![]() My question is: What particles are predicted at the GUT temperature and PLANCK temperature by supersymmetry and string (or M) theory ? How many degrees of freedom do these contribute ? The number of degrees of freedom at the Planck time may be of particular interest because it determines the current temperature of the background of gravitons left over from the big bang. At yet higher temperatures, heavier particles may be expected to contribute. At temperatures ~ TeV all of the particles in the standard model contribute to a total of just over 100 degrees of freedom. The number of degrees of freedom is thus higher at earlier times. When kT>mc^2 particles of mass m behave as radiation (rather than cold matter), and contribute to the number of relativistic degrees of freedom. As you look earlier and earlier, things get hotter. Here is a brief intro: The early universe was radiation dominated. Leonard Susskindĭear All, My query is from Cosmology (& Particle Physics). ![]() So as I said, there are more states than you might expect. The space of states is 4 dimensional (uu, ud, du, dd). Then as you say, the number of parameters is 2N-2 = 2. The space of states has dimension 2 (up, down). Now consider the spin of a single electron. Therefore the number of real parameters is 2N-2. But there is a constraint that the sum of squares is 1. Here is the rule: If the dimension of the space of states is N then it takes N complex numbers to specify the components of a general vector. The extra states are of course the entangled ones. This means that there are states of the two electron system that are more general than the "product states" of two un-entangled electrons. One would think that if it takes 2 real parameters to specify the state of an electron spin, then it would take 4 to specify the state of two electron spins. If not perhaps someone else can answer.ĭear jpr, Your question gets to the heart of the matter. If I know the answer to your question I will post it. Some are more broadly about physics and science. Some are about the material in the courses. Since the videos went up, I have received many emails with good questions. ![]() The response was overwhelming and it was suggested that Stanford put them up on the internet. The courses are specifically aimed at people who know, or once knew, a bit of algebra and calculus, but are more or less beginners. So I started a series of courses on modern physics at Stanford University where I am a professor of physics. Fat advanced textbooks are not suitable to people who have no teacher to ask questions of, and the popular literature does not go deeply enough to satisfy these curious people. The authors provide vivid explanations that, to borrow a phrase from Einstein himself, are as simple as possible (but no simpler).Īn approachable yet rigorous introduction to one of the most important topics in physics, General Relativity is a must-read for anyone who wants a deeper knowledge of the universe's real structure.A number of years ago I became aware of the large number of physics enthusiasts out there who have no venue to learn modern physics and cosmology. They delve into black holes, establish Einstein field equations, and solve them to describe gravity waves. Starting from the equivalence principle and covering the necessary mathematics of Riemannian spaces and tensor calculus, Susskind and Cabannes explain the link between gravity and geometry. Now, physicist Leonard Susskind, assisted by a new collaborator, André Cabannes, returns to tackle Einstein's general theory of relativity. He taught us classical mechanics, quantum mechanics, and special relativity. ![]() The latest volume in the New York Times bestselling physics series explains Einstein's masterpiece: the general theory of relativity ![]()
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