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Course Information

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Video Lectures
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Course

Subject:	Physics
Topic:	Special Relativity
Views:	65,082

Educator

Stanford University

Name:	Stanford University (Stanford)
Type:	University

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Instructor

Name

Leonard Susskind

Modern Physics: Special Relativity

Video Lectures

Displaying all 8 video lectures.

Lecture 1 Play Video	Inertial Reference Frames The laws of physics are the same in any inertial reference frame. The Lorentz transformation is the transformation between two inertial frames. Galilean transformation is appropriate for small velocities. Proper time is the time an observer measures with a clock traveling with the observer, and is an invariant under a Lorentz transformation.
Lecture 2 Play Video	Principle of Least Action Review Lagrangian techniques in Classical Mechanics. Coordinates describe the state of a system, position, momentum. Euler's equations. Fields exist throughout space-time. Example: point masses connected by springs. The Action integral and the Principle of Least Action
Lecture 3 Play Video	Invariance of the Laws of Nature Laws take the same form in every reference frame. Define the infinitesimal distance between two points. Contravariant, covariant vectors, invariant inner product. Summation convention. Examples of fields in Nature. The four-dimensional Lagrangian. The Action Principle in four dimensions.
Lecture 4 Play Video	Lagrangian Mechanics Define the Action integral in four dimensional space-time. Kinetic and potential energy appear in the Lagrangian. Symmetries and Conservation Laws Time invariance implies energy conservation. Define the canonical momentum. Invariance under a space transformation implies conservation of the sum of the momentum of the particles.
Lecture 5 Play Video	Conservation of Charge and Momentum Two ideas of momentum: Mechanical and canonical. Conservation of momentum and energy in field theory. Interaction of fields and particles, mechanical momentum vs. canonical momentum. Invariance under a phase transformation implies conserved electric charge.
Lecture 6 Play Video	Relativistic Wave Equation and Conservation Laws The conservation of charge relates to the mathematical statement of a vanishing divergence of the charge current. Study an example: the conservation of charge for a complex wave function. Conservation of charge can be derived using the infinitesimal change of phase of a complex wave function. By “conserved” a physicist means there exists a current, conserved quantity and a continuity equation for the current and charge. Isotopic spin has three components. Study the relation between the energy and momentum of a particle.
Lecture 7 Play Video	Invariance under Gauge Transformations Gauge theory. Phase transformation of a complex wave function. The electromagnetic vector potential appears in the covariant derivative. The Action for the relativistic wave equation is invariant under a phase (gauge) transformation. The electromagnetic field tensor is gauge invariant.
Lecture 8 Play Video	Gauge Theory A global gauge transformation has the same phase shift everywhere whereas a local gauge transformation has a phase shift as a function of location. Benjamin Franklin fixed the convention for positive and negative charge and the direction of current flow. Lorentz invariance of the equation of motion implies that the Lagrangian must be a scalar. Gauge invariance of the Lagrangian implies conservation of charge. The Lorentz force is the force of the electromagnetic field upon a charge. No magnetic monopoles have been observed although some theories allow for them. A field approximating a magnetic monopole can be constructed using a very long solenoid.