In this post, we will see the book *Space and Time in the Microworld* by D. I. Blokhintsev .

About the book

In comprehending the physical content of dynamic variables which have geometric meaning, for example, the space-time particle coordinates x, y, z, t it is often necessary to have recourse to gedanken experiments which, although not feasible in practice, can nevertheless be compatible with the basic principles of geometry and quantum mechanics. In a desert sea of abstract constructions there is a still larger distance between macroscopic concepts of space-time and the way of employing the coordinates x, y, z and t in relativistic quantum field theory.

It is shown in this monograph that if elementary particles have a structure it is doubtful whether the coordinates of elementary particles, x, y, z, t, can even be defined exactly, let alone the coordinates of the elements which make up these particles (if they do not exist only in our imagination). This important fact is revealed in even the most favourable gedanken experiments.

From this fact, doubt arises about the logical validity of using the symbols x, y, z, t as the space-time coordinates to describe phenomena inside elementary particles. This allows theoreticians a certain freedom of choice of space-time and causal relationships within elementary particles; in other words, an arbitrariness of choice of the geometry in

the small.The last chapters of this book describe some models used to illustrate the situation described above. In concluding, experimental data and experimental possibilities relating to geometric and causal problems in the microworld are discussed.

The book was translated from Russian by *Zdenka Smith* and was published in 1970.

Credits to the original uploader.

You can get the book here.

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**Contents**

INTRODUCTION

**I. GEOMETRICAL MEASUREMENTS IN THE MACROWORLD 1**

1. The Arithmetization of Space-Time 1

2. The Physical Methods of Arithmetization of Space-Time 3

3. On Dividing the Manifold of Events into Space and Time 10

4. The Affine Manifold 19

5. The Riemann Manifold 23

6. The Physics of Arithmetization of the Space-Time Manifold 28

7. Arithmetization of Events in the Case of the Non-Linear Theory of Fields 33

8. The General Theory of Relativity and the Arithmetization of Space-Time 37

9. Chronogeometry 42

**II. GEOMETRICAL MEASUREMENTS IN THE MICROWORLD 44**

10. Some Remarks on Measurements in the Microworld 44

11. The Measurement of Coordinates of the Microparticles 46

12. The Mechanics of Measuring Coordinates of Microparticles 52

13. Indirect Measurement of a Microparticle Coordinates at a Given Instant in Time 64

**III. GEOMETRICAL MEASUREMENTS IN THE MICROWORLD IN THE RELATIVISTIC CASE 69**

14. The Fermion Field 69

15. The Uncertainty Relation for Fermions 74

16. The Boson Field 77

17. The Localization of Photons 82

18. The Diffusion of Relativistic Packets 86

19. The Coordinates of Newton and Wigner 89

20. The Measurement of a Microparticle’s Coordinates in the Relativistic Case

**IV. THE ROLE OF FINITE DIMENSIONS OF ELEMENTARY PARTICLES 95**

21. The Polarization of Vacuum. The Dimensions of an Electron 95

22. The Electromagnetic Structure of Nucleons 99

23. The Meson Structure of Nucleons 108

24. The Structure of Particles in Quantized Field Theory 114

**V. CAUSALITY IN QUANTUM THEORY 124**

25. A Few Remarks on Causality in the Classical Theory of Fields 124

26. Causality in Quantum Field Theory 132

27. The Propagation of a Signal “Inside” a Microparticle 141

28. Microcausality in the Quantum Field Theory 147

29. Microcausality in the Theory of Scattering Matrices 153

30. Causality and the Analytical Properties of the Scattering Matrix 159

**VI. MACROSCOPIC CAUSALITY 173**

31. Formal S-matrix Theory 173

32. Space-Time Descriptions Using the S-matrix 182

33. The Scale for the Asymptotic Time T 187

34. Unstable Particles (Resonances) 191

35. Conditions of Macroscopic Causality for the S-matrix 200

36. Examples of Acausal Influence Functions 207

37. An Example of Constructing an Acausal Scattering Matrix 211

38. The Dispersion Relation for the Acausal S_{a},-Matrix 219

**VII. A GENERALIZATION OF CAUSAL RELATIONSHIPS AND GEOMETRY 226**

39. Two Possible Generalizations 226

40. Euclidean Geometry in the Microworld 232

41. Stochastic Geometry 237

42. Discrete Space-Time 243

43. Quasi-Particles in Quantized Space 250

44. Fluctuations of the Metric 255

45. Nonlinear Fields and the Quantization of Space-Time 261

**VIII. EXPERIMENTAL QUESTIONS 269**

46. Concluding Remarks on the Theory 269

47. Experimental Consequences of Local Acausality 270

48. Experimental Results of Models with the “External” Vector 278

**APPENDICES 282**

**BIBLIOGRAPHY 326**

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