הרצאות מוקלטות

The aim of these 10 lectures is to present the models in modern physics to able to bridge the gap between mathematics and physics. These lectures can help anyone who wants to understand Modern Physics. It can be helpful for students studying course on Modern

Motivation for use of tensors Einstein's summation convention Vectors, co-vectors Matrices and metrics Levi-Civita symbol Vector analysis in 3D

Transformation of tensors of different rank 1:39
Determinant of 3x3 matrix by use Levi-Civita symbol 8:00
Prove of the determinant of the product 10:06
Formula for the inverse matrix 12:25
Proof of Kramer's rule 16:38
Calculation of curl and div of a vector field 17:43
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Overview of lecture 4
Conservation of angular momentum for central force 7.10
Geodesics on the globe 10:22
On a sphere, geodesics are great circles 11:25
Geodesics near the North pole 13:06
Geodesics from New York to Madrid 13:26
The right direction for the shortest route on globe 14:07
Angle between the geodesic and North 15:04
Examples of Generalized Principle of inertia 16:01

Lorentz transformations from principle of relativity
Invariant metric, Preserved Speed; Velocity addition, Fizeau experiment; Fiber Optic Gyroscope and Sagnac effect

Overview of lecture 5
Meaning of Lorentz transformations 5:50
Eigenvectors of Lorentz transformations 8:40
Space travel and proper time example using SR 10:44
Symmetric velocity 12:55
Rapidity 14:40

Real bounded symmetric domains (BSD)
The ball of admissible velocities D is a BSD 11.39
The Lie algebra aut(𝐷) 14.50
Minkowski spacetime 18.49
Four-velocity 26.56
Generators of homogeneous Lorentz group and its Lie algebra 34.13
Four-acceleration and electro-magnetic tensor 37.05
Four-momentum for massive and massless objects 46.05
Relativistic Dynamics Equation

Overview of lecture 6
The velocity ball as a BSD 2:04
The generators of dynamic equation 2:49
Embedding 3D into 4D 3:33
Appearance of magnetic field 6:00
Symmetric velocity addition 7:00
Conformal geometry and symmetric velocities 9:15
Analytic relativistic dynamics 9:58
The meaning of negative length 11:20

Shortcoming of differential equation description of evolution 1.45
Use of fields to describe action at a distance 5.34
Field generated by a single source 8.35
Bi-polar coordinates in spacetime 12.40
Astronomy Observations and bi-polar coordinates 16.24
Local basis in bi-polar coordinates 23.16
Matrix Representations of Spacetime 27.09
Spin-half Lorentz group representation 32.42
Commutation relations of representation 36.13
Invariance of the complex angle under spin-half representation 46.10
Pre-potential of single source field 50.20

Light cone in Cartesian and Bi-polar coordinates 0:20
Local basis and dual basis in Bi-polar coordinates 3:55
The conjugation in complex Minkowski space 7:11
Boosts in spin-half representation 9:15
Rotations spin-half representation 11:50

Bi-polar coordinates 2.28
Pre-potential of a single source field 5.25
Complex spacetime conjugation 8.09
Derivatives of the relative position 9.20
Diamond product 16.02
Gradient of the relative position vector 19.25
The four potential of the field 30.30
The electromagnetic field tensor 37.00
Near and radiation fields 48.57
Electromagnetic field from several sources 50.53
Maxwell equations 1.00.38
Meaning of complexification 1.14.35

Why there is a need for General Relativity?
Relativistic Newtonian Dynamics for a gravitational field 03:32
The metric of a spherically symmetric body 15:41
Gravitational time dilation 34:24
Equation of planetary motion in RND 39:13
Solving the planetary motion equation an precession of Mercury 50:30
Deflection of light 1:06:22

The Need of Quantum mechanics 0:22
State space of an object 11:04
Observables 23:28
Quantum harmonic oscillator 32:52
Hydrogen atom 43:40
Lectures overview 52:05
Open problems 1:08:05

הרצאה פומבית " תורת היחסות של איינשטיין והתנהגות אנושית" (ברוסית)