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Chinaxiv:201910.00072V3 The Uncertainty Principle and the Certainty Rule Delong DUAN (Aerospace Information Research Institute, Chinese Academy of Sciences; Institute of Electronics, Chinese Academy of Sciences， Beijing 100190， China) Abstract Objective: Analyze and resolve differences between the uncertainty principle and quantum theory in physical interpretation. Methods: The original derivation and physical meaning of the mathematical relationship of Heisenberg's uncertainty principle were re-examined, and the limits of the relationship under different action scenarios were investigated. Results: Under the electromagnetic interaction scenario, through the analysis of the statistical distribution of quantum mechanical quantities and its full probability space, the result of the destruction of the uncertainty relationship under non-statistical interpretation is obtained; Using Fourier transform, the standard deviation constraint relation of the corresponding conjugate mechanical quantity under the virtual action scene is derived; By investigating the collection of electromagnetic interaction scenarios, gravitational interaction scenarios, and virtual interaction scenarios, the deterministic criterion of the mechanical state of microscopic quantum objects is chinaXiv:201910.00072v3 obtained. Limitations: Unanalyzed Entanglement. Conclusions: ①The non-statistical interpretation has logical contradictions；the uncertainty relationship, and the current quantum mechanics theory can properly describe the mechanical state of the microscopic quantum object only in the electromagnetic interaction scene under the statistical interpretation; ② The deterministic criterion shows that the mechanical state of microscopic particles is objectively certain, and its wave function is an *Corresponding author: De-Long DUAN (E-mail: [email protected]) 1 / 15 20200920(2012) expression of the statistical appearance of the mechanical state of microscopic particles in the context of electromagnetic interaction. The quantum probability of non-statistical interpretation refers in essence to the description of the statistical probability of the interaction between microscopic particles and the interaction scene. Keywords: quantum mechanics, uncertainty principle (relation), Copenhagen interpretation of quantum mechanics, probability distribution，gravitational waves PACS: 03.65.Ca, 03.65.Ta, 05.30.ch, 02.50.Sk, 04.40.Dg 1. Introduction 1.1 Background introduction and problem elicitation Quantum mechanics is called by Jammer M. as the only logically consistent theory about the micro-primitive process. It has laid the foundation of modern science, is the cornerstone of the development of contemporary material and information science-technology, and has achieved unprecedented success in the history of science1234. At the same time, the dispute between the interpretation of quantum mechanics and the physical interpretation of Heisenberg's uncertainty principle-the fundamental difference between the two interpretations represented by Bohr and Einstein, has been existing for a long time. The uncertainty principle, as a proposition called "principle" in the theoretical system of quantum mechanics5, is called the cornerstone of the quantum mechanics theory by Pauli and Dirac of the Bohr school. The construction of the mathematical formal system of quantum mechanics is ahead of its physical interpretation. In order to solve the quantum mechanics formal system ①whether the position and velocity of a particle can only be determined with limited accuracy at a given moment, ②whether the accuracy the theory allows is compatible with the best accuracy obtained in the experimental measurement1346, Heisenberg derived the uncertainty relation and proposed the uncertainty principle in March 1927. The proposal of the uncertainty principle is considered to be a major achievement in the history of science-it demonstrates the sharp contrast between the indeterminacy of quantum mechanics and the determinism in classical mechanics. It is the theory of quantum mechanics which signs of essential differences with classical mechanics theory57. chinaXiv:201910.00072v3 As soon as Heisenberg's uncertainty relation and its physical interpretation were put forward, it immediately attracted the attention of Einstein and Bohr. At the Solvay Conference held in October of that year, Einstein and Bohr had a heated debate on it. From the logical consistency of the uncertainty principle, which is equivalent to the logical self-consistency of quantum theory, to the completeness of the quantum mechanics theory targeted by the EPR theory, from 1927to the end of their lives, the ongoing debate between Einstein and Bohr lasted for decades. Although after the debate with Bohr in 1927 and 1930 at