Question of relativity - MA thesis (ENG version - fully revised)

QUESTION OF RELATIVITY: AN OPEN COMPARISON BETWEEN ALBERT EINSTEIN AND ERNST CASSIRER Elisa Belotti AN HONOUR THESIS in Philosophy and History of Natural and Human Sciences Curriculum in Philosophy and History of Natural Sciences Fields of interest: Philosophy and History of Physics and Cosmology Presented to the Department of Letters, Philosophy, Communication of the University of Bergamo in fulfilment of the Requirements for the Degree of Master of Art with honours 2021 Enrico Renato Antonio Calogero Giannetto, thesis supervisor and Head of Department II. III. There is no knowledge of the absolute, but rather there is absolutely certain knowledge. E. Cassirer, History of Modern Philosophy IV. V. To me and to all my dreams. To those who remain close to my heart. To my never-ending passion for the history of science. May this work be the first of a long, fruitful and, most importantly, joyful career. VI. VII. Acknowledgments Words cannot express my gratitude to all the Professors and researchers I encountered during that amazing and thrilling path this Master degree at the University of Bergamo has been. I am extremely grateful to each of them because without their professionalism, competence, deep passion, and excitement for their studies and research, I would not have been able to choose the right direction of journey, for both me personally, and my academic career specifically. In particular, I am deeply indebted to Professor Enrico R.A.C Giannetto, PhD, for his patience and guidance throughout the entire planning and writing process, and for having shared parts of his limitless knowledge with me while diving in the complex word of physics and its philosophy and for showing true dedication to research, science and innovation as well as to philosophical consulting. I am also thankful to visitor research fellow at the University of Bergamo, Sasha Freyberg from the Max Plank-Institute for the History of Science, Berlin, Germany, for having provided advice and suggestions while editing major parts concerning Cassirer and Schlick so to enrich and complete the origins of relativity. Moreover, I would like to mention my parents for their practical support during these two years and in general, I would like to thank my family, particularly my significant one and friends for their endless support and for being there, providing me hope, happiness, and tranquillity when I needed it the most: their belief in me and my capabilities has kept my spirit and motivation high for the entire time of this path. Lastly, I would like to thank my cat for all the emotional support. Table of content ACNOWLEDGEMENTS………………………………………………. VII INTRODUCTION………………………………………………………. 1 CHAPTER 1. Continuum spatii et temporis est absolutum.…………... 15 1.1 On the cosmological problem …………………………... 22 1.2 God does not play dice… does He? ……………………... 27 1.3 An Einstein’s revision by…Einstein himself ………….... 32 1.4 The answers to philosophers and scientists ……………… 38 CHAPTER 2. A new, problematic face of the world …………………... 45 2.1 The problem of space and time …………………………. 56 CHAPTER 3. Open comparison between Einstein and Cassirer ………. 61 3.1 Truth: where do its boundaries lie? ……………………… 64 3.2 If truth has blended boundaries, reality gets problematic ………………………………………………………………. 71 CHAPTER 4. Albert Einstein at the creation of relativity’s origins …. 75 4.1 A step forward: Einstein and Moritz Schlick …………. 79 CHAPTER 5. Conclusions …………………………………………… 83 BIBLIOGRAPHY ……………………………………………………. 85 Introduction: On the theory of relativity, its roots, and its formulation, over the years much has been written and thought. Still, despite this, its possible interpretations and redefinitions are always in potential development and the deployment of my paper I will try my hand at just that: a revisiting of it in a philosophical key following the gaze of the German philosopher adherent to neo-Kantianism, Ernst Cassirer (18741925), within an open confrontation between the two. Starting from the beginning of the question, the theory of general relativity was presented by Albert Einstein (1879-1955) in 1916 and the heart of the problem, not only epistemological but also physical, revolves around the concept of no longer having the possibility to distinguish whether a body is at rest or in uniform motion, so the laws of physics would be equal for all the reference systems, both inertial and non-inertial ones, which leads to consider within Einstein's theory that heliocentric and geocentric systems are mathematically equal because, from within the solar system, we would not be able to discern the motion of the Earth with respect to the Sun and vice versa. Certainly, these are the final considerations that we can draw from the postulation of this theory, however, its origin is much more complex than we can believe, because in fact it is already defined in the work "Science and Hypothesis" by Henri Poincaré (1854-1912), published in 1902, where he, thanks also to the introduction of the use of Chronogeometry (a nonEuclidean geometry that assumes a four-dimensional space-time), completely reinterprets the mechanistic physics of Newton in a relativistic perspective, postulating as relative motion , space and time, and then in 1904, Poicaré presents an article at a conference in Saint Luis in which are contained the two principles for the constitution of a new mechanics, which would later form the basis of Einstein's writing: the principle of relativity of motion, expressed in terms of invariance of the laws of physics to the variation of the inertial reference system and the principle according to which the motion of light occurs at a speed of three hundred thousand kilometres per second, called C because it is constant for all inertial reference systems, which means that it does not depend on the radiation rise. In addition to this, the radical change in Poincaré's thought, which will accompany Einstein from 1907 onwards, lies in the different conception of nature: it is no longer simply the mechanistic one, but the electromagnetic one, derived from the discovery of the existence of the electromagnetic field, pure energy that would be transmitted from one body to another and that would go right to coincide with nature itself, which then would no longer include only matter, but together with it now would be added also light, which clearly would move in terms of electromagnetic waves (indicated by λ)1, because satisfying the wave equations thought by Jean Baptiste d'Alembert (1717-1783). So, an electromagnetic field would be an immaterial entity because it is light and also because it is in line with vacuum equations elaborated by James Clerk Maxwell (1831-1879), that is it could perfectly continue to exist even where matter would not exist, that is in vacuum. All this leads to a disruption in the ontology concerning physics because a whole series of qualities that in previous periods were considered as objective, first of all those related to the amount of matter and then to the mass, now are replaced by those of the electric field that, summarizing what we have seen so far, would exist only in motion and never at rest and would find its deepest expression in the value of C, that is the constant indicating the speed of light, because if it were to vary, then this would lead to a system that would be in motion and not at rest, it would move at the same speed, where the wave then would be equal to zero and therefore at rest, but it can never exist in a state of rest by its definition. Just this impossibility of describing the wave in a state of quiet has led, as seen above, to the use of Chronogeometry of the invariance group of laws, which would explain the description in a dynamic way of spaceThe wavelength λ represents the distance between the corresponding points of two successive waves (two successive crests), its unit of measure is the meter or its submultiples (micrometre, nanometre, etc) and can vary depending on the change of transparent material crossed (vacuum, air, glass, etc). (via: IFAC, Institute of Applied Physics "Nello Carrara") 1 time quantities. Pulling the sums of what was then declared by Einstein, the general relativity would carry out the imposition precisely of this specific new type of nonEuclidean geometry, in which the space is a curved spherical type and therefore he realizes mathematically what already assumed conceptually by Poincarè, and moreover it is reputed as usable because related to the characteristics of the electromagnetic field and correspondingly to the fictitious fields to which it is related, because, in fact, the new theory, in order to be relational, that is to establish a relation at a distance between bodies, should refer us to a conception of nature, just as a pure field, where in fact the mathematical entities, called tensors, used by Einstein with the letter G to represent space-time and with the letter T for energymatter, in the new Einsteinian gravitational field equation, are equivalent. Ernst Cassirer places himself, as already mentioned, on the strand of neo-Kantian thought and already from the writing "Substance and function" of 1910, he intends to show how Kantian philosophy is intrinsically inserted in the development of modern science since Galileo Galilei (1564-1642), asserting that ontology must give way to the analytics of the intellect, or the study of a priori conditions that govern the formation of the object of investigation of the various sciences: “Thus a new evaluative criterion comes forward: what from the point of view of metaphysics appears accidental and extrinsic, from the point of view of knowledge is the proper and legitimate object. Galilei could have already pronounced the words with which Robert Mayer characterizes the spirit and purpose of his method: The strict indication of the natural limits of human research is for science a task that has a practical value, while the attempts to penetrate the depths of the cosmic order, using hypotheses, constitute feedback for the efforts of the adept.”2 In the analysis of modern science that he proposes, he notes that the conceptsubstance has gradually replaced the concept of function and so terms such as energy, space-time, ether, atom, would no longer designate concrete realities but would represent only symbols for the description of a context of possible Ernst Cassirer, The Concept of Substance and the Concept of Function, 1910, edited by R. Pettoello, Small Fires, Editrice Morcelliana, Brescia, 2018, p. 36. 2 relationships and from here would arise the importance that he emphasizes language compared to other objects of epistemological analysis, given its relational nature affects the constitution of the objective world. In this context, he states that the consequence that seems to him to derive from the relativisation so far implemented of space and time has led to the removal of thought about the explicit determination of the object, because it would seem that the unity of experience, on which epistemology based the unity of the object, is far exceeded: “The nearest consequence that seems to derive from the relativisation of all spatial and temporal measures seems to be that with this is generally removed the thought of the clear determination of the object. The unity of experience, as understood by previous physics and on which epistemological consideration founded the unity of the object, now seems to have been superseded. There is but one experience, so Kant summarizes the result of his transcendental deduction of the categories.”3 He emphasizes this by basing it precisely on what Kant brought forward, and thus, if one were to consider so many different spaces and times, variations from reference system to reference system, to the common synthetic unity of experience would be destroyed at its base. This led Cassirer to the extreme conclusion that then, the concept of "truth" would be valid only and only concerning itself, according to the point of view of the person expressing it, there would no longer be a single truth that can be said to be original, precisely the theory of relativity would develop the principle that there is no longer any system that can be considered privileged over another and in fact, and he also argues that space and time as conditions of physical judgments, they in the theory of relativity are maintained, although eliminated as physical "things": “The world, the objective reality, so would teach the contemporary physical principle of relativity, like the old philosophical principle of relativity, for each are as they appear to him; the perceptions of one subject have no superior "objective" value with respect to those Ernst Cassirer, The Philosophical Problems of the Theory of Relativity, Lectures 1920-1921, edited by R. Pettoello, Mimesis Edizioni, MIM Edizioni SRL, Sesto San Giovanni, 2015, p. 125. 3 of another.”4 Starting from this general introduction to the multiple problems and implications found within the very constitution of the theory of relativity both in more strictly scientific terms and in philosophical validity, I would like to continue my paper by bringing to the surface the animated discussion in Cassirer's thought about the advancement of natural philosophy, which as introduced earlier, is radically revolutionized by the introduction of the electromagnetic field, also clarifying the dynamics 4 Ibidem, p. 126 of Albert Einstein's philosophical and religious thought. Chapter I. Continuum Spatii et Temporis Est Absolutum With this statement opens the writing of Albert Einstein on the theory of general relativity, preceded by considerations on the status concerning space and time conveyed in the theory of special relativity, in fact he states that if with Isaac Newton (1642-1726) was possible to assert that spatium est absolutum and the same for time, because the universe in Newton's vision coincided with the socalled sensorium Dei, the way God perceives nature, now instead we can postulate, starting from the theory of special relativity, that continuum spatii et temporis est absolutum, where absolute means not only physically existing but also not deviated from its own physical conditions: “The preceding considerations (referring to the theory of special relativity) are based on the assumption that, in order to describe physical phenomena, all inertial systems are equivalent but that, in order to formulate the laws of nature, they are privileged with respect to reference systems in different states of motion. However, the previous considerations do not allow to justify this preference for particular states of motion, neither based on properties of bodies nor based on the concept of motion; this preference must therefore be considered as an independent property of the space-time continuum. The principle of inertia, in particular, seems to force us to attribute physically objective properties to the space-time continuum. Just as it was consistent from the Newtonian point of view to state the two concepts tempus est absolutum and spatium est absolutum, so from the point of view of the theory of special relativity we must say continuum spatii et temporis est absolutum. In this statement, absolutum means not only physically real, but also independent in its physical properties, having a physical effect, but not affected by its physics conditions”.5 This is because, according to his point of view, classical mechanics brought to light an internal deficiency, and this makes that the principle of relativity must be 5 Albert Einstein, The Meaning of Relativity, 1922, edited and translated by E. Vinassa de Regny, Edizioni Integrali, Newton Compton Editori, Rome, 2019, p. 61. extended to reference systems that do not have inertial properties. This leads the German physicist to be convinced of the possibility of being able to numerically equal inertia with gravitation through the unification of their own nature and this would give to the theory of general relativity a clear superiority with respect to classical mechanics, in addition to the fact that inertial systems would present a series of consequences that would lead directly to the development of a vicious circle: a mass (m) would move in fact without acceleration (a) if it was far enough from other bodies, but we know that it would do so only because it would move precisely without acceleration. At the conclusion of a series of mathematical considerations, Einstein comes to affirm that a reference system not at rest, can be considered inverse, with respect to which there could be a gravitational field, composed of "fictitious" forces or centrifugal forces and those said of Coriolis 6, thus arriving to say that the gravitational field would influence and even determine the metric laws of the space-time continuum, in the presence of which, Einstein underlines very openly, the geometry becomes non-Euclidean, because in this particular case it would be impossible to introduce on a surface coordinates having a simple metric meaning: “However, according to the principle of equivalence, K' can also be considered as a system at rest, with respect to which there is a gravitational field (field of centrifugal forces and Coriolis forces). Therefore, we arrive at this result: the gravitational field influences and even determines the metric laws of the spacetime continuum. If the laws of the configuration of an ideal rigid body must be expressed geometrically, then in the presence of a gravitational field the geometry is not Euclidean. The case we have considered is analogous to that which arises in the two-dimensional treatment of surfaces. Also, in this case it is in fact impossible to introduce on a surface (for example on the surface of an ellipsoid) some coordinates that have a simple metric meaning, while on a plane the Cartesian Coriolis force: an apparent force to which a body is subjected when observing its motion from a reference system that is in rotational motion with respect to an inertial reference system. (via: Treccani encyclopedia). 6 coordinates, correspond directly to the lengths measured by a ruler-sample"7. For this reason, Einstein introduces arbitrary coordinates x1, x2, x3, x4, which are going to identify the points of space-time so that events in succession are associated with values close to them. Therefore, it would be clear that the theory of general relativity, requires a generalization of the theory of invariants and the theory of tensors, the latter is referred to what was structured by mathematicians such as Bernhard Riemann (1826-1866)8, long before the formulation of relativity. In the continuation of the text, at the end of the elaboration of the necessary mathematical apparatus, Einstein continues with the development of individual results: starting from the principle of inertia, a particle of matter on which no forces act, would move with uniform velocity along a straight line, which in the fourdimensional continuum of the theory of special relativity, was seen to be a real straight line and its natural generalization, that is the simplest one derived from the invariants of Riemann, is a of geodesic line: "Geodesics. A line can be constructed in such a way that its successive elements derive from each other by parallel displacements. This is the natural generalization of the straight line of Euclidean geometry.... We get the same line when you look for the line for which the value of the integral is minimum: ∫ ds or ∫ √gμυ dxμ dxυ between two points (geodesic line)".9 Deriving so a series of equations, he was able to show how they express the influence of inertia and gravitation on the material particle previously indicated, and then the unity between inertia and gravitation would be expressed by the fact that the entire first member of the equation, obtained by applying the principle of equivalence, has tensorial character. So, Einstein would be able to take over the position that would allow him to state that, the matter would be then constituted by electrically charged particles and that therefore should be by considered itself, as in fact it is done, the main part of the electromagnetic field itself. Albert Einstein, The Meaning of Relativity, 1922, edited and translated by E. Vinassa de Regny, Edizioni Integrali, Newton Compton Editori, Rome, 2019, p. 65. 8 Ibidem, p. 68. 9 Ibidem, p. 79. 