What is meant by uniform relative movement

Space and Time in Contemporary Physics

About the reflection of light in an inhomogeneous layer / space and time in contemporary physics pp 159-286 | Cite as

As an introduction to understanding [the theory of relativity and gravity]
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Part of the Moritz Schlick. Complete edition book series (MSKG, volume 2)

abstract

The rapid exhaustion of the third German edition of this little book shows that despite the abundance of recently published writings on the theory of relativity, it still has a right to exist.1 It can only owe its justification for continued existence to its peculiarity, which distinguishes it from other writings on the same subject, and so I tried to preserve and reinforce this peculiarity for the fourth edition. The presentation still places the greatest emphasis on a tangible, illuminating elaboration of the basic ideas and introduces the reader to the main questions from that side which seemed to be the most accessible. In order to clarify such points, which experience has shown to cause difficulties for understanding, the new edition has been extended by a whole series of insertions. Other improvements and additions have also been made. The main purpose of writing is to describe the scientific doctrines presented in it in their relationship to knowledge in general, i.e. in their philosophical meaning. The greatest emphasis is therefore placed on the general theory of relativity, which is of particular importance for natural philosophy and the worldview. The last one, | explicitly philosophical, chapters have received some additions, but I have resisted the temptation to give a detailed exposition of the philosophical consequences of Einstein's teachings; it would have been neither necessary nor desired in the context of this document

X, A: 〈of general relativity〉

X: 〈Privatdozent Dr. Moritz Schlick, Rostock〉

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  1. With regard to the verifiability of the general theory of relativity, Schlick had expressed himself much more cautiously in his essay on the philosophical meaning of the principle of relativity. Compare with Schlick, Relativity principle, Pp. 169-171. Later, however, it reads elsewhere: “No more doubt: the general theory of relativity is brilliantly confirmed; one of the greatest triumphs of the human spirit has been achieved. Albert Einstein is rightly praised [...] all over the world as a new Newton today. The transformation of the most fundamental concepts (space, time, matter) brought about by his genius has no equal in the history of science. "(Schlick, confirmation, P.8) Google Scholar
  2. So also Schlick, theory of relativity, 58f. Google Scholar
  3. With the year 1905, Schlick refers to Einstein's first publication on the special theory of relativity (see Einstein, Electrodynamics) .Google Scholar
  4. Compare with Larmor, Ether.Google Scholar
  5. See Newton, Principles, P. 25. There it says: “The absolute, true and math time flows in itself and by virtue of its nature uniformly, and without relation to any external object. [... ] The absolute space by virtue of its nature and without any relation to an external object, it always remains the same and immobile. ”Google Scholar
  6. See Leibniz, Nouveaux Essais, Livre II, Chapitre XXVII, § 1. Google Scholar
  7. The qualitative formulation of this physical hypothesis can originally be found in Fitzgerald, Ether, P. 390. It is presented in mathematical form for the first time in Lorentz, Relative motion, P. 221 and more in detail in the same., attempt, Pp. 119-124. The effect of molecular forces is connected with the assumption of the Lorentz contraction. It reads: "Now, some such change in the length of the arms in Michelson's first experiment and in the dimensions of the slab in the second one is so far as I can see, not inconceivable. What determines the size and shape of a solid body? Evidently the intensity of the molecular forces; any cause which would alter the latter would also influence the shape and dimensions. Nowadays we may safely assume that electric and magnetic forces act by means of the intervention of the ether. It is not far-fetched to suppose the same to be true of the molecular forces. "(Lorentz, Relative motion, P. 221) Google Scholar
  8. What is meant here in particular is the light and ether concept of Augustin Fresnel, against the background of which Lorentz in particular worked out his concept of a “dormant” ether. See Lorentz, attempt, Pp. 120-122. Google Scholar
  9. Schlick is referring here to Einstein's analysis of the assumptions under which we make length and time measurements. As a result of his kinematic considerations, Einstein arrives at terms of length and simultaneity, which do not have absolute validity, as previously assumed, but are to be understood relative to a certain coordinate system. See Einstein, Electrodynamics, Sections 1–2.Google Scholar
