Epistemic Processes: A Basis for Statistics and Quantum Theory

This book discusses a link between statistical theory and quantum theory based on the concept of epistemic processes. The latter are processes, such as statistical investigations or quantum mechanical measurements, that can be used to obtain knowledge about something. Various topics in quantum theory are addressed, including the construction of a Hilbert space from reasonable assumptions and an interpretation of quantum states. Separate derivations of the Born formula and the one-dimensional Schrödinger equation are given.

In concrete terms, a Hilbert space can be constructed under some technical assumptions associated with situations where there are two conceptual variables that can be seen as maximally accessible. Then to every accessible conceptual variable there corresponds an operator on this Hilbert space, and if the variables take a finite number of values, the eigenspaces/eigenvectors of these operators correspond to specific questions in nature together with sharp answers to these questions. This paves a new way to the foundations of quantum theory.

The resulting interpretation of quantum mechanics is related to Hervé Zwirn's recent Convivial Solipsism, but it also has some relations to Quantum Bayesianism and to Rovelli's relational quantum mechanics. Niels Bohr's concept of complementarity plays an important role. Philosophical implications of this approach to quantum theory are discussed, including consequences for macroscopic settings.
The book will benefit a broad readership, including physicists and statisticians interested in the foundations of their disciplines, philosophers of science and graduate students, and anyone with a reasonably good background in mathematics and an open mind.

本書討論了統計理論和量子理論之間的聯繫，基於認識過程的概念。後者是指可以用來獲取關於某事物的知識的過程，例如統計調查或量子力學測量。本書涵蓋了量子理論的各種主題，包括從合理假設中建構希爾伯特空間以及對量子狀態的解釋。書中還提供了波恩公式和一維薛定諾方程的獨立推導。

具體而言，希爾伯特空間可以在某些技術假設下構建，這些假設與存在兩個被視為最大可訪問的概念變量的情況相關。然後，對於每個可訪問的概念變量，都對應著這個希爾伯特空間上的一個算子，如果這些變量取有限數量的值，這些算子的特徵空間/特徵向量對應於自然界中的具體問題以及對這些問題的明確答案。這為量子理論的基礎奠定了一條新的道路。

所得到的量子力學解釋與Hervé Zwirn最近的Convivial Solipsism有關，但也與量子貝葉斯主義和Rovelli的相對性量子力學有一些關聯。尼爾斯·玻爾的互補性概念起著重要作用。本書討論了這種對量子理論的方法的哲學意義，包括對宏觀環境的影響。

本書將對廣大讀者受益，包括對自己學科基礎感興趣的物理學家和統計學家、科學哲學家和研究生，以及具有相當良好的數學背景和開放心態的任何人。