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The Theoretical Minimum: OverviewShort and Sweet

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DoD Higher Education

• Tell them what you’re going to tell

them.

• Tell them what you told them you were

going to tell them.

• Tell them what you told them.

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The Original Theoretical Minimum

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Lev Davidovich Landau, 1908 - 1968

One of the great Russian physicists of the 20th century

Tested prospective students in theoreticalphysics.

43 students passed, the 2nd of whom washis famous collaborator, Ilya Lifshitz.

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Our Theoretical Minimum

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Leonard Susskind, 1940-

Prominent American physicist atStanford University: “brilliant imaginationand originality”

Received many awards and honors(but not yet The Big One)

Devotes substantial efforts to a series oflectures aimed at the physics-oriented public

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Susskind’s Target Audience

“The courses are specifically aimed at

people who know, or once knew, a bit

of algebra and calculus, but are more

or less beginners.”

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The Core Sequence of Courses

• Classical Mechanics

• Quantum Mechanics

• Special Relativity and Electrodynamics

• General Relativity

• Cosmology

• Statistical Mechanics6

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Mechanics

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Principal Elements (1)

State Model of Physics Laws

• Determinism

• Reversibility

• Allowed vs Disallowed Forms

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Mathematical Infrastructure (I)

• Spaces

• Trigonometry

• Vectors

Principal Elements (2)

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x

y

z

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Principal Elements (3)

Description of motion (kinematics)

Where particles move but not why:

• position

• velocity (and speed)

• acceleration10

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Principal Elements (3.5)

Mathematical Infrastructure (III)

Differential calculus

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_W = dW (t)dt

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Principal Elements (4)

Mathematical Infrastructure (IV)

Integral calculus

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Q =Ra

b q(x)dx

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Principal Elements (5)

Dynamics of motion

Forces and their effects

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d(m~v)dt = m~a = ~F

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Principal Elements (6)

Mathematical Infrastructure (V)

Partial differentiation (just more

differentiation)

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p(x;y) = @P (x;y)@y

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Principal Elements (7)

Extremum principles

• the whole rest of the course

• the Promised Land

• the heart of classical mechanics

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Principal Elements (7.1)

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L = T ¡ V

ddt

³ @L@_qi

´= @L

@qi

Example: Lagrangian Mechanics

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do.

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