Reply to  Comment on   Timelike flows of energy momentum and particle trajectories for the Klein Gordon equation   

2002 ◽  
Vol 35 (37) ◽  
pp. 7963-7964 ◽  
Author(s):  
George Horton ◽  
Chris Dewdney
Keyword(s):  
Gordon Equation ◽  
Particle Trajectories ◽  
Klein Gordon ◽  
Klein Gordon Equation

Pilot-Wave Theory for a Relativistic Spin Zero Particle

2020 ◽  
Author(s):  
Dan N. Vollick
Keyword(s):  
Gordon Equation ◽  
Wave Theory ◽  
Particle Trajectories ◽  
Superluminal Motion ◽  
Pilot Wave ◽  
Nonlinear Generalization ◽  
Klein Gordon ◽  
Hamilton Jacobi Equation ◽  
Klein Gordon Equation ◽  
Pilot Wave Theory

In the usual approach to the pilot-wave theory for a spin zero particle one starts with the Klein-Gordon equation, which is the relativistic generalization of the Schrodinger equation. This approach encounters several difficulties including superluminal motion and particle trajectories that move backwards in time. In this paper I start with the relativistic classical Hamilton-Jacobi equation and introduce the quantum potential in a way that avoids the above mentioned difficulties. Particle trajectories are timelike or null and are future pointing. The wave equation satisfied by the field is a nonlinear generalization of the Klein-Gordon equation.

scholarly journals Fractional Klein-Gordon equation with singular mass

2021 ◽  
Vol 143 ◽  
pp. 110579
Author(s):  
Arshyn Altybay ◽  
Michael Ruzhansky ◽  
Mohammed Elamine Sebih ◽  
Niyaz Tokmagambetov
Keyword(s):  
Gordon Equation ◽  
Klein Gordon ◽  
Klein Gordon Equation
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