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Dianzi Ke-ji Daxue xuebao

Quantum Interpretation of Signal’s Uncertainty Principle

Jianping Li

Published Jan 1, 2008• 7 citations
OpenAlex

Abstract

The uncertainty principle of signal is proved according to the uncertainty principle of quantum mechanics,and is further interpreted by quantum mechanics.The signal can be considered as a kind of the quasi quantum system with wave-particle dualism.Because of the wave-particle dualism of the signal,time and frequency can not be measured at the same time.The frequency operator(FO) of signal is defined in this study,and it can be widely used in signal theory and,especially in wavelet research.The quantum interpretation for the signal explains the essence of the signal and provides the theory support for applying the framework of quantum mechanics to the signal processing.

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The uncertainty principle of signal is proved according to the uncertainty principle of quantum mechanics,and is further interpreted by quantum mechanics.The signal can be considered as a kind of the quasi quantum system with wave-particle dualism.Because of the wave-particle dualism of the signal,time and frequency can not be measured at the same time.The frequency operator(FO) of signal is defined in this study,and it can be widely used in signal theory and,especially in wavelet research.The quantum interpretation for the signal explains the essence of the signal and provides the theory support for applying the framework of quantum mechanics to the signal processing.
The frequency operator of signal is obtained in this paper. It reflects the quantum characteristics of signal. It is a linear and Hermitian operator. Eigenfunctions, eigenvalues and superposition principle of signal are researched by using the frequency operator. The frequency operator is used to prove the uncertainty principle of signal. The uncertainty principle of signal indicates that the signal can be considered as a kind of the quasi quantum system with wave-particle dualism. The frequency operator is a powerful tool to research the quantum characteristics of signal. The quantum interpretation of frequency operator explains the essence of signal and provides the theory support for applying the framework of quantum mechanics to the signal processing.
Quantum certainty mechanics is a theory for measuring the position and momentum of a particle. Mathematically proven certainty principle from uncertainty principle, which is basically one of the most important formulas of quantum certainty mechanics theory. The principle of uncertainty can be proved by the principle of certainty and why uncertainty comes can also be proved. The principle of certainty can be proved from the theory of relativity and in the uncertainty principle equation, the principle of certainty can be proved by fulfilling the conditions of the principle of uncertainty by multiplying the uncertain constant with the certain values of momentum-position and energy-time. The principle of certainty proves that the calculation of θ ≥π/2 between the particle and the wave involved in the particle leads to uncertainty. But calculating with θ=0 does not bring uncertainty. Again, if the total energy E of the particle is measured accurately in the laboratory, the momentum and position can be measured with certainty. Quantum certainty mechanics has been established by combining Newtonian mechanics, relativity theory and quantum mechanics. Quantum entanglement can be explained by protecting the conservation law of energy.
Quantum certainty mechanics is a theory for measuring the position and momentum of a particle. Mathematically proven certainty principle from uncertainty principle, which is basically one of the most important formulas of quantum certainty mechanics theory. The principle of uncertainty can be proved by the principle of certainty and why uncertainty comes can also be proved. The principle of certainty can be proved from the theory of relativity And in the uncertainty principle equation, the principle of certainty can be proved by fulfilling the conditions of the principle of certainty by multiplying the uncertain constant with the certain values of momentum-position and energy-time. The principle of certainty proves that the calculation of θ π/2 between the particle and the wave involved in the particle leads to uncertainty. But calculating with θ=0 does not bring uncertainty. Quantum certainty mechanics has been established by combining Newtonian mechanics, relativity theory and quantum mechanics. Quantum entanglement can be explained by protecting the principle of conservation of energy.
The principle of uncertainty is one of the essential principles of quantum mechanics as it outlines that there is a reflective limit to the measurement of microscopic particle motion. However it is impossible to measure at once and accurately both the position and momentum data of any microscopic particle no matter what means are used to do so. This paper starts by discussing the notion and mathematical derivation of the uncertainty principle as put forth by Heisenberg explaining the physical relevance of the principle. It introduces the natural uncertainty the principle introduces to the dynamics of particles in the microscopic world, and the significant part it plays in the theory of quantum mechanics. The article overviews the explanations of the principle on phenomena including atomic stability and scanning tunneling microscopes, and the interference of measurement actions on the states of particles and the shortcomings of measurement precision. According to the wave-particle duality of quantum mechanics, this article gives a required theoretical basis of microscopic phenomena. Likewise, the use of the research theory on the uncertainty principle by distinguished scholars in the physics fraternity helps the readers in achieving the knowledge in related subjects more easily.
Interpreting quantum mechanics is a hard problem basically because it means explaining why and how the mathematics exploited to formulate wave-particle duality are related to observations or reality in classical physics (due to Newtonian mechanics, special relativity, gravity and entropy). Here, we first prove the limitation of the Heisenberg uncertainty principle by invoking the wave-particle duality and apply it to revise and/or extend the Copenhagen postulates. In particular, even though the said uncertainty exists due to non-commuting operators, but these operators do not commute simply because one of the operators is well-defined in classical physics (particle-like), while the other is wave-like (well-defined in quantum mechanics), or the eigenvalue is not at all defined in classical physics. We also construct a new quantum mechanical postulate (Postulate 9) to deduce why the forbidden gap between discrete energy levels should exist in atoms, molecules and condensed matter phases. In fact, we tackle all the problems arising from the Copenhagen interpretation without violating established experiments and without proposing ideas that violate physical reality.