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On Probabilities in Quantum Mechanics

Inge Svein Helland

Published Feb 2, 2024• 1 citation
Publisher

Abstract

This is an attempt to clarify certain concepts related to a debate on the interpretation of quantum mechanics, a debate between Andrei Khrennikov on the one side and Blake Stacey and R\(\mathrm{\ddot{u}}\)diger Schack on the other side. Central to this debate is the notion of quantum probabilities. I first take up the probability concept in the QBist school, and then refer to my own arguments for the Born formula for calculating quantum probabilities. In that connection, I also sketch some consequences of my approach towards the foundation and interpretation of quantum theory. I discuss my general views on QBism as a possible alternative interpretation before I give some final remarks.

DOI
10.32388/7wjtql

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This is an attempt to clarify certain concepts related to a debate on the interpretation of quantum mechanics, a debate between Andrei Khrennikov on the one side and Blake Stacey and R(\mathrm{\ddot{u}})diger Schack on the other side. Central to this debate is the notion of quantum probabilities. I first take up the probability concept in the QBist school, and then refer to my own arguments for the Born formula for calculating quantum probabilities. In that connection, I also sketch some consequences of my approach towards the foundation and interpretation of quantum theory. I discuss my general views on QBism as a possible alternative interpretation before I give some final remarks.
This is an attempt to clarify certain concepts related to a debate on the interpretation of quantum mechanics, a debate between Andrei Khrennikov on the one side and Blake Stacey and Rüdiger Schack on the other side. Central to this debate is the notion of quantum probabilities. I first take up the probability concept in the QBist school, and then give my own arguments for the Born formula for calculating quantum probabilities. In that connection I also sketch some consequences of my approach towards the foundation and interpretation of quantum theory. I discuss my general views on QBism as a possible alternative interpretation before I give some final remarks.
This is an attempt to clarify certain concepts related to a debate on the interpretation of quantum mechanics, a debate between Andrei Khrennikov on the one side and Blake Stacey and Rüdiger Schack on the other side. Central to this debate is the notion of quantum probabilities. I first take up the probability concept in the QBist school, and then give my own arguments for the Born formula for calculating quantum probabilities. In that connection I also sketch some consequences of my approach towards the foundation and interpretation of quantum theory. I discuss my general views on QBism as a possible alternative interpretation before I give some final remarks.
This is an attempt to clarify certain concepts related to a debate on the interpretation of quantum mechanics, a debate between Khrennikov on the one hand and Stacey and Schack on the other hand. Central to this debate is the notion of quantum probabilities. I first take up the probability concept in the QBist school, as seen from my point of view, and then give my own arguments for the Born formula for calculating quantum probabilities. In that connection, I also sketch some consequences of my approach toward the foundation and interpretation of quantum theory. I discuss my general views on QBism as a possible alternative interpretation of quantum mechanics before I give some final remarks.
QBism is currently one of the most widely discussed 'subjective' interpretations of quantum mechanics. Its key move is to say that quantum probabilities are personalist Bayesian probabilities and that the quantum state represents subjective degrees of belief. Even probability-one predictions are considered subjective assignments expressing the agent's highest possible degree of certainty about what they will experience next. For most philosophers and physicists this means that QBism is simply too subjective. Even those who agree with QBism that the wave function should not be reified and that we should look for alternatives to standard Psi-ontic interpretations often argue that QBism must be abandoned because it detaches science from objectivity. The problem is that from the QBist perspective it is hard to see how objectivity could enter science. In this paper, I introduce and motivate an interpretation of quantum mechanics that takes QBism as a starting point, is consistent with all its virtues, but allows objectivity to enter from the get-go. This is the view that quantum probabilities should be understood as objective degrees of epistemic justification.
Abstract Over a dozen constructions have been proposed to untangle the foundations of quantum mechanics (QM). The authors have spent a lot of energy in establishing formal solutions but, to the best of my knowledge, have not carefully examined the methodological problems that arise before beginning a theoretical construct in QM. This paper argues on the following methodological obstacles: 1. The definitional and computational formulas. 2. The different theories of probability. We have also tried to solve problems 1 and 2, but the complete illustration of this attempt exceeds an article’s length, so this paper is limited to presenting 1 and 2, and discussing the intellectual and formal assumptions that should be necessary to unify the theories of probability.