Let's look at what's implied by

the way Einstein talks about gravity.

If mass-energy tells space-time how to curve and

space-time curved tells mass-energy how to move,

then we should see this effect on

particles or radiation traveling through the universe.

That's in fact how the first prediction of

general relativity in his confirmation happened in 1916.

Using Einstein's theory which had

only been published less than a year ago,

Eddington and others decided that the sunlight from

a distant star grazing

the sun's surface should be bent

around the Sun to come to the earth,

and show a slightly different deflection

than predicted in Newton's theory.

This is the gravitational lensing effect.

In an eclipse expedition of that year,

Eddington and his team

observed this deflection as Einstein predicted.

An extraordinary situation or a frontier new theory,

was affirmed within 12 months of being published,

and this is part of what cemented

Einstein's reputation as a brilliant scientists.

Since then, gravitational lensing

has been observed in hundreds,

even thousands of situations.

Space-time is curved and

light follows the curvature

of space-time and so is deflected,

when there's sufficient gravity.

These effects are very small,

tiny fractions of a percent in a situation like the Sun.

But for a compact object

like a neutron star or black hole,

these effects can be extreme.

In more recent decades,

gravitational lensing has been seen

in other situations far beyond our galaxy.

There are super massive black holes or compact objects,

billions of light years from the Earth,

where the light passes along

different paths around the galaxy

and is lensed by that galaxy,

producing huge gravitational optic experiments

in the universe where multiple images are formed.

A mirage essentially caused by gravity.

Gravitational lensing is the most routine way

we see the general relativity applies in the universe.

There are however other effects of general relativity,

they've also been observed.

General relativity predicts that time

slows down in an intense gravitational field.

At the event horizon of a black hole time

actually stands still.

But general relativity was confirmed in

a more mundane terrestrial situation.

If time slows down in a gravitational field,

then an atomic clock

carried high above the Earth's surface,

should actually run slightly

faster than an atomic clock at the Earth's surface.

This experiment was actually first done in the

1950's using high-flying spy planes,

and early versions of

atomic clocks confirming general relativity.

The sensitivity of a such experiments

is such that in the last year,

it's been confirmed even in a laboratory where

a super precise atomic clock has been shown to

operate or keep time very slightly

faster above the lab than in the lab itself.

Time slows down in an intense gravity,

just as space and time are curved in intense gravity.

Let's look in a bit more detail at

the curvature of space-time implied by relativity.

In Newton's view of the universe,

space is infinite and flat.

Objects and light do not deviate

traveling through space which is euclidean.

In Einstein's view of space,

space is curved by local gravity or

even by global gravity of the universe itself.

So we can think of the universe as

a slightly crazy fun house mirror where there are

subtle distortions of light radiation

or particles traveling through the universe,

being warped and deflected

slightly by the gravity they encounter along the way.

In relativity, there are simple ways

to characterize curved space-time.

Now in relativity, the curvature is in

three-dimensional space-time, the space we live in.

But it's easier to visualize this in a lower number of

dimensions by projecting it onto a surface.

Familiar to us, is

the euclidean space of a flat sheet of paper,

where parallel lines stay

parallel and where the angles in

a triangle add up to

a 180 degrees as Euclid said 2,000 years ago.

In relativity, if space is curved,

it can have two signs.

Can have different amounts of curvature,

but the two fundamental differences are whether

the space is positively or negatively curved.

In positively curved space,

in the analogy in two-dimensions,

it's like the surface of a sphere or

some other contain space-like that.

As we know, if you draw parallel lines on the surface of

a sphere such as two lines

projected north from the equator of the Earth,

which would meet at the pole, those lines converge.

So parallel light does not remain parallel,

there's a focusing or convergence

caused by the curvature.

We also know that a triangle drawn on the surface of

a sphere has angles that add

up to more than a 180 degrees,

so Euclid geometry does not apply.

By contrast, we can imagine in

two-dimensions and it can exist in three-dimensions.

Negatively curved space.

In negatively curved space,

the analogous shape is like a saddle.

Parallel lines drawn on a saddle shape will actually

diverge and if you draw a triangle on a saddles shape,

the angles in the triangle add up

to less than a 180 degrees.

So we can violate

Euclidean geometry in these curved space-times.

Now what this means in three-dimensional space,

is that if space were truly flat in Euclidean,

parallel light beam sent out into

the universe would never get closer or further apart,

they would stay parallel.

If we lived in

a universe that had positively curved space-time,

those light beams would actually

eventually meet or converge,

and if we lived in a universe

with negatively curved space-time,

those parallel light beams would diverge.

This in principles in experiment we can hope to

do to learn about the curvature of our universe.

The analogy in two-dimensions is limited,

remember we exist in

three-dimensional space and that space

can be positively or negatively curved too,

and we can do experiments while trapped in

that three-dimensional space to

tell us what kind of universe we live in.

Going back to the positively

curved analogy in two-dimensions,

we can see another feature of general relativity.

The surface of a sphere is

a bounded surface but it has no edge.

If we believe this operates in three-dimensions too,

we could have a positively curved universe

where light could be

infinitely trapped and travel around and

around in that universe and never encounter an edge.

Yet where the universe would have a finite volume just as

the surface of this sphere has a volume or

a surface area that you can calculate.

In general relativity, our best theory of gravity,

space and time are related and they

occur by the existence of mass and energy.

This is a quite different concept

from Newton's theory of Gravity,

where space and time are distinct

and mass and energy are distinct.

In Newtonian Gravity, space

is infinite and linear and time also.

In Einstein's theory they are coupled and they can be

distorted by the presence of matter or objects.

The predictions of general relativity started with

a slight deflection of starlight

caused by the curvature of space time near the Sun.

That was confirming his theory

within a year of it being published.

Since then, this phenomenon of

gravitational lensing has been

observed thousands of times.

Another prediction of relativity,

is that time is slowed down by

stronger gravity fields and

this has also been observed many times.

The strongest exposition of

general relativity occurs when gravity is

intense such as around collapsed

objects like neutron stars and black holes.

We'll see later in the course that

these extreme distortions of

space-time are exciting and dramatic.

But even the subtle distortions of space and time can be

observed in the perimeter of

the Earth and in observations,

for example the GPS satellite network incorporates

general relativity to give

accurate distance measurements on the Earth.

General relativity is a profound theory of

gravity based on beautiful and subtle mathematics,

and it's been multiply confirmed by

many types of observation over the last century.