7 However, the form of the tensor is left in this case undetermined because it would not be known for the moment with enough precision the electromagnetic field produced by these charges, but on the other hand it is just it that would transfer energy and momentum to the matter because it exerts on it forces and then it would provide energy. So, from equations would be evident the emergence of a differential tensor, completely determined by three conditions (it cannot contain any derivative gμν of order higher than the second, it must be linear and homogeneous in the second derivatives and its divergence must be zero). From a phenomenological point of view, this tensor would be composed by the tensor of the electromagnetic field and by the tensor of the matter in the strict sense and if we consider the different parts of the energy tensor according to their order of magnitude, from the results of special relativity, it would follow that the contribution of the electromagnetic field would be an absolutely negligible quantity compared to the contribution of the ponderable matter. The space we are going to consider here, as previously said but it is good to underline it, is curved and not Euclidean and from the relations previously indicated, it would show that the interval between two beats of the unit clock, in the units used in our coordinate system, would correspond to "time": 1 + χ/8π ∫ σdV0/r. 10 Here, the rate of progress of a clock is therefore the smaller the mass of ponderable matter in its vicinity. Another great consequence of the theory, which would be glimpsed from these studies, would concern the path of light and light rays. In the theory of general relativity in fact, the speed of light would be at every point the same concerning a local inertial system and this speed unitary, and also in it, the law of propagation of light in general coordinates would be characterized by the equation: ds² = 0, and in the coordinate, system chosen previously, the speed of 10 Ibidem, p. 90. light would be composed in: (1 + χ/4π ∫ σdV0/r ) (dx²1 + dx²2 + dx²3) = (1 - χ/4π ∫ σdV0/r ) dl².11 From this, it would be then possible to conclude that a luminous ray would bend when it passes in proximity of a great mass and therefore, if it was taken as valid that the mass M of the Sun was concentrated all in the system of coordinates taken in consideration, this analysed ray would be bent altogether over it. We can already see from these considerations, how the theory of general relativity flows in the great space occupied by astronomy because it is in this space that it finds its most direct application and in fact from here would emerge also the other great consequence of the theory, that is the one concerning the planet Mercury, particularly in the analysis of its perihelion12 motion. Einstein affirms that the secular changes in the orbits of the planets would be so well known that the approximation used until now, would no longer be sufficient to conjugate the theory with the experimental observations and therefore would be necessary to return to the general equations of the field. The major result that the German physicist from these premises would be able to obtain would be made explicit by a secular rotation of the elliptical orbit of the planet in the same direction of the motion of revolution of the planet, which is expressed in radians per revolution, would be equivalent to: 24 π³ α² / (1 - e²) c² T² Where13: o α is the semi-major axis of the orbit, expressed in centimetres Ibidem, p. 91. Perihelion: point on the major axis of the ellipse described by a planet around the Sun, at which the planet is at the minimum distance from the Sun. (via: Treccani encyclopedia). 13 Albert Einstein, The Meaning of Relativity, 1922, edited and translated by E. Vinassa de Regny, Edizioni Integrali, Newton Compton Editori, Rome, 2019, p. 94. 11 12 o e is the numerical value of eccentricity o c is the value of the speed of light in vacuum o T is the period of revolution, expressed in seconds This equation would then allow, according to Einstein's ideas, to explain the reason for the motion of Mercury's perihelion, for which theoretical astronomy had not yet been able to find an effective explanation. In any case, the question of whether the universe is non-Euclidean or not would have already been discussed for a long time and well before the development of his theory, for admission of Einstein himself, but on the other hand he would affirm that the problem, thanks to his studies, would have entered in a new phase and in the next level, just because in it the geometric properties of bodies would depend on the same distribution of masses. To sustain moreover that the universe is infinite and totally Euclidean, from relativity point of view, according to Einstein would be a very complex and complicated enterprise. Therefore taking into account the equations of the principle of Ernst Mach (1838-1916)14, which he follows and sees in the development of his reasoning, the scientist brings to the surface the fact that the inertial mass would be proportional to the factor 1+ σ¯, and therefore it would be increasing if the masses approached the body under analysis, as well as by a part of the masses accelerated, then on the said body there should be an action of induction of the of the same sign and finally a material particle that, inside a hollow body, moves perpendicularly to the axis of rotation, would be deflected in the direction of rotation (that is, the field of Coriolis forces). Unfolding these ideas to their ultimate consequences, Einstein would conclude that all inertia, that is all the gμυ → gravitational field, is determined by the matter of the universe: “Although it is impossible to have an experimental demonstration of these effects because of the smallness of x, following the theory of general relativity they certainly exist. We can indeed consider them a strong confirmation of Mach's idea of relativity of all 14 Ibidem, p. 97. inertial actions. If we develop these ideas to their ultimate consequences, we must expect that all inertia, i.e., all the gμυ field, is determined by the matter of the universe and not only by the boundary conditions at infinity.”15 It seems very satisfactory given his reasoning to show the hypothesis that the universe is spatially limited and that therefore, in agreement with the hypothesis of the constancy of σ, it has constant curvature, either spherical or elliptical. In case this is adequate, the conditions at the edges of infinity, which is, as one can easily imagine complex from the point of view of general relativity, could be replaced by the conditions for a closed space and would be, from Einstein's point of view, much more natural. What about matter? In this case, it is thought as constituted by electrically charged particles, which according to the theory developed by James Maxwell (1831-1879), cannot be considered electromagnetic fields without singularity and for this, it would be necessary for Einstein to introduce energy terms that in Maxwell instead were not present, to allow these particles to remain united despite the mutual repulsion between their behaviours as they have charges of the same sign, then he would then pass to the indication of a pressure term suitable only for the energetic representation of the dynamic replace in the matter. In the last analysis, Einstein is expressly in favour of a conception of a universe spatially limited, therefore finite and for which he lists several arguments: first of all, for the theory of relativity, postulating such a universe, closed, is much simpler than stating the contrary, after which the idea made explicit by Mach, according to which inertia would depend on mutual actions between bodies, would already be contained in the equations of the theory of relativity itself and this would also result, on a more strictly epistemological level, in a more satisfying determination of matter in the mechanical properties of space, and finally an infinite universe would be possible only if it would be satisfied the hypothesis that the average density of matter in it is zero, which would also be logically correct, but certainly 15 Ibidem, p. 99. less likely than the one that in the universe there is a finite average density of matter. I.I. On The Cosmological Problem This just outlined, was Einstein's first elaboration of the theory of general relativity, resulting in a complete remake of the gravitational field equations predicted by Newton. He was strictly convinced that, as we have already explained, the universe was not only finite and closed, for the reasons listed above, but also that it was completely unchanging, frozen in a non-expansive state. This vision of the universe, although discussed and supported by equations and rigorous arguments, must be sought in its philosophical and religious convictions. Albert Einstein, as is well known, was in fact of Jewish origin and very attached to them and the construction, in a metaphysical sense, of the world by Baruch Spinoza (1632-1677), who wanted to demonstrate in the posthumous work of 1677 Ethica ordine geometrico demonstrate that God, the only infinite substance, is manifested through infinite attributes: “6. With God, I mean an infinite entity or a substance that consists of infinite attributes, each of which expresses an eternal and infinite essence. I say infinite absolutely, and not infinite: because of everything that is infinite only in its own kind one can deny an infinity of attributes, while to the essence of what is infinite belongs everything that expresses an essence and does not imply any denial.”16 Therefore, since these statements of his concerning God, that being infinite and to maintain these attributes as such, must also belong to immutability, not to submit to the movement of becoming, ideas as already explained, that Albert Einstein makes his in unfolding the theory of general relativity. This situation, however, is reversed at the dawn of 1929 when the young American astronomer Edwin Hubble, 16 Benedictus de Spinoza, Ethica ordine geometrico demonstrata, 1677, care, translation and notes by S. Landucci, Biblioteca universale Laterza, Urbino, Editori Laterza, 2009, p. 6. who in 1924 had already demonstrated a constant relationship between the period of variation of brightness of a variable Cepheid (Star V1) in the Andromeda Galaxy and its average brightness, thus sanctioning the existence of spiral galaxies outside the Milky Way, gave to the press what in time became better known as Hubble's law, which places in linear relation the redshift of light emitted by galaxies, or more specifically redshift, and their distance: in particular, the effect of redshift was already known in spectroscopy also under the name of Doppler effect 17, indicates precisely the going, the move, towards the zone red of the spectrum by the lines composed by the electromagnetic waves put by the body under observation, a phenomenon that highlights that the universe is now considered as an entity in becoming, in constant expansion, because the area of red would indicate that this body examined, is moving away from the point of observation. Considering these discoveries, Albert Einstein was forced to re-discuss his thesis in an appendix to the second edition of the theory of general relativity, which is marked in a particular way for the introduction of the cosmological constant in the equations of the gravitational field. In fact, he points out that the problem of cosmological character can be introduced in terms of safety given now that the system in which the stars are located does not resemble at all an island floating in an infinite empty space and consequently, would not exist based on this, nothing that can be designated as a centre of gravity of all matter, for which, moreover, we are led to think that we have an average density other than zero in space: “The problem may be formulated more or less in this way: thanks to our observations of the fixed stars we have become quite convinced that, as a whole, the system of such stars does not resemble an island floating in an infinite empty space and that, therefore, there is nothing like a centre of gravity of all existing matter; 17 Doppler effect: compared to a stationary observer, the wavelength of light emitted by a moving source increases or decreases depending on whether the source is approaching or moving away. Discovered by physicist Christian Doppler, is well known in everyday life: just think of the difference in the sound of an ambulance siren depending on whether it is approaching or moving away from us: the effect is more evident the faster the medium is. It became then fundamental in astronomy and it is thanks to it that it is possible to measure the speed of galaxies, stars, and celestial bodies in general. (via INAF: National Institute of Astrophysics). furthermore, we are led to think that we have a non-zero average density of matter in space. At this point a question arises: can this hypothesis, which is suggested by experience, be reconciled with the theory of general relativity?”.18 So, on the basis of these considerations, Einstein passes to the attempt to make these problems collide with the theory of general relativity and appeals to the way found by Russian mathematician and cosmologist Aleksandr Fridman (18881925)19, who proposed a model of homogeneous and isotropic universe, calculated with positive, neutral and negative curvature, leading him already in 1922 to guess the actual expansion of the universe with matter in motion. For the German physicist, there would then be the possibility to observe how the star systems, are distributed with the same density in all directions and this leads us to assume that the spatial isotropy of these systems is valid for all observers, or for every point and time of an observer at rest for the surrounding matter, where the hypothesis that the density of matter is constant over time, no longer maintain its validity. This would also imply the abandonment of the independence of the metric field concerning time, consequently a new need would arise, or to seek a mathematical equation that allows to show that the universe is isotropic 20 with respect to the four-dimensional space, concluding that there would be a family of surfaces orthogonal to geodesics, with constant curvature, whose segments between pairs of them, would be equal to those of geodesics. Faced with these results, Einstein, proceeding in his mathematical analysis, now wants to arrive at satisfying the gravitational field equations without, however, the cosmological term, or cosmological constant, which is presented in this form: Albert Einstein, The Meaning of Relativity, 1922, edited and translated by E. Vinassa de Regny, Edizioni Integrali, Newton Compton Editori, Rome, 2019, p. 105. 19 Writings featured in "Über die Möglichkeit einer Welt mit konstanter negative Krümmung des Raumes" (On the possibility of a world with constant negative curvature of space), published in Zeitschrift für Physik (Vol. 21, pp. 326- 332) by the Berlin Academy of Sciences on January 7, 1924. 20 Property of a body to exhibit the same values of a physical quantity in all directions. In general, amorphous bodies and crystalline bodies are isotropic only for some properties (such as optical and thermal) that belong to the monometric system. (via: Treccani encyclopedia). 18 (Rik - ½ gik R) + χ T ik = 0 .21 Thanks to it, the scientist would be able to analyse the space in the three cases already indicated above: non-zero curvature (i.e. positive), null and negative curvature. Following the results obtained in this way, he would be able to draw some conclusions about the matter, namely that, first of all, the introduction of the cosmological constant in the equations of gravity, although admissible at a level of relativistic realization, should be rejected from the point of view of logical economy and for this statement, Einstein gives reason to Fridman, who would have been the first to first reconciled the original form of the field equations with a finite density of matter everywhere, and secondly, he admits that the hypothesis of the spatial isotropy of the universe discussed above, naturally leads to the formulation of Fridman. In addition, he takes note of the relationship between average density and expansion supported by Hubble that, if neglected the influence of space curvature, would be confirmed empirically and experimentally, and emphasizes that in the known physical facts, there would be no support that avoid connecting the Doppler effect with the red shift phenomenon always identified by Hubble himself. Einstein asserts that according to those who try in vain to prove this, it would be possible to establish a said connection between two stars S1 and S2, by a rigid ruler. By doing so, the monochromatic light sent from S1 to S2 and reflected back to the first star, would arrive with a different frequency, if the wavelength number of light along the straightedge would change with time during the trip, but this would lead to a contradiction for the special relativity theory: the speed of light, C, measured at a point would depend on time: “Some try to explain the shift of spectral lines discovered by Hubble without resorting to the Doppler effect, but this does not find any support in the known physical facts. According to such a hypothesis, it would be possible to connect two stars, S1 and S2 with a rigid ruler. The monochromatic light that is sent from S1 to S2 and reflected back to S1 would 21 Albert Einstein, The Meaning of Relativity, 1922, edited and translated by E. Vinassa de Regny, Edizioni Integrali, Newton Compton Editori, Rome, 2019, p. 110. arrive with a different frequency if the wavelength number of the light along the ruler changed with time during the path. However, this would mean that the speed of light measured at a point depends on time, which is contradictory to the theory of special relativity. Also, it should be noted that a light signal going back and forth between S1 and S2 would itself constitute a “clock” which however would not be in constant relationship with a clock placed on S1.”22 Einstein points out that these observations are based on the wave theory of light, whose nature would be explained in a radiation of electromagnetic waves as recognized by Maxwell's equations, while some supporters of this idea could have gone into a description of light through an effect similar to the one exposed by Compton, but it is clear that a hypothesis that does not include diffusion of waves, could not have any justification, from the point of view of knowledge of the time. Moreover, Einstein raises doubts about the Big Bang hypothesis, the possible original explosion that should have given origin to the expansion of the universe, as proposed first by George Gamow (1904-1968)23 and then by Fridman and Georges Lemaître (1894-1966)24, because this should be made to go back only 109 years ago and moreover he supports the fact that this type of theory of the evolution of the universe, is based on claims weaker than those of the field equations, also because the main theoretical doubts, would derive from the fact that in the instant of the beginning of the expansion, the metric should have presented a singularity and the density σ should have been infinite. Certainly, Einstein does not deny the presence of empirical arguments in favour of the dynamic conception of space, such as the continuous existence of uranium despite its continuous and perennial decay and the impossibility at the time of being able to recreate it or wonder why the night sky does not appear as the day sky from the amount of radiation present in space. In conclusion, for the German physicist it is necessary to analyse one last aspect of great importance: the age of the universe, previously indicated with the Ibidem, p. 119. Peter Bowler e Iwan Rhys Morus, Making modern science. A historical survey, the University of Chicago Press, Chicago, p. 323. 24 Ibidem, pp. 324, 325. 22 23 term 109, must certainly exceed by far that detected by the crust of the earth, obtained through the examination of radioactive minerals in Earth's crust, obtained through the examination of radioactive minerals, because otherwise the cosmological theory so far exposed, should be abandoned, as contradictory, but despite this, Einstein also clarifies the fact that in the case, he could not find another solution logically acceptable. I.II. God Does Not Play Dice ... Does He? As noted above, the very constitution of the theory of general relativity in Einstein results in a cosmological outpouring that has reverberations in his way of seeing the world, through the aid of Spinozian metaphysics. In the writing entitled "Cosmic religion", published for the first time in 1931 with the original title of On cosmic religion and other opinions and aphorisms, his vision takes full shape and in fact, God and universe come to fully coincide, in a peaceful union between science and religion, as suggested also by the afterword of the essay by Enrico R.A.C. Giannetto and Audrey Taschini. On the other hand, what Einstein achieved here is not a novelty, in fact in the history of science and philosophy there have been many systems of thought which, even though developing extremely rigorous physical and scientific theories, have shown a strong attachment to theology. One name above all is certainly that of Newton, whose period of retirement from the public scene is well known to devote himself to biblical exegesis and in particular to the interpretation in a prophetic key of the book of Revelation, in which he described the origins of the Christian Church in the light of his own subordinatist conception of Christ, that is, according to the great English theologian, he was not at all omniscient by his very nature because at the moment when the Lamb (Christ) takes the sealed book from the one who sits on the heavenly throne (God), the content would be so excellent that it could not be communicated to anyone except the Lamb himself, deserving of this through his own death. This prophetic scene, contained in Rev. 5:6-825, represented for Newton the symbol of the greatest apostasy, begun precisely by corrupting the truth about the relationship between the Father and the Son, equalizing them, while God should have been the supreme King on the throne, full of every perfection, and Christ should have been second in dignity, as well as the only one deserving to communicate with Him.26 The history of this plot is long and complex, but Einstein takes on an even different character, asserting first that the religious feeling in man unfolds for different reasons, the first of which would be the fear, established in primitive peoples, after which there would be the so-called social feelings, that is the desire to have a guide and a help from which would arise an idea of a protector and consoler God, which would characterize the religions of civilized people, which would all share the anthropomorphic character of God. For Einstein, only those who are able to abandon this idea, reach the third form of religious experience, or the sense of cosmic religion and, according to his peculiar point of view, all religious geniuses would have reached this stage, without dogmas and without a God in the image of man and, therefore, without a church. Precisely for these reasons, Einstein maintains that "the experience of cosmic religion is the strongest and noblest driving force of scientific research" as well as "the most important function of science is to arouse and keep alive this feeling of those who are receptive "27. Therefore, he feels able to assert with reason that only those men who demonstrate a deep religiousness, are also the only honest men of research and therefore, of science: “Anyone who understands scientific research only in its practical The Holy Bible, Edizioni Paoline, Pia società San Paolo, Rome, 1968: "Then I saw standing between the throne the four Living Ones and the Watchmen, a Lamb as if slain, with seven horns and seven eyes, which are the seven Spirits of God ... Now, he came forward and took the book from the right hand of him who is seated on the throne. After he had taken the book, ... they prostrated themselves before the Lamb, each holding in his hand a zither and golden cup filled with perfume, which are the prayers of the saints." 