the two Solvay Conferences, Einstein no longer publicly questioned the validity of the uncertainty principle, but in fact he never agreed with Bohr-Heisenberg's interpretation basis. Moreover, it should be noted that until the end of his life in 1962, Bohr was not completely confident and affirmed of the uncertainty principle and the non-statistical interpretation of quantum mechanics that he and Heisenberg had been insisting on18. The physics community has no objection to the mathematical derivation of the uncertainty relation. The fundamental difference lies in the physical interpretation of the uncertainty principle that began in the Einstein-Bohr era. The physical interpretation of the uncertainty relationship is divided into the following two schools according to Jammer’s research 1： Ⅰ Statistical Interpretation-the interpretation insisted by Einstein and Schrödinger: the uncertainty relationship describes the ensemble composed of identically prepared quantum systems, and the lower limit of the product of the standard deviation of the statistical distribution 2 / 15 20200920(2012) of the regular conjugate variables is ħ⁄2. Its essence is to insist on rather than give up the precise description of the classic cause and effect. Ⅱ Non-statistical Interpretation-Bohr-Heisenberg interpretation: The uncertainty relationship is a description of an individual quantum system, whose regular conjugate variables cannot be accurately determined at the same time, and the lower limit of the product of uncertainty is ħ⁄26, this is the mainstream interpretation of quantum mechanics, also known as the orthodox interpretation of quantum mechanics or the Copenhagen interpretation. Its essence is to adhere to the individual probability of quantum mechanics. 1.2 Problem solution and meaning At present, the application technology of quantum mechanics is developing rapidly, but the theoretical interpretation is still binary oppositions and cannot be unified. This awkward situation has caused great troubles for the further improvement of new theories and new technologies based on quantum mechanics. In view of the history and current status of the physical interpretation of the quantum mechanics theory marked by the uncertainty principle, this article will first examine the original derivation and physical meaning of the uncertainty principle relation, the probability analysis and discussion of the non-statistical interpretation of the uncertainty relation are carried out under the electromagnetic interaction; then the corresponding mathematical relations are deduced by analogy in the picture of gravitational action scene, and finally, the uncertainty relation and the evolution of the mathematical form of the wave function are investigated through the limit analysis of the basic action unit of the virtual action picture. The research results of this paper show that the orthodox non-statistical interpretation of quantum mechanics is difficult to maintain its theoretical the self-consistency and logical consistency, negating the theory that quantum mechanics is the only logical consistency of the fundamental process, and restoring the original statistical appearance of uncertainty relations and quantum mechanics. 2. The formulation and non-statistical interpretation of the uncertainty principle Literature review Heisenberg published "On the Intuitive Content of Quantum Theory's Kinematics and Mechanics"16in March 1927, proposing the Heisenberg uncertainty principle and giving the mathematical derivation of the relationship, 1929 HP Robertson use quantum mechanics operators to express the normative proof of uncertainty relations. Heisenberg derives the following relationship in 6 through the mathematical form of quantum mechanics: chinaXiv:201910.00072v3 ħ ∆ ∆ ≥ (1) q p In the formula(1), ∆ ≡ ∆ − ∆ ≡ 2 ∆ − . At the same time, a 2 2 2 2 physical interpretation of thqe un(ceqrt)ai=nty pxrinxcip,lepwas c(arpr)ied=outpbx y ptaxking γ-ray microscope and electronic single slit position determination and other thought experiments as examples12. The definition of uncertainty relation is the accuracy limit of quantum theory for simultaneous measurement of several different physical quantities, emphasize that any experiment measuring position Q, every observation must interfere in some way with the velocity (momentum)P (and vice versa)；and the degree of uncertainty of this change must limit the knowledge (accuracy) of the electron motion with respect to position Q and velocity (momentum) P to the uncertainty relation after the experiment is completed6，"Any exact observation (accuracy) must be subject to the uncertainty relationship 8. It is considered that the uncertainty principle protects the logical self-consistency of quantum mechanics10, the emphasis
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