  10. Regarding the distinction made here by Schlick between the principle of relativity and the theory of relativity (as the epitome of the conclusions that can be derived from the principle of relativity) cf. Relativity Principle, Pp. 133 and 142. Google Scholar
  11. Einstein also speaks in this context of an "epistemological deficiency" of the special (compared to the general) theory of relativity. See Einstein, basis, P. 771.See also ders., Relativity problem, P. 344. Google Scholar
  12. Elsewhere, Schlick goes so far as to claim that these terms have "a completely different meaning" for Einstein than for Newton. See Schlick, confirmation, 6 Google Scholar
  13. This was precisely what the contemporary opponents of the theory of relativity disputed. See e.g. B. Farsky, Relative, P. VI: "Copernicus' merit lies in the fact that he took a step forward in the direction from the subjective (relative) to the objective (absolute), contrary to what Einstein does. [...] The newer theory of relativity [is therefore] nothing more than a return to the times of Ptolemy [sic!]. "Google Scholar
  14. Schlick understands the difficult mathematical apparatus in particular as the tensor calculus. This leads to a significant simplification of the mathematical representation of the special theory of relativity and is also a necessary prerequisite for the development of the formalism of the general theory of relativity. The tensor theory was worked out in the 19th century based on Carl Friedrich Gauß and Georg Friedrich Bernhard Riemann, in particular by Elwin Bruno Christoffel, Gregorio Ricci-Curbastro and Tullio Levi-Civita. For a detailed description of the historical context and the importance of the tensor calculus for general relativity, see Klein, lectures, Chap. 3. Google Scholar
  15. Against this background, cf. also Einstein, Do, P. 102: “Concepts which have proven useful in the ordering of things easily acquire such an authority over us that we forget their earthly origin and accept them as unchangeable givens. They then become ’necessities for thinking’, ’given a priori’, etc. stamped. Such errors often make the path of scientific progress impassable for a long time. It is therefore by no means an idle gimmick if we are trained to analyze the concepts that have long been familiar and to show the circumstances on which their justification and usefulness depend, how they have grown out of the givens of experience. This breaks their overly great authority. They are removed if they cannot legitimize themselves properly, corrected if their assignment to the given things was overly negligent, replaced by others if a new system can be set up, which we prefer for whatever reason. ”Google Scholar
  16. The interference experiment cited by Schlick was first carried out in 1881 by Albert Abraham Michelson on Astrophysical Observatory carried out in Potsdam. The experiment was repeated with greater precision six years later by Michelson and Edward Williams Morley in Cleveland and subsequently by others. The explanation of its negative outcome - the experimental proof of the ether as a stationary carrier medium of the wave propagation of the light could not be provided - gave rise to the discussion of the prevailing ether hypothesis as an absolutely excellent reference system. Nevertheless, it is controversial whether the Michelson-Morley experiment had a decisive influence on the establishment of the special theory of relativity in 1905.Google Scholar
  17. See e.g. B. Lorentz, ask, P. 101: “Aether, ponderable matter, and we want to add electricity, are the building blocks from which we assemble the material world, and if we once knew whether matter, as it moves, carries the aether with it or not, so we would be given a way on which we can delve a little further into the essence of these building blocks and their mutual relationships. ”Google Scholar
  18. See an illustration in a mug, Natural philosophy, P. 316. Google Scholar
  19. See z. B. Lodge, grade, P. 344: “[T] he aether is a physical standard of rest; and motion relative to it, which is cognisable by us, is in that sense an ascertained absolute motion. "Google Scholar
  20. See Lorentz, attempt, P.4: “That of absolute It goes without saying that there is no question of the calm of the aether; the phrase wouldn't even make sense. When I say, for the sake of brevity, that the ether is at rest, I only mean that one part of this medium does not shift towards the other and that all perceptible movements of the heavenly bodies are relative movements in relation to the ether. "Google Scholar
  21. See Michelson, The relative motion and Michelson / Morley, On the relative motion. Further Lorentz, Interference attempt.Google Scholar
  22. Michelson, The relative motion, P. 122.See also Born, Theory of relativity, P. 162, fig. 106. Google Scholar
  23. For the mathematical details see ibid., Pp. 160–163.Google Scholar
