Albert Einstein explained his way of thinking and the reason why he was so appealed for reaching the truth. He had the impression that « youth is intentionally being deceived by the state through lies. » Thence, « [His] mistrust of every kind of authority grew out of this experience . ». This attitude never left him and has been tempered by a better insight into causal connections. His epistemological credo was : « I see on the one side the totality of sense experiences and, on the other, the totality of the concepts and propositions that laid down in books.". The latter block get meaning or content only through its connection with the former. The degree of certainty with which this connection, or intuitive linkage, can be undertaken, and nothing else, differentiates empty fantasy from scientific "thruth". The system of concepts is a creation of man, together with the rules of syntax, which constitute the structure of the conceptual systems. A proposition is correct if , within a logical system, it is deduced according to the accepted logical rules. So, a correct proposition borrows its "truth" from the truth-content of the system to which it belongs. In reference to David Hume, Albert Einstein underline that certain concepts, as for example that of causality, cannot be deduced from the material of experience by logical methods. Even more, he said : "All concepts, even those closest to experience, are from the point of view of logic freely chosen posits, just as is the concept of causality, which was the point of departure for this inquiry in the first place."
At the beginning of the XX century, "all physicists of the previous century saw in classical mechanics a firm and definitive foundation for all physics, indeed for the whole of natural science, and that they never grew tired in their attemps to base Maxwell's theory of electromagnetism, which, in the meantime, was slowly beginning to win out, upon mechanics as well."
After, this remark, he gave us two points of view from which physical theories should be analyzed :
1) (scope) the theory must not contradict empirical facts;
2) (inner perfection) the "naturalness" or "logical simplicity" of the premises (the basic concepts and the relations between them)
Then, he starts the critique of mechanics as the basis of physics.
1) From the confirmation by experiment point of view, the incorporation of wave optics into the mechanical picture of the world, interpreted as undulatory motion in a elastic body (ether), implies two types of matter with complicated interactions between them. The ether had to lead a ghostly existence alongside the rest of matter and it seemed to offer no resistance whatever to the motion of "ponderable" bodies.
At the beginning of the XXI century, an attentive reader could have asked if such a critique is always written on the agenda of today theories or not (dark matter, dark energy) ?
2) From the inner perfection point of view:
- (a generalization of Newton's like theory - masses and their interaction - has no future) First in line, he said, is Mach's argument: " From a purely geometrical description stanpoint, all "rigid" coordinate systems are logically equivalent. However, the equations of mechanics (i.e. the law of inertia) claim validity only when referred to a specific class of such systems (i.e. the "inertial systems") for which there is no significance as material object. So, the need for this specific choice has to be searched by someting that exits beyond the objects (masses, distances) included in the theory. Thence, it appeared at first glance that a reasonable theory of inertia would have to depend upon the interaction of the masses. However, it presupposes implicitly that the basic theory should be of the general type of Newton's mechanics: masses and their interaction as the original concepts. But, such an attempt at a resolution does not fit into a consistent field theory, as will be recognized;
- (having to turn away from the theory of action at a distance) the second argument referred to the contrast between the precision of the law of motion and the arbitrariness of the expression for the force or the potential energy when one dropped the argument that the forces depend only on the coordinates and not on their derivatives with respect to time. This insightsuggests a turning away from the theory of action at a distance;
- Third in place : one internal asymetry of the theory is that inertial mass that occurs in the law of motion also appears in the law of the gravitational force, but not in the expresions for the other forces;
- Fourth argument : the division of energy into two essentially different parts, kinetic and potential energy, must be felt to be unatural as H. Hertz felt this and attempted to free mechanics from the concept of potential energy (i. e. from the concept of force);
After this analysis, Albert Einstein defined what he considered to be an impressive theory: "the more impressive, the greater the simplicity of its premises.". Hence the deep impression that classical thermodynamics made upon him.
At student time, the Maxwell's theory was his most fascinating subject since it appeared revolutionary because of the transition from action at a distance to fields as a fundamental variables (i.e. expression of the elementary law through differential equations). He underlined that the relation of the speed of light to the electric and magnetic absolute system and the relation of the index of refraction to the dielectric constant and the relation between the reflection coefficient of a body and its metallic conductivity were like a revelation;
The insight into the essence of electromagnetic theory was difficult since electric and magnetic "field intensities" and displacements" were treated as equally elementary variables. Matter appeared as the bearer of the field, not space. This implied that the carrier of the field should have velocity, and this was naturally to apply to the vacuum (ether).
