Everything attracts everything else.

Ouch!

Including you.

Ow!

In this final lesson,

we'll explore what gravity means for space-time,

or rather what space-time means for gravity.

Until now, we've been dealing with things moving at constant speeds,

with straight world lines in space-time.

But once you add gravity,

if you measure a speed at one moment,

then again a bit later,

the speed may have changed.

In other words, as I discovered, gravity causes acceleration,

so we need the world line to look different from one moment to the next.

As we saw in the last lesson,

the correct way to tilt an object's world line is using a Lorentz transformation:

Einstein's stretch and squash trick.

So, to map out what gravity is doing to Tom's motion,

we need to create a whole load of little patches of space-time,

each transformed by different amounts.

So that my world line is at a different angle in each one.

And then, we're ready to stitch everything together.

We assemble a cozy quilt of space-time

where world lines look curved.

Where the world lines join, the objects collide.

By making these connections between the patches,

a curvature gets built into space-time itself.

But Einstein's true genius

was to describe precisely how each patch is stretched and squashed

according to nearby mass and energy.

The mere presence of stuff curves the space-time,

and curving space-time moves the stuff around.

This is gravity, according to Einstein.

Previously, Isaac Newton had explained gravity using the ideas of force and acceleration,

without any wibbly wobbly space-time,

and that did pretty well.

But Einstein's theory does just slightly better at predicting,

for example, the orbit of Mercury around the Sun,

or the way that light rays are deflected by massive objects.

More importantly, Einstein's theory predicts things that simply don't exist in older theories

where space, time and gravity were separate.

The stitching can leave wrinkles in the space-time material.

These are called gravitational waves,

which should be detectable as tiny, repetitive, subtle squashes and stretches in space.

So we're building experiments to check if they are there.

In the meantime, indirect evidence,

most recently in the polarization patterns of light left over from the Big Bang,

strongly suggest that they are.

But despite Einstein's successes,

when too much stuff gets concentrated in too small a space,

like in a black hole,

the curvature of space-time becomes so large,

that his equations collapse.

We need a new picture of space-time that incorporates quantum mechanics

to unlock the secret at the heart of black holes.

Which means there's plenty more to be discovered about space, time, and space-time in the future.