26 Robert Iliffe, Newton: the Priest of Nature, translation by S. Di Biella, The biographies, Hoepli editori spa, Milan, 2019, pp. 301-302. 27 Albert Einstein, Cosmic Religion, edited by E. R. A. C. Giannetto and A. Taschini, Red Pelican, Morcelliana Publisher, Brescia, 2016, pp. 22-23. 25 applications can easily come to a misinterpretation of the state of mind in men who, surrounded by sceptical contemporaries, have shown the way to kindred spirits scattered throughout all nations in all centuries. Only those who have devoted their lives to such ends can have a living conception of the inspiration that gave these men the energy to remain loyal to their goal, despite countless failures. It is the sense of cosmic religion that grants this energy. A contemporary has rightly said that it is the deeply religious individuals, in our largely materialistic age, who are the only honest men of research.”28 Einstein's cosmic religion then proposes an abandonment of both a devotion based on terror and one that proposes a vengeful, acting God in human moral life, to make explicit instead a form of reverence for the whole universe and empathy, and compassion, toward all forms of life, exactly as Spinoza had also argued. It is also characterized by feeling a dimension of mystery and inviolability, by fully perceiving the beauty of the world as a universe and life, which remains inaccessible to us, leaving behind every attempt of anthropomorphic and selfish reading. In short, the theory of general relativity (but also special) would be the final result of an intimate introspection by Einstein because in fact the same order of the cosmos, formulated in the laws that make up the theory of general relativity, would be the clear demonstration of the divinity, which opens then a real reinterpretation of physics in theological terms, which also allows to understand the denial by the German physicist of the constitution of quantum physics and in particular of the theory Werner Heisenberg’s (1901-1976) indeterminacy, because he could not conceive a God-universe that is compatible with the complete quantum randomness. Consequently, if Nature is configured with God himself, the curvilinear motion, also called geodesic, discussed in the previous paragraphs, should be configured as natural and not due to an external cause, thus composing the main formation of non-Euclidean geometry, going to delineate a “purer” and “by heart”29 rectitude that would belong to the law of God. On the other hand, the 28 29 Ibidem, pp. 23-24 Ibidem, p. 84 and refer to The Book of Psalms, Psalm 18 verse 10: "He incurved the heavens and image of the unlimited straight line had been the most evocative and marking for the philosophy of nature of the seventeenth and eighteenth century, but with the theory of general relativity, it is cracking more and more, establishing instead a curved and free line in a pseudo-Riemannian space, now linked at the conceptual level to the electromagnetic field described, as already seen by Maxwell. The cosmic religion proposed by Einstein, would then undermine the Calvinist doctrine of the absolute sovereignty of God 30, an idea also brought forward by René Descartes (1596-1650) and Newton, thus causing the disappearance of the mechanical god, already announced by Nietzsche through the words of Zarathustra: “But when Zarathustra was alone, so he spoke ... << ... he has not yet heard that God is dead! >>. And the parable of the insane man in "The Joyous Science": << Where has God gone? >> he shouted, << I want to tell you! We have killed him - you and I! We are all his murderers! ... God is dead! God remains dead! And we have killed him ... >>”31 . For the German physicist, the force would not belong only to God, but it would be the energy of Nature itself, in its perfect Chronogeometric order, because as already underlined many times, God and Nature identify each other in a Spinozian way. In addition to this, the light, of which we have already spoken extensively and of which we have already underlined the importance related to the new electromagnetic conception of Nature itself would be identified here with the very nature of God, in a so-called electromagnetic theology where light would take the place of intelligence and soul. In conclusion, for Einstein at the origin of science itself, there is an amor dei intellectualis32 and it must be considered as the knowledge of Nature-God itself, a descended, and dark cloud was under his feet" and Psalm 119 1-7: "Blessed are those whose way is spotless, who walk in the law of God … I will praise you with righteousness of heart, instituted of your righteous decrees." 30 Albert Einstein, Cosmic Religion, edited by E. R. A. C. Giannetto and A. Taschini, Red Pelican, Morcelliana Publisher, Brescia, 2016, p. 87. 31 Friedrich Nietzsche, Thus Spoke Zarathustra, 1883, introduction by F. Masini, translation by A.M. Carpi, Unabridged Edition, Newton Compton Publishers, Rome, 2016, p. 45. F. Nietzsche, The Joyous Science, 1882, edited by F. Masini, introductory note by G. Colli, Adelphi e-Book, Adelphi editions spa, Milan, 2015, pp. 107-108. 32 This expression refers directly to the Ethica ordine geometrico demonstrata, 1677, edited by S. vision that allows him to go beyond Newtonian mechanicism and the theory of general relativity itself leads to the contemplation of God, which must be added to a Chronogeometric order of the cosmos completely deterministic, in which the human free will would be a pure illusion while the true freedom would reside in adapting precisely to this order, in a wink to theological rationalism, while, in contrast, the emerging quantum physics is structured in a Franciscan-style voluntarism, in which the action, or better to say the Love 33, of God would not be predictable and could not be enclosed in a series of predictions, leading to what is called chaos physics34 that would be configured with the complete indeterminacy of phenomena and this would be reflected on what concerns the microcosm and the initial phase of the universe, called Big Bang because space and time would be by now said infinite matrices, sanctioning, therefore, the impossibility to represent the expansion of the universe. Therefore, contrary to what Einstein claimed, God in this idea would not only play dice, but as said by the great cosmologist Stephen Hawking (1942-2018), sometimes he would throw them where it is not possible to see the result35: this is the last real consequence of the uncertainty principle associated with quantum theory, in addition to the intrinsic entropy36 that would bring gravity to a further level of non-predictability. Landucci, Biblioteca universale, Urbino, Publishers Laterza, 2009, p. 38, proposition 31: "the intellect in act, whether it is finite or infinite so also the will, desire and love and so on - have to be brought back to the natura naturata, and not already to the natura naturante." 33 The Holy Bible, Edizioni Paoline, Pia società San Paolo, Rome, 1968: First Letter of St. John 4:8 and 16: "He who does not love has not known God, for God is love! ... God is love: and he who abides in love abides in God, and God abides in him." 34 Theorized for the first time by Henri Poincaré in his study of three-body problems (1890) and some of its aspects were analysed by Jacques Hadamard in his study of the behaviour of geodesic flows on compact varieties with negative curvature (1898). after which the advent of the theory of relativity relegated this field to a single area of classical mechanics called the theory of dynamical systems. The importance of chaos theory was fully rediscovered only in the seventies when Ilya Prigogine extended the concepts of the predictability limit to the study of non-equilibrium systems giving the basis for the theory of complex systems (1977). Chaos, in the language of modern physics and mathematics, identifies the situation of impossibility to estimate a priori with certainty the future value of the quantities that characterize a physical system in evolution. (via encyclopedia Treccani). 35 Stephen Hawking and Roger Penrose, The Nature of Space and Time, 1996, translated by L. Sosio, Le Scoperte, le Invezioni, Biblioteca universale Rizzoli, Milan, 2017, pp. 28-29. 36 Entropy is the measure of the degree of molecular disorder of the system or the degree of indetermination with which molecular positions and velocities of the system are known. As a measure of the degree of disorder or indeterminacy of a system, entropy has been used in application fields far from physics, first the theory of information. (via Treccani encyclopaedia). I.III. A Review of Einstein by ... Einstein In 1949, aged 67, Albert Einstein wrote a rather peculiar but extremely interesting text, both from a literary and, more importantly, from a scientific point of view. The work in question is called Scientific Autobiography37, although the German physicist, described it more than once as a sort of obituary that should have the purpose of showing to students and, more generally, to those who stay with scholars for a long time, the exhausting effort and research that are hidden behind the immense and continuous work to which physicists are called. Retracing the stages of his life, Einstein describes how his thought has evolved since when, at 12 years old, he abandoned religion because he was convinced by the science books, he read that many biblical episodes, could not find effective feedback in history. He became an ardent supporter of free thought, transforming himself also into a sceptical and suspicious boy, towards every authority and towards those of the convictions of the different environments of society. But Einstein wanted more: he wanted the contemplation of this world of ours which thought cannot be traced back simply to memory with the surfacing of certain images, and not even when these form a succession, but when an image recurs in many of these successions, it then becomes a real ordering element because it connects these alternations that otherwise would not be, and this element becomes what we call "concept" or tool. So, Einstein says: “Here is my defence. All our thoughts have this nature of free play with concepts, and the justification of this play consists in the greater or lesser help it can give to reach a general view of the experience of the senses. The concept of "truth" cannot yet be applied to this mechanism: in my opinion, this concept can be taken into consideration only when there is already a general agreement (a convention) concerning the elements and 37 Albert Einstein, Scientific Autobiography, translation by A. Gamba, Bollati Boringhieri publisher, Turin, 2014. the rules of the game.”38 He is also convinced that thought goes on even without the strict use of words, in fact, many times it happens unconsciously and in this way would explain the wonder, which happens spontaneously, without warning, like the time when he was 5 years old he was kidnapped by the operation of a compass shown to him by his father: the operation of the needle that did not need a contact to move, was extremely amazing, for the conceptual world that clearly possessed at that age. This came back vividly and strongly, again at the age of 12, when at school he was able to read a manual of Euclidean geometry, and this is how Einstein tried to recount his experience: “It seemed to me that there was a need for some kind of demonstration only for things that did not appear as "obvious". Also, it seemed to me that the things that geometry deals with were not essentially different from those that can be perceived with the senses, that can be seen and touched. This rudimentary idea, probably the same one that underlies the well-known Kantian problem on the possibility of "synthetic a priori judgments," is obviously since the relationship existing between geometric concepts and the objects of sensible experience was unconsciously present to me. ”39 Having said that, he emphasizes that concepts and propositions would acquire content only through their direct link with the sensitive, everyday experience, and this link is only intuitive, not logical, and just this would distinguish the mere fantasy from the scientific truth because the latter would show a degree of certainty with which this link can be carried out and nothing else. As for the truth of a system, it would correspond to the completeness and solidity with which it would be possible to coordinate and relate it to the totality of experience. A correct proposition for Einstein can repeat the truth contained in the system to which it belongs. Returning then to his autobiography, Einstein does not disdain some words of criticism towards the educational system in general, which instead of making students' minds blossom, places them under obligations that asphyxiate 38 39 Ibidem, p. 12. Ibidem, p. 13. their creativity and their desire to study, learn and improve. He felt the same way when he attended the Zurich Polytechnic to study mathematics and physics: too many notions that did not directly interest him to put in his head anyway to pass the exams. As I have already pointed out several times, the physics that still dominated Einstein's university days was Newtonian physics, despite the appearance of more and more new openings: “In spite of the luxuriance of particular research, a dogmatic rigidity prevailed in matters of principles: at the beginning (if there was an origin) God created Newton's laws of motion along with the necessary masses and forces. That is all.”40 Then, it would not be surprising if many physicists and scientists of the previous century had tried repeatedly to lead back for example Maxwell's electromagnetic theory to mechanics, failing miserably. The only one, according to Einstein, who succeeded in shuffling the cards was the well-known Mach who, as already said, influenced Einstein himself in the construction of the special relativity theory, but not only, because his young age fascinated him also from the epistemological point of view, from which he detached himself. According to Einstein, before criticizing any physical theory, it would be necessary to clarify two principles: the first would be, of course, the fact that the theory must not contradict empirical facts, and the second would have instead to do with the premises of the theory itself or with what we could also call "logical simplicity"41 of the premises. Based then on these two principles, Einstein shows that what dissuaded physicists from trying to bring everything back to Newtonian mechanics was precisely Faraday's and Maxwell's electrodynamics, experimentally demonstrated by Heinrich Rudolf Hertz (18571894): this caused physics to enter a state of transition in which the historical basis was completely lost. In addition, there was also a methodological interest that shows a type of argumentation that in the future of physics will be essential for the choice of theories, because the more the concepts and axioms will be detached from what is testable, the more complex will be to compare the implications of the 40 41 Ibidem, p. 17. Ibidem, p. 19. given theory with the facts. And so Newton finished his journey: “And now enough Newton, forgive me, you have found the only way that in your time, was possible for a man of high intellect and creative power. The concepts which you have created still guide our thinking in the field of physics, although we now know that they will have to be replaced by others far more removed from the sphere of immediate experience if a deeper knowledge of the relations between things is to be attained.”42 One might ask: is this an autobiography or a treatise on physics? Well, for Einstein this is indeed an obituary because what really matters to him is what he thinks and how he thinks, not what he does or what he suffers in his life. And therefore, consequently, this autobiography can deal with what was paramount to him and with what inspired him most. At that time, however, to accept that electromagnetism existed, it was very complex, even if it was experimentally demonstrated because it was clear that it was not the space to be the carrier of the field, but the matter and consequently that it had a speed that had to be applied to vacuum, and it is on this that was based the whole Hertz electrodynamics. From a general picture, we can now pass to Einstein's path, who, also in the light of the creation of the Planck constant, at the beginning of his career, saw all his attempts to adapt the theoretical basis of physics to these new explorations and research, fail. It is for this reason that when Niels Bohr (18851962) was able to discover, in spite of these bases, the spectral lines emitted by atoms, this seemed to him almost a miracle, so much to affirm “this is the highest form of musicality in the sphere of thought”.43 The main problem that afflicted Einstein was to understand what general conclusions could be drawn about the structure of radiation, and in general, the electromagnetic basis of physics, starting from the formula of radiation. So, in his path, he developed statistical mechanics and the kinetic-molecular theory of thermodynamics that was based on it. More and more desperate for the lack of these, he slowly convinced himself that the discovery of a universal principle could 42 43 Ibidem, p. 24. Ibidem, p. 31. lead him to certain results: here, in his autobiography, we find the core of special relativity: “After ten years of reflection, such a principle: resulted from a paradox in which I had come across at the age of 16 years: if I could follow a ray of light to speed c, the light ray would appear to me as an electromagnetic field oscillating in space, in a state of quiet. But nothing of the kind seems to be able to subsist based on experience or Maxwell's equations. From the beginning, it seemed to me intuitively clear that, from the point of view of such a hypothetical observer, everything must happen according to the same laws that apply to a stationary observer concerning the Earth. Otherwise, how would the first observer know, i.e. how could he establish, to be in a state of rapid uniform motion? In this paradox is already contained the germ of the theory of special relativity.” 