Chapter S3 Spacetime and Gravity

General Relativity

Introduction
         Einstein 1915

         There is no "superior reference frame" -- we cannot claim to know
         who is accelerating.
         We cannot tell the difference between (distinguish between) feeling weighty
         and feeling accelerated

Room example
                  Spaceship example: part 1 part 2

         Einstein's Equivalence Principle: "The effects of gravity are exactly
         equivalent to the effects of acceleration"
         The laws of physics are the same in all reference frames

We will need to think in terms of Spacetime

         There are 4 dimensions:
                  3 spatial dimensions (up-down, left-right, forward-backward)
                  + 1 time dimension

         We can only see the 3 spatial dimensions
                  So, it isn't surprising that different people (i.e. different perspectives)
                  "see" things differently (we think Jackie accelerates, and vice verse)
2 dimensional analogy

         Plotting with a spacetime diagram:
                  It is hard to squish 4 dimensions into 2, but we will try
                  This daily life example
                  becomes this spacetime diagram
                           constant velocity => straight worldlines
                           acceleration velocity => curved worldlines
                  Here are more trajectories ("worldlines")

Einstein's Logic

         Travelling at constant velocity, far from gravitional field => straight worldline
         Cannot tell the difference between "" and being in free fall around a
                  massive object
         So, being in free fall around a massive object => straight worldline, too

         How can that work --:
         It works even if spacetime is not flat, but is curved

         Einstein suggests that the straight worldline business above still applies
         except that now "straight" => straightest (shortest) possible path
         So, a freely falling object will take the shortest, straightest possible
                  worldline path

         If that path seems bent to us, it is because spacetime is curved
Diagram of curved spacetime near a massive object

         Einstein's revolutionary thinking:

                  "What we perceive as gravity arises from the curvature of spacetime"

                  "Mass causes spacetime to curve, and the curvature of spacetime"
                  "determines the paths of freely moving masses"

Some Effects

         Light travels with constant velocity, so takes shortest, straightest path
                  So, from our point of view, light appears to bend around massive objects
                  Gravitational lensing: diagram, image
More spectacular image
Close up of a similarly spectacular example

         Time runs slower for things that are closer to a massive object

         Do wormholes exist? (They haven't been ruled out)

Supplimental Material:

Rubber sheet views. 1 2 3 black holes and event horizons.

Time dilation 1 2

Mercury’s orbital precession

Gravitational lensing total solar eclipse multiple images 2

Gravity waves gravitational radiation PSR 1913+16

Detection by LIGO