Dynamics of a particle is formulated from classical principles that are amended by the uncertainty principle. Two best known quantum effects: interference and tunneling are discussed from these principles. It is shown that identical to quantum results are obtained by solving only classical equations of motion. Within the context of interference Aharonov-Bohm effect is solved as a local action of magnetic force on the particle. On the example of tunneling it is demonstrated how uncertainty principle amends traditional classical mechanics: it allows the momentum of the particle to change without the force being the cause of it.Dynamics of a particle is formulated from classical principles that are amended by the uncertainty principle. Two best known quantum effects: interference and tunneling are discussed from these principles. It is shown that identical to quantum results are obtained by solving only classical equations of motion. Within the context of interference Aharonov-Bohm effect is solved as a local action of magnetic force on the particle. On the example of tunneling it is demonstrated how uncertainty principle amends traditional classical mechanics: it allows the momentum of the particle to change without the force being the cause of it.

Jan 1, 20001 citation

The Spin

Slobodan Danko Bosanac

It is shown that the spin is naturally introduced into classical mechanics if the latter is formulated as dynamics of the phase space density. It is shown that the uncertainty principle, as the amendment in this dynamics, restricts possible spins, and in particular equation for the particle with the spin $\hbar /2$ is derived. Also equation for the charge with this spin is derived when electromagnetic field is included. In one example it is shown that the modulus of the spin changes with the gradient of the magnetic field.It is shown that the spin is naturally introduced into classical mechanics if the latter is formulated as dynamics of the phase space density. It is shown that the uncertainty principle, as the amendment in this dynamics, restricts possible spins, and in particular equation for the particle with the spin $\hbar /2$ is derived. Also equation for the charge with this spin is derived when electromagnetic field is included. In one example it is shown that the modulus of the spin changes with the gradient of the magnetic field.

arXiv:quant-ph/0110090Oct 15, 20010 citations

The Spin

Slobodan Danko Bosanac

Oct 15, 20010 citations

The Spin

Slobodan Danko Bosanac

It is shown that the spin is naturally introduced into classical mechanics if the latter is formulated as dynamics of the phase space density. It is shown that the uncertainty principle, as the amendment in this dynamics, restricts possible spins, and in particular equation for the particle with the spin ħ/2 is derived. Also equation for the charge with this spin is derived when electromagnetic field is included. In one example it is shown that the modulus of the spin changes with the gradient of the magnetic field.It is shown that the spin is naturally introduced into classical mechanics if the latter is formulated as dynamics of the phase space density. It is shown that the uncertainty principle, as the amendment in this dynamics, restricts possible spins, and in particular equation for the particle with the spin ħ/2 is derived. Also equation for the charge with this spin is derived when electromagnetic field is included. In one example it is shown that the modulus of the spin changes with the gradient of the magnetic field.

Fortschritte der PhysikDec 1, 20010 citations

Aharonov-Bohm Effect—Quantum Effects on Charged Particles in Field-Free Regions

Herman Erlichson

The Aharonov-Bohm effect is relatively little known, but it poses fundamental questions in quantum theory. It concerns physical effects on charged particles in field-free regions. The present paper provides an over-all critical review and commentary on the literature of the Aharonov-Bohm effect. The two fundamental questions raised by the effect concern the role of the force concept in quantum mechanics, and the localizability of physical effects principle. A recent letter from Professor Bohm concerning his evaluation of the significance of the effect is included in the Appendix.The Aharonov-Bohm effect is relatively little known, but it poses fundamental questions in quantum theory. It concerns physical effects on charged particles in field-free regions. The present paper provides an over-all critical review and commentary on the literature of the Aharonov-Bohm effect. The two fundamental questions raised by the effect concern the role of the force concept in quantum mechanics, and the localizability of physical effects principle. A recent letter from Professor Bohm concerning his evaluation of the significance of the effect is included in the Appendix.

American Journal of PhysicsFeb 1, 197048 citations

More variations on Aharonov-Bohm

A. I. Ershkovich

The article about Aharonov-Bohm effects is interesting and comprehensive. The primary and best-known effect shows that the vector potential A of the electromagnetic field is a physical reality rather than a mathematical artifice. That reality was implicit in the Schrödinger equation, as the Hamiltonian H depends on A instead of the electric field E and magnetic field B = ∇ × A. But the same statement also refers to the Hamilton-Jacobi equation in classical mechanics, so one may expect that a similar effect exists in classical physics as well.Indeed, classical mechanics is governed by the fundamental Hamilton-Jacobi equation for the action S: δS/δt + H = 0, which naturally follows from William Hamilton’s principle of least action. Both H and S depend on A (even with E = B = 0). Thus it is quite possible that the vector potential is also a physical reality in classical physics. Erwin Schrödinger arrived at his famous equation in 1926 by using a mechanics-optics analogy, the so-called eikonal equation. Hamilton in 1834 proved that eikonal and Hamilton-Jacobi equations are equivalent, so that the Schrödinger equation actually follows from Hamilton-Jacobi.Had Hamilton known that classical mechanics does not always hold, quantum mechanics might have appeared a century earlier. 1 1. H. Goldstein, C. Poole, J. Safko, Classical Mechanics, 2nd ed., Addison-Wesley, Reading, MA (1980), p.484 . The analogy between the equations of classical and quantum mechanics provides a reason to search for experiments that might prove whether a classical analogue of the Aharonov-Bohm effect exists.REFERENCESSection:ChooseTop of pageREFERENCES <<CITING ARTICLES1. H. Goldstein, C. Poole, J. Safko, Classical Mechanics, 2nd ed., Addison-Wesley, Reading, MA (1980), p.484 . Google Scholar© 2010 American Institute of Physics.The article about Aharonov-Bohm effects is interesting and comprehensive. The primary and best-known effect shows that the vector potential A of the electromagnetic field is a physical reality rather than a mathematical artifice. That reality was implicit in the Schrödinger equation, as the Hamiltonian H depends on A instead of the electric field E and magnetic field B = ∇ × A. But the same statement also refers to the Hamilton-Jacobi equation in classical mechanics, so one may expect that a similar effect exists in classical physics as well.Indeed, classical mechanics is governed by the fundamental Hamilton-Jacobi equation for the action S: δS/δt + H = 0, which naturally follows from William Hamilton’s principle of least action. Both H and S depend on A (even with E = B = 0). Thus it is quite possible that the vector potential is also a physical reality in classical physics. Erwin Schrödinger arrived at his famous equation in 1926 by using a mechanics-optics analogy, the so-called eikonal equation. Hamilton in 1834 proved that eikonal and Hamilton-Jacobi equations are equivalent, so that the Schrödinger equation actually follows from Hamilton-Jacobi.Had Hamilton known that classical mechanics does not always hold, quantum mechanics might have appeared a century earlier. 1 1. H. Goldstein, C. Poole, J. Safko, Classical Mechanics, 2nd ed., Addison-Wesley, Reading, MA (1980), p.484 . The analogy between the equations of classical and quantum mechanics provides a reason to search for experiments that might prove whether a classical analogue of the Aharonov-Bohm effect exists.REFERENCESSection:ChooseTop of pageREFERENCES <<CITING ARTICLES1. H. Goldstein, C. Poole, J. Safko, Classical Mechanics, 2nd ed., Addison-Wesley, Reading, MA (1980), p.484 . Google Scholar© 2010 American Institute of Physics.

Physics TodayApr 1, 20102 citations

\hbar /2

is derived. Also equation for the charge with this spin is derived when electromagnetic field is included. In one example it is shown that the modulus of the spin changes with the gradient of the magnetic field.

\hbar /2