  24. See Michelson, The relative motion, P. 128: "The result of the hypothesis of a stationary ether is thus shown to be incorrect, and the necessary conclusion follows that the hypothesis is erroneous." Google Scholar
  25. On the capacitor experiment by Frederick Thomas Trouton and Henry R. Noble cited by Schlick here, see Trouton / Noble, Forces. Schlick goes into the condenser rotation tests carried out in the years 1901–1903. In this experiment, originally proposed by FitzGerald, the torque exerted on a plate capacitor is determined by suspending the capacitor so that the axis of rotation is parallel to the plane of the plate and perpendicular to the direction of motion of the earth. The magnetic field of the capacitor tends to be perpendicular to the direction of movement. The influence of an ether wind as a result of the movement of the capacitor with the earth through a stationary ether as a second order effect on the torque of the capacitor at the moment of its charging could not be proven, as stated by Schlick. Google Scholar
  26. Similar to silt, Einstein's theory of relativity, Pp. 109-111. Laue provides a detailed overview of the experimental basis of the special theory of relativity, theory of relativity, § 3 Google Scholar
  27. Newton himself discusses the problem of whether one could experimentally prove a straight line motion to be an absolute motion in the notes to the chapter "Mathematical Principles of Natural Science" of his Principia and comes to the conclusion that one cannot determine by observing movements (displacements) alone whether a rectilinear uniform movement is an absolute movement. See Newton, Principles, P. 30. So did Galileo, dialog, P. 121. Google Scholar
  28. See Einstein, Electrodynamics, P. 891: “[T] he unsuccessful attempts to establish a movement of the earth relative to the 'light medium' lead to the assumption that the concept of absolute rest not only in mechanics but also in electrodynamics does not have any properties of Phenomena correspond, but rather that the same electrodynamic and optical laws also apply to all coordinate systems to which the mechanical equations apply, as has already been proven for the quantities of the first order. We want to make this assumption (the content of which will be called the “Principle of Relativity” in the following) as a prerequisite [...]
  29. See also Einstein, theory of relativity, P.9: "Is K′ A relating to K Uniform and rotation-free moving coordinate system, this is how natural occurrences run in relation to K′ According to exactly the same general laws as with respect to K. We call this statement the 'principle of relativity' (in the narrow sense). ”Google Scholar
  30. See also Einstein for the following, theory of relativity, § 7 and Schlick, Relativity principle, Pp. 138-140. Google Scholar
  31. Newton first developed this conception, also known as the “corpuscular theory” of light, in 1675 and then v. Chr. a. in his Opticks from the year 1704. See Newton, Opticks, esp. Query 31. Google Scholar
  32. See Ritz, Research.Google Scholar
  33. See Einstein, Electrodynamics, P. 895, where the principle of invariance (or constancy) of the speed of light is introduced for the first time and is defined as follows: “Every ray of light moves in the 'resting' coordinate system at a certain speed V. [here: c], regardless of whether this light beam is emitted by a body at rest or in motion. ”See also the detailed (primarily against Neo-Kantianism) discussion of this principle in Schlick, Relativity Principle, Pp. 156-163. Google Scholar
  34. See Einstein, Electrodynamics, P. 892: “The introduction of a 'light ether' will prove to be superfluous, as, according to the conception to be developed, neither an 'absolutely calm space' equipped with special properties nor a point of empty space in which electromagnetic processes take place is introduced , a velocity vector is assigned. ”Google Scholar
  35. See also Einstein on the following, theory of relativity, Sections 8–12.Google Scholar
  36. See Einstein, Electrodynamics, P. 896: “The generally used kinematics tacitly assumes that [...] a moving rigid body in the time epoch t completely through in geometrical relation same Body when in certain position rests, is replaceable. ”Google Scholar
  37. In this context, however, see the relevant writings of Poincaré and Cohn, Electrodynamics. On the latter cf. also the explanations above, p. 166, note c-1.Google Scholar
  38. See Einstein, basis, P. 774, note: “We assume that 'simultaneity' can be determined for spatially immediately adjacent events, or - more precisely - for spatiotemporal adjacentness (coincidence) without giving a definition for this fundamental term." Google Scholar
  39. See in detail MSGA I / 1, A209 f., B. 224 f.Google Scholar
  40. See Einstein, Electrodynamics, P. 897: “So we see that we have no concept of simultaneity absolute We are allowed to attach importance, but that two events, which, viewed from a coordinate system, are simultaneous, viewed from a system moving relative to this system, are no longer to be understood as simultaneous events
