…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),

(px,py,pz,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

2nd Law of Thermodynamics…entropy increases (unless you do work)

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/r2 forces

2 Ds: 1/r1 too weak, 4Ds: 1/r3 too strong

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 particlesexistence of negative energy in vacuum between plates by extension, positive vacuum energy outside plates

GR + QM: no singularities in quantum world extended objects may exist? “strings”?

GUT = Grand Unified Theories: EM + Weak + Strongunification scale = 1015 GeV

Planck: time…size = 10-30 cmmass = energy = temperature = 1019 GeV, a black hole?

Relativistic γ factor quantifies life near c Lorentz contraction: observed objects shortened along path

observed length = Lrest / γ

time dilation: observed clocks run slower, time intervals longerobserved tick period = Trest γ

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