According to Einstein, the merit of H. A. Lorentz was to explain that action at the distance is replaced by the field, which also decribes the radiation. Taking into account gravitation was possible by enriching the structure of the field by expanding Maxwell's field laws. By this step, others could follow. Here, Einstein mentionned a key point about dualism : material point in Newton's sense and the field as continuum are used as elementary concept side by side. Kinetic energy and field energy appear as essentially different things. However, according to Maxwell's theory, the magnetic field of a moving electric charge represents inertia. "Why not then the whole of inertia ?", he asked. Then only field energy would be left, and the particle would be merely a domain containing an especially high density of field energy. In that case, one could hope to deduce the concept of the mass point together with the equations of motion of the particles from the field equations - the disturbing dualism would have been removed. But, the linearity of Maxwell's equations did not permit the derivation of the equilibrium of the electricity that constitutes a particle. Only different, nonlinear field equations could possibly accomplish such a thing. Even if, no method existed for discovering them, one could believe that it would be possible to find a secure foundation for all of physics upon the path so successfully initiated by Faraday and Maxwell.
So, the revolution begun by the introduction of the field will continue.
Independently, an other fundamental crisis took place, which was owned to Max Planck's investigations into heat radiation (1900).
From the starting point of Kirchhoff results, the energy density and the spectral composition of radiation in a cavity enclosed by impervious walls of the temperature T, must be independent of the nature of the walls. In other words, the monochromatic density of radiation is a universal function of the frequency and of the absolute temperature. What is this function ? According to Maxwell's theory the radiation had to exert a pressure on the walls determined by the total energy density. Boltzmann connected the empirical Stefan's law with the basis of Maxwell's theory by means of pure thermodynamics. Thence, W. Wien found that the universal function of two vaiables v and T have a form which exlusively depends on a universal function of one variable v/T. So, Planck found a statement that rendered the measurements very well. This statement relies on h and k, two fundamental constants. The first led to quantum theory. What is possible to derive it theoretically ?
The Planck's resaonning : by using the kinetic theory of gases and the relations between a irreversible macrostate and reversible microstates, Plank applied the Boltzmann's principle to a system consisting of a very many resonators of the same frequency v. Then, he expressed the finite number of microstates belonging to the macrostates by dividing the total energy into a large but finite number of identical microenergy elements, which have the magnitude of hv, a finite value, a quanta.
However, according to A. Einstein, this form of reasonning contradicts the mechanical and electrodynamic basis. The energy of a mechanical structure capable of oscillations as well as the energy of radiation can be transferred only in quanta - in contradiction to the laws of mechanics and electrodynamics. So, without having a substitute for classical mechanics, A. Einstein could nevertheless see to what kind of consequences this law of temperature radiation leads for the photoelectric effect and for other phenomena of the transformation of radiation energy, as well as forthe specific heat of solid bodies. But, all of his attempts to adap the theoritical foundation of physics to this new knowledge failed completly.
As a miracle, as the highest form of musicality in the sphere of thought, from this insecure and contradictory foundation, N. Bohr's unique instinct and sensitivity discovered the principal laws of the spectral lines and the electron shelles of the atoms, together with their significance for chemistry.
During these years, A. Einstein's main question was : "what general conclusion can be drawn from radiation formula concerning the structure of radiation and even more generally concerning the electromagnetic foundation of physics ?
As a prerequisite, A. Einstein had investigated fluctuation phenomena related to the Brownian motion in order to find facts that would guarantee as much as possible the existence of atoms of definite finite size. Hence, he developped the statistical mechanics and the molecular kinetic theory of thermodynamics based upon the previous investigations of Boltzmann and Gibbs.
After this success of the theory of Brownian motion, he went back to the study concerning the constitution of radiation from Planck's formula. First, he considered the average kinetic energy of a freely moving, quasi-monochromatically reflecting mirror in a space filled by radiation. This mirror would have to go through a kind of Brownian movement. Thence, he calculated its mean kinetic energy. Thence, from the Maxwell's theory, he calculated the random fluctuation of the pressure exerted upon the mirror because the wave packets, constituting the radiation, interfere with one another. He found that, in such a case, these pressure variations are by no means sufficient to impart to the mirror the average kinetic energy of its Brownian motion. So, as a logical consequence, there exist a second type of pressure variations, not derivable from Maxwell's theory. As a consequence, He guessed that radiation energy consists of indivisible point-like localized quanta of energy hv, and momentum hv/c, which are refected individed. He underlined that this way of looking give an type of immediate reality to Planck's quanta. Therfore, the radiation must possess a kind of molecular structureas far as its energy is concerned, which contradicts Maxwell's theory. The other approach about radiation based on Boltzmann's entropy probability relation, probability taken to equal to statistical temporal frequency, lead to the same result. So, the dual nature of radiation, and of material corpuscule, is a major property of reality.
Shortly after 1900, A. Einstein had the conviction, from reflections of the type above, that neither mechanics nor electrodynamics could claim exact validity.
After, desesperately trying to extract the true laws from the facts, he came to the conviction that only the discovery of a universal formal principle could lead us to assured results.
Here, the attentive reader wonder if data analysis approaches have aleready learnt lessons or not from this return on experience.