44 The universal principle of the theory of special relativity would then be contained in the postulate: the laws of physics would be invariant to the Lorentz transformations. Einstein does not stop here, he wants to make clear what are the characteristics of the four-dimensional space: according to him, it would be divided into a three-dimensional continuum and a one-dimensional one, that is time, so the four-dimensional point of view would not be necessary. Physics is indebted, obviously for Einstein, to his theory of special relativity, especially for two concepts: the first would be that there would be no immediate action at a distance, in the sense of Newton's mechanics, and the second would state that the two principles of conservation of momentum and conservation of energy would merge into a single principle: the inert mass of a closed system would coincide with its energy and mass would be eliminated as an independent concept. But this, as of course can be imagined, was nothing more than the first step towards a later development that culminated in the theory of general relativity, which became apparent in Einstein's mind as early as 1908. This occurred, on the admission of the physicist himself, that in the theory of special relativity, there was actually no place for a satisfactory elaboration of a new theory of gravitation, and in fact, states 44 Ibidem, p. 34. that: “Then it occurred to me this: the equality of the inner and the heavy mass, that is the independence of the gravitational acceleration from the nature of what falls, can be expressed as follows: in a gravitational field everything happens as in a space free from gravitation, as long as you introduce, instead of "inertial system", a reference system accelerated concerning an inertial system”.45 It took him a few years to arrive at this construction because it was not easy for him to detach himself from the idea that coordinates had an immediate metric meaning. The theory of general relativity then, had only to proceed according to the principle that natural laws should be expressed by equations that were covariants concerning the group of continuous transformations of coordinates. This group would then replace the group of Lorentz transformations of special relativity theory. Einstein outlines exhaustively the heuristic meaning of the principles of general relativity, which would be in the fact that they lead us to look for systems of equations that, in their general covariant formulation, are as simple as possible, including the famous equations of the gravitational field. However, about the mature formation of general relativity, Einstein feels compelled to stop on a great complication in the physics of the time: quantum physics, in whose mechanics it is impossible to find the representation of reality in such an easy way as it had been in the past. On the other hand, Einstein had to admit some contrasts with this theory, especially about its future use: “It is my opinion that today's quantum theory, utilizing certain exactly defined fundamental concepts, which all come from classical mechanics, constitutes the best possible formulation of the various connections. I believe, however, that the same theory does not offer any useful starting point for future development. This is the point where my predictions diverge from those of most contemporary physicists. They are convinced that it is impossible to interpret the essential aspects of quantum phenomena by a theory which describes the actual state of things by continuous functions of space for which differential equations apply. They believe, moreover, that the atomic 45 Ibidem, p. 40. structure of matter and radiation cannot be understood in this way.”46 Einstein certainly does not deny that all these questions are incredibly serious for physics, but the decisive question seems to him another and that is what attempt is possible to make with hopes of success, given the current situation of physical theory, being guided by the experiences connected with the new theory of gravitation: his equations would be, according to Einstein, the most natural generalization of the equations of gravitation, even if the application and then the demonstration of their physical usefulness will be a very exhausting task because they will not be enough only approximations. He concludes his work thus: “This exposition will have answered its purpose if it has shown the reader the connection which unites the efforts of a lifetime, and the reason why they have led to expectations of a definite nature.”47 I.IV. Answers to Philosophers and Scientists Einstein's scientific autobiography, was not, however, simply published by the physicist without obtaining any further repercussions, in fact, a host of eminent philosophers and scientists read and criticized Einstein's obituary, in a continuous search for a more and more general field theory, for the protagonist of the writing, and the opposite conception, perpetrated instead by most physicists of the time. Not for this Einstein remained impassive he wrote a reply to the observations of all the authors who expressed themselves in his text. Surely this operation was not easy for him, on the contrary! For a whole a series of reasons, starting from the fact that the arguments in the essays are, as it is easy to understand, too many and not always connectable among them. So, Einstein tries to reorganize everything according to a logical criterion, even if the mentality of many is an insuperable obstacle for him so that he would not be able to express himself about them. Starting from the beginning, the first ones to be taken into consideration are 46 47 Ibidem, p. 51. Ibidem, p. 55. Wolfgang Pauli (1900-1958) and Max Born (1882-1970), who describe the part about quanta and statistics following their logical coherence and their path in the evolution of physics of the 20th century. Both these thinkers would complain that he does not accept the fundamental idea of the current statistical quantum theory because he does not believe that it can be used as a valid basis for physics in general. But quantum physics finds its heart in Heisenberg’s uncertainty principle, as mentioned before. According to Einstein, all the others would be completely convinced that the mystery of the double nature of corpuscles (undulating and corpuscular) has found its solution in this theory and that it is the fundamental presupposition of all the physical theories thinkable and reasonable. The thought on which Einstein is directed instead is oriented to support that the statistical character of contemporary quantum theory must be attributed to the fact that it deals with an incomplete description of physical systems. Moreover, it does not seem to satisfy him fully, his attitude towards what seems to him to be the purpose of physics itself: "The complete description of any real situation that is supposed to exist independently from any act of observation or verification. Whenever the modern physicist with positivistic sympathies hears such a formulation, his reaction is a smile of pity.”48 Furthermore, he believes that this revolves around quantum mechanics in the sense of claiming difficulty, which would derive from the fact that one should always postulate as "real" something that is not observable. What Einstein did not like about this, is precisely the fundamental positivistic attitude which for him would be literally untenable and that, among other things, it would be attributable to the same principle of Berkeley 'esse est percipi'. Being then is always something that we construct with the mind, or something that we assume, in freedom, but in a logical sense. So, according to the physicist: “In simple words, the conclusion is this: in the framework of quantum statistical theory there is nothing like a complete description of the single system. Wanting to be more cautious, one could say this: the attempt to conceive of quantum-theoretical 48 Ibidem, p. 20. description as a complete description of individual systems leads to unnatural theoretical interpretations, which immediately become unnecessary if one accepts the interpretation that the description refers to sets of systems and not to individual systems.”49 Then for Einstein, there would be a psychological reason for the fact that this interpretation, however, is rejected: if quantum theory gave up describing the individual system completely, it would then be inevitable to look somewhere else for a complete description of the system and in doing so, then it would be clear from the beginning that the elements of this description could not be part of the conceptual territory of quantum theory. According to him, it would be more natural to think that an adequate formulation of the laws of the universe, has always to do with the use of all the conceptual elements necessary for a complete description. But also, Bohr, together with Pauli, besides recognizing Einstein's work in a historical sense, attacked him on a common point: the rigid adherence to classical theory. The defence that he deploys is to say that nowadays, anything even similar to a classical field theory and therefore it could not be strictly adhered to, but this does not mean that it does not exist as a program and then yes Einstein can be attributed and the justification would be that follows: “The theory of gravitation has shown me that the nonlinearity of these equations implies that the theory admits in general interactions between structures. But the theoretical search for nonlinear equations is hopeless unless the principle of general relativity is used. At the same time, however, it does not seem possible to formulate this principle if one tries to deviate from the above program. The result is a compulsion from which I cannot escape.”50 Subsequently, Einstein goes on to consider the work of Hans Reichenbach (18911953)51, which instead invests the territory of the relationship between philosophy and the theory of relativity, particularly the issue of truth. First, it is necessary to Ibidem, p. 214. Ibidem, p. 219. 51 Ibidem, p. 220. 49 50 examine the dynamics of the problem related to geometry, i.e. whether it is verifiable or not. This is because the positions are divided on two fronts: Reichenbach approves, and Helmotz too, while Poincaré does not, and then a short dialogue takes place in Einstein's text in which the latter states that bodies empirically given, would not be rigid and therefore, they could not be used to materialize geometric intervals, therefore theorems of geometry would not be provable. The first one replies then that it is fine to admit that nobody can be immediately used as the "true definition"52 of the interval, but this would not remove the fact that it can be obtained through relationships such as the influence of temperature on volume, etc., and that classical physics would have easily demonstrated this without contradiction. Poincaré shows, however, that to do this, Reichenbach has used Euclidean geometry and then the verification of which he spoke, is not simply addressed to the geometry but to the whole system of physical laws that are the foundation. So, why then could he not depend on himself on the choice of a geometry that is suitable for his purposes and to whose choice he will adapt the consequent laws? In this way, contradictions between this speech and experience would be avoided. Reichenbach then replies that it should be noted, however, that sticking to the objective meaning of length and the interpretation of the differences in coordinates, has never brought, in pre-Relativistic physics, any complication. In any case, he points out that for Einstein it would have been possible to build a theory of general relativity, even if he had not accepted the objective meaning of length. Against Poincaré, it could also be observed that what would matter, is not the greater simplicity of geometry, but of physics, including geometry, and that is why then it would be inappropriate to adopt Euclidean geometry. Reichenbach's essay is then really stimulating for Einstein and can be easily connected to Percy Bridgman's one (1882-1961)53: to consider a logical system as a physical theory, it is not necessary to set the condition that all its statements can be verified one by one, but it is necessary only that it contains 52 53 Ibidem, p. 220. Ibidem, p. 222. empirically verifiable statements in a general sense. The essay of Henry Margenau (1901-1997)54, however, according to Einstein, contains original observations: a logical conceptual system is a physical science insofar as its concepts and statements are necessarily related to the world of experience, but all those who try to establish such a system will certainly find a dangerous obstacle in the arbitrariness of the choice, and this would be the reason, for Einstein, why he tries to connect his concepts as directly as possible with experience, thus showing an empirical attitude. Nevertheless, a part of his essay does not convince him at all: “In this case, which has always existed in physics, we must limit ourselves to give objective meaning to the general laws of the theory, that is, we must set the condition that these laws are valid for every description of the system that is recognized as valid in the function of the group. It is not true, therefore, that objectivity presupposes a group characteristic but, on the contrary, the group characteristic imposes a refinement of the concept of objectivity.”55 We now turn, in Einstein's remarks, to the essays of Lenzen and Northrop56 who both deal systematically with the occasional epistemological content of some of his expressions: the former would have constructed an accurate general picture of them, and everything written in them is, for Einstein, convincing, while Northrop would have used them as a starting point for a critique of epistemological systems and which Einstein himself greatly admires. What Einstein states here is: “The mutual relationship between epistemology and science is very important. They depend on each other. Epistemology without contact with science becomes an empty scheme. Science without epistemology is primitive and formless.”57 In these various essays, there is also a brief mention of the cosmological problem, a theme he has already dealt with in this paper and therefore it can be an excellent enrichment, with Edward Milne (1896-1950), Lemaître and Leopold Infeld (18981968), for which Einstein says: “On the ingenious reflections of Milne I can only Ibidem, p. 223. Ibidem, p. 224. 56 Ibidem, p. 227. 57 Ibidem, p. 227. 54 55 say that I find their theoretical basis too limited. From my point of view, it is not possible to arrive theoretically at results that are, at least, reliable, in the field of cosmology, if you do not make use of the principle of general relativity. As for Lemaître's arguments in favour of the so-called "cosmological constant" in the gravitational equations, I must admit that they do not seem to be convincing enough, at the present state of our knowledge... Infeld's essay is a very good introduction, understandable even if taken by itself, to the so-called "cosmological problem" of the theory of relativity, which critically examines all the essential points.”58 The last essay considered by Einstein is that of Kurt Gödel (1906-1978)59, in which there would be an important contribution to the theory of general relativity, especially in the analysis of the concept of time, a problem that worried Einstein since the first formulation of the theory of general relativity and, without going too much into technicalities that belong to Gödel's writing, it is possible to see how the distinction between "before" and "after", is not valid for all the points of the universe very distant from each other in a cosmological sense and indeed, Gödel himself would have found cosmological solutions to gravitational equations, which for Einstein would be very interesting to analyse in case they should not be discarded by physical reasons. This roundup of Einstein's answers to other physicists and philosophers is concluded with his decision not to write anything more on this subject and not to add anything more to his already existing comments, because they have already become too long 60. Ibidem, p. 229-230. Ibidem, p. 231. 60 Ibidem, p. 233. 58 59 Chapter II. A New, Problematic Face for The World In the previous chapter, I have dealt with laying the necessary gnoseological foundation for a thorough understanding of the discussion between Albert Einstein and Ernst Cassirer, showing the formulation and implications, including cosmological ones, of the theory of special relativity. Instead, in the chapter that opens here, I would like to pass more in detail to what Cassirer sealed in the lectures he gave in the winter semester, from October 13 th, 1920 to January 26th, 1921, in which he brought to the surface a regulative principle, in the strictly Kantian sense of the term, of a general maxim for the study of nature, which goes to compose the fundamental philosophical nucleus of the theory of relativity, without denying the experimental and empirical bases because the postulate of general covariance, is placed as a rule of the intellect: a principle that would be used precisely by the intellect hypothetically for the investigation and interpretation of experiences and following only this rule it is possible to reach the so-called synthetic unity of phenomena understood in a temporal relationship. First of all, the problems related to relativity are presented by Cassirer, as philosophical, which invests in particular the relationship between science and philosophy itself, the latter in fact would be revised in principle as "philosophy of nature", already present in reality since the times of ancient Greece, where it would emerge a common trait, not so much directed towards the search of the so-called αρχή, but rather towards the common conjugation of physiology, φύσις and λογος, exasperated towards an attempt to explain the world. In this period, it would be considered under the description of κοσμος, a united whole, in which matter would come to elucidate the structure of the universe, which would be at the mercy of the motions of becoming, generating, in turn, the process of natural history, also identified in the theory of nature. The first separation between philosophy and the science of nature would occur with the advent of the thought of Pythagoras, which would highlight a new necessary feature: the mathematics that is so preponderant in the discourse of science, along with an empirical basis of departure, a character then exasperated by Democritus in the explication of the atomic theory, where the atoms and the vacuum would reign supreme. Moreover, according to Cassirer, the same fundamental moments should be found in the subsequent development of modern philosophy in which the historia naturalis takes the place of the science of nature and is realized in the work of Francis Bacon (1561-1626), who would like to divert attention from scholastic metaphysics, which would have the pretension of wanting to detach itself from the guide of experience. Nature, therefore, would be known only in an inductive way that would allow us to connect the various cases in a rigorous system to define the understanding of the "form": “The same fundamental moments of the philosophical consideration of nature are then presented in the development of modern philosophy. The empirical consideration of nature, in which the science of nature is transformed into historia naturalis is embodied by Bacon. Bacon fights the empty abstractions of mathematicians, just as he fights scholastic metaphysics, which believes that it can free itself from the guidance of nature, from the guidance of experience. Nature can be known only by inductively enumerating cases, connecting them, ordering them according to similarities and differences; and grasping them systematically, that is, in an empirical-encyclopaedic way. Thus, the Instauratio Magna, the great renewal, takes its starting point from the encyclopaedia, to arrive, through the doctrine of method, which contains the doctrine of induction as its main part, at the history of nature and from this philosophia naturalis... all these treatises seek to go as far as the knowledge of form, just as the understanding of form constitutes the goal of Baconian induction.”61 This is violently countered by Descartes, who rails in favour of a mathematical, hence Pythagorean-Democratic, ideal of nature and knowledge of it, in a slow progression toward what would later be defined as mechanicism based solely on: extension, form, and motion: “Descartes' main work immediately denies both: by 61 Ernst Cassirer, The Philosophical Problems of the Theory of Relativity, 1921, edited and translated by R. Pettoello, Mimesis edizioni, MIM Edizioni srl, Sesto San Giovanni, 2015, p. 42-43. far the largest part of the work to which Descartes gave the title Principia Philosophiae, deals with the principles of physics, namely, the derivation and mechanical explanation of all happening, based solely on extension, form, and motion.”62 In opposition to both the purely empirical and the mechanical conception, then, there is in the last analysis, the one by Friedrich Schelling (1775-1854), who proposes instead a dusting at Heraclitus' ideal off, namely that of an understanding and a lived experience of nature in the total fullness of its manifestations: “To the merely empirical conception, as to the mathematical-mechanical conception of nature, Schelling finally contrasts again, in the philosophy of nature, the Heraclitan ideal, the ideal of the understanding and lived experience of nature in the concrete fullness of its manifestations. Only here must be found the reconciliation between universal and between intuition and concept. The philosophical intuition of nature, that intuition which Schelling found embodied in poetic vision ... is the unity of universal and particular; in it intuition itself appears as intellectual, the intellect itself as intuitive”.63 In light of this evolution concerning the philosophy of nature, science on the other hand can be seen to have taken an independent path and made to stand out by Newton's work, namely the Philosophiae Naturalis Principia Mathematica of 1687, in which he makes explicit the will to eliminate the moments of pure hypothesis, speculation of the philosophy of nature, placing in fact as his famous motto, the expression: "hypotheses non fingo"64. A pupil of Newton, John Keill65 (1671-1721), coined in one of his works the most suitable definition that will lead to the division of the purely scientific method, from the philosophical one, namely: descriptio phaenomenorum, that is a simple but effective description of phenomena. This resolution is more suitable than in Ibidem, p. 43. Ibidem, p. 43. 