Opposed Views on the Reality of Time

Is time real or is it an illusion? Lee Smolin’s answer is that time is real but Carlo Rovelli has no definite answer.

Contents

1. Carlo Rovelli the Sceptic
2. Lee Smolin the Convert
3. And Me how I see the Space-Time

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Testimony

Quotes as abstract

„Why are numbers beautiful? It’s like asking why Beethoven’s Ninth Symphony is beautiful. If you don’t see why, someone can’t tell you. I know numbers are beautiful. If they aren’t beautiful, nothing is.” (Paul Erdős)

“Pure mathematics is, in its way, the poetry of logical ideas.” (Albert Einstein)

“Mathematics is the most beautiful and most powerful creation of the human spirit.” (Stefan Banach)

“Many who have had an opportunity of knowing any more about mathematics confuse it with arithmetic, and consider it an arid science. In reality, however, it is a science which requires a great amount of imagination.” (Sofia Kovalevskaja)

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Axiomatized Probability Theory in Physics – the beginning of a beginning

Contents

1. Introduction
2. The axiomatic system of the probability theory with the basic concepts of physics
3. Summary and conclusions
4. Appendix – The modified Kolmogorov’s axiomatic system of the probability theory
5. Appendix – Table of the parallels between different concepts of the probability theory

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In memoriam Attila József's death

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One of my favorite Ady verse; The straight star.

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The Universal Axioms of the Probability Theory

Contents

1. History
   1. The root equation of the probability theory
   2. The probability theory and the spacetime
   3. The probability theory and the continuum hypothesis (CH)
   4. Connection between CH and spacetime models
2. The universal axioms of the probability theory
3. Summary
4. Appendices

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The Key to Solving these Two Problems

„Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts.”
(David Hilbert, „Mathematical problems”)

Contents

1. Hilbert's 1st problem, continuum hypothesis (CH) and its current status
2. Quantified version of CH and its alternatives
   1. About infinity in other way – by the helps of positional numeral system
   2. About infinity in other way – by the methods of projective geometry
   3. Extensions of number lines and the lessons of CH’s alternatives
3. Hilbert's 6th problem, the axiomatization of mathematical physics and its current status
4. The basic concepts of the probability theory and the spacetime character of events
   1. The two-element numbers and the probability theory
   2. The two-element numbers and the spacetime
5. Summary

Appendix

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A poem from the past

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Quantum superposition, as I see

“The assumption of superposition relationships between the states leads to a mathematical theory in which the equations that define a state are linear in the unknowns. In consequence of this, people have tried to establish analogies with systems in classical mechanics, such as vibrating strings or membranes, which are governed by linear equations and for which, therefore, a superposition principle holds. Such analogies have led to the name 'Wave Mechanics' being sometimes given to quantum mechanics. It is important to remember, however, that the superposition that occurs in quantum mechanics is of an essentially different nature from any occurring in the classical theory, as is shown by the fact that the quantum superposition principle demands indeterminacy in the results of observations in order to be capable of a sensible physical interpretation. The analogies are thus liable to be misleading.” (P. A. M. Dirac, Principle of Quantum Mechanics)

Contents

1. Introduction
2. Dirac and the superposition
   1. Photon absorption
   2. Photon interference
3. Feynman path integrals and the superposition
4. Conclusions

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“It has often been said, and certainly not without justification, that the man of science is a poor philosopher. Why, then, should it not be the right thing for the physicist to let the philosopher do the philosophizing? Such might indeed be the right thing at a time when the physicist believes he has at his disposal a rigid system of fundamental concepts and fundamental laws which are so well established that waves of doubt cannot reach them; but, it cannot be right at a time when the very foundations of physics itself have become problematic as they are now.” (Albert Einstein, Physics and Reality)

Contents

1. Introduction
2. Newton vs. Huygens – Particle or wave
3. Bohr–Einstein debates –Non-locality or locality
4. Concluding comments

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