  41. See Schlick, Relativity Principle, P. 141: “One must not say that a staff 'appears' to be shorter in relation to one system than in relation to another; a distinction between the apparent and real length of the rod must not be made in this sense. Rather, all observers resting in any authorized system can join same Rights refer to the 'real' length of the rod as the one that you determine from your own system, because none of the various authorized systems has an exceptional special position. There is no such thing as an 'absolute' duration or an 'absolute' length; the term length is a relative one, as are the terms 'longer' and 'shorter'. "Similar to Born, theory of relativity, Pp. 186-192. Google Scholar
  42. On the "clock paradox" referred to by Schlick below, see Einstein, Electrodynamics, P. 904 f. And Born, theory of relativity, Pp. 190-192. Google Scholar
  43. Compare with the following v. a. Einstein, Electrodynamics, § 3. See also Born, theory of relativity, Pp. 175-178. Google Scholar
  44. The term "Lorentz transformation" comes from Poincaré (cf. Electron, P. 1505). In their current form, the equations can be found in Lorentz, Apparitions, P. 9 Google Scholar
  45. See Einstein, Electrodynamics, P. 903: “Our considerations become meaningless for faster than light speeds; Incidentally, we will find in the following considerations that the speed of light physically plays the role of the infinite speed in our theory. ”Google Scholar
  46. Schlick's assertion that the law of mass and the law of conservation of energy stood side by side on an equal footing in pre-relativistic physics cum grano salis to understand. Georg Helm, for example, had postulated - albeit with different intentions - that mass could be traced back to the law of conservation of energy almost 20 years before Einstein. See helmet, Teaching, Pp. 56-66. Similar to Ostwald, Studies.Google Scholar
  47. For the following, see Einstein, inertia.Google Scholar
  48. Schlick is thinking here of radioactive elements, the decay of which converts part of the mass of the atomic nucleus into radiation energy of high intensity. See Hahn, Meitner, Radioactive substances, Meitner, radioactivity and this., Energy development.Google Scholar
  49. See Einstein, theory of relativity, P. 31: “Pre-relativistic physics knows two conservation laws of fundamental importance, namely the law of conservation of energy and the law of conservation of mass; these two fundamental propositions appear to be quite independent of one another. The theory of relativity fuses them into one sentence. ”Google Scholar
  50. Schlick agrees with Becher's considerations here. In a letter from Becher to Schlick it says: “[...] with regard to the concept of substance, we are objectively very close. But I think we can too the Hold on to the concept of substance, which makes it the bearer of properties. The electromagnetic field 'carries' properties, e.g. B. spatial. Nevertheless, I agree with you that there is much justification in Locke-Humean's criticism. The mistake lies in the fact that the 'carrier' relationship has often been misunderstood. It is not the substance that stands 'behind' the properties as a special, mysterious carrier, but this is the independently existing epitome of the same, which carries the individual dependent properties. [...] The philosopher's task remains to eliminate incorrect versions of this useful term, absolutizations to which the human spirit tends, which turn the relatively independent into something absolutely independent, eternal, a causa sui and the like. In terms of philosophy and history, the term substance is admittedly badly burdened; but that doesn't have much to say for natural science. ”(Erich Becher to Moritz Schlick, December 26, 1915) Cf. also MSGA I / 1, A244 f., B260 f. And Schlick, Relativity Principle, Pp. 172–175 as well as Becher, World buildings, P. 10. Google Scholar
  51. See also Petzoldt, space and time. Also the introduction above, p. 38, note 111. Google Scholar
  52. Schlick is probably thinking here of the (usually referred to as "relationalism") views of Gottfried Wilhelm Leibniz, George Berkeley and, as will become clear later, Ernst Mach. Leibniz (in his correspondence with the Newtonian Samuel Clarke) z. B. writes: “As far as my own opinion is concerned, I have said more than once that I consider space as well as time to be something purely relative, namely an order of coexistence, just as time is an order of succession. Namely, space is a possible order of things that exist at the same time, whereby one regards them as existing together without asking about their particular way of existing. "Leibniz, Correspondence, Third letter to Dr. Clark, § 4, p. 37 f. Google Scholar
  53. See in detail MSGA I / 1, A152 f., B159 f.Google Scholar
  54. Planck, Lanes, P. 44. In the original: “Because what can be measured also exists.” Google Scholar
  55. A critical discussion of this criterion can be found in Cassirer, theory of relativity P. 14 f. But see also Schlick's own restriction, below, p. 284. Google Scholar