64 Isaac Newton, The Mathematical Principles of Natural Philosophy, 1687, edited by F. Giudice, Piccola Biblioteca Einaudi Scienza, G. Einaudi Editore spa, Turin, 2018, p. 95. 65 Ernst Cassirer, The Philosophical Problems of the Theory of Relativity, 1921, edited and translated by R. Pettoello, Mimesis edizioni, MIM Edizioni srl, Sesto San Giovanni, 2015, p. 44. 62 63 Gustav Kirchhoff (1824-1887)66, who in his mechanics, highlights that its precise purpose is to describe optimally and clearly, the motions and changes that nature shows. What about relativity? What space does it occupy in these considerations of Cassirer? He affirms that it pushes towards the dissipation of the primary facts of consciousness, much further than what happened in mechanistic physics alone: a motion, it is no longer possible to think, without considering it as something belonging to a mass, a subject, even if it was only a point and without space being interpreted as homogeneous, uniform, in which there is an equally uniform time. On the contrary, space and time in relativity would become part of that content which definitively disappears in the logical-mathematical form of this physics: “Relativistic physics is characterized by the fact that it pushes the dissolution of the fundamental facts of consciousness, of the "given" far beyond what happened in the mechanistic conception of the world. This resolves all "subjective qualities" into quantities, everything that is the object of sensation into something numerable and measurable. The vision of the day is turned into vision of the night; the world of colours and sounds disappears for us and passes into a world of pure quantities. But if you look more carefully, you see that at the foundation of this world of mere quantities there are still qualitative differences that are completely determined. It is about those differences that are placed precisely in the fundamental concepts of the mechanism itself. The motion, to which all sensible contents and all sensible differences are brought back, cannot be thought without us, placing something that moves, a mass, as the subject of motion, even if we think of this mass as reduced to a mere material point without our also thinking of a homogeneous, uniform, continuous space too, in which it proceeds and a uniform time, in which it flows.”67 So where would the epistemological knot of relativity lie? In the concept of reality, which would accord with the one of philosophy in its form of conceptual analysis. Its philosophical content and merit, according to Cassirer, would consist precisely in shedding effective light on the boundaries between physics and philosophy, 66 67 Ibidem, p. 44. Ibidem, p. 52. between the problems of nature and its actual knowledge exactly as they are perceived by the philosopher and the physicist: “Does this concept of reality agree with the one of philosophy, with the criterion of measurement with which philosophy, in its form of conceptual analysis, measures the things of nature and the contents of consciousness, or are they already originally, already as a thinkable criteria of measurement, in conflict with each other? This is the essential epistemological problem that the theory of relativity raises. Its essential philosophical content and its philosophical merit, as we shall try to show, consists not so much in its ultimate results, as in the fact that it has raised with full determinacy this question... and here, in the theory of relativity, we can finally make clear the boundaries between physics and philosophy, between the problem of nature, objective knowledge, as they present themselves to the philosopher and the physicist. The first great physicists of the Modern Age, Galilei, and Kepler, had not yet drawn these boundaries rigorously.”68 For Cassirer, the duty then that contemporary physics would pose to scholars would be to find a way to escape that leads to philosophical truth and reality , that could keep us safe between the Scylla of nominalism and relativism and the Charybdis of the absolutist conception of the world and things. To trace the contours of this path then, we need to analyse in a more detailed way the concept of truth and the concept of physical reality. So, how could reality and truth behave within this panorama? First, the theory of realistic copy is placed by Cassirer: physical concepts would be endowed with a certain amount of reality in the moment in which they would reflect the object present in nature. This theory, however, would show a very naive conception of nature because, basing itself exclusively on this, it would have a claim to knowledge and in fact, since the early days of the philosophy of nature, but if we want to see from those of human knowledge in general, it is noted that the changeability and relativity of "real" objects, are also something concrete and cannot be attributed to them directly. 68 Ibidem, p. 53. From this, there later arose an agreement between empiricism and rationalism, initiated by John Locke (1632-1704), namely that these objects would be characterized primarily by the so-called primary qualities: “The first conception concerning the essence and meaning of physical concepts that arises is the theory of the realistic copy: physical concepts possess "truth" insofar as they reproduce the "real" object present in nature. The naive conception of the world believes in grasping immediately the reality of things, of nature in the sensory perceptions; but already from the very beginning of the scientific considerations of the world, the relativity, and the changeability of the contents of the sensible perception are discovered and it is shown that they cannot be attributed to the "same" object... But Locke still concludes that, on the contrary, the primary qualities belong to the object itself; the representations of number, of form, of motion are in the objects, in the object as well as in us: here a perfect similarity takes place.”69 However, continuing the analysis, it became clear that these qualities, while belonging to the object, were also subject to the trend of relativity, and, thinkers such as George Berkeley (1685-1753)70, objected that both primary and secondary qualities should be considered equivalent from a psychological point of view. These issues are the ones that would then run through the world of our perception. Looking into the past and turning to ancient philosophy, it had been reconstructed, among the various theories that followed over the centuries, also based on atoms, by Democritus and placed as the very basis of reality and matter. During the centuries, the development of this theory changed and consolidated, from Descartes to Newton, from Leucippus (beginning of V century B.C. - third quarter of V century B.C.) to Gustav Fechner (1801-1887) from Max Planck to James Maxwell, and the same for other concepts such as ether, that in the theory of relativity is even largely eradicated from its original function of subsidy of electromagnetic and optical events. According to Cassirer, this point of the discussions about perception and everything else, would open a further gap: a contradiction within the development 69 70 Ibidem, p. 57. Ibidem, p. 58. of physics itself, in fact it would have as its supreme purpose to bring to the complete knowledge of perceptions, sensations, describing them as a whole, but to fully fulfil it, it must necessarily take a path away from this, or its entire course would be constituted by a real detachment from this task: “The path of physics starts from sensations and returns again to sensations: all its concepts, its hypotheses are nothing but attempts to describe, evaluate, order sensory data. Their theoretical value consists exclusively in enclosing within themselves this reduction, an abbreviation of the content of sensations and thus save intellectual labour. The function of physical concepts is resolved in the economy of thought. Thus, the ether, the atom, force, mass, and energy are not concepts of things, they are not reproductions of real objects that we can presuppose as real somewhere in the nature of things; they are nothing more than computational instruments, than conceptual fictions - insofar as they can have in general a sense - which in the end must be reconverted into factuality of sensation, into elements and relations between elements. But at this point, a new problem arises. If the description, the understanding of concrete sensations constitutes the authentic end of scientific thought, it must be admitted that physics, to achieve this end, must take a particular road, a road that, instead of bringing it closer to it, threatens to take it further and further away. It should know no other task than that of describing sensations, according to their concrete content, as faithfully and immediately as possible. But instead of even attempting such a description of the sensible data, its whole procedure consists rather in a distancing from this content.”71 The element that more than any other is detached in the study of physical concepts, would be, according to Planck72, the anthropological one and according to him, only the primitive stages of the evolution of physics, would have still involved this aspect: the progress instead would show the setting aside of the human-historical principle from the definitions of physics, for example, Planck shows how the characterization of seeing, therefore related to the sense of sight, is given in the 71 72 Ibidem, p. 63. The Unity of the Physical Worldview, Leipzig 1909. language with "light" or "colour "73, while this is fundamentally different from the true nature of the light ray. The sensation, therefore, would present only qualitative differences, while physics would have as focus the attainment of quantities 74 that can be defined as such and consequently a concreteness of the concepts of measurement: “Such an extraordinary enlargement of the theory (see Planck's optical theory) is also presented to us in the theory of relativity, which distances itself even more than classical mechanics did, not only from the point of view of sensation but also from the one of immediate intuition, from our usual view of space and time. About the theory of special relativity, it has already been said that its essence consists in transforming all realities, even "tangible realities", in "mathematical constructions" and the development in the theory of general relativity has further accentuated and strengthened this fundamental tendency... all that physics aims at consists in obtaining exact concepts of magnitude and therefore exact concepts of measurement; sensation, however, based on its immediate content, is neither measurable nor, by itself, can it serve as a means and principle of measurement. Sensation as such presents only qualitative differences, ... in which the possibility of establishing comparisons of quantities or determinations of quantities is not at all immediately given.”75 Up to this point, Cassirer is giving a negative connotation of perception and in particular of vision and this leads him to emphasize the positive aspects, especially taking into account that physics from the Nineteenth century onwards is transformed from physics of images to physics of principles, with a peak in the pervasion of electromagnetic physics, where the mechanical models used should be considered only as an ideal representation of the given phenomenon studied. At this point of the discussion, Cassirer wonders which are the invariable Lecture "Das Wesen des Lichtes," delivered on October 28th, 1919, at the general meeting of the Kaiser Wilhelm Society for the Advancement of Science. 74 A physical quantity is any measurable physical property of a body, object, or phenomenon, and that given measurement must be able to be uniquely expressed through a number and a unit of magnitude. They can be either extensive or intensive and also scalar or vector. (via: YouMath). 75 Ernst Cassirer, The Philosophical Problems of the Theory of Relativity, 1921, edited and translated by R. Pettoello, Mimesis edizioni, MIM Edizioni srl, Sesto San Giovanni, 2015, p. 65-66. 73 component of the hypothesis and of the physical theories, since the sensitive one is no more usable: according to him, it should be found not in the single objects, events, and so on, but in the relationships based on the laws that bind the phenomena, therefore the physical concepts would be understandable only thanks to the position that they assume in the complex of physical judgments, that is the physical laws themselves. Here clearly arises a further dilemma, namely the one concerning the achievement, the systematization of these laws where, the simplest and most direct answer to it, seems to be found in the measurement, which takes place thanks to the space-time measurements that we assume to be always constant, although the concept of constancy presupposes the universal value of the laws of nature, so that they are already part of our measurement, and compose the result, but at the same time they are part of it as a condition itself: “We ask ourselves then, what is the constant component of physical hypotheses and theories, if certainly, their sensible component is not? What still generates between them some objective link? ... in truth it is easy to indicate the element "object" and "constant" of the various theories that we were looking for: it is not found in individual "things", whatever they are, to which our physical concepts resemble or reproduce faithfully, but in the relationships based on laws of phenomena, which they express. Physical concepts are never comprehensible by themselves, but they become so only because of their position in the general complex of physical judgments; the form of the physical judgment is that of the physical law. Therefore, every concept has insofar content as it represents a building stone for the formulation of laws.”76 Turning now to a more detailed discussion of the theory of special relativity instead, Cassirer shows the importance of two experiments in particular: the one by Hippolyte Fizeau (1819-1896)77: it was used to measure the relative speed of light in water, when it is kept moving at a constant speed, using a special 76 77 Ibidem, p. 73-74. Fizeau experiment: via SPIE: the International Society for Optics and Photonics, excerpted from Fundamentals of Optical Engineering, second edition, B.H.Walker, 2009. arrangement of the interferometer to measure the effect of motion in an optical medium on the speed of light, and the one by Albert Michelson (1852-1931)78: conducted in 1857, it is still considered one of the most famous and important experiments in the history of science. He succeeded in demonstrating the independence of the speed of light for the hypothetical "ether wind" and it was the great proof against this one, also called luminiferous ether (a theory of the XIX century that indicated the medium through which it was thought to pass the electromagnetic waves). Michelson's interferometer was used, which allowed him to get the result. They seemed to bring rather contradictory results, and just from this feature that would permeate the experience, it would open the way to the theory of relativity because the scientific thought could not accept this problem, but it could not even overcome it without operating on itself a deep revolution of its assumptions that resulted in a real critical consciousness of the forms of measurement itself both of space and time 79. What these two experiments brought to light was a study on the hypothetical existence of the luminiferous ether and its motion, first of all comparing the speed of light when it propagates in a moving medium and when it propagates in a medium at rest: the general conclusion would show how the motion of the light ray, actually is not at all influenced by the one of the medium and therefore, supposing the existence of this ether, we should speak of "absolute" motion of the Earth during the period of revolution around the Sun because this substance than would be at rest. As for the problem concerning pure theoretical physics, then we would have on one hand Fizeau's experiment that showed how the ether was not dragged by bodies with refraction quotient80 1, while on the other there would be the one of Michelson who seemed to show instead, Michelson-Morley experiment: via SapereScienza, The ether paradox and the Michelson-Morley experiment, by A. Frova, June 25, 2020. 79 Ernst Cassirer, The Philosophical Problems of the Theory of Relativity, 1921, edited and translated by R. Pettoello, Mimesis edizioni, MIM Edizioni srl, Sesto San Giovanni, 2015, p. 82. 80 Refraction consists of a variation in the trajectory of waves as they pass between one medium and another. The variation of the trajectory is produced by the variation of the speed of propagation of the waves in the two media. The refraction index indicates how much a medium modifies the speed of a certain type of wave (in particular, electromagnetic waves). Fraction indices are called absolute and are always pure numbers greater than 1. (via encyclopaedia Treccani). 78 how the ether would be completely transported by the air in motion, together with the Earth. Since both were performed and the conclusion was a drift without actual results, we can now move on to methodical and philosophical considerations, especially concerning a diatribe of long duration: that between experience and thought! Both Einstein's and Hendrik Lorentz's theory (1853-1928), fundamental for the following development of electromagnetism and electrodynamics and as the basis for Einstein himself to formulate the concept of space and time in special relativity, start from a new concept of measure and measuring principle, even if for the latter, space and time become concept of thing. Relating this to what was explained before about the two experiments, we can deduce, according to Cassirer, that it is by introducing an objective ether that we could explain why we must stick only to the rules of measurement, valid for each reference system: “In fact, everything that until now was not explainable at all, or it was only explainable by resorting to extremely difficult and arbitrary hypotheses, through the introduction of an objective ether, understood as a particular substance, is explained as long as we stick only to the rules of measurement valid for each physical reference system. The unity of the physical image of the world is now founded in these rules and not in a substantial thing that exists absolutely, and in this unity, there is no contrast with the diversity of observations, which can be obtained from different reference systems in uniform motion for each other, but rather the key to this diversity is found there.”81 However, on the other hand, Einsteinian theory incorporates perfectly the unitary criterion of measurement, on which the material values of space and time could be discerned, putting at the centre the principle of the invariance of the speed of light. This united with the principle of relativity, gives a complete explanation of the mechanical, electromagnetic and optic-electrical phenomena: they formulate together a unitary fundamental relation to which all the laws of nature obey, representing in this way a universal gnoseological moment 81 Ernst Cassirer, The Philosophical Problems of the Theory of Relativity, 1921, edited and translated by R. Pettoello, Mimesis edizioni, MIM Edizioni srl, Sesto San Giovanni, 2015, p. 90. for us, being in reciprocal coordination, even if it must be underlined that the theory of special relativity itself cannot step too far, but it should stick precisely to the principle of invariance of light. For Cassirer, the relationship between classical mechanics and the theory of relativity should be stabilized in thinking of this last one as the fulfilment of the concept of object in classical mechanics, but at the same time as an overcoming of it: “Here the postulate of the constancy of the speed of light is stripped of its absolute meaning; the principle of measurement is moved to another place. So, to say, no single procedure is no longer valid as a fundamental constant in general; rather, all that remains now is the "law of legality", the norm according to which invariants cannot be given in general. Precisely, these we call the laws of nature and precisely to these we refer as the ideal "motionless poles". The relationship of classical mechanics with the theory of relativity from this perspective: the fundamental thought of the theory of relativity as the fulfilment of the concept of the object of classical mechanics and at the same time as its overcoming, because it transfers all objectivity in the determined fundamental relations.”82 II.I. The Problem of Space and Time To analyse its developments, as usual, it is necessary to start from the beginning and therefore from Isaac Newton's mechanics. Space and time in his theoretical construction are, as it is well known, of absolute character and that therefore they would come to transcend our sensibility and the possibility to know the world. From these perspectives, started the first criticisms not on a mere physical level, on the metaphysical one by Gottfried Wilhelm Leibniz (1646-1716) and George Berkeley, who opposed Newton because, they saw mixed in a wrong way, according to them, the intelligible being with the sensitive, with the perception, transferred then in the phenomenological dimension of space and time. 82 Ibidem, p. 101. Newton himself will be able to admit that absolute space and time, remain directly unknown to us in the sensibility, but this does not take away that he was convinced by this: he never doubted their existence, in fact behind all the different relative metric determinations, there would still have to be the determination of being, that is space and time precisely, also indicated as the “true causes"83, even if in a perspective of experience, none can give us evidence of it, and this statement can lead us, as Cassirer states in his discussion, to wonder why in the Eighteenth century. then absolute space and time are so rooted in the common thought of many philosophers, even though we cannot confirm them through our senses: “Why then, despite everything, the whole mathematical-physical thought of the Eighteenth century persists in accepting this assumption; why does it seem so difficult, even almost impossible to abandon the hypothesis of absolute space and absolute time? Perhaps this thought has not seen the difficulties inherent in these two concepts. This is not the case: it highlights them instead most rigorously and firmly. But after pointing out all these difficulties, the thought always returns anyway to its initial point, to its starting point.”84 The answer that he gives, could be found in the construction of another Swiss scholar, considered one of the greatest mathematicians of the entire history: Leonhard Euler, or better, Euler (1707-1783)85. He in fact, in his 1765 work Theoria motus corporum solidorum seu rigidorum, would reserve to philosophers the role of metaphysicians who would tend to invent the concepts of reality, without considering the "real" data coming from the rules of nature, so for Euler they are not the ones to decide about things that only empirical natural science, together with mathematics, can abrogate or not. Philosophy, from its peculiar point of view, must therefore certainly remain in constant dialogue with physics and Isaac Newton, The Mathematical Principles of Natural Philosophy, 1687, edited by F. Giudice, Piccola Biblioteca Einaudi Scienza, G. Einaudi Editore spa, Turin, 2018, p. 76: "Rules of Philosophizing, Rule I: No more causes of natural things should be admitted than those which are true and sufficient to explain their phenomena." 