Epistemic Processes: A Basis for Statistics and Quantum Theory
暫譯: 認識過程：統計學與量子理論的基礎
Inge S. Helland
- 出版商: Springer
- 出版日期: 2021-10-16
- 售價: $5,640
- 貴賓價: 9.5 折 $5,358
- 語言: 英文
- 頁數: 244
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 3030819221
- ISBN-13: 9783030819224
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相關分類:
機率統計學 Probability-and-statistics、量子 Quantum
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商品描述
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.
商品描述(中文翻譯)
這本書探討了基於認識過程概念的統計理論與量子理論之間的聯繫。後者是指一些過程，例如統計調查或量子力學測量，這些過程可以用來獲取有關某事的知識。書中涉及了量子理論的各種主題，包括從合理假設構建希爾伯特空間以及對量子態的詮釋。對於波恩公式和一維薛丁格方程的推導也分別給出了。
具體而言，可以在一些與兩個概念變數相關的技術假設下構建希爾伯特空間，這些變數可以被視為最大可接觸的。然後，每個可接觸的概念變數都對應於這個希爾伯特空間上的一個算子，如果變數取有限個值，這些算子的特徵空間/特徵向量則對應於自然界中的特定問題以及這些問題的明確答案。這為量子理論的基礎鋪平了一條新路。
所得到的量子力學詮釋與Hervé Zwirn最近的《共生唯我論》有關，但它也與量子貝葉斯主義和Rovelli的關係量子力學有一些關聯。尼爾斯·玻爾的互補性概念在其中扮演了重要角色。這種對量子理論的詮釋的哲學意涵也被討論，包括對宏觀環境的影響。
這本書將使廣泛的讀者受益，包括對其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，以及任何具有相當數學背景和開放思維的人。
作者簡介
Inge S. Helland completed his cand.mag (B.S.) in mathematics and physics at the University of Bergen in 1970. After a research fellowship at The Niels Bohr Institute, Copenhagen in fall 1971, he turned to statistics, and completed his cand.real. (M.S.) at the University of Bergen in 1973. He was a fellow at the University of Bergen from 1973 to1978, including a research stay at the University of California, Berkeley in 1977 and 1978. He was then an Associate Professor of Statistics at the Agricultural University of Norway, later Norwegian University of Life Sciences, from 1978 to 1983, and Professor at the same university from 1983 to 1996.
He obtained his dr. philos. degree on limit theorems for stochastic processes from the University of Oslo in 1980, and was Professor of Statistics at the University of Oslo from 1996 to 2012, when he went took on an emeritus position. His research covers a large area of theoretical and applied statistics, including proposing a statistical model connected to the chemometricians' partial least squares algorithm.
作者簡介(中文翻譯)
Inge S. Helland 於1970年在卑爾根大學完成數學和物理學的 cand.mag (學士) 學位。1971年秋季，他在哥本哈根的尼爾斯·玻爾研究所進行研究獎學金後，轉向統計學，並於1973年在卑爾根大學完成 cand.real. (碩士) 學位。他在卑爾根大學擔任研究員，期間為1973年至1978年，包括在1977年和1978年於加州大學伯克利分校的研究停留。隨後，他於1978年至1983年擔任挪威農業大學（後來的挪威生命科學大學）的統計學副教授，並於1983年至1996年擔任該大學的教授。
他於1980年在奧斯陸大學獲得有關隨機過程極限定理的 dr. philos. 學位，並於1996年至2012年擔任奧斯陸大學的統計學教授，之後轉為名譽教授。他的研究涵蓋了理論和應用統計學的廣泛領域，包括提出與化學計量學家部分最小二乘法算法相關的統計模型。
