General
Relativity

1905
Einstein works out theory of relativity

Gravity
didn’t work in well with his theory

1911
the happiest thought in his life

“If I
jumped of a barn and I was falling, I would cancel gravity”

The principle of
equivalence

This
is why there is weightlessness, when only gravity is working on you

F=ma
(principle of inertia)

qE =
ma therefore a = qE/m

F=
GMm/R2

^{ }

Why
every object gets the same acceleration is that gravitation principle of
equivalence

Rocket
ship and things falling, if the floor rises to meet the falling objects

Both
gravity and centrifugal forces are not real, they are
changes in coordinate systems

The
Principle of equivalence is local

If your
lab is falling toward the earth,

The lab
can’t be too big or falling for too long

As it
falls towards the earth, the distance between them get smaller

The size
depends on the accuracy of the measuring devices

If
they are stacked on each other then they experience tidal acceleration

And they
will pull apart as they fall

Tide:
Closer to moon, stronger gravity pull

1911-1913
Figures out how to patch all of the situations together

Used
Riemannian geometry

Wrote a
paper with Grossmon that has Einstein's equation but
doesn’t know how to use them yet

But they
didn’t figure out coordinate system yet

1915-
Hilbert had a great math tutor but Einstein was working on it too

Both of
them are trying to find the theory as a race

Now
Einstein understood his equations

In solar
system, planet's orbit shifts 1.5 degrees each century

There was
extra around mercury

Hilbert
turned his paper in a day before Einstein

Clock
is in rocket ship that sends a beam of light up to the other clock

Low clock
+ H/C is about = high clock

As the
rocket launches, the light still goes at C, but the relative time is

Low
clock2 + H/C-gt = high clock2

The clock
at