  56. In addition to the metric (measuring) and the projective geometry, there is the analysis situs or purely qualitative geometry in the Poincaré sense. In contrast to metric geometry, which uses measurable quantities to characterize space, Analysis situs dispenses with any dimensional determinations in geometry. See Poincaré, Value of science, First part, third chapter, § 2 and v. a. ders., Pensées, Chapitre III, § 1. See also Schlick's remarks in Helmholtz, Axioms, P. 28, Erl. 21. Google Scholar
  57. Schlick is probably referring here to the controversy in mathematics of the late 19th century between supporters and opponents of an axiomatic (and to that extent no longer descriptive) Objects acting) geometry in the sense of David Hilbert. See Hilbert, geometry, §§ 1–8 and Pasch, geometry. See also MSGA I / 1, B § 7 Google Scholar
  58. Against the background of the following, see v. a. also Einstein, geometry.Google Scholar
  59. See Helmholtz, Axioms, Pp. 18-22. Google Scholar
  60. See Poincaré, Science et method, Livre II, Chapitre I, v. a. Pp. 96-103. Google Scholar
  61. See Mongré, chaos, Pp. 72-123, especially pp. 84-89 and pp. 92-101. The German mathematician Felix Hausdorff hides behind the pseudonym Paul Mongré. As can be seen from the received correspondence, Hausdorff first approached Schlick in 1919 and asked him about his book The chaos in cosmic selection pointed out (cf. Felix Hausdorff to Moritz Schlick, February 23, 1919). Schlick's reply has not survived. But see Felix Hausdorff to Moritz Schlick, July 17, 1920, where Hausdorff thanks Schlick for his benevolent assessment of his book. See also the reference to Hausdorff's book in MSGA I / 1, B229.Google Scholar
  62. Poincaré, Science et method, P. 97: "En réalité, il vaudrait mieux dire que l’espace étant relatif, il ne s’est rien passé du tout et que c’est pour cela que nous ne nous sommes aperçus de rien." Google Scholar
  63. See also Mongré on the following, chaos, Pp. 85-89. Google Scholar
  64. Regarding the connection between measurement and spatiotemporal coincidence mentioned by Schlick, see also his explanations in Helmholtz, Fonts, P. 29, Erl. 30 and p. 32, Erl. 39. See also, below, p. 231. Google Scholar
  65. Similar to the résumé in Mongré, chaos, P. 105 f. Google Scholar
  66. See Helmholtz, Axioms, Pp. 20-24. Google Scholar
  67. See Poincaré, Value of science, P. 46 f Google Scholar
  68. See also the representation in Born, theory of relativity, Pp. 227-234. Google Scholar
  69. See Gauss, Investigations. On the concept of "Gaussian coordinates" see Hilbert, physics, P. 58 f., Where this term is probably used for the first time.Google Scholar
  70. See Born, theory of relativity, P. 228, fig. 126. Google Scholar
  71. See also Schlick's comment on Helmholtz, Axioms, P. 33, Erl. 45: "Recognizing the pointlessness of the question of which of the two described worlds is the 'real' and which is the deformed one is of the utmost importance for the entire problem. There is no real ’difference at all between the two worlds, but only one of the description, in that both cases are based on a different coordinate system [...]. In other words: in both cases we are dealing with the same objective reality, which is represented by two different systems of signs. ”Google Scholar
  72. That Schlick is concerned here with the simplicity of the scientific system is expressed even more clearly elsewhere. This is what his commentary on Helmholtz reads, Axioms, P. 32, Erl. 38: “But it is not the simplicity of a single branch or aid of science that is decisive, but ultimately the simplicity of the system of science, which is identical with the unity of the knowledge of nature. This supreme simplicity is more perfectly achieved today by dropping Euclidean geometry than by keeping it. ”Google Scholar
  73. See Poincaré, Value of science, P. 44: “Obviously, when we say that the Euclidean straight line is a real Even though the non-Euclidean straight line is not, just say that the first intuition gives one more important Subject corresponds to as the second. ”Google Scholar
  74. Poincaré says in this connection: “One sees that experience plays an inescapably necessary role in the genesis of geometry; but it would be a mistake to conclude from this that geometry, even if only in part, is an empirical science. [...] Experience guides us in this choice, but does not impose it on us; it does not let us know which geometry is the most correct, but which it does most convenient is. "(Poincaré, Science and hypothesis, P. 72 f.) Google Scholar
  75. See MSGA I / 1, A299, B322 for Google Scholar
  76. In the original: "[L]’ espace est en réalité amorphous et les choses qui sont dedans lui donnent seules une forme. " (Poincaré, Science et method, P. 102 f.) Google Scholar
  77. On the following, see also Schlick's comments in Helmholtz, Axioms, P. 36 f.Further Schlick, Helmholtz, Pp. 36-38. Google Scholar