Thence , He underlined, for the second time the example of thermodynamics and its general theorem: "the laws of nature are such that it is impossible to construct a perpetuum mobile of the first and second kind. So, A. Einstein spent ten years of reflections to find an answer to the question : How could such a universal principle be found ?
In classical physics, in the transition from one intertial system to anather, the two assumptions below are mutually incompatible:
1) the constancy of the light velocity;
2) the independence of the laws from the choice of inertial system;
After an in-depth reflexions about the signifcance of the spatial coordonates and time fixation of an event in physics, A. Einstein reach the following result. The insight for the special theory of relativity is this : "the assumptions, mentionned above, are compatible if relations of a new type ("Lorentz transformation) are postulated for the conversion of coordinates and times of events.".
A. Einstein mentionned the importance of philosophers like David Hume whom support his type of critical resasonning required for the discovery of the axiom of the absolute and arbitrary character of time . A. Einstein had the need to go beyond Saint-Augustine's observation: "So what is time?" If no one asks me, I know; if I want to respond to this request, I ignore it. In that sense, David Hume was certainly a great help.
Soon after this, he mentionned the contribution of Minkowsky. Before Minkowsky's investigation it was necessary to carry ou a Lorentz trnsformation on a law in order to test its invariance under such transformations. After his contribution , the mathematical form of the law itself guarantees its invariance under Lorentz transformations. Thence, the four dimensional tensor calculus achieved the same thing for the four dimensionnal space that the ordinary vector calculus achived for the three spatial dimentions. So, the Lorentz transformation is nothing but a rotation of the coordinate system in the four dimensionnal space.
A this stage of the development of the theory, one must admit its inconsistency because it introduced two kinds of physical things: 1) mesuring rods and clocks; 2) all other things like the electromagnetic field, the material point. These things should emerge from the basic equations as theoretically sekf-syfficient entities. However, this is only a step beyond a more general and complete theory since, at this stage, the postulates of the theory are not strong enough to deduce from them equations of events sufficiently complete and sufficiently free from arbitrariness in order to base upon such a foundation a theory of measuring rods and clocks. From this, one must not fall in a trap which consists of perceiving that distances are physical entities of a special type, intrinsically different from other physical variables. Thence reducing physics to geometry.
Nevertherless, physics owes two insights of definitive nature to the special theory of relativity:
1) there is no such thing as simultaneity of distant events;
2) the principles of the conservation of linear momentum and of energy are fused into one single principle. The inert mass of an isolated system is identical with its energy, thus eliminating mass as an indemendent concept.
The special theory of relativity owes its origin to Maxwell's equations of the lectromagnetic field. Conversely, the latter can be grsped formally in satisfactory fashion only by the way of the special theory of relativity. Maxwell's equations are the simplest Lorents-invariant field equations that can be postulated for an antisymmetric tensor derived from a vector field.
However from quantum phenomena, one knows that Maxwell's theory does not do justice to the energetic properties of radiation. So, Maxwel's theory would have to be modified in a naturel fashion. However, the special theory of relativity offers no adequate foothold. Moreover, it offers non answer to Mach's question : "how does it come about that inertial systems are physically distinguised above all other coordinate systems ?
A. Einstein tries to find the total physical field which consists of a scalar field (gravitation) and a vector field (electromagnetic field) as a starting point, and might be more complicated types of fields. However a good theory must satisfy the condition that: the acceleration of a system falling freely in a given gravitational field is independent of the nature of the falling system. This must be aligned with the following things :
1) the intial mas of a physical system increases with the total energy;
2) the gravitational mass of a body is exactly equal to its inertial mass;
A key for the problem was : In a gravitational field, things behave as they do in space free of gravitation, if one introduces into it, in place of an "intertiel system", a frame of reference accelerated relative to the former. Then, if one interprets the behavior of a body with respect to the latter frame of reference as caused by a "real" gravitational field, it is possible to regard this frame as an "inertial system" with as much justification as the original reference systems. As a consequence, th concept of "inertial system" becomes completely empty. The concept of "acceleration relative to space" then loses all meaning and with it the principle of inertia along with the paradox of Mach.
As a fundamental consequence of the equality of inertial and gravitational mass, one must postulate an invariance of laws relative to nonlinear transformation of the coordinates in for-dimensional continuum. This is the general principle of relativity.
A remark of fundamental importance from A. Einstein : "The group of general relativity is the first one requiring that the simplest invariant law be no longer linear and homogeneous in the fields variables and their derivatives.". Moreover, A. Einstein claims that the true laws cannot be linear nor can they derived from such.
As a result, the 21st century reader wonders in what kind of cases cloud computing, edge computing, and all of those might be most useful. It seems that expecting to find a new foundations from data analytics, big data and AI would not be fruitful. On the contrary, the ability to calculate nonlinear equations as simply as linear equations with a smartphone would give new opportunities to traverse nonlinear reality without difficulty by considering nonlinear borderline cases as, in the past, we used linear borderline cases.
Have a nice reading !
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