# 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

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

3

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