YAML Title: - Photonic_Toroidal_Vortex_Architecture Desription: - An_exact,_semi-classical,_geometric_alternative_to_probabilistic_theories._It_replaces_point_abstractions_with_a_local,_mechanical_conservation-of-action_principle,_within_a_structured_rotating-photon-framework. Aim: - Obtain_a_visualisable_mechanical_model_of_the_unobservable_world_beyond_the_senses - Interpret_anthropocentric_theories_using_a_universal_model Core_achievements: - obtains_energy_levels_for_an_electron_without_an_external_potential - reproduces_the_Sommerfeld-Dirac_fine_structure_hydrogen_atom_energy_levels_to_2_parts_in_10^10 - obtains_the_hyperfine_half_splitting_for_hydrogen_across_30_states_with_a_median_error_of_0.0014_MHz - provides_explicit_local_physical_mechanisms_for_intrinsic_spin,_the_Lorentz_force_deflection,_mass_generation,_charge_invariance,_and_Bose_Einstein_statistics_with_distinguishable_photons Main_research_and_documentation: - https://barryispuzzled.com/physics Relevant_publications: - Reinterpretation_of_the_Grangier_experiment_using_a_multiple-triggering_single_photon_model,_Modern_Physics_Letters_B,_(2023),_DOI:_10.1142/S0217984923500422 - A_photonic_toroidal_vortex_model_of_the_hydrogen_atom_fine_structure,_Quantum_Studies:_Mathematics_and_Foundations,_(2025),_DOI:_10.1007/s40509-025-00364-9 Preprints: - Geometrical_interpretation_of_the_hydrogen_atom_hyperfine_structure,_(2026),_DOI:_10.20944/preprints202603.1719.v1 - The_Lorentz_force_and_the_nature_of_charge_from_a_photonic_toroidal_vortex_model,_(2026),_DOI:_10.20944/preprints202603.2233.v2 - A_heuristic_model_of_the_Bose-Einstein_distribution_with_distinguishable_photons,_(2026),_DOI:_10.20944/preprints202605.1447.v1 Author: Name: Dr Barry R. Clarke Curriculum_vitae: - The_Vortex_Atom,_World_Scientific_Publishing,_(2021) - The Quantum_Puzzle,_World_Scientific_Publishing,_(2017) - Puzzle_compiler_for_the_Daily_Telegraph_with_over_1800_mathematics_and_logic_puzzles - Challenging_Logic_Puzzles_Mensa,_Sterling,_(2003),_over_100,000_sold - MSc_by_thesis_in_matrix_mechanics_perturbation_methods_with_two_publications_in_J._Phys._A. - PhD_in_Shakespeare_attribution_studies website: - https://barryispuzzled.com HS: type: fundamental_construction_unit description: finite-length_string Sp-1: derived_from: HS description: optical_spin_angular_momentum_(optical_SAM) structure: HS_helical_trajectory Sp-2: derived_from: Sp-1 description: optical_orbital_angular_momentum_(optical_OAM) structure: Sp-1_helical_trajectory Sp-3: derived_from: Sp-2 description: toroidal_rotation structure: Sp-2_rotation_around_toroidal_axis constants: alpha: fine_structure_constant c: speed_light mo: electron_rest_mass m'o: proton_rest_mass h: Planck's_constant hbar: h/(2*pi) M: mo/m'o Ry : Rydberg_frequency An: nuclear_mass_number Zn: nuclear_charge variables: na: Sommerfeld_azimuthal_quantum_number nr: Sommerfeld_radial_quantum_number n: total quantum number - n = na + nr r2o: Sp-2_radius - r2o = 3.86159268*10^(-13) m r3o: Sp-3_radius - r3o = 5.291631210153*10^(-11) m v2: Sp-2_speed v2f: Sp-2_field_speed v3: Sp-3_speed v3f: Sp-3_field_speed p2f: Sp-2_field_momentum p3f: Sp-3_field_momentum xbar: bound-state_distance_between_proton-electron_toroidal_centers_as_fraction_of_r3o dbar2: