General Relativity PH1012

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					                                                                                       Scope and Aims of Course:
           General Relativity: PH1012
                                                                                           “In this class, I hope you will learn not merely
                                                                                           results, or formulae applicable to cases that may
                                                                                           possibly occur in our practice afterwards, but the
                                                                                           principles on which those formulae depend, and
                  Dr. Andrew G. Green                                                      without which the formulae are mere mental
                                                                                           rubbish.
                  Rm 213
                  Andrew.green@st-andrews.ac.uk                                            I know the tendency of the human mind is to do
                                                                                           anything rather than think. But mental labour is not
                                                                                           thought, and those who have with labour acquired
                                                                                           the habit of application, often find it much easier
                                                                                           to get up a formula than to master a principle”

                                                                                           James Clerk Maxwell 1860
                                                                                           Inaugural Lecture UCL




Scope and Aims of Course:                                                             Outline:

         •Non-mathematical Introduction to GR                                             7 lectures in total:
         •General Relativity:
                      Relationship between measurements                                   2 Galilean Relativity +Special Relativity

         •Emphasis:   observation                                                         3 General Relativity: Main ideas + consequences
                      deduce general principles                                           2 Cosmological consequences + open questions
                      mathematical formulation                                            (non-examinable)
                      test with thought experiments
         Basic ideas are few and quite simple.
         The consequences are surprising.                                                 Notes:       Handout and on web
                          ASK!                                                            Problem Set: Handout and on Web
                                                                                                       Solutions on Web later




Synopsis:

 The Principle of Galilean                  The General Theory of Relativity
   Relativity                               n   The Weak Principle of Equivalence
                                                Inertial Forces
                                                                                                      Lecture 1:
                                            n
 n   Frames of Reference
                                            n   The Strong Principle of Equivalence
 n   Galilean Transformations               n   Gravitational Time Dilation, Length

                                                                                                  Galilean Relativity
 n   Galilean Invariance of Newton's            Contraction and Red Shift
     Laws                                   n   Gravitational Bending of Light
 n   Universal Time                         n   Spacetime Curvature
 n   The Failure of Galilean Relativity



 Special Relativity                         The Edge of Relativity
                                            n          Principle/Gravetomagnetism
                                                Mach's Principle/ Gravetomagnetism
 n   The Principles of Special Relativity   n   Black Holes
                                                Cosmological Expansion
     Time Dilation + Length Contraction
                                            n
 n
                                            n   Quantum Mechanics + GR
 n   The Lorentz Transformation
                                            n   General Relativistic Analogue
 n   Lorentz Invariance of Maxwell's            Systems
     Equations
                                            n   …
 n   The invariant interval




                                                                                                                                                  1
Galilean Relativity:                                                  Galilean Relativity
           A few words on philosophy:                                  Principle of Galilean Relativity:
              •Describe relationship between observations
              •“ Caputuring the appearances” ( data compression)
              •Thought Experiment- very important tool                   “The Results of Measurement depend only
          “The only justification for our concepts and system of         upon the relative velocity of observer and
          concepts is that they serve to represent the complex of          observed and not upon their absolute
          our experiences; beyond that they have no legitimacy”
                                                                                         velocities”
          “I am convinced that the philosophers have had a
          harmful effect upon the progress of scientific thinking
          in removing certain fundamental concepts from the                       First communicated in a letter by Galileo
                                                                                  Thought Experiment: Motion of Ship…
          domain of empiricism…”

          A. Einstein “The Meaning of Relativity”




Galilean Relativity                                                   Galilean Relativity
 Frames of Reference:
                                                                       Galilean Transformation:
                                                                                                                                (x,y,z,t) in O
 •Galilean (and special and general) Relativity
         all about measurement of time and space
                                                                             x’=x-vt                                            (x’,y’,z’,t’) in O’
 •Carefully define measurement                                                                                      v
                                                                             y’=y
                                                                             z’=z
    Imaginary grid of rulers + clocks
                                                                             t’=t
    Synchronise clocks with light pulse
           know distance, use t=l/c                                                                    Frame O                Frame O’
    Measure:
           -position determined by
                   nearest clock                                              Assumptions:       Universal time    -Main assumption
           -time by time on clock




Galilean Relativity                                                   Galilean Relativity

 Galilean Invariance of Newton’s Laws:                                 Assumption:

         •Solve some dynamical problem with Newton’s laws                                 Universal time            -Main assumption
         •Add constant velocity to every component
                                                                                          Invariant mass
         •Calculate with Newton’s Laws again
         •Answer as before with velocity added to it                                      Invariant Force

              F=ma depends only upon acceleration
                                                        Galilean
         •See Q1 on example sheet                    Transformation
         •Consider cannon ball…




                                                                                                                                                      2
Galilean Relativity                                           Galilean Relativity

 Failure of Galilean Relativity:                               Failure of Galilean Relativity:

       •Maxwells Equations                                           •Michelson Morely experiment

       •Light, radio etc travelling waves of E and B fields
       •Rearrange Maxwell: (∂t2+c^2 ∂x2)E=0
       •Wave equation same for water waves, sound, etc
       •All other waves travel in medium
       •Led to postulate the ether    -permeates all space
                                -supports EM waves
       •Michelson-Morely Experiment




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