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Chongqing Shifan Daxue xuebao. Ziran kexue ban

The Uncertainty Principle and Basic Hypothesis and Constant

Gou Xian

Published Jan 1, 2000• 0 citations
OpenAlex

Abstract

The uncertainty principle is one of the objective natural laws. It is an important relative formula in physics. The uncertainty principle can be obtained from the commutator of operators or from the diffraction of electron. In this papar, the various expressions are obtained from plank postulates and Bohr pestulates and de Broglie postulates. And then ,if can be obtianed from every espression of the uncertainty principle corresponding to one constand. [WT5HZ]

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The uncertainty principle is one of the objective natural laws. It is an important relative formula in physics. The uncertainty principle can be obtained from the commutator of operators or from the diffraction of electron. In this papar, the various expressions are obtained from plank postulates and Bohr pestulates and de Broglie postulates. And then ,if can be obtianed from every espression of the uncertainty principle corresponding to one constand. [WT5HZ]
This paper is a small discussion about the uncertainty principle. With the great discoveries and researches made by predecessors, I try to answer some questions within the uncertainty principle. Using the definition of momentum, the momentum in de Broglie wave, the property of cosine function, the Euler’s formula, the basic property of plane wave, the law of derivative, the energy of quantum discovered by Max Planck, the photon energy discovered by Albert Einstein, the energy equation of a system and the Hamiltonian operator, I figure out the Schrodinger equation successfully. With the help of Schrodinger equation, the possibility density of a wave function, the concept of normalization, the average value of position and momentum, the Fourier transform, the integration by parts and the limit of normalized wave functions, I find the position operator and the momentum operator. Then using some knowledge of the standard deviation and the variance, the concept of inner product of vectors, some property of Dirac symbol, the law of calculation of complex number and the law of operator calculation, I obtain the general uncertainty relationship of abstract mathematical quantities. According to the general relationship, I get the inequality of uncertainty principle, and discuss the specific relationship between the position and the momentum. After getting the inequality, I use Heisenberg’s experiment of measuring an electron by using the γ ray to hit the electron to explain why we cannot measure the position and the momentum simultaneously. Based on Heisenberg’s experiment, I give my own explanation by discussing the earth and a spacecraft. Transforming the perspective, we can easily see how the accuracies of position and momentum change. In addition, I attempt to figure out why the uncertainty exists. However, I can only explain it by discussing the time and frequency in mathematical method and have no idea to work it out in a pure physics approach.
The uncertainty principle is the most important for the foundations of quantum mechanics but it still remains failed to reach a consensus of its interpretation, which gives rise to debates upon its physical nature. In this work, we address the problem of its foundation from a different aspect to present an alternative formulation for proving the uncertainty relations in a general way in terms of commutation relations and action function. The relationship between the de Broglie relation and the uncertainty principle is studied from a new angle. As a result, it is demonstrated that the de Broglie relation is the foundation of the uncertainty principle. Starting with the origin of the problem, we show that the de Broglie relation provides the form of the wave function and the determined form of the wave function in turn leads to the conception of operators for quantum mechanics, and thus it is possible to provide with the help of the operators and wave function a generalized proof of the uncertainty principle as the law governing ensemble of states. As a decisive solution to the problem, the interpretation of the uncertainty principle in terms of the action function is offered that gives one self-consistent explanation in agreement with the known physical phenomena. Eventually, we show the necessity and possibility of reassessing and improving the foundation and interpretation of the uncertainty principle as a leading principle of quantum mechanics.
The more scientists learned about the atom, the less categorical became the questions they put to nature. The uncertainty relation is a strict law of nature, which is in no way related to some imperfections of our devices. The uncertainty relation is directly opposed to intuition and everyday experience. Heisenberg explained the matter by discarding still another idealization of classical physics — the concept of observation. It turned out that in quantum mechanics it had to be revised, along with the concept of motion. The concepts of “phenomenon”, “measurement”, and “observation” are closely related to one another but they are by no means identical. Any measurement is essentially interaction between the instrument and the object to be studied. The principle that Bohr named complementarity is one of the most fundamental philosophical and scientific ideas of our time, which can only be compared to the principle of relativity and the concept of a physical field.
Heisenberg’s uncertainty principle is a milestone of twentieth-century physics. We sketch the history that led to the formulation of the principle, and we recall the objections of Grete Hermann and Niels Bohr. Then we explain that there are in fact two uncertainty principles. One was published by Heisenberg in the Zeitschrift für Physik of March 1927 and subsequently targeted by Bohr and Hermann. The other one was introduced by Earle Kennard in the same journal a couple of months later. While Kennard’s principle remains untarnished, the principle of Heisenberg has recently been criticized in a way that is very different from the objections by Bohr and Hermann: there are reasons to believe that Heisenberg’s formula is not valid. Experimental results seem to support this claim.