bound-state_distance_between_proton-electron_Sp-2_centers_as_fraction_of_r3o E3: fine_structure_formula_with_reduced_mass E3D: fine_structure_formula_with_reduced_mass_and_velocity_adjustment nu_midpoint: hyperfine_midpoint_frequency_(MHz) nu_magnetic_potential: magnetic_potential_frequency_(MHz) nu_shift: hyperfine_half-interval_shift_from_midpoint_(MHz) nu: frequency_(MHz)_includes_fine_structure_with_reduced_mass_and velocity_adjustment,_magnetic_potential,_and_hyperfine_half-interval_shift capital_gamma: searchable_parameter_in_fine_structure_velocity_adjustment A: Searchable_parameter_in_magnetic_potential B: Searchable_paremeter_in_magnetic_potential k: muliplier_in_hyperfine_half-shift_(k=1_for_nS1/2_states) Fundamental_postulates: - Sp-1_and_Sp-2_rotations_tend_to_preserve_action_h - rotational_and_translational_action_are_interchangeable_when_Sp-1_or_Sp-2_action_is_overloaded_or_underloaded used_in: - dispersive_media_when_photon_speed_slows_due_to_translational_action_redistributed_into_Sp-1_action - hyperfine_shift_when_changing_magnetic_momentum_field_overloads_or_underloads_electron_Sp-2_action_into_or_out_of_Sp-3_action - Lorentz_force_when_Sp-2_circuit_in_toroid_is_underloaded_or_overloaded_due_to_field_gradient_across_it_and_change_in_Sp-3_translational_action_gives_deflection Attraction_mechanism: - proton_and_electron_Sp-3_have_opposite_rotations - proton_Sp-3_field_momentum_intrudes_in_electron_Sp-3_rotation - electron_Sp-3_action_reduced_by_field_momentum_so_toroid_attempts_to_find_next_lowest_integer_action - electron_seeks_stronger_proton_field_to_reduce_action_further - electron_Sp-3_energy_redistributed_into_translational_motion_towards_proton - translational_energy_emitted_as_radiation_at_bound-state_distance Repulsion_mechanism: - same_charges_have_same_sense_Sp-3_rotations - action_in_target_Sp-3_is_overloaded_by_intruding_Sp-3_field_momentum - toroid_attempts_to_find_next_lowest_integer_action - toroid_seeks_weaker_source_field_to_reduce_action_further - Sp-3_energy_redistributed_into_translational_motion_away_from_source rest_mass: derived_from: Sp-2 structure: circular_Sp-2_rotation condition: inversely_proportional_to_Sp-2_radius equation: mo = h/(2*pi*r2o*c) relativistic_mass: derived_from: - Sp-2 - Sp-3 condition: Sp-2_helical_trajectory_due_to_Sp-3_momentum_component magnetic_momentum_field: derived_from: Sp-2 structure: - permanent_field_emission_due_to_Sp-2_rotation - p2f_field_momentum - r2f_field_radius - radius_taken_from_Sp-2_center - mass_of_field_invariant - speed_inversely_proportional_to_r2f - field_cuts_line_joining_source-target_Sp-2_centers_at_pi/4 - field_lines_are_parallel used_in: - changing_p2f_field_momentum_creates_hyperfine_splitting formula: - p2f = hbar/r2f - v2 = c*sqr(1 - alpha) electric_momentum_field: derived_from: Sp-3 structure: - permanent_field_emission_due_to_Sp-3_rotation - p3f_field_momentum - r3f_field_radius - radius_taken_from_Sp-3_center - electric_field_momentum_perpendicular_to_magnetic_field_momentum used_in: - Coulomb_field - Ampere's_law: aligned_Sp-3_field_rotations_around_current-carrying_conductor formula: - p3f = hbar*alpha/(r2f*sqr(1 - alpha^2)) - v3 = alpha*c dbar2: name: - bound-state_distance derived_from: - electron_Sp-3_residual_energy_after_field_intrusion - proton_Sp-3_momentum_field_energy