用Clifford代数探讨量子力学的基本概念基础
An Investigation on the Basic Conceptual Foundations of Quantum Mechanics by Using the Clifford Algebra
摘要：
我们回顾了我们的量子力学的方法，也增加了一些新的有趣的结果。我们首先证明了两个重要定理的存在性和Clifford代数。这最后一个代数证明冯诺依曼基本假设的量子测量解释，从而在代数方式的波函数崩溃假设在标准量子理论。通过这种方式，我们达到了揭示量子力学自洽版本的目的。证明了量子类海森堡测不准关系、量子马赫-曾德尔干涉现象以及在某些物理意义下的量子坍缩，讨论了量子系统的时间演化和空间位置的变化问题。我们还给出了Kocken-Specher定理的证明，并给出了EPR的代数公式和解释。用同样的方法，我们还得到了贝尔不等式.我们的制定是强烈的基础上使用的幂等元，包含在Clifford代数。它们在量子力学中的对应物由投影算符表示，这些算符被解释为逻辑陈述，遵循基本的冯·诺依曼结果。利用Clifford代数，我们可以将这一结果反演.根据Orlov在1994年得到的结果，我们可以证明量子力学是从逻辑学中推导出来的。我们表明，不确定性和量子干涉有其起源的逻辑。
英文摘要：
We review our approach to quantum mechanics adding also some new interesting results. We start by giving proof of two important theorems on the existence of the and Clifford algebras. This last algebra gives proof of the von Neumann basic postulates on the quantum measurement explaining thus in an algebraic manner the wave function collapse postulated in standard quantum theory. In this manner we reach the objective to expose a self-consistent version of quantum mechanics. We give proof of the quantum like Heisenberg uncertainty relations, the phenomenon of quantum Mach Zender interference as well as quantum collapse in some cases of physical interest We also discuss the problem of time evolution of quantum systems as well as the changes in space location. We also give demonstration of the Kocken-Specher theorem, and also we give an algebraic formulation and explanation of the EPR . By using the same approach we also derive Bell inequalities. Our formulation is strongly based on the use of idempotents that are contained in Clifford algebra. Their counterpart in quantum mechanics is represented by the projection operators that are interpreted as logical statements, following the basic von Neumann results. Using the Clifford algebra we are able to invert such result. According to the results previously obtained by Orlov in 1994, we are able to give proof that quantum mechanics derives from logic. We show that indeterminism and quantum interference have their origin in the logic.
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