84 Ernst Cassirer, The Philosophical Problems of the Theory of Relativity, 1921, edited and translated by R. Pettoello, Mimesis edizioni, MIM Edizioni srl, Sesto San Giovanni, 2015, p. 106. 85 Ibidem, p. 107. 83 must continually refer to it, even if it cannot certainly limit itself to it to find the answers to its fundamental questions. This aspect is truly evident if we think that contemporary science today continues to ask questions and to give answers, which are also found in the science of past centuries. For Euler, in any case, absolute space and time remain an undeniable and certain physical reality, whereas Einstein will later state that they are deprived of "the last remnant of physical objectivity"86, bringing us back to a dialectic (a term that Cassirer uses without Hegelian implications) in empirical science itself. Interestingly, Cassirer then mentions two other names, more precisely a mathematician and a physicist: Carl Neumann (1832-1925) and Ernst Mach (1838-1916)87. In particular, the first expressed a very peculiar point of view that gave a more than surprising turn to the conflict between absolute space-time or not, namely through the use of a paradox: the principle considered so far the basis of mechanics, and therefore of science in general, not only would not have had any meaning from the sensible point of view but even no logical sense!: “His solution (ref. Neumann) of the problem was to tell the truth a paradox, but one of those paradoxes which contain in themselves the kernel of a fruitful truth. The paradox consisted in the fact that the principle that until now was considered as the foundation of mechanics and with that of the science of nature in general too, in the formulation that is usually given to it, not only does not possess any immediate empirical meaning but even no comprehensible logical sense.”88 This is especially so about the law of inertia. Neumann states that this principle would be obtained only if we assume that in some unknown place in the universe, there is an equally unknown rigid body, called Alpha Body, on which to relocate the inertia itself. The immediately apparent problem is to consider the existence of this body as acceptable, leads to further complications, instead of solving the question more easily because obviously, we should think of a body Albert Einstein, The Foundations of the Theory of Relativity, 1922, edited by E. Vinassa de Regny, translation by W. Mauro, Edizioni Integrali, Newton Compton publishers, Rome, 2019, p. 61. 87 Ernst Cassirer, The Philosophical Problems of the Theory of Relativity, 1921, edited and translated by R. Pettoello, Mimesis edizioni, MIM Edizioni srl, Sesto San Giovanni, 2015, p. 112. 88 Ibidem, p. 112. 86 completely unknown to us that possesses all the characteristics of a metaphysical being, then we must look for some reference system that is empirically representable and for which are valid the equations of mechanics both of Galileo and Newton. An attempt at this search is in Ernst Mach89, who identifies this system in what can be called the sky of fixed stars because a free body would move of uniform rectilinear motion concerning them and this is an empirically observable fact. The peculiarity in the thought of the Austrian physicist would be in the principle of rotational motion, in which Newton believed he could find the existence of motion in absolute space, so it would be necessary to re-establish that in the motions with respect to fixed stars, the principle of inertia would be valid only for a certain approximation: “Of particular importance is the application Mach makes of this his general principle to rotary motion. In this motion, Newton believed that he had the immediate empirical mark of the existence of a motion, with respect to absolute space; for the centrifugal phenomena, which we observe in rotation, occur, as he asserts, only in the case of a "real" rotation with respect to absolute space, not in the case of a mere relative motion. Thus, in particular, the crushing which we observe in a rotating mass, may be taken as a sign of its absolute rotation.”90 Where does the theory of relativity then stand here? Surely it has had the merit of having turned the problem of relative motion into a postulate, then of all the difficulties and obstacles that until this moment the physical thought has met, it makes a real virtue even if the assumption on which it is based is all of epistemological nature: if we analyse only the reference systems that have a uniform translation, then the inertial ones, they are not defined univocally through the phenomena, but their relationship is defined by Lorentz transformations, thanks to which we obtain the overcoming of the absolute meaning of the concept of simultaneity: “two events in a system K, measured according to clocks belonging to the same system, appear simultaneous, determined according to clocks of the 89 90 Ibidem, p. 115. Ibidem, p. 116. system K' do not proceed simultaneously”.91 Ergo, if two twin living being, one of which departed and the other instead remained in the system of belonging, the first would return from that voyage, younger than his brother, who is remained on Earth. The same applies to other quantities: length, shape, volume, and energy, in different systems, would be measured differently: “That is, to express even more concretely: a living being returns from such a journey "younger" than his former peer (let's imagine two twins, one of which remains at home and the other travels around the world on a ray of light or, whatever, on a channel ray, which has 1/1000 of the speed of light, the latter will return back who is a young man, while his twin brother became an old man). The same applies to the extent of length, shape, volume, and even to the temperature and to the energy of a body: in different systems they are measured differently.”92 91 92 Ibidem, p. 122. Ibidem, p. 124. Chapter III Open Comparison Between Einstein and Cassirer After showing the position of Einstein and then, the one of Cassirer and after introducing assumptions and problems, it is now time to go into more detail about what the latter writes about relativity. I would like to emphasize that the relationship between Ernst Cassirer and Albert Einstein, was never conflictual but of open dialogue and, at the beginning of the work Einstein's Theory of Relativity of 1920, Cassirer highlights how the purpose of his writing and his work in general, is to bring philosophers and physicists towards a deep understanding on issues, such as that of the object, truth and much more, where their first opinion diverges deeply, opening instead a debate of enrichment for both categories: “In this book, I have the sole purpose of trying to initiate such a collaboration, to give birth to a discussion, and if possible, in the face of the uncertainty that still characterizes the different evaluations, to initiate it along precise methodological guidelines. The paper will have reached its goal if it succeeds in opening the way to a mutual understanding between philosophers and physicists on issues around which their respective judgments diverge substantially.”93 In addition, Albert Einstein himself would have read the manuscript and would have affixed notes and criticisms: two great minds that do not come into conflict with each other, but in the debate enhance each other. From the very beginning, Cassirer's neo-Kantian training is loud and clear he begins with the introduction of the great work of Immanuel Kant (1724-1804)94, the Critique of Pure Reason (1781), which highlights that all the knowledge we have, comes from experience, especially if this knowledge precisely concerns the phenomena of nature. Considering this, how does the theory of relativity, both general and special, relate to our senses? First of all, the events that we experience are nothing but single Ernst Cassirer, Einstein's Theory of Relativity, 1920, foreword by G. Giorello, Castelvecchi, Lit Edizioni srl, Rome, 2015, p. 13. 94 Ibidem, p. 29. 93 observations, that added together will give rise to what we call experience, on the other hand, however, the role of thought and the application of an abstraction, are undoubtedly essential and no type of empiricism will ever deny it, as well as no idealism will ever deny the importance of the senses, as well as not even the Platonic one has ever done. Therefore, Einstein's theory brought to the surface a new way to cooperate between thought and perception, because it finds its roots in the contradiction of physical experiments, exactly the ones we have already talked about in the previous chapter: Fizeau's and Michelson's, which eventually led Einstein to issue the principle of the constancy of the speed of light, which, assisted by relativity in mechanics, became the real generator of the theory itself in the 1905 work, The Electrodynamics of Moving Bodies. Resuming what is said at the end of chapter two, we can now discuss the discourse regarding the measurements and the mathematical strategy used by Einstein himself to do this, namely the transformations of the already mentioned Lorentz: 't' = t - (v/c²) x / √1-v²/c².95 This means that the laws by which the states of physical systems change, no longer come to depend on the reference of these changes from one state to another, provided that they move in a uniform motion, so what the theory of relativity then tried to do was to abandon the belief that the measured values of the quantities of space and time, really remain uniform, thus discovering the well-known simultaneity of two processes, exactly as seen for the hypothetical journey of the twin brothers, in which every single quantity then must be measured according to the system in which we are moving at that moment, mathematically demonstrated by the equation just described, especially the final part 96 √1-v²/c² : “.. the theory of relativity has abandoned the belief that the values of measurement of spatial and temporal quantities remain uniform in different systems....by resorting to the 95 96 Ibidem, p. 34. Ibidem, p. 37. method of measuring time and the fundamental part that the speed of light plays in all our physical measurements of time, it discovers the relativity of the simultaneity of two processes and shows that, as results from the Lorentz transformations, even the value-measurement of the length of a body, its volume, its shape, its energy and temperature, and so on, is to be determined differently according to the reference system in which the measurement is chosen to be made.”97 Cassirer also points out that Einstein was right in rejecting the criticism, addressed to him by other physicists of the time, that the theory of general relativity is based on the contradiction of the theory of special relativity because the latter is based only on the consideration of phenomena that belong to the gravitational field: the very heart of general relativity leads to highlight that the very phenomena of nature are not the singular eventualities that we experience (as Newton and Galileo intended) but of the determined relations and dependencies that we explicate through the use of mathematics and physics. In this statement, there is the sense, according to Cassirer, of relativity as a natural conclusion of the scientific thought that has dominated the modern age, teaching us that in the measurement of certain quantities, we must always calculate the state of the physical system that we are analysing at that moment. Einstein’s theory wants to get rid of the residue of the presupposition regarding rigid bodies and systems at rest, by replacing the unit indicated by the constant c, which is the speed of light. The criticism that is made here by relativity, according to Cassirer, was born from the context of the already mentioned Critique of Pure Reason by Kant and addresses the concept of object, this is because the theory of 1905 does nothing but detach itself, as we have already had to see, from a naive view of the world and its facts, so it stands on a profoundly different gnoseological plan, which springs in a much broader discourse that directly touches on the metamorphosis of the concept of truth itself, in a heated debate with purely questions of pure logic: “Having dissolved both the concept of matter proposed by classical mechanics and the concept of ether elaborated by 97 Ibidem, p. 35. electrodynamics, the theory of general relativity has moved these "independent and permanent relations" elsewhere, but it has not denied them as such at all: rather, it has reaffirmed them most firmly in its invariants that remain indifferent to variations in the reference system. The criticism addressed by the theory of relativity to the physical concepts of object derives therefore from that methodology of scientific thought that led to the formation of such concepts: the theory of relativity does not do anything but push a step further this methodology, releasing itself more and more from the assumptions of the naive, sensitive conception of the universe as a world of things. In order to understand this fact in its full extent, we must necessarily go back to the more general question that the theory of relativity poses to us at the gnoseological level: to the transformation of the concept of the truth of physics that the theory contains within itself and that allows it to confront immediately a fundamental problem of logic.”98 III.I. Truth: Where Do its Boundaries Reside? If we took a step back in time, to be exact around the sixth century B.C. in what was then Magna Graecia, we would stumble upon what was then defined as the Eleatic School99 to which belonged personalities such as Parmenides, Zeno of Elea, Xenophanes of Colophon, and many others. In it, as in most of the ancient logic, the main clash was held between subject and predicate: the core was in the relationship between the given concept and its attributes, having as its ultimate goal, in general, to grasp the essential features of absolute substances, or even better of being. For example, if we look at the Eleatic logic, the will of its members was to eliminate regardless of the senses and their epistemological validity (the δοχα) and, instead, to assume criteria of necessity, such as those of truth and thus reach the being, one, eternal and immutable, opposed therefore to non-being. If instead, we moved to the modern field, we would see that logic has undergone a 98 99 Ibidem, p. 46. Eleatism: founded in the sixth century BC by Parmenides in Elea. The main feature is the profound difference between the sensible and changeable world and the intelligible world, object of reason, the only one that really exists and that can be identified with the Being. rather radical change: abandoned this opposition, it turns, on the contrary, its attention to concepts such as forms and relations, thus making the possibility of any determinacy of the content to be thought of depend on the validity of the forms, where the truth from being simply the direct expression of an image, it turns into the expression instead of a function. This turning point takes place thanks to Gottfried Leibniz100, although he was still bound in his vision, to monads and the world they constitute even though they are worlds closed in themselves: then, they would also express a common truth too. The theory of general relativity would have the merit according to Cassirer, of not claiming at all, that for every living being is true what appears to the senses, but on the contrary, not to take as truth the expression of the validity of which science is the guardian because, as we have already said, the natural phenomena themselves are valid only from the single reference system that we are considering at that moment. It would like to show how can issue utterances around this totality of events, in an overview: nothing arbitrary or accidental belongs to the phenomenon anymore : “The theory of relativity abandons this privileged position: not as if it could or would renounce the postulate of the univocal determinacy of the happening, but because it has new conceptual tools to satisfy this postulate... the physical theory of relativity does not want at all to claim that for everyone, that is true what appears to us, but on the contrary, it warns not to take already for truth, in a scientific sense, that is for an expression of the overall and definitive legality of experience, phenomena for which they are valid only starting from a single determined system of reference. The theory of general relativity shows the way that allows us to conceive a statement about this totality, the way that allows us to rise from the dispersion of individual views to an overall view of the happening.”101 The consequences then that Einstein's theory brings in terms of logical application must be treated in terms of the object and its determination, in fact if we would Ernst Cassirer, Einstein's Theory of Relativity, 1920, foreword by G. Giorello, Castelvecchi, Lit Edizioni srl, Rome, 2015, p. 51 101 Ibidem, p. 53. 