QM motion of Classical Particle and probable link to GRW Theory Konstantin Lukin Laboratory for Nonlinear Dynamics of Electron Systems, LNDES, Usikov IRE NASU, Kharkov, UKRAINE V. Rusov and D. Vlasenko Department of Theoretical and Experimental Nuclear Physics, Odessa National Polytechnic University, Ukraine

QM motion of Classical Particle and probable link to GRW Theory Konstantin Lukin Laboratory for Nonlinear Dynamics of Electron Systems, LNDES, Usikov IRE NASU, Kharkov, UKRAINE V. Rusov and D. Vlasenko Department of Theoretical and Experimental Nuclear Physics, Odessa National Polytechnic University, Ukraine

OUTLINE Motivations Schrödinger-like Equation from Newtonian mechanics Introduction Schrödinger-like Equation from Newtonian mechanics Link to GRW model ? What is primary in physical theory: Physics or Mathematics? Conclusions

”The progress so made is immensely impressive. J. S. Bell, ”Speakable and unspeakable in quantum mechanics. Collected papers on quantum philosophy”, Cambridge University Press, Cambridge, 1987, p. 169 Bell noted : “ This progress is made in spite of the fundamental obscurity in quantum mechanics. Our theorists stride through that obscurity unimpeded... sleepwalking?” ”The progress so made is immensely impressive. If it is made by sleepwalkers, is it wise to shout ’wake up’? I am not sure that it is.

”The progress so made is immensely impressive. J. S. Bell, ”Speakable and unspeakable in quantum mechanics. Collected papers on quantum philosophy”, Cambridge University Press, Cambridge, 1987, p. 169 Bell noted : “ This progress is made in spite of the fundamental obscurity in quantum mechanics. Our theorists stride through that obscurity unimpeded... sleepwalking?” ”The progress so made is immensely impressive. If it is made by sleepwalkers, is it wise to shout ’wake up’? I am not sure that it is. So I speak now in a very low voice”. J. S. Bell, 1987

Diffusive oscillatory waves Quantum Corral Q. Potential Diffusive oscillatory waves Donald Eigler and Erhard Schweizer of IBM Almaden Labs, 1994

Quantum Corral Donald Eigler and Erhard Schweizer of IBM Almaden Labs,

SCHRÖDINGER EQUATION AS EQUATION FOR STABLE MOTION OF CLASSICAL PARTICLES IN FLUCTUATION-DISSIPATIVE ENVIRONMENT

Newton’s equation for a point-like particle Back-Ground fluctuation force - the particle action work against Back-Ground fluctuation force - kinetic energy

Introduce a new function where is the action related to the phase is a real constant is the Amplitude

Introduce a new function where is the action related to the phase is a real constant is the Amplitude Ansatz : Introduction of the Amplitude is equivalent to introduction of Quantum Potential in QM

Newton’s equation In more detail

Equation of Motion in terms of -function

Equation of Motion in terms of -function Condition for compensation of perturbations due to zero-point fluctuations by Quantum Potential force

Equation of Motion in terms of -function Condition for compensation of perturbations due to zero-point fluctuations by Quantum Potential force

Condition for compensation of perturbations due to zero-point fluctuations by Quantum Potential force After separation of real and imaginary parts

The Schrödinger equation as the stability condition of trajectories in classical mechanics If we assume where h is Plank’s constant we obtain Schrödinger equation

The Schrödinger equation as the stability condition of trajectories in classical mechanics If we assume where h is Plank’s constant we obtain Schrödinger equation Quantum Potential

Particle + environment Q. Potential

The Bohm-Madelung system of equations Hence, it follows that the Bohm-Madelung quantum potential is equivalent to Chetaev’s dissipation energy Q where S is the action; h = 2 is Plank constant; А is amplitude, which in the general case is the real function of the coordinates qi and time t.

Condition for compensation of perturbations due to zero-point fluctuations by Quantum Potential force After separation of real and imaginary parts

Stochastic Schrödinger Equation where GRW operator ?

Fisher information and F/D Quantum Potential Heisenberg Inequality

Conclusions Schrödinger Equation may be derived from classical physics

Conclusions Schrödinger Equation may be derived from classical physics if taking into account background fluctuations

Conclusions Schrödinger Equation may be derived from classical physics if taking into account background fluctuations

What is primary: Physics or Mathematics?

What is primary: Physics or Mathematics What is primary: Physics or Mathematics? New physics may be seen from these derivations