condition: electron_Sp-3_residual_energy == proton_Sp-3_momentum_field_energy used_in: - fine_structure_velocity_adjustment_D-function - magnetic_potential - hyperfine_shift - neutron_construction formula: - dbar2 = sqr(xbar^2 + (1 - M)^2) charge: derived_from: - Sp-2 - Sp-3 - Lorentz_force_deflection_analysis structure: - view_rotations_in_v2_and_v3_directions - two_chiralities_for_each_charge - negative_charge: clockwise_Sp-2_and_counter_clockwise_Sp-3 - negative_charge: counter_clockwise_Sp-2_and_clockwise_Sp-3 - positive_charge: counter_clockwise_Sp-2_and_counter_clockwise_Sp-3 - positive_charge: clockwise_Sp-2_and_clockwise_Sp-3 principle: - charge_invariance_when_viewing_it_moving_away_from_other_side fine_structure_reduced_mass: formula: - MHz_frequency - Y = nr^2 + sqr(na^2 - alpha^2) - mu = mo/(1 + M) - E3 = (10^(-6)/h)*(mu/sqr(1 - alpha^2/(2*(Y^2 + alpha^2))))*alpha^2*c^2/(2*(Y^2 + alpha^2)) fine_structure_velocity_adjustment: formula: - MHz_frequency - D = (1 + capital_gamma*M/n)^2 - YD = nr^2 + sqr(na^2 - D*alpha^2) - mu = mo/(1 + M) - E3D = (10^(-6)/h)*(mu/sqr(1 - D*alpha^2/(2*(Y^2 + D*alpha^2))))*D*alpha^2*c^2/(2*(Y^2 + alpha^2)) - alpha^2_in_E3_replaced_by_alpha^2*D - relative_speed_adjustment_of-electron_along_line_joining_Sp-2_centers magnetic_potential: formula: - MHz_frequency - nu_magnetic_potential = A*(dbar2)^B nature: - with_B=-3.000_(to_three_decimal_places_for_all_states)_it_resembles_a_dipole_moment - boundary_term_that_remains_when_differentiated_field_momentum_with_respect to spatial_coordinates_is_integrated_over_trajectory_from_infinity_to_bound-state_distance_dbar2 - cumulative_effect_of_Sp-2_field hyperfine_midpoint: - used_instead_of_the_hyperfine_centroid used_in: base-line_for_equal_magnitude_hyperfine_half-interval_shift_each_side formula: - MHz_frequency - nu_midpoint = E3D + nu_magnetic_potential parameter_constraints: B: - capital_gamma_in_E3D_is_varied - found_by_minimizing_difference_between_experimental_value_of_nu_midpoint_and_E3D - for_all_60_hydrogen_states - B = -3.000 (3_decimal_places) A: - once_B_is_found_A_is_lined_up_on_lowest_n_of_set_for_example_1S1/2_in_nS1/2,_it_must_then_work_for_all_other_states_in_that_set - it_then_has_to_work_on_other_five_tested_states_in_that_set - two_values_for_each_states_with_A>0_and_A<0,_corresponding_to_two_values_of_capital_gamma_<0_and_>0 universal_scaling_law: - A/capital_gamma = -28651713/(An*Zn) - law_has_0.03%_error_for_deuterium - law_has_0.04%_error_for_tritium - law_has_0.05%_error_for_3He+ - law_has_0.01%_error_for_7Li2+ hyperfine_shift: - two_cases_per_state_depending_on_whether_the_proton-electron_have_same_or_opposite_sense_rotations - same_sense_proton-electron_Sp-2_rotations_as_they_approach_gives_red-shift,_capital_gamma_>0 - opposite_sense_proton-electron_Sp-2_rotations_as_they_approach_gives_blue-shift,_capital_gamma_<0 formula: - nu_shift_value_can_be_plus_or_minus - nu_shift = 2*k*pi*n^2*alpha^3*Ry/(sqr(2)*Y^2*sqr(1 + alpha^2/Y^2)*(1 - alpha^2)^(3/2)*dbar2^3) - k=1_for_nS1/2_states_but_varies_for_other_sets_due_to_Sp-2_eccentricity_which_reduces_field_receptivity nature: - effect_of_changing_Sp-2_field_at_electron_Sp-2_location_in_one_electron_Sp-2_time_period complete_calculation: formula: - nu = E3D + nu_magnetic_potential + nu_shift