WED

Symplectic Topology meets Celestial and Quantum Mechanics via Weber Electrodynamics

Advanced School February 2020
IMECC UNICAMP

Videos and PDFs

They key videos concerning history and motivation for this Advanced School are

Assis Video-4 Weber's Planetary Model of the Atom
Frauenfelder Video-4 Neumann functionals and Weber’s Hamiltonian

Weber's Electrodynamics (WED), Relational Mechanics and Weber's Planetary Model of the Atom

André Assis (Campinas, Phys)

Video-1   pdf-1 Ampère's Electrodynamics
                                   - Oersted’s Experiment and Its Interpretation - Ampère’s Deduction of His Force between Current Elements
                                         - Ampère’s Unification of Magnetism, Electromagnetism and Electrodynamics
                                           - Modern Experiments to Distinguish Ampère’s Force from Grassmann-Biot-Savart’s Force

Video-2 pdf-2     Weber's Electrodynamics
                                 - Weber’s Force and Potential Energy - Deduction of the Laws of Gauss, Amp`ere and Faraday
                                 - The Meaning of the Velocity in Lorentz’ Force and the Several Definitions of the Field Concept
                                           - Modern Experiments to Distinguish Weber’s Force from Lorentz’ Force

Video-3 pdf-3 The Electric Force of a Current
                                           - Weber and the Surface Charges of Resistive Conductors Carrying Steady Currents
                                         - The Force Between a Closed Circuit Carrying a Constant Current and an External Charge at Rest Relative to the Resistive Circuit
                                       - Potential and External Electric Field in Circuits with Different Geometries: Straight Wire, Coaxial Cable, Twin-Lead, Solenoid, Ring
                                           - Propagation of Electromagnetic Signals at Light Velocity from Weber’s Law

Video-4 pdf-4 Weber's Planetary Model of the Atom
                                         - Evolution of Weber’s Model of the Atom - The Two-Body Problem in Weber’s Electrodynamics
                                           - The Critical Distance and the Possibility of a Negative Effective Inertial Mass in Weber’s Law
                                         - Weber’s Model of the Atom and the Stability of the Nucleus with his Electrodynamic Force

Video-5 pdf-5 Relational Mechanics and the Diurnal Rotation of the Earth
                                           - Newtonian Mechanics: Absolute Space and the Free Fall of an Apple - The Kinematic Rotation of the Earth Relative to the Stars and Galaxies
                                           - The Dynamic Rotation of the Earth as Measured by Its Flattening at the Poles and by Foucault’s Pendulum
                                           - Relational Mechanics and Implementation of Mach’s Principle with Weber’s Gravitational Force
                                         - The Rotation of the Earth According to Newton, Mach, Einstein and Relational Mechanics

Symplectic Aspects of Celestial Mechanics

Kai Cieliebak (Augsburg, Math)

Video-1   The N-body problem
                                - Newtonian and Hamiltonian formulation - Conserved quantities
                                  - Noether's theorem
Video-2 Symplectic geometry and the Kepler problem
                                - Symplectic structures - Hamiltonian systems
                                  - Completely integrable systems - Kepler problem
Video-3 Runge-Lenz vector and regularizations of the Keper problem
                                - Runge-Lenz vector
                                - Moser regularization - Levi-Civita regularization
Video-4 The restricted 3-body problem
                                - Restricted 3-body problem - Sitnikov's system and symbolic dynamics
                                - Planar circular restricted 3-body problem and its limit cases
Video-5 Stark-Zeeman systems and J+ like invariants of their periodic orbits
                                - Stark-Zeeman systems - Periodic orbits and plane curves
                                  - Arnold’s invariant J+ - Invariants under Stark-Zeeman homotopies

Non-local Floer homology

Urs Frauenfelder (Augsburg, Math)

Video-1   Morse homology
                                - Morse chain complex - Broken gradient flow lines
                                - Morse inequalities
Video-2 Classical Floer homology
                                - The action functional of classical mechanics
                                  - Floer's gradient flow equation - The bubbling phenomenon
Video-3 Rabinowitz Floer homology
                                - Rabinowitz action functional - Non-locality of the gradient flow equation
                                  - Bound on the Lagrange multiplier
Video-4 Delayed potentials and Weber’s Hamiltonian
                                - Neumann's action functional - Taylor approximation - Derivation of the Weber Hamiltonian
                                  - Weber's atomic modell and its connection to Lorentz geometry
Video-5 The fine structure of Weber's hydrogen atom
                                - The atomic modell of Helmholtz, Kelvin and Tait and Zöllner's attempt to prove the existence of a fourth dimension
                                  - Old quantum mechanics - Symmetries of the Weber Hamiltonian and its connection to the fine structure
                        - Comparison with the work of Sommerfeld and Glitscher

Celestial mechanics and systolic geometry

Pedro Salomão (São Paulo, Math)

Video-1 Systolic inequalities for geodesics flows - The special case of the two-sphere - The Calabi-Croke example - Pinching conditions - Surfaces of revolution - Zermelo navigation data.
Video-2 Systolic inequalities for Reeb flows - The case of the tight three-sphere - A conjecture of Viterbo - Unboundedness of systolic ratio for general Reeb flows.
Video-3 Some systolic inequalities for the circular planar restricted three body problem and the rotating Kepler problem

Introduction to Lorentzian geometry

Stefan Suhr (Bochum, Math)

Video-1   First examples of spacetimes
                                  - Minkowski -, Robertson-Walker -, Schwarzschild -, and Misner spacetimes
                                  - Existence of Lorentzian metrics on closed manifolds
Video-2 Global hyperbolicity and the Ave-Seifert Theorem
                                  - Basic definitions of Lorentzian causality - Global hyperbolicity
                                  - Avez-Seifert Theorem - Lorentzian distance function
Video-3 Geodesics in Lorentzian Geometry
                                  - Geodesics in spacetimes - Generic incompleteness of Lorentzian surfaces
                                  - Morse theory for causal geodesics

Viscoelastic tides and dissipative forces in celestial mechanics

Clodoaldo Ragazzo (São Paulo, Math)

Video-1   In this talk we present equations of motion for a system of linear visco-elastic bodies interacting under gravity.
                The equations are obtained within a finite dimension Lagrangian framework with dissipation function.
                The main dynamical consequences of the dissipative tidal forces will be discussed.

Poster

João Chaib (Minas Gerais, Phys)

Poster "How to defend the validity of Newton’s 3rd law in electrodynamics with four experimental results"

Hints to upload videos to YT

Our videos were in format m2ts and extremely large (1h ~ 8GB), so uploading was just impossible (1 video took more then 12hs and usually upload crashed just shortly before the end..).
With the free software ffmpeg, installation on iMac nicely explained here
https://www.youtube.com/watch?v=-wKkcxYpCoY
the video compressed by a factor of 12(!!) and was saved in mp4 format.
Upload was then less than an hour and worked pretty well.

Command:
ffmpeg -i inputfilename.m2ts outputfilename.mp4

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Atualização: 9.11.1984