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GENERAL RELATIVITY II CURVED SPACE-TIME. Intrinsic Curvature. Airlines follow the shortest path This is not a straight line because the Earth’s surface is intrinsically * curved. *Cannot be made flat without stretching or tearing. Intrinsic curvature measured by triangulation.

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GENERAL RELATIVITY II

CURVED SPACE-TIME


Intrinsic Curvature

Airlines follow the shortest path

This is not a straight line because the Earth’s surface is intrinsically* curved

*Cannot be made flat without

stretching or tearing


Intrinsic curvature measured by triangulation
Intrinsic curvature measured by triangulation

Draw any triangle = 3 points joined by geodesics*

*Geodesic – line of shortest distance in curved space (in flat space this is a straight line)

Σ angles > 180o Σ angles < 180oΣ angles = 180o

The first 2 shapes cannot be made from a flat

piece of paper without tearing or stretching


General Relativity’s

BIG IDEA

Generalization of curved space to more than 2 dimensions Mathematician -> Riemann, Einstein used this work for GR.

Space & Time are

intrinsically curved by mass.

This alters motion `as if’

there is a force of gravity

(there isn’t).


Worldine

t

t

Spacetime

y

At rest

TABLE

x

Worldine

t

  • Minkowskispacetime

  • has 3 space and 1 time

  • = 4 dimensions

  • Spacetime is intrinsically

  • curved by mass

Constant

velocity


In free fall, objects are following

geodesics in 4-dimensional spacetime

General Relativity’s Law of Motion

E.g. planetary orbit

t

y

y

x

x

Note: Path in space

only is not geodesic

Spacetime curved by Sun’s mass.

Planet’s geodesic is not `straight’.



What general mathematical name is given to the shortest path between two points?

a) Line

b) Geometric

c) Worldline

d) Geodesic


What general mathematical name is given to the shortest path between two points?

a) Line

b) Geometric

c) Worldline

d) Geodesic


How many dimensions does our spacetimehave?

a) 2

b) 3

c) 4

d) 5


How many dimensions does our spacetimehave?

a) 2

b) 3

c) 4

d) 5


Which of the following is not part of Einstein’s General Relativity model

  • Gravity is due to the curvature of the Earth’s surface

  • Spacetimeis curved by the presence of mass

  • Free fall due to gravity is equivalent to being in an inertial frame

  • Objects in free fall follow geodesics in spacetime


Which of the following is not part of Einstein’s General Relativity model

  • Gravity is due to the curvature of the Earth’s surface

  • Spacetimeis curved by the presence of mass

  • Free fall due to gravity is equivalent to being in an inertial frame

  • Objects in free fall follow geodesics in spacetime


Which of the following is evidence that General Relativity is better than Newton’s models?

a) The measured advance of the perihelion of Mercury

b) The phase of Venus

c) That the Earth orbits the Sun, not vice versa

d) The existence of Jupiter’s moons


Which of the following is evidence that General Relativity is better than Newton’s models?

a) The measured advance of the perihelion of Mercury

b) The phase of Venus

c) That the Earth orbits the Sun, not vice versa

d) The existence of Jupiter’s moons


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