Difference between revisions of "Sub-Quantum Physics 4: Oscillator Ground State from Aether Stochastic White Noise"
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| − | A standard treatment of the motion of the classical simple harmonic oscillator driven by a ?kinetic gas?-type white noise stochastic process is shown to have direct relevance to the quantum oscillator ground state. When the driving excitation involves normally distributed impulses, the position probability density of the oscillator is normal, just as for the quantum oscillator ground state. For both the classical oscillator and the quantum oscillator ground state, the position probability density function has the functional form exp[-V(y)/E<sub>0</sub>]. In each case the argument numerator function V(y) is Ky<sup>2</sup>/2 , where is the position variable (the distance from the neutral point) and K is the force constant. The argument denominator for the classical oscillator is E<sub>0</sub> = kT where k is Boltzmann?s constant and T is the absolute temperature. The denominator for the quantum oscillator ground state is just the quantum zero-point energy E<sub>0</sub> = h<em>v</em>/2 where h is Planck?s constant and <em>v</em> is the oscillator natural frequency. The resemblance between the densities for the stochasitcally-driven classical oscillator and the quantum oscillator ground state lends support to the author?s previous assertion that the quantum oscillator can be seen as an essentially classical object driven by stochastic bombardment from an underlying aether. The article presents the stochastic methodology.[[Category:Scientific Paper]] | + | A standard treatment of the motion of the classical simple harmonic oscillator driven by a ?kinetic gas?-type white noise stochastic process is shown to have direct relevance to the quantum oscillator ground state. When the driving excitation involves normally distributed impulses, the position probability density of the oscillator is normal, just as for the quantum oscillator ground state. For both the classical oscillator and the quantum oscillator ground state, the position probability density function has the functional form exp[-V(y)/E<sub>0</sub>]. In each case the argument numerator function V(y) is Ky<sup>2</sup>/2 , where is the position variable (the distance from the neutral point) and K is the force constant. The argument denominator for the classical oscillator is E<sub>0</sub> = kT where k is Boltzmann?s constant and T is the absolute temperature. The denominator for the quantum oscillator ground state is just the quantum zero-point energy E<sub>0</sub> = h<em>v</em>/2 where h is Planck?s constant and <em>v</em> is the oscillator natural frequency. The resemblance between the densities for the stochasitcally-driven classical oscillator and the quantum oscillator ground state lends support to the author?s previous assertion that the quantum oscillator can be seen as an essentially classical object driven by stochastic bombardment from an underlying aether. The article presents the stochastic methodology. |
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| + | [[Category:Scientific Paper|sub-quantum physics oscillator ground state aether stochastic white noise]] | ||
Latest revision as of 11:07, 1 January 2017
| Scientific Paper | |
|---|---|
| Title | Sub-Quantum Physics 4: Oscillator Ground State from Aether Stochastic White Noise |
| Author(s) | Alan McCone |
| Keywords | {{{keywords}}} |
| Published | 2000 |
| Journal | Galilean Electrodynamics |
| Volume | 11 |
| Number | 3 |
| Pages | 49-53 |
Abstract
A standard treatment of the motion of the classical simple harmonic oscillator driven by a ?kinetic gas?-type white noise stochastic process is shown to have direct relevance to the quantum oscillator ground state. When the driving excitation involves normally distributed impulses, the position probability density of the oscillator is normal, just as for the quantum oscillator ground state. For both the classical oscillator and the quantum oscillator ground state, the position probability density function has the functional form exp[-V(y)/E0]. In each case the argument numerator function V(y) is Ky2/2 , where is the position variable (the distance from the neutral point) and K is the force constant. The argument denominator for the classical oscillator is E0 = kT where k is Boltzmann?s constant and T is the absolute temperature. The denominator for the quantum oscillator ground state is just the quantum zero-point energy E0 = hv/2 where h is Planck?s constant and v is the oscillator natural frequency. The resemblance between the densities for the stochasitcally-driven classical oscillator and the quantum oscillator ground state lends support to the author?s previous assertion that the quantum oscillator can be seen as an essentially classical object driven by stochastic bombardment from an underlying aether. The article presents the stochastic methodology.
