Abstract
This review presents results obtained from our group’s approach to model quantum mechanics with the aid of nonequilibrium thermodynamics. As has been shown, the exact Schrödinger equation can be derived by assuming that a particle of energy is actually a dissipative system maintained in a nonequilibrium steady state by a constant throughput of energy (heat flow). Here, also other typical quantum mechanical features are discussed and shown to be completely understandable within our approach, i.e., on the basis of the assumed sub-quantum thermodynamics. In particular, Planck’s relation for the energy of a particle, the Heisenberg uncertainty relations, the quantum mechanical superposition principle and Born’s rule, or the “dispersion of the Gaussian wave packet”, a.o., are all explained on the basis of purely classical physics.
Highlights
This review presents results obtained from our group‘s approach to model quantum mechanics with the aid of nonequilibrium thermodynamics
Planck‘s relation for the energy of a particle, the Heisenberg uncertainty relations, the quantum mechanical superposition principle and Born‘s rule, or the ―dispersion of the Gaussian wave packet‖, a.o., are all explained on the basis of purely classical physics
We shall more generally summarize the results of our works relating to the derivation from purely classical physics of the following quantum mechanical features: Planck‘s relation E for the energy of a particle, the Schrödinger equation for conservative and non-conservative systems, the Heisenberg uncertainty relations, the quantum mechanical superposition principle, Born‘s rule, and the quantum mechanical ―decay of a Gaussian wave packet‖
Summary
Equation (2.2.1) describes a forced oscillation of a mass m swinging around a center point along x(t) with amplitude A and damping factor, or friction,. If m could swing freely, its resonant angular frequency would be 0. The time-derivative of the sum must be zero since the sum is the whole energy of the system and has to be of constant value. To derive the stationary frequency , we use the right-hand side of Equation (2.2.6) together with Equation (2.2.2) and obtain. The system is stationary at the resonance frequency 0 of the free undamped oscillator. From Equation (2.2.16), an invariant quantity is obtained: it is the angular momentum L(t) = mr (t). With = 0 , the quantity of Equation (2.2.17) becomes the time-invariant expression of a basic angular momentum, which we denote as
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