Introduction to foundations of probability and randomness (for students in physics), Lectures given at the Institute of Quantum Optics and Quantum Information, Austrian Academy of Science, Lecture-1: Kolmogorov and von Mises

TL;DR

This paper emphasizes the importance of a deep understanding of probability and randomness in physics education, especially for quantum information and foundations, and introduces foundational concepts through lectures to improve comprehension.

Contribution

It provides an accessible introduction to the foundations of probability and randomness tailored for physics students, based on lectures addressing classical and quantum interrelations.

Findings

High student interest in foundational probability issues

Lectures clarify classical and quantum probability relations

Educational gaps in physics curricula highlighted

Abstract

The education system for students in physics suffers (worldwide) from the absence of a deep course in probability and randomness. This is the real problem for students interested in quantum information theory, quantum optics, and quantum foundations. Here the primitive treatment of probability and randomness may lead to deep misunderstandings of theory and wrong interpretations of experimental results. Since during my visits (in 2013 and 2014) to IQOQI a number of students (experimenters!) asked me permanently about foundational problems of probability and randomness, especially inter-relation between classical and quantum structures, this year I gave two lectures on these problems. Surprisingly the interest of experiment-oriented students to mathematical peculiarities was very high. This (as well as permanent reminding of prof. Zeilinger) motivated me to write a text based on these lectures which were originally presented in the traditional black-board form. I hope that this might be useful for students from IQOQI as well as other young physicists.