Universe Without Things: Physics in an Intangible Reality PDF
Preview Universe Without Things: Physics in an Intangible Reality
Jan-Markus Schwindt Universe Without Things Physics in an Intangible Reality Universe Without Things Jan-Markus Schwindt Universe Without Things Physics in an Intangible Reality Jan-Markus Schwindt Dossenheim, Germany ISBN 978-3-662-65425-5 ISBN 978-3-662-65426-2 (eBook) https://doi.org/10.1007/978-3-662-65426-2 © Springer-Verlag GmbH Germany, part of Springer Nature 2022 The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content. This work is subject to copyright. 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Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer-Verlag GmbH, DE, part of Springer Nature. The registered company address is: Heidelberger Platz 3, 14197 Berlin, Germany Contents 1 I ntroduction 1 2 P hilosophy 11 2.1 Philosophy and Language 12 2.2 World and Mind: Schrödinger’s Dilemma 16 2.3 Devaluation of Philosophy 19 2.4 Wittgenstein vs. Jaspers 22 3 M athematics 27 3.1 Sets and Structures 30 3.2 Proofs 33 3.3 Mathematics: Man-Made or Man-Independent? 36 3.4 Numbers and Spaces 40 3.5 Differential Calculus 42 4 N atural Science 45 4.1 Our Common World 54 5 R eductionism 59 5.1 Reduction by Decomposition 66 5.2 Reduction by Generalization or Unification 75 5.3 Reduction by Replacement 76 5.4 Reduction of Effective Theories 77 5.5 The Special Role of Physics 79 v vi Contents 6 P hysics 81 6.1 History and Overview 81 6.2 Physical Theories and Experiments 84 6.3 Physics and Mathematics 98 7 The Pillars of Physics 101 7.1 Classical Mechanics 102 7.2 Classical Field Theory 107 7.3 Special Theory of Relativity 113 7.4 General Theory of Relativity 126 7.5 Statistical Mechanics 137 7.6 Quantum Mechanics 148 7.7 Quantum Field Theory 171 7.8 The Standard Model of Particle Physics 182 7.9 Cosmology 190 8 Th e Unknown 207 8.1 The Hunt for the Theory of Everything 207 8.2 Open Questions 213 8.3 The Crisis of Physics 223 8.4 The Multiverse 233 9 Th ings and Facts 237 9.1 Facts 237 9.2 Things 250 9.3 World and Reality 253 9.4 Time 256 10 The Practical Limits of Physics 261 10.1 Once Again: Scales 264 11 The Fundamental Limits of Physics 269 11.1 The Hard Problem of Consciousness 270 11.2 The Flow of Time 274 11.3 Qualia and Physicalism 277 Contents vii 12 C onclusion 283 12.1 Physics and Reality 283 12.2 The Richness of Physics 287 12.3 Practical Limits and Crisis of Physics 288 L iterature 291 I ndex 293 List of Figures Fig. 7.1 Modified Pythagorean theorem in spacetime. (i) “Normal” Pythagorean theorem in two spatial dimensions. (ii) and (iii) Modified theorem with a cathetus a in space and a cathetus b in the time direction, where b is longer than a in one case and shorter in the other 115 Fig. 7.2 If the coordinate system is rotated, distances are preserved and can be calculated according to the same rule. Here B has coordinates (3, 4) in the coordinate system (x, y), and coordinates (5,0) in the coordinate system (x′, y′). The distance to A is 5(cid:31) 32(cid:30)42 (cid:31) 52(cid:30)02 117 Fig. 7.3 By the modified Pythagorean theorem, the distance between events A and B is not 52(cid:31)42 (cid:30)6,4, but 52(cid:31)42 (cid:30)3 119 Fig. 7.4 Otto’s time axis runs through A and B. Due to the modified Pythagorean theorem, it appears to be stretched out to a certain extent (“time dilation”) 120 Fig. 7.5 “Twin paradox”. Otto has aged by six time units on the way A-B-C, Erwin on the direct way from A to C by ten. In the direction of time, the direct path is not the shortest but the longest 121 Fig. 7.6 Lorentz transformation. (x, t) is the reference frame of Erwin, (x′, t′) that of Otto on his way from A to B. A ray of light travels along the diagonal (or angle bisector), in both reference frames 122 Fig. 7.7 A macrostate A evolves to a macrostate B with higher entropy. Higher entropy means that many more possible microstates belong to B than to A. Because of time reversal invariance, all processes can also run backwards on the level of microstates. So there are just as many microstates running from A to B as from B to A. However, these make up only a tiny fraction of all micro- states in B. If B is given, the probability that B will evolve to A is therefore virtually zero 146 ix x List of Figures Fig. 7.8 Simple example of a Feynman diagram. Two electrons (e−) are scattered by each other. The diagram symbolizes a certain math- ematical contribution to the scattering, which can be understood as the exchange of a single “virtual photon” (γ). The time runs from the bottom to the top 177 Fig. 10.1 Finite section of an in principle infinite “scale line”. The LHC scale refers to the length scale that is just resolved by the LHC particle accelerator 266 1 Introduction I think there are basically two different motivations to deal more intensively with physics. One is the engineering approach. You want to understand how the technology around you works, the car, the refrigerator, the lamp, the mobile phone, the energy supply; what natural laws underlie it and how you can use these laws to design something new and thus solve practical problems. The other is the philosophical approach. Here one is driven by questions like: What is the world? How did it come into being? Will it end one day? What is the “reality” behind things? Is everything ultimately mathematically comprehensible? And what am I? A lump of atoms? Some kind of computer program running on a brain? Or something else entirely? How are space and time related? And so on. For me, the motive was clearly philosophical. When I was little, my father used to take me to shows at the Mannheim Planetarium. The stars and planets themselves weren’t that important to me; I wanted to know how big the uni- verse was, whether it had a boundary, how it started. I wanted mysterious words like the “big bang”, “expansion” and “space-time” explained to me. And because they were mentioned mostly only in passing, I often became impatient. At 13, I took matters into my own hands, learned special relativity, began devising my own thought experiments and drawing conclusions, most of which were complete nonsense. Feverishly driven by my questions, over the next 2 years I devoured every popular science book on fundamental physics I could get my hands on. At 16, I lost sight of physics for a while in the turmoil of a typical teenager’s life. But at least I remained faithful to mathematics, which had always © Springer-Verlag GmbH Germany, part of Springer Nature 2022 1 J.-M. Schwindt, Universe Without Things, https://doi.org/10.1007/978-3-662-65426-2_1
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