1. 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

2. 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

3. 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

4. ”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.

5. ”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

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

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

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

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

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

11. 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

12. Newton’s equation
In more detail

13. Equation of Motion in terms of -function

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

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

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

17. 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

18. 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

19. Particle + environment
Q. Potential

20. 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.

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

22. Stochastic Schrödinger Equation
where
GRW operator ?

23. Fisher information and F/D Quantum Potential
Heisenberg Inequality

24. Conclusions Schrödinger Equation may be derived from classical physics

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

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

27. What is primary: Physics or Mathematics?

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