The Theoretical Minimum: What You Need to Know to Start Doing Physics
Leonard Susskind, George Hrabovsky
Language: English
Pages: 256
ISBN: 0465075681
Format: PDF / Kindle (mobi) / ePub
If you ever regretted not taking physics in college—or simply want to know how to think like a physicist—this is the book for you. In this bestselling introduction, physicist Leonard Susskind and hacker-scientist George Hrabovsky offer a first course in physics and associated math for the ardent amateur. Challenging, lucid, and concise, The Theoretical Minimum provides a tool kit for amateur scientists to learn physics at their own pace.
Symmetries in Physics: Philosophical Reflections
How Physics Confronts Reality: Einstein Was Correct, but Bohr Won the Game
The Shape of Inner Space: String Theory and the Geometry of the Universe's Hidden Dimensions
Paradox: The Nine Greatest Enigmas in Physics
The Character of Physical Law (Messenger Lectures, 1964)
Landau. The TM in Russia meant everything a student needed to know to work under Landau himself. Landau was a very demanding man: His theoretical minimum meant just about everything he knew, which of course no one else could possibly know. I use the term differently. For me, the theoretical minimum means just what you need to know in order to proceed to the next level. It means not fat encyclopedic textbooks that explain everything, but thin books that explain everything important. The books
as a particle that moves along the x axis, subject to a force that pulls it toward the origin. The force law is Fx kx. The negative sign indicates that at whatever the value of x, the force pulls it back toward x 0. Thus, when x is positive, the force is negative, and vice versa. The equation of motion can be written in the form x or, by defining k m k m x, Ω2 , x Ω2 x. (6) Exercise 4: Show by differentiation that the general solution to Eq. (6) is given in terms of two constants A and B
to label the points of the state-space. When the state-space is described this way, it has a special name—phase space. The phase space of a particle is a six-dimensional space with coordinates xi and pi (see Figure 1). p x, p x Figure 1: A point in phase space. Why didn’t we call this space configuration space? Why the new term phase space? The reason is that the term configuration space is used for something else, namely, the threedimensional space of positions: Just the ri ’s. It might have
to manipulate Poisson Brackets (from now on I’ll use the abbreviation PB) without all the effort of explicitly calculating them. You can check (consider it homework) that the rules really do follow from the definition of PB’s. Let A, B, and C be functions of the p’s and q’s. In the last lecture, I defined the PB: A, C i A C A C qi pi pi qi . (1) The first property is antisymmetry: If you interchange the two functions in the PB it changes sign: A, C C, A . (2) In particular, that
subtended by an arc equal to the radius of the circle. Φ c a Θ b Figure 7: A right triangle with segments and angles indicated. We define the functions sine (sin), cosine (cos), and tangent (tan), as ratios of the various sides according to the following relationships: sin Θ cos Θ tan Θ a c b c a sin Θ b cos Θ . We can graph these functions to see how they vary (see Figures 8 through 10). Spaces, Trigonometry, and Vectors 21 We can graph these functions to see how they vary (see