100 start by stating that for all sentient subjects there are many different spaces and times, the synthetic unity (in the Kantian sense of the term) would be practically invalidated and only the individual perceptions would remain: by doing so, however, for Cassirer, we would return to the long-standing diatribe that Plato already opposed in the Theaetetus against Protagoras and sophistry in general.102 Each measure, taken by each observer, represents a single truth and the problem, instead of finding a point of arrival, continues to be interpreted. In the theory of general relativity, however, Cassirer points out that it confirms what Kant said about space and time as "forms of intuition" because, for the theoretical physicist, they are nothing more than simply systems of coordinates that take an immediate physical meaning and the synchronism of points-events remains possible and indeed, tends to express the laws of nature. It appears then clear to the neo-Kantian philosopher that the theory of general relativity, nothing else would do, but move in space and time as sources of knowledge, where however they would be eliminated as things in a physical sense. Therefore, the theory of 1915 tries to find the unity of nature according to a new sense that gathers the gravitational phenomena with those then electrodynamic, under a single fundamental principle of the knowledge of nature, which must be admitted, even if not explicitly, the concept of coincidence to which the theory itself refers when a certain content is traced back to the laws of nature: “The theory of relativity does not oppose in any way the logical universality of such an idea: on the contrary, it begins precisely with the consideration of all movements in space as simply relative, because otherwise it is not able to collect them in a certain empirical concept that unites all phenomena. Since the postulate of the totality of determination, it rejects any attempt to make a single determinate element, of a particular reference system, the norm of all others. The only valid norm remains the idea of the unity of nature, that is, of univocal determination itself. In this conception, the mechanistic conception of the universe has no more reason to exist. The theory of general relativity founds 102 Ernst Cassirer, The Philosophical Problems of the Theory of Relativity, 1921, edited and translated by R. Pettoello, Mimesis edizioni, MIM Edizioni srl, Sesto San Giovanni, 2015, p. 126. the unity of nature in a new sense, grasping the gravitational phenomena, which constitute the authentic field of investigation of the previous mechanics, together with the electrodynamic phenomena under a supreme fundamental principle of the knowledge of nature. One can precisely indicate the point at which the theory of general relativity must implicitly admit that methodical premise which in Kant goes under the name of "pure intuition." It is the concept of coincidence, to which the theory ultimately traces the content and form of all laws of nature.”103 Relativity then brings to the surface that, it is the functional thought to be part of the necessary motivations for any space-time determination: in this way, physics never knows its concepts in the form of a logical self, but only between their mutual connection. The whole physics then, is placed in the middle of two areas between which to mediate, without wondering what the origin might be: the multiplicity of sensitive data that each of us collects and the multiplicity instead of functions of form and order, because it comes to depend both on the material content of our experience, as well as formal and general principles. The history of physics therefore is not the simple discovery of facts, but the history of the discovery of specific conceptual tools in continuous renewal, where, however, it constantly wants to feel "safe" on the ground of a science that, however, represent nothing but the very birth of the problems that emerge in it: “Before we can analyse the coincidence of events and try to establish it with special methods of measurement, we must necessarily have already grasped the concept of "event" as a space-time event, we must have understood the sense that is expressed in it. As for its fundamental problem, physics is placed from the beginning between two areas that it must recognize and between which it must mediate without wondering further what is the "origin". On one hand we have the multiplicity of sensitive data, and on the other hand a multiplicity of pure functions of form and order. As an empirical science, physics is bound as much to the "material" contents offered to it by sensory perception as to these formal principles, in which the general 103 Ernst Cassirer, Einstein's Theory of Relativity, 1920, foreword by G. Giorello, Castelvecchi, Lit Edizioni srl, Rome, 2015, p. 76 conditions of the "possibility of experience" are experienced. It does not have to "discover" or deduce either one or the other field, but its task is resolved in putting progressively the realm of "forms" about the data of empirical observation and, vice versa, these to those. The history of physics is thus not the history of the discovery of a simple series of "facts", but the history of the discovery of specific and always new conceptual tools. Nevertheless, in each change of these conceptual tools, as physics moves along the "sure path of a science," it also confirms the unity of those methodological principles on which the same problem is founded.”104 In Einstein's theory, then, the core of the question would emerge only when it is a matter of connecting in the dimension of time, events that however are far apart in space. Einstein dedicates the first chapter of the part reserved to kinematics, to the definition of simultaneity and to the problems that are generated in the article that concerns the theory of relativity, that is On the Electrodynamics of Moving Bodies: if we consider a system of coordinates in which the equations of Newtonian mechanics are valid, this would be called "at rest" and if we consider a material point at rest concerning it, its position can be measured by rigid rulers in terms of coordinates, but still Cartesian type. If we wanted to describe the movement of a material point, then we would give the values of coordinates in function to time. But what does Einstein mean by "time"? Well, it is a description of simultaneous events and hence the famous example: “This train arrives here at 7 o'clock, this means something like the small hand of my watch on 7 and the arrival of the train are simultaneous.”105 Despite this, the definition of simultaneity does not seem to be completely sufficient when we consider events that take place in places far from where the clock is located, and not in the same place (such for example, the station where we are and where we read the timetable of trains and, obviously, the train itself). If we assume that at point A there is a clock so that an observer at the same point can 104 105 Ibidem, p. 80. Albert Einstein, On the Electrodynamics of Bodies in Motion, June 1905, published in the famous academic journal Annalen der Physik, in the cycle of four articles known as Annus Mirabilis Papers, Bern, p.2. evaluate the events that occur in the vicinity of A as simultaneous with the hands of the clock. At point B, then, there is a clock built exactly like the one at A, such that the same observations are possible as at A. We can then evaluate a time of A and one of B, but an overall time for A and B has not yet been defined: the latter must be described as the time that light takes from A to B and vice versa, i.e. the two clocks are simultaneous if: tB- tA = t1A - t1B . If we assume that, this contains no contradiction, then the timing of an event is the simultaneous indication of the event of a clock that is at rest at the event location and that is synchronized with a clock which is at rest too and which is maintained in this status for all the characteristics listed above. We could then establish this magnitude: 2AB / t1A - tA = V, where V is the constant, one and only, of the speed of light in vacuum, already seen and discussed in this paper repeatedly: “Consider a coordinate system in which the equations of Newtonian mechanics are valid. We call this coordinate system "system at rest" to distinguish it, in words, from other coordinate systems that will be introduced later and to represent it precisely. If a material point is at rest concerning this coordinate system, then, its position relative to it can be determined using rigid rulers and the use of Euclidean geometry methods and is expressed in Cartesian coordinates. If we want to describe the motion of a material point, then we give the values of its coordinates as a function of time. Now, we must pay attention to the fact that such a mathematical description makes physical sense only if we have first clarified what is meant here by "time". We must consider the fact that all our assertions, in which time enters, are always assertions about simultaneous events. When I say, for example, "This train arrives here at 7 o'clock," this means something like "The small hand of my watch on 7 o'clock and the arrival of the train are simultaneous events." It might seem, that all the difficulties encountered by the definition of "time" could be overcome if I used, instead of "time", "the position of the small hand of my watch". Such a definition is sufficient when it comes to defining time exclusively by the position of the small hand of the clock itself; however, the definition is no longer sufficient when it comes to temporally combining a series of events that occur in different places, or - which is the same thing - temporally evaluating events that happen in places far from the clock. On the other hand, we might be content to temporally evaluate these events through an observer, who stands at the origin of the coordinate system along with the clock, and who associates the corresponding position of the clock hands with each light signal that reaches him through the space and that represents an event to be evaluated. Such an association carries with it, however, the drawback of not being independent of the point of view of the observer provided with the clock, as we know from experience. We would arrive at a more practical determination through the following considerations. Let there be a clock at point A in space so that an observer who is at A can temporally observe events that occur near A by detecting the position of the hands of the clock, which is simultaneous with these events. A clock is also present at point B - we want to add "a clock built the same as the one at A" - so that a temporal evaluation of events is also possible near B, by an observer who is B. However, it is not possible, without further imposition, to compare an event in A with an event in B; so far, we have only defined a "time -A" and a "time-B", but not an overall time for A and B. The latter can be determined by establishing that the "time" that light takes to go from A to B is the same as the "time" that light takes to go from B to A. That is, a ray of light starts from A to B at "time-A" ta, is reflected in B to A at "time-B" tb and returns to A at time-A" t1a. The two clocks are synchronized if: tb - ta = t1a - tb. Suppose that this definition of synchronism is possible in a contradiction-free way, and certainly, for many arbitrary points, and that therefore, these relations are valid, in general: 1. If the clock in B is synchronized with the clock in A, then the clock in A is synchronized with the clock in B. 2. If the clock in A is synchronized as much with the clock in B as with the clock in C, then the clocks in B and C are also synchronized with each other. We have then established, with the help of a certain physical (just thought), experiment what is meant by synchronized clocks that are at rest in different positions, and thanks to that, we have obtained a definition of "simultaneity" and "time". The "time" of an event is the simultaneous indication to the event of a clock that is at rest in the position of the event and that is synchronized with a given clock at rest, and that clearly, keeps itself synchronized with this for all determinations of time. Based on the experience, we could also establish that the magnitude: 2AB/t1a - ta = V, is a universal constant (the speed of light in vacuum). It is essential to define time by means of clocks at rest in a system at rest; we can call this time we have just defined "the system time at rest," because it corresponds to the system at rest."106 Within this framework, then, it is confirmed the possibility of drawing and defining a "here" and a "now" distinct from each other, absolutely necessary to arrive at a delineation of space and time and their totality based on measurements made in them, which, however, the theory of relativity itself is not able to define on which it bases its space-time values. Thus, the boundaries of truth are not drawn in a strict sense from the logical point of view, but they are blurred in the relative position of an observer for whom the truth of his system applies. III.II. If Truth Has Blurred Boundaries ... Reality becomes Problematic After addressing the question of space, time, and truth, it is now time to face another discussion, the one concerning reality, which hides in itself the sum of the previous concepts and the questions they pose. Einstein's theory of general relativity, according to Cassirer, must be used as the last word of physics, because the relativization that it brings to all the notions listed above and the disintegration of the concept of nature itself in the measurements, is precisely the fulcrum of the physical process itself, the very gnoseological function of physics: to know nature in an "absolute" way, which is now unimaginable. Relativity, for Cassirer, can be well interpreted as the pure and as the general expression of the concept of a 106 Ibidem, p. 2-3. physical object, but the latter, on the other hand, no longer corresponds to reality itself: to believe that there are ideas of simple concrete reality, is an illusion. Only when we resist the desire to bring all the complexity to a kind of metaphysical, absolute, unwavering unity, to be placed at the foundation of the universe, only there, at that moment, reality itself will manifest to us its authentic content and with all of its wealth: “The general relativity of all places, all times and all measures must be the last word of physics, because the relativisation, the dissolution of the object "nature" in pure metric relations, is the very core of the physical procedure, the fundamental cognitive function of physics. However, if this is the sense in which to understand how the content of the thesis of relativity comes, according to an intrinsic necessity, from the form of physics, at the same time a precise critical limitation of this thesis emerges. The postulate of relativity may well be the purest, most general and rigorous expression of the physical concept of object, but precisely this physical object, from the point of view of general gnoseological criticism, does not immediately coincide with reality... every original direction taken by knowledge, every interpretation to which it subjects phenomena to gather them into the unity of a historical nexus - that is, a precise unity or unity of meaning - implies a particular version and representation of the concept of concrete reality... The task of a truly general gnoseological critique does not level this multiplicity, this polymorphous richness of forms of knowledge and intelligence of the universe, not crushing it in a purely abstract unity, but letting it subsist as such. Only when we resist the temptation of compressing it into an ultimate metaphysical unity, into the unity and the simplicity of an absolute "foundation" of the universe and deduce from this the complex of forms that manifest themselves, the authentic concrete content and its concrete richness is revealed to us.”107 And so, the task of philosophy will be precisely that of making us resist this temptation, so strong and so rooted in so many systems of thought, to escape from 107 Ernst Cassirer, Einstein's Theory of Relativity, 1920, foreword by G. Giorello, Castelvecchi, Lit Edizioni srl, Rome, 2015, p. 104. the one-sidedness to which it would lead us, and it is a task that goes beyond gnoseology itself: philosophy, particularly the systematic one, should embrace the complex, the totality of forms and associate with each form its role in the whole. Einstein's relativity has led physics to set a radically different explanation of phenomena and therefore of reality: every happening, is explained as corresponding to each point of the space-time continuum of four numbers, x1, x2, x3, x4, (the same seen in chapter one about arbitrary coordinates that allow Einstein to associate events to values that are close to them) which have no immediate physical meaning but are used to give a determination to the given event in the space-time, then it is clear that every single quality of space and time is reported in pure numerical values, the same that Pythagoras (V-VI sec. BC) and his School hoped for. Relativity thus seeks not only the differences of different experiences, and sensations but also those of space-time determination. At the end of this process, the professional physicist will affirm the priority of objective space and time, instead of subjective, while it seems quite clear that the philosopher and the psychologist, will draw the the opposite conclusion because they will turn to the immediacy of experience and lived experience: “In that complex which we call our 'world', the being of our ego and the being of things enter as equally necessary moments. We cannot exclude from this complex either of the two moments in favour of the other, but we can only assign to each the determined place that is due to it in the totality. In this regard, the physicist, whose task is all about objectification, affirms the priority of "objective" space and time over "subjective" space and time; the psychologist and the metaphysician, turned as they are to the immediacy of lived experience and totality, draw the opposite conclusion.”108 It is good to underline, however, how both positions are wrong because a false absolutisation, in one sense or the other, would be operated. In any case, the theory of relativity cannot fulfil the task of philosophy, and neither has the claim, because it turns its gaze, from the beginning to only one of the determinations of space and 108 Ibidem, p. 111. time, namely that of our empirical measurements. After this discussion, it is possible then to affirm that philosophy and gnoseology, should welcome with optimism the alternative and especially innovative impulses that the theory of general relativity gives to the principles of physics itself: “What space and time are, would be defined for us in a philosophical sense only if we could grasp together all the richness of their shades of meaning and establish the formal law that founds them and to which they obey. The theory of relativity cannot claim to fulfil this philosophical task, because from the beginning, according to its scientific formation and tendency, it addresses and limits itself to only one specific reason for the concepts of space and time. As a physical theory, it develops only the meaning that space and time have in the system of our physical-empirical measurements. And in this case, even the final judgment on it belongs exclusively to the physical science. It will be this, in the continuation of its history, to decide whether the image of the world proposed by the theory of relativity is stable on its theoretical foundations and finds a full experimental confirmation. Gnoseology is not able to anticipate the verdict that it will give on this matter, but as of now it can gratefully welcome the new impulses that the general doctrine of the principles of physics has received from the theory of relativity.”109 109 Ibidem, p. 113. Chapter IV. Albert Einstein at The Origin of the Creation of Relativity: Stories of Collaborations and Debates The core of my thesis was aimed at the direct comparison between Albert Einstein and Ernst Cassirer, who, as we have already been able to well notice, begins to be interested in the philosophical implications concerning the main concepts that relativity invests (space, time, truth, object and reality), since 1920 when in Berlin he publishes the essay Einstein's Theory of Relativity: Gnoseological Considerations, in which he argues a comparison between the general relativity and the immense work of Immanuel Kant. Within this work, of which I will report the bibliography too, Cassirer highlights many intrigues that the general relativity brings with it, but on the other hand, as I have already had the opportunity to point out, he also highlights the advantageous aspects and merits, such as wanting to simplify the system of nature. Cassirer's essay is certainly short, but extremely dense, so much to touch a bit on the whole history of epistemology and philosophy itself. What I would like to cast light on in this last chapter, is certainly the fact that, usually, when we talk about the theory of relativity (with reference always to the general one), we tend to consider it as a work of almost solitary origins, the work of a genius closed in his sphere, whom with a sudden illumination, sweeps away the secular antecedent classical physics. This is false, in fact, I have already mentioned in the introduction and in chapter one the many theories that Einstein himself used and modified to get to the composition of relativity: see for instance Riemann, Mach, Maxwell, and Hubble, but also those before him and one on them all, is certainly Newton's one and the deep criticism addressed to him. History, as we all know, is always much more complex and intricate than it is sometimes presented: the theory of relativity itself was born a few years earlier and belongs, actually, to Henri Poincaré (1854-1912), and specifically to the 1902 writing Science and Hypothesis 1902 and the subsequent article The Dynamics of the Electron, presented in June 1905 at the French Academy of Sciences. A young Albert Einstein, just twenty-three years old, came into contact for the first time with these issues when in 1902, together with two friends, Conrad Habicht (18761958) and Maurice Solovine (1875-1958), he founded in Bern a club known as the Olympia Academy, to discuss physics and philosophy, while his job was still that of an expert at the Patent Office of the city. This job was certainly monotonous and uninspiring, but it gave him plenty of time to work out his ideas, derived from the readings and discussions in his circle, which he kept in what he called his department of theoretical