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…new vocabulary from Hawking Chaps 9-11 Space-like, time-like variables…subject to Heisenberg time: an imaginery dimension; spacelike & timelike conjugate variables 4 space-time vectors: e.g. (x, y, z, ict), (p x,p y,p z,iE/c) CPT maximal P and C violation: Madam Wu looking at radioactive decay CP good to high level of accuracy…but fails at amplitude 10 -3 T, microscopic time reversal CP violation leads to matter asymmetry in early universe …and proton decay today, though not yet observed Entropy…increase of disorder in an isolated system, more phase space in a disordered system than in an ordered one 2 nd Law of Thermodynamics…entropy increases (unless you do work)

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GR+QM: no singularities in the quantum world extended objects, “strings,” world sheets and tubes 3 spatial Ds: planetary and atomic stability thanks to 1/r 2 forces 2 Ds: 1/r 1 too weak, 4Ds: 1/r 3 too strong

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Kurt Gödel’s incompleteness theorem: cannot formulate arithmetic from a set of axioms =impossible to prove all true statements …by extension the case for all theories based on math Feynman graphs: particle going forward in time = antiparticle going backward Casimir force between 2 metal plates: macro proof of virtual particles existence of negative energy in vacuum between plates by extension, positive vacuum energy outside plates

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GR + QM: no singularities in quantum world extended objects may exist? “strings”? GUT = Grand Unified Theories: EM + Weak + Strong unification scale = 10 15 GeV Planck: time… size = 10 -30 cm mass = energy = temperature = 10 19 GeV, a black hole? Relativistic γ factor quantifies life near c Lorentz contraction: observed objects shortened along path observed length = L rest / γ time dilation: observed clocks run slower, time intervals longer observed tick period = T rest γ

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Relativistic γ factor: Lorentz contraction, time dilation natural unit of velocity, dimensionless β = v/c natural unit of relativity, dimensionless γ = 1/√(1-(v/c)) 2 watch her go c fast? a) she’s squashed, in direction of motion, and b) her watch time slowed

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