|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'504'928
Articles rated: 2609
25 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
From probabilistic mechanics to quantum theory | | Ulf Klein
; | | Date: |
19 Jul 2019 | | Abstract: | We show that quantum theory (QT) is a substructure of classical probabilistic
physics. The central quantity of the classical theory is Hamilton’s function
$H(q,p)$, which determines canonical equations, a corresponding flow
$phi_{t}^{H}$, and a Liouville equation for the probability density
$
ho(q,p,t)$. We extend this theory in two respects: (1) The same structure is
defined for arbitrary observables $A(q,p)$. Thus, we obtain entities
$phi_{alpha}^{A}$, and $
ho_{A}(q,p,alpha)$, where $alpha$ is the
independent variable in the canonical equations. (2) We introduce for each
$A(q,p)$ an action variable $S_{A}(q,p,alpha)$. This is a redundant quantity
in a classical context but indispensable for the transition to QT. The basic
equations of probabilistic mechanics take a "quantum-like" form, which allows
for a simple derivation of QT by means of a projection to configuration space
reported previously [Quantum Stud.:Math. Found. (2018) 5:219-227]. We obtain
the most important relations of QT, namely the form of operators,
Schr"odinger’s equation, eigenvalue equations, commutation relations,
expectation values, and Born’s rule. Implications for the interpretation of QT
are discussed, as well as an alternative projection method allowing for a
derivation of spin. | | Source: | arXiv, 1907.8513 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER