dorsal/arxiv
View SchemaQuantum Mechanics
| Authors | Hitoshi Kitada |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0410061 |
| URL | https://arxiv.org/abs/quant-ph/0410061 |
| Journal | Lectures in Mathematical Sciences vol. 23, The University of Tokyo, 2005, ISSN 0919-8180, ISBN 1-000-01896-2 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
I consider in this book a formulation of Quantum Mechanics. Usually QM is formulated based on the notion of time and space, both of which are thought a priori given quantities or notions. However, when we try to define the notion of velocity or momentum, we encounter a difficulty as we will see in chapter 1. The problem is that if the notion of time is given a priori, the velocity is definitely determined when given a position, which contradicts the uncertainty principle of Heisenberg. We then set the basis of QM on the notion of position and momentum operators as in chapter 2. Time of a local system then is defined approximately as a ratio $|x|/|v|$ between the space coordinate $x$ and the velocity $v$. In this formulation of QM, we can keep the uncertainty principle, and time is a quantity that does not have precise values unlike the usually supposed notion of time has. The feature of local time is that it is a time proper to each local system, which is defined as a finite set of quantum mechanical particles. We now have an infinite number of local times that are unique and proper to each local system. Based on the notion of local time, the motion inside a local system is described by the usual Schr\"odinger equation. We investigate such motion in a given local system in part II. This is a usual quantum mechanics. After some excursion of the investigation of local motion, we consider in part III the relative relation or motion between plural local systems. In the final part IV, we will prove that there is at least one Universe wave function $\phi$ in which all local systems have local motions and thus local times. This concludes our formulation of Quantum Mechanics.
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"abstract": "I consider in this book a formulation of Quantum Mechanics. Usually QM is\nformulated based on the notion of time and space, both of which are thought a\npriori given quantities or notions. However, when we try to define the notion\nof velocity or momentum, we encounter a difficulty as we will see in chapter 1.\nThe problem is that if the notion of time is given a priori, the velocity is\ndefinitely determined when given a position, which contradicts the uncertainty\nprinciple of Heisenberg. We then set the basis of QM on the notion of position\nand momentum operators as in chapter 2. Time of a local system then is defined\napproximately as a ratio $|x|/|v|$ between the space coordinate $x$ and the\nvelocity $v$. In this formulation of QM, we can keep the uncertainty principle,\nand time is a quantity that does not have precise values unlike the usually\nsupposed notion of time has. The feature of local time is that it is a time\nproper to each local system, which is defined as a finite set of quantum\nmechanical particles. We now have an infinite number of local times that are\nunique and proper to each local system. Based on the notion of local time, the\nmotion inside a local system is described by the usual Schr\\\"odinger equation.\nWe investigate such motion in a given local system in part II. This is a usual\nquantum mechanics. After some excursion of the investigation of local motion,\nwe consider in part III the relative relation or motion between plural local\nsystems. In the final part IV, we will prove that there is at least one\nUniverse wave function $\\phi$ in which all local systems have local motions and\nthus local times. This concludes our formulation of Quantum Mechanics.",
"arxiv_id": "quant-ph/0410061",
"authors": [
"Hitoshi Kitada"
],
"categories": [
"quant-ph"
],
"journal_ref": "Lectures in Mathematical Sciences vol. 23, The University of\n Tokyo, 2005, ISSN 0919-8180, ISBN 1-000-01896-2",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Quantum Mechanics",
"url": "https://arxiv.org/abs/quant-ph/0410061"
},
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