able to examine a sufficiently great part of the surface:
But if this part is very small indeed, they will no longer be able to demonstrate that they are on a "spherical" world and not on a Euclidean plane, for a small part of a spherical surface differs only slightly from a piece of a plane of the same size.
Thus if the spherical-surface beings are living on a planet of which the Solar System occupies only a negligibly small part of the spherical Universe, they have no means of determining whether they are living in a finite or an infinite Universe, because the "piece of the Universe" to which they have access is in both cases practically plane, or Euclidean.
To this two-dimensional sphere-universe there is a three-dimensional analogy, namely, the three-dimensional spherical space which was discovered by Riemann. Its points are likewise all equivalent. It possesses a finite volume which is determined by its "radius".
It is easily seen that the three-dimensional spherical space is quite analogous to the two-dimensional spherical surface. It is finite (that is, of finite volume) and has no bounds.
It may be mentioned that there is yet another kind of curved space, "elliptical space". It can be regarded as a curved space in which the two "counterparts" are identical.... An elliptical universe can thus be considered to some extent as a curved universe possessing central symmetry.
It follows from what has been said that closed spaces without limits are conceivable. From amongst these, the spherical space (and the elliptical) excels in its simplicity, since all points in it are equivalent. As a result of this discussion, a most interesting question arises for astronomers and physicists, and that is whether the Universe in which we live is infinite, or whether it is finite in the manner of the spherical universe. Our experience is far from being sufficient to enable us to answer this question. But the general theory of relativity permits of our answering it with a moderate degree of certainty, and in this connection the difficulty mentioned earlier (from the point of view of the Newtonian theory) finds its solution.
The structure of space according to the general theory of relativity differs from that generally recognised:
According to the general theory of relativity, the geometrical properties of space are not independent, but they are determined by matter. Thus we can draw conclusions about the geometrical structure of the Universe only if we base our considerations on the state of the matter as being something that is known. We know from experience that ... the velocities of the stars are small as compared with the velocity of transmission of light. We can thus as a rough approximation arrive at a conclusion as to the nature of the Universe as a whole, if we treat the matter as being at rest.
We might imagine that as regards geometry, our Universe behaves analogously to a surface which is irregularly curved in its individual parts, but which nowhere departs appreciably from a plane: something like the rippled surface of a lake. Such a universe might fittingly be called a quasi-Euclidean universe. As regards its space it would be infinite. But calculation shows that in a quasi-Euclidean universe the average density of matter would necessarily be nil. Thus such a universe could not be inhabited by matter everywhere: it would present to us an unsatisfactory picture.
If we are to have in the universe an average density of matter which differs from zero, however small may be that difference, then the Universe cannot be quasi-Euclidean. On the contrary the results of calculation indicate that if matter be distributed uniformly, the universe would necessarily be spherical (or elliptical). Since in reality the detailed distribution of matter is not uniform, the real Universe will deviate in individual parts from the spherical, i.e. the Universe will be quasi-spherical. But it will be necessarily finite. In fact the theory supplies us with a simple connection between the space-expanse of the Universe and the average density of matter in it.
The last proposition is treated in a somewhat different manner by Prof. A. S. Eddington in his book, Space, Time and Gravitation:
After mass and energy there is one physical quantity which plays a very fundamental part in modern physics, known as Action. Action here is a very technical term, and is not to be confused with Newton's "Action and Reaction". [Action is determined as energy multiplied by time (Chwolson) PDO] In the relativity theory in particular this seems in many respects to be the most fundamental thing of all. The reason is not difficult to see. If we wish to speak of the continuous matter present at any particular point of space and time, we must use the term density. Density multiplied by volume in space gives us mass, or what appears to be the same thing, energy. But from our space-time point of view, a far more important thing is density multiplied by a four-dimensional volume of space and time; this is action. The multiplication by three dimensions gives mass or energy; and the fourth multiplication gives mass or energy multiplied by time. Action is thus mass multiplied by time, or energy multiplied by time, and is more fundamental than either.
Action is the curvature of the world. It is scarcely possible to visualise this statement, because our notion of curvature is derived from surfaces of two-dimensions in a three-dimensional space, and this gives too limited an idea of the possibilities of a four-dimensional surface in space of five or more dimensions. In two dimensions there is just one total curvature, and if that vanishes the surface is flat or at least can be unrolled into a plane.
Wherever there is matter there is action and therefore curvature; and it is interesting to notice that in ordinary matter the curvature of the space-time world is by no means insignificant. For example, in water of ordinary density the curvature is the same as that of space in the form of a sphere of radius 170,000,000 kilometres. The result is even more surprising if expressed in time units; the radius is about half an hour.
It is difficult to picture quite what this means; but at least we can predict that a globe of water of 170,000,000 km. radius would have extraordinary properties. Presumably there must be an upper limit to the possible size of a globe of water. So far as I can make out, a homogeneous mass of water of about this size (and no larger) could exist. It would have no centre, and no boundary, every point of it being in the same position with respect to the whole as every other point of it like points on the surface of a sphere with respect to the surface. Any ray of light after travelling an hour or two would come back to the starting point. Nothing could enter or leave the mass, because there is no boundary to enter or leave by; in fact it is co-extensive with space. There could be no other world anywhere else, because there isn't an "anywhere else".
An exposition of the theories of new physics which stand apart from "relativity" would take too much space. The study of the structure of light and electricity, the study of the atom (the theories of Bohr), and especially the study of the electron (the quantum theory), lead physics along entirely right lines, and if physics really succeeded in freeing itself from the above-mentioned impediments which arrest progress, and also from unnecessarily paradoxical theories of relativism, it would some day discover that it knows much more about the true nature of things than might be supposed.
OLD PHYSICS: