Abstract For a long time, the academic community believes that quantum mechanics and classical mechanics are two greatly different mechanical systems, and the algorithms of quantum mechanics cannot be used to solve classical mechanics problems [1] . However, starting from classical mechanics, this paper proves through rigorous mathematical methods that classical mechanics and quantum mechanics have exactly the same mathematical algorithms. For example, concepts such as wave function, probability amplitude and superposition state can also describe the random motion states of macroscopic objects. This paper mainly adopts mathematical calculation, supplemented by computer simulation experiments, and verifies the correctness of the mathematical calculation process from both theoretical and experimental perspectives. No assumptions are needed in this paper, and all concepts are derived and proved through strict mathematical deduction. These derivation steps show that concepts such as probability amplitude and wave function are universal concepts applicable to random motion processes, which can be used for both macroscopic objects and microscopic particles, and are not unique calculation methods of quantum mechanics. PACS: 03.65.Ta, 03.50.Kk
Abstract For a long time, the academic community believes that quantum mechanics and classical mechanics are two greatly different mechanical systems, and the algorithms of quantum mechanics cannot be used to solve classical mechanics problems [1] . However, starting from classical mechanics, this paper proves through rigorous mathematical methods that classical mechanics and quantum mechanics have exactly the same mathematical algorithms. For example, concepts such as wave function, probability amplitude and superposition state can also describe the random motion states of macroscopic objects. This paper mainly adopts mathematical calculation, supplemented by computer simulation experiments, and verifies the correctness of the mathematical calculation process from both theoretical and experimental perspectives. No assumptions are needed in this paper, and all concepts are derived and proved through strict mathematical deduction. These derivation steps show that concepts such as probability amplitude and wave function are universal concepts applicable to random motion processes, which can be used for both macroscopic objects and microscopic particles, and are not unique calculation methods of quantum mechanics. PACS: 03.65.Ta, 03.50.Kk
Abstract The theoretical framework of quantum mechanics consists of five assumptions, and academic circle generally believed that the correctness of the assumptions can only be proved by experiments and cannot be proved theoretically. In this paper, according to the stochastic process problem in probability theory, we used Fourier transform, delta function and other methods to study stochastic motion, derived the wave function, superposition state and other concepts, thus giving the theoretical proof process of five assumptions. This paper is based on the basic concepts of quantum mechanics, the derivation process further improves the mathematical basis of quantum mechanics, but the derivation conclusion can be applied to both quantum mechanics and classical mechanics.
Abstract The theoretical results of quantum mechanics (QM) have been verified by experiments, but the probabilistic Copenhagen interpretation is still controversial, and many counterintuitive phenomena are still difficult to understand. To trace the origin of probability in QM, we construct the superimposed amplitudes of a space-time position in a multiparticle quantum objective system and find that the probability in QM originates from the particle number distribution rate in a unit volume near position r at time t in the multiparticle quantum objective system. Based on the origin of probability, We find that the state function of an elementary particle (hereinafter called particle for short) has precise physical meaning; that is, the particle periodically and alternately exhibits the particle state and wave state in time and space, obtain the localized and nonlocalized spatiotemporal range of the particle, the apparent trajectory of the particle motion. Based on this, through rigorous mathematical derivation and analysis, we propose new physical interpretations of the quantum superposition state, wave-particle duality, the double-slit experiment, the Heisenberg uncertainty principle, and the quantum tunnelling effect, and these interpretations are physically logical and not counterintuitive.
Abstract The theoretical results of quantum mechanics (QM) have been verified by experiments, but the probabilistic Copenhagen interpretation is still controversial, and many counterintuitive phenomena are still difficult to understand. To trace the origin of probability in QM, we construct the amplitudes of a space-time position in a multiparticle quantum objective system and find that the probability in QM originates from the particle number distribution rate in a unit volume near position r at time t in the multiparticle quantum objective system. Based on the origin of probability, the quantization conditions of action and the principle of least action for an elementary particle (referred to as particle) , we find that when a particle moves in space-time, it periodically and alternately exhibit particle and wave state. We have derived the formula for the fringe positions in the double-slit experiment with particles, a new certainty relation and the uncertainty relation, obtain the localized and nonlocalized spatiotemporal range of the particle, the apparent trajectory of the particle motion. Based on this, through rigorous mathematical derivation and analysis, we propose new physical interpretations of the quantum superposition state, wave-particle duality, the double-slit experiment, the Heisenberg uncertainty principle, and the quantum tunnelling effect, and these interpretations are physically logical and not counterintuitive.
Aiming at the quantum mechanics wave function description probability feature, statistical interpretation, randomicity, uncertainty, nonlocality and agnosticism etc fundamental principles and concepts, based on the mass-space interaction, mass-space space-time view, microscopic mass-energy systems correlating with space-time model etc principles and theories, and the quantum entanglement particle experiments etc facts, present the matter-ordering-energy conservation laws and the Dong Pei innovating group interpretation of quantum mechanics. Simultaneously indicate: In the universe there exists the ordering- and disordering-energy matter, together known as matter. Existing the absolute space and absolute time. The absolute space-time is continuous. Matter and the absolute space-time together create and compose the objective world. The objective world is a harmonious and unified whole. Physical laws are completely unified. The objective world and matter are all finite. Matter exists, evolves and moves in the absolute space-time. Interactions are the most essential and most root basic attribute of matter. The interaction among matter is the mass-space interaction. The mass-space interaction is continuous and stable, is not random and intermittent. Macroscopic and microscopic regions all observe the identical physical laws. Elementary particles and they compose the microscopic mass-energy systems are all the ordering-energy matter, their mass-energy space-time is a interdependent whole, their feature, state, structure and motion laws are all entirely determined by the mass-space interaction, correspond with the determinism and causality, the motion state and feature, motion orbitals, position and speed of particles in the absolute space-time are all absolutely determined and could be measured exactly, their quantum states could be approximately described by the wave function of quantum mechanics. The wave functions are the simplified mathematical function approximate expression of quantum system states of adopted interaction, can be used to calculate the correlative physical quantities. The wave functions could approximately describe the state of the mass-energy space-time whole of a microscopic mass-energy system with the mass-space interaction acting and continuously moving. An eigenstate just is the state making the system energy minimum and in rather stable existence. Scientific theories are the abstract simplified approximate expression for the essential of natural phenomena. Physical theory is the abstract simplified approximate representation for the matter structure and its motion laws. Whereas the mathematical formulation then is the further simplified approximate representation for physical contents. All of theories, include quantum mechanics and relativity, only when the assumed approximate condition is satisfied, just are the applied correct scientific theory, could describe the objective world good enough but not exactly. Develop scientific theory, correctly cognize and reasonably interpret the objective world, without the end.
Usually, the idea of probability is applied only to the random motion in physics. Here, the instant probability concept is obtained by applying the probability approach to objects with deterministic motion trajectories via a coin falling to the ground as an example. Applied this concept to understand quantum mechanics, the following conclusions are inferred: The wave function/quantum state represents an instant probability distribution of physical quantities after taking into account Planck's constant; the collapse of the wave function is a special case of any function on time-dependent probability prediction has to collapse when performing measurement. The arrangement of measurements will affect the observed results; Quantum mechanics reveals the existence of non-local effects, which have nothing to do with the interaction in classical physics. Quantum mechanics cannot answer questions such as whether the cat is dead or alive before opening the box. The correct answer to this kind of question has to be from classic physics.
Abstract The theoretical results of quantum mechanics (QM) have been verified by experiments, but the probabilistic Copenhagen interpretation is still controversial, and many counterintuitive phenomena are still difficult to understand. To trace the origin of probability in QM, we construct the state function of a multiparticle quantum objective system and find that the probability in QM originates from the particle number distribution rate in a unit volume near position r at time t in the multiparticle quantum objective system. Based on the origin of probability, We find that the state function of an elementary particle (hereinafter called particle for short) has precise physical meaning; that is, the particle periodically and alternately exhibits the particle state and wave state in time and space, obtain the localized and nonlocalized spatiotemporal range of the particle, the apparent trajectory of the particle motion. Based on this, through rigorous mathematical derivation and analysis, we propose new physical interpretations of the quantum superposition state, wave-particle duality, the double-slit experiment, the Heisenberg uncertainty principle, and the quantum tunnelling effect, and these interpretations are physically logical and not counterintuitive.