physics110, namely the second drawer of his desk. The first time they read together Poincaré's work was in 1904 and this peculiar edition presented an enrichment at the beginning of chapter VI: an article by the mathematician in which he discussed for the first time the relativity of time and the concept of simultaneity. One can easily imagine the astonishment of these young scholars in front of this kind of relativistic conjectures with which the author undermined Newtonian physics, using a new kind of geometry: the non-Euclidean geometry, as mentioned in the first chapter of this thesis, particularly the chronogeometry. Poincaré, however, in turn, did not start from scratch, in his investigation of physics: primarily, he adhered to the philosophy of Leibniz, whom harshly criticised Newton, opened for the first time a hypothesis of relativity in the physical sense, and the conception of nature in the electromagnetic sense. The major consequence that he obtained was from an epistemological point of view: the invariance of the laws in correlation to the invariance of the same physical reality for all the systems of reference: “In other words, the state of the bodies and their reciprocal distances at any time will depend only on the state of these same bodies and their mutual distances at the initial instant, but they won't depend at all on the initial absolute position of the system and its initial absolute orientation. In short, I could define this, as the law of relativity. Up to this point, I have spoken like a Euclidean geometer. But, as I have said, an experiment, whatever it may be, 110 Pedro G. Ferreira, The perfect theory: general relativity, a century-long adventure, translated by C. Caparro and A. Zucchetti, Rizzoli Editore, RCS Libri spa, Milan, 2014, p. 21. involves an interpretation according to the Euclidean hypothesis and likewise, it involves another one, according to the non-Euclidean hypothesis. Well, we have performed a series of experiments, we have interpreted them according to the Euclidean hypothesis, and we have recognized that such experiments, so interpreted, do not violate the law of relativity.”111 Moreover, thereby, a whole series of qualities that before were thought as objective, now would belong to the electromagnetic field itself, which would exist only in motion and never at rest. The case (or not?), however, wanted that the work written in a more extensive and detailed form, was presented by Poincaré on July 23, 1905 at the Mathematical Circle in Palermo112, but it was printed only in 1906, when the German physics journal Annalen der Physik, on September 30, 1905 had already published the well-known article, already mentioned, by Einstein "The electrodynamics of moving bodies". This delay was one of the reasons why Poincaré's work became less important than Einstein's, when he was the first to define the contours. The profound difference that separates the French physicist from the German is that the latter does not present in his work a new equation of mechanics, as the first one does: Einstein is limited to a mathematical loop whole for which, in any reference system at rest we can consider the equation F = m a, as valid, while Poincaré elaborates a new equation: F = dP/dt , i.e. force is translatable as the relation between the difference of momentum (P) and the differential of time (t). It will follow that: P = mem v , i.e., the momentum is equal to electromagnetic mass times velocity, and then F = v d mem /dt + mem dv/dt . Thereafter, Poincaré proposes a new elaboration for gravity as a force linked to a gravitational field that works just like an electromagnetic field and that propagates in electromagnetic waves, well before Einstein who will arrive only about ten years later, when he will publish the theory of general relativity in 1916. Einstein's situation, from of the fame's point of view, that these publications brought him, is much further Henri Poincaré, La Scienza e l'Ipotesi, 1902, preface by P. Odifreddi and translation by M.G. Porcelli, Edizioni Dedalo srl, Bari, 2012, p. 82. 112 Academic organization of mathematics, founded in 1884 by Giovanni B. Guccia and is the oldest Italian society of its kind. (via: Treccani encyclopedia). 111 complicated if we think that in the ten years following Poincarè's writing, other scholars presented the same ideas, but before, of course, Einstein himself, as for example David Hilbert (1862-1943) who published the same equations of the gravitational field, sometime before113. Moreover, in Einstein's theory there are many contributions of other physicists, which led to the completion of general relativity, such as that of Marcel Grossman (1878-1936), Swiss physicist and schoolmate of Einstein, who helped him thanks to his application of another type of a non-Euclidean geometry, the elliptic one114, as mentioned at the beginning and as well as in the first chapter. One of the most important reasons why Einstein was finally celebrated as the one and only genius creator of the theory of relativity, is actually a political one: when in 1933 Hitler's National Socialist Party took power in Germany, which led Einstein not to return to Europe but to settle in Princeton, New Jersey, where he taught at the homonymous University, the anti-Semitic discrimination did not concern only the Jewish population, but also its academic and cultural products and therefore there was a strong battle against relativity seen as a result of a "perverse" vision of the Jews towards reality. This extremely negative fact, however, brought Einstein to the forefront in the post-war period, when the opposite thought to the anti-Semitic one was established and this resulted in the simplification for which the extremely competent theorists that preceded him were almost set aside. Moreover, as is well known, in 1922 Einstein was awarded the prestigious Nobel Prize for Physics, but not for the theory of relativity, but for his studies on the photoelectric effect 115. According to a study conducted by Science, the authoritative scientific journal, in 1997, Hilbert would have sent his article with the equations on November 20, 1915, while Einstein five days later. That of the latter was published on December 2, while those of the former, only on December 6 without the equations. 114 Geometry constructed primarily by Bertrand Riemann. In it, there are no parallel lines and surfaces have positive curvature and the sum of the interior angles of a triangle is greater than a flat angle. (via: Treccani Encyclopedia). 115 Photoelectric effect: consists in the emission of electrons by a metal when it is hit by electromagnetic radiation having a certain energy. The frequency of this radiation is called critical v0 and is characteristic of each metal. It helped Einstein to understand how light was not only describable in wave terms, but also in corpuscular terms. (via: ChimicaOnline) 113 IV.I. A Further Step Forward: Einstein and Moritz Schlick116 From the beginning of the first decade of the 20th century, Moritz Schlick (18821936)117 was aware of what Albert Einstein was working out, both from of relativity's point of view and the so-called "hole argument "118. He was interested, a bit like Cassirer later, in the implications that Einstein's theory should have in particular on the concepts of object and reality and between the two there was an intense exchange of essays and meetings in person too, and it is for this reason Einstein was able to find a motivation to the fact that there would not be an exact equivalence between reference systems in relativity, assuming the multiplicity, complexity of space-time, in fact according to Schlick the reality of the object inside this conception, would be possible to support only starting from the explicit description of this object precisely in space-time. Briefly, what Schlick sustained was a bit a compendium of what Mach argued in his principle, used as a foundation by Einstein to arrive to the new gravitational field equations, and then, of an ontological and a cognitive points of view. The academic relations between Einstein and Schlick, however, were not restricted only to this and to the theory of relativity seen according to a physical and gnoseological point of view, but even invested a certainly new field, founded only at the beginning of the 20th century, For the elaboration of this paragraph, I would particularly like to thank Prof. Sascha Freyberg of the Max Planck Institut in Berlin, who provided me with valuable material, useful for the composition of this paper, especially with the text La ragione scissa, by Jürgen Renn. 117 Best known as the founder of the Vienna Circle in 1924, at the center of whose discussions there was for a long time the "Tractatus logico-philosophicus" of Ludwig Wittgenstein (1889-1951). 118 Hole argument: elaborated in August 1913, is the result of a series of physical and theoretical reflections. Einstein started from the fact that in a region of space-time, without matter (the hole), it was possible to distinguish two space-time points in a four-dimensional complexity only on the basis of their coordinates: he wanted to show that the field equations could not give any clear solution because of the hole. Nowadays this kind of solution, is proposed by the existence of the black hole body: a celestial body with a gravitational field so high that neither matter nor electromagnetic radiation can escape, from relativistic point of view is a region of space-time with a curvature so large that nothing can escape from its interior, including light because the escape velocity is greater than c. (via: The split reason by Jürgen Renn and GlobalScience, from "How to feed a black hole", by I. Marciano, July 30, 2021). 116 that is the Gestaltpsychologie119, the Gestalt psychology. In fact, Einstein wrote in 1922 a letter to the founder of the Vienna Circle, regarding the figure of Max Wertheimer (1880-1943), founder of this new discipline, in which he expressed the judgement that German psychology itself seemed to be neglected compared to the theory of knowledge. This opening to an area that seems so far from mere physics, was possible thanks to the very complications of relativity, which did not simply invest a certain area of restricted knowledge, but it expanded in many areas, even the one of the everyday life and emotions that affect the human being. To Schlick, space and time were then not only a mere mathematical construction, but it was even linked to the experiential foundation itself and to space-time coincidences. At the end of 1915, Albert Einstein and Moritz Schlick agreed that in physics the coincidences of the point as the only reality were observable in such a way, they were useful in the measurements as they were confluent from a mixture of mathematics, physics and psychology, as well as of maximum importance for the cognitive point of view. In brief, it appears plain that when we talk about theory of relativity, we enter in a much wider and articulated discussion, because it is not rare to find in manuals or anything else, the message that, as mentioned before, relativity was born only from the mind of one person. The complications, the unspoken, the implications, but surely also the resolutions that this theory exposes, are of ancient origin, they have a history behind them that it is surely worth to deal with, not to stop simply to a superficial resolution. It is enough to see the quantity (and the quality) of the names mentioned in this work: there is much more than you can believe and a quantity of contributions that have led Einstein to elaborate what he did, much more expanded than those usually reported on non-specific books. Therefore, the theory of relativity may have been published in 1916 by Einstein, but surely, it is the result of studies, criticism, material and mental 119 Gestaltpsychologie: focused on perception and experience, it is literally the psychology of form/representation in which the whole is different from the sum of the parts. The studies of those who adhered to it focused primarily on perceptual aspects, but also on problem solving skills. The discipline contributed to the investigation of learning, memory, thought and the interrelationship between subject and society. Nowadays it finds a great application in marketing strategies. (via: InPsiche). experiments, of long duration and great complexity. Chapter V. Conclusions: The core of my thesis, as I have had the opportunity to highlight over and over again, was the comparison, the transparent debate between Albert Einstein and Ernst Cassirer. The two of them, had the opportunity to confront each other several times and the work of the German philosopher was corrected and enriched by the physicist: this is not in this case of a bitter conflict between two very different minds, but an open dialogue, made of mutual exchanges, additions, constructive criticism and explicit gratitude for this exchange of ideas. Relativity, as seen in the introduction, is always a thorny issue to be addressed: many are the uncertainties that it opens, the shades of meaning that can take and the fields that are influenced, from physics in the strict sense, mathematics and geometry, philosophy, until even psychology and literature. In fact, in Modernism, to which belong writers such as Italo Svevo, Eugenio Montale, Luigi Pirandello and many others, the very vision of the world, reality and truth are deeply revolutionized because everything becomes relative, the laws that until the previous decade seemed unshakable, now instead are destroyed, in this case it is the gaze of the subject that affects reality, it then comes from a mental process. The tentacles that this theory is able to extend can then cover the major branches of human knowledge and culture, but despite this, Ernst Cassirer, in addressing the philosophical problems that it presents, does not have the pretension and the arrogance to dissect them all: he is aware of the scope of relativity. In the same way, he is perfectly aware of the fact that the tasks posed by relativity to a gnoseological critique, can be accomplished only thanks to the collaborative work of physicists and philosophers, together, not separated in their attitudes and in their paths of study: neither of the two categories should make a prevarication on the other one! The only thing Cassirer is concerned with, is to direct their work along a correct methodology120. 120 Ernst Cassirer, Einstein's Theory of Relativity, 1920, foreword by G. Giorello, Castelvecchi, Lit Edizioni srl, Rome, 2015, p. 13. Nowadays this collaboration, in my opinion, is certainly more evident even if not very accentuated because on the other hand it is easily explainable: who studies philosophy, usually deals with issues closer to logic, hermeneutics, ontology and so on, who studies physics instead, does not have a deep attraction for the cognitive and perceptive point of view that we have towards nature, they deal with the evisceration of issues that meet subjects as technology, climatology and much, much more. However, it is also true that this mixture of interests, if cultivated not only at an academic level, but also at a professional one, can lead to an extremely important baggage for the advancement of the unified human knowledge (just think of the recent Nobel Prize for Physics, Professor Giorgio Parisi who, between his various studies on complex systems and the search for the understanding of chaos, is able to range in many fields of knowledge), which I sincerely hope for my future, along with all those who are part of this research program, vast and complex, with the goal turned towards the future. Bibliography. Primary sources: Bowler P. J. and Morus I. R., Making modern science. Second edition, Chicago, University of Chicago Press, 2020. Cassirer E., Determinism and indeterminism in modern physics, edited and translated by G. Borbone, Sesto San Giovanni, Mimesis Editions, MIM Editions Srl, Filosofia/Scienza series n.28, 2020. Cassirer E., The Philosophical Problems of the Theory of Relativity. Lectures 19201921, edited by R. Pettoello, Sesto San Giovanni, Mimesis Editions, MIM Editions Srl, series Ricercare n. 10, 2015. Cassirer E., The concept of substance and the concept of function, edited by I. Bertoletti, translation by R. Pettoello, Brescia, Editrice Morcelliana, Small fires, 2020. Cassirer E., Einstein's theory of relativity, preface by G. Giorello, translation by N. Zippel, Rome, Lit Editions Srl, Castelvecchi, 2015. Einstein A., Scientific Autobiography, translation by A. Gamba, Turin, Bollati Boringhieri publisher, 2014. Einstein A., The meaning of relativity - The world as I see it, edited by E. Vinassa de Regny, translation by W. Mauro, Rome, Newton Compton Editori Srl, eleventh edition, 2019. Einstein A., The electrodynamics of bodies in motion, from the website of the National Institute of Nuclear Physics, Rome, PDF format. Einstein A., Cosmic Religion, edited by E.R.A.C. Giannetto and A. Taschini, Brescia, Morcelliana publisher, Red Pelican, 2016. Ferreira P. G., The perfect theory. General relativity: a century-long adventure, translated by C. Capararo and A. Zucchetti, Milan, , Rcs Libri Spa, Rizzoli, 2014. Fridman A., On the possibility of a world with constant negative curvature in space, published in the journal Zeitschrift für Physik by the Berlin, Academy of Sciences, January 7th, 1924, Vol.21 pp. 326-332. Hawking S. W. and Penrose R., The Nature of Space and Time. What the human mind can understand about the universe, translation by L. Sosio, Milan, Mondadori Libri Spa, BUR Rizzoli, third edition, 2018. Iliffe R., Newton. The Priest of Nature, translation by S. Di Bella, Milan, Hoepli publisher Spa, Le Biografie, 2017. The Holy Bible, edited by Sac Dr. F. Pasquero, translation from the Original Texts, Rome, Pia Società San Paolo, Book of Psalms and Book of Revelation, 1968. Newton I., Mathematical Principles of Natural Philosophy, edited and translated by F. Giudice, Turin, Giulio publishers Spa, Piccola biblioteca Einaudi Scienza, 2018. Nietzsche F. W., Thus Spoke Zarathustra. A book for everyone and no one, introduction by F. Masini, translation by A. M. Carpi, Rome, Newton Compton Editori Srl, Edizioni Integrali, fourth edition, 2016. Nietzsche F.W., The Gaia Science, edited by F. Masini, introduction by G. Colli, Milan, Adelphi Edizioni Spa, Adelphi e-book, 2015. Planck M., The unity of the physical worldview, Lecture presented in Leipzig, 1909. Planck M., The Essence of Light, Lecture delivered on October 28, 1919 at the general meeting of the Kaiser Wilhelm Society for the Advancement of Science. Poincaré J. H., Science and Hypothesis , preface by P. Odifreddi, translation by M. G. Porcelli, Bari, Edizioni Dedalo Srl, new edition. 2012. Renn J. and Engler F. O., The split reason. Of the end of a dialogue between science and philosophy, n.p., n.d. Spinoza B., Ethics, edited, translated and annotated by S. Landucci, Urbino, Editori Laterza Spa, Biblioteca universale, 2009. Secondary sources: ChimicaOnline, Photoelectric effect, https://www.chimica- online.it/download/effetto_fotoelettrico.htm , 04/09/2021. Global Science, Marciano I., black hole, https://www.globalscience.it/28322/come-si-nutre-un-buco-nero, 06/10/2021. IFAC National Institute of Applied Physics "Nello Carrara", Mugnai D., wavelength and refraction, http://www.ifac.cnr.it/index.php?option=com_content&view=article&id=123%3 Atoq-un-esperimento-diffrazione&catid=52%3Atoq&Itemid=146&lang=it 17/07/2021. INAF National Institute of Astrophysics, ABC of the Universe, Doppler effect, http://glossario.oa-cagliari.inaf.it/Doppler.html, 19/07/2021. INFN National Institute of Nuclear Physics, Compton effect, https://virgilio.mib.infn.it/~terranova/compton_2013_2014.pdf, 20/07, 2021. InPsiche, Dr. Calabretti G., Gestalt psychology, https://www.inpsiche.it/lapsicoterapia-della-gestalt-spunti-storici-epistemologici-e-teorici/, 06/10/2021. SapereScienza, Frova A., Michelson-Morley experiment, http://www.saperescienza.it/rubriche/fisica-e-tecnologia/il-paradosso-delletere-e-l-esperimento-di-michelson-morley , 09/09/2021. SPIE International Society for Optics and Photonics, Walker B.H., https://spie.org/Publications/Book/818136 https://spie.org/publications/tt82_25_speed_of_light , 09/09/2021. Treccani Encyclopedia, online Encyclopedia, chaos physics, https://treccani.it/enciclopedia/caos , 23/07/2021. Treccani Encyclopedia, online Encyclopedia, Coriolis force, https://treccani.it/enciclopedia/forza-di-coriolis , 17/07/2021. Treccani Encyclopedia, online Encyclopedia, elliptic geometry, https://treccani.it/enciclopedia/geometria-ellittica , 14/09/2021. Treccani Encyclopedia, online Encyclopedia, entropy, https://www.treccani.it/enciclopedia/entropia , 22/07/2021. Treccani Encyclopedia, online Encyclopedia, Mathematical Circle of Palermo , https://www.treccani.it/enciclopedia/giovan-battista-guccia , 04/09/2021. Treccani Encyclopedia, online Encyclopedia, perihelion, https://www.treccani.it/enciclopedia/perielio , 18/07/2021. Treccani Encyclopedia, online Encyclopedia, refraction, https://treccani.it/enciclopedia/rifrazione , 12/08/2021. Treccani Encyclopedia, online Encyclopedia, spatial isotropy, https://www.treccani.it/enciclopedia/isotropia , 19/07/2021. YouMath, FQA, https://www.youmath.it/domande-a-risposte/view/4067- grandezze-fisiche.html , 09/09/2021.