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Compton-Wavelength Minimum Position Uncertainty Due to Diversion of Momentum Uncertainty to Increased Particle Number

Steven Kenneth Kauffmann

In single-particle quantum mechanics there is no impediment to a particle's wave function having a significant amplitude for arbitrarily short wavelengths, i.e., for arbitrarily large momenta, so the iconic single-particle uncertainty relation permits a particle's position to be arbitrarily accurately ascertained. Once a single-particle theory is second quantized, however, the physics of imparting a particle's wave function with ever larger momenta eventually encounters stiff competition from the formation of multiparticle states wherein none of the individual particles is characterized by high momentum. In fact, the single-particle uncertainty principle itself is modified by the presence of the expectation value of the particle number operator on its right side. Since the threshold for the high-momentum-diverting formation of additional particles is set by the particle's rest mass, it stands to reason that particles have an irreducible position uncertainty of the order of their Compton wavelength, for which we develop a specific model.In single-particle quantum mechanics there is no impediment to a particle's wave function having a significant amplitude for arbitrarily short wavelengths, i.e., for arbitrarily large momenta, so the iconic single-particle uncertainty relation permits a particle's position to be arbitrarily accurately ascertained. Once a single-particle theory is second quantized, however, the physics of imparting a particle's wave function with ever larger momenta eventually encounters stiff competition from the formation of multiparticle states wherein none of the individual particles is characterized by high momentum. In fact, the single-particle uncertainty principle itself is modified by the presence of the expectation value of the particle number operator on its right side. Since the threshold for the high-momentum-diverting formation of additional particles is set by the particle's rest mass, it stands to reason that particles have an irreducible position uncertainty of the order of their Compton wavelength, for which we develop a specific model.

Jun 1, 20190 citations

On the Experimental Verification of the Uncertainty Principle Of Position and Momentum

Thomas Schürmann, Ingo Hoffmann, Winfrid Görlich

arXiv:2211.14724Physics Letters AJan 1, 20223 citations

Uncertainty relation and simultaneous measurements in quantum theory

Paul Busch

May 15, 19820 citations

A thought experiment violating Heisenberg's uncertainty principle

M. C. Robinson

In principle, it is possible to make simultaneous and precise measurements of a particle's velocity using two different methods, which should give identical results. It is shown that these results permit the calculation of the particle's position and momentum with a combined error [Formula: see text] at every instant of time in an arbitrarily large interval. It is also shown that, in the special case considered, the statistical interpretation of the wave function is invalid.

Canadian Journal of PhysicsMay 1, 196913 citations

Why does uncertainty come in quantum mechanics?

Muhammad Yasin

In 1927 Heisenberg has invented the uncertainty principle. The principle of uncertainty is, "It is impossible to determine the position and momentum of a particle at the same time."The more accurately the momentum is measured, the more uncertain the position will be. Just knowing the position would make the momentum uncertain. Einstein was adamant against this principle until his death. He thought that particles have some secret rules. Einstein thought, "The uncertainty principle is incomplete. There is a mistake somewhere that has resulted in uncertainty. Many did not accept Einstein then. But I'm sure Einstein was right then, there are secret rules for particles. Heisenberg's uncertainty principle is also 100% correct . I recently published a research paper named "Quantum Certainty Mechanics"[1], which shows the principle of measuring the momentum and position of particles by the quantum certainty principle. Why uncertainty comes from certainty is the main topic of this research paper. When the value of the energy absorbed by the electron in the laboratory is calculated, the uncertainty is removed. The details are discussed below.In 1927 Heisenberg has invented the uncertainty principle. The principle of uncertainty is, "It is impossible to determine the position and momentum of a particle at the same time."The more accurately the momentum is measured, the more uncertain the position will be. Just knowing the position would make the momentum uncertain. Einstein was adamant against this principle until his death. He thought that particles have some secret rules. Einstein thought, "The uncertainty principle is incomplete. There is a mistake somewhere that has resulted in uncertainty. Many did not accept Einstein then. But I'm sure Einstein was right then, there are secret rules for particles. Heisenberg's uncertainty principle is also 100% correct . I recently published a research paper named "Quantum Certainty Mechanics"[1], which shows the principle of measuring the momentum and position of particles by the quantum certainty principle. Why uncertainty comes from certainty is the main topic of this research paper. When the value of the energy absorbed by the electron in the laboratory is calculated, the uncertainty is removed. The details are discussed below.

Mar 2, 20210 citations

Uncertainty relations in simultaneous measurements for arbitrary observables

Shiro Ishikawa

Reports on Mathematical PhysicsJun 1, 199165 citations

Note on the Uncertainty Principle

Abstract

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Note on the Uncertainty Principle

Abstract

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