Table Of ContentJan-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
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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
