Derivation of the Universal Electrodynamic Force Law

1. Derivation of the Universal Electrodynamic Force Law Charles W. Lucas, Jr CHURCH COMPUTER SERVICES 29045 Livingston Drive Mechanicsville, MD 20659-3271 bill.lucas001@gmail.com

2. Euclid’s Axiomatic Method in Science • Logical procedure by which theories are deduced using logic from basic propositions (axioms) • Propositions are constructed from a few primitive terms • Terms may be defined arbitrarily or empirically • Science consists of a collection of arbitrary and empirical propositions and all the logically derived theories from those axioms

4. Problems with Axiomatic Method • Identification of primitive terms • Determination of fundamental axioms

5. Newton’s Scientific Assumption ALL OF THE UNIVERSE CAN BE EXPLAINED IN TERMS OF FORCES ALONE

6. Newton’s Empirical Scientific Method • Systematic observation of forces • Experiments with forces • Measurement of forces • Mathematical formulation of force laws • Determine additional phenomena implied by force law • Experimental testing of force laws and additional phenomena • Modification of force laws as required by experiment

7. MathematicsThe Primary Tool of Science • Enables an analysis of forces • Helps identify the primitives • Helps identify the causes of forces • Adds credibility to scientific theories

8. Newton’s Conditions for Physical Force • Direction of the force must be determined by some material body other than the one it is acting on • All aspects of the force’s magnitude must be given by a general force law that is dependent on the forces of action and reaction • Some of the physical quantities in a force law must pertain to the other body in a way that determines the direction of the force

9. Newton’s Conditions for Physical Force • The force law must hold for some forces that are indisputably real • If the forces acts on a macroscopic body, then it must be composed of forces acting on the microphysical parts of that body.

10. Newton’s Rules of Natural Philosophy • No more causes of phenomena are allowed than are true and sufficient to explain them • The same natural effects should always be assigned the same causes • The qualities of bodies within reach of our experiments are assumed to be universal qualities of all bodies • Propositions inferred by induction from experiment are to be considered as accurate or true until disproven or modified by other phenomena

11. Maxwell’s Axiomatic Method • Based on 4 empirical laws of electrodynamics • Based on point particle idealization • Based on logic to derive a more comprehensive theory

12. 1887 Michelson-Morley Experiment

13. Photoelectric Effect

14. Photoelectric Effect Na Crystalline Metal Plate

15. Waves not Quanta

16. Einstein’s Special Relativity Theory • Based on quanta from photoelectric experiment • Based on Michelson-Morley experiment

17. Covariant Version of Electrodynamics LorentzForceLaw

18. Discovery of Extinction Effect 1912

19. HOFSTADTER ELECTRON SCATTERING DATA Finite Size of Elementary Particles 2.0 1.5 4pr2 x charge density 1.0 Proton 0.5 0 0.5 1.0 1.5 2.0 2.5 Radius r (10-13cm) -0.5 Neutron

20. A More Perfect Union ofAxiomatic & Empirical Scientific Methods • Based on empirical laws • Ampere’s circuital law • Faraday’s electromagnetic induction law • Gauss’s static electric & magnetic field laws • Galilean Invariance -> Lorentz Force Law • Based Lenz’s empirical law • Conservation of energy for magnetic fields • Newton’s 3rd Law • Finite Size particles

21. Lenz’s LawHow Electrodynamics Obeys Newton’s 3rd Law and Conservation of Energy “An induced current is always in such a direction as to oppose the motion or change causing it”

22. Improved Version of Electrodynamics LorentzForceLaw From Galilean Invariance

23. Definition of Electrodynamic Potential • Conservation of electric & magnetic energy allows definition of electrodynamic potential Definition of Force from Potential Extension of Electromagnetic Force to Include Acceleration a

24. Significance of Force Terms (v/c)0 Static Coulomb Force (v/c)2 Induction Forces a Inertial Forces (v/c)4 Gravitational Forces r x (r x v) Quantization of Orbits r x (r x a) Radiation Emission/absorption da/dt Radiation reaction

25. R x (R x A)  Relativistic Larmor Radiation Formula For v ┴r

26. Galilean InvarianceorPrinciple of Relativity The Laws of Physics are the same in all inertial frames of reference

27. FIELDS OF CHARGESRemain Attached to Charges

28. Patterns of Magnetic Fields

29. Extension of Electrodynamic Forceto Radiation Reaction da/dt terms • Based on periodic motion within the toroidal structures of a charged particle Radiation Reaction Term

30. Union of Euclid’s Axiomatic andNewton’s Empirical Scientific Method • Based on empirical laws • Ampere’s circuital law • Faraday’s electromagnetic induction law • Gauss’s static electric & magnetic field laws • Based Lenz’s empirical law • Conservation of energy for magnetic fields • Newton’s 3rd Law • Finite Size particles - periodic charge structure

31. Improved Electrodynamic Force • Conserves Energy for Magnetic Fields • Satisfies Newton’s 3rd Law • Allows Definition of Electrodynamic Potential • Allows Extension to Acceleration a Terms • Allows extension to Radiation Reaction da/dt Terms • Can Replace Einstein’s Special Theory of Relativity

32. Improved Electrodynamic Force • Can Replace Newton’s Universal Law of Gravitation • Can Replace Newton’s Force of Inertia • Can Replace Quantum Electrodynamic Standard Model of Elementary Particles • Can Replace Quantum Electrodynamic Model of Atom • Can Replace Quantum Electrodynamic Model of Nucleus • Can Replace Quantum ElectrodynamicModel of Molecules

33. Albert EinsteinNobel Prize Award Address “A theory is the more impressive the greater the simplicity of its premises is, the more different kinds of things it relates, and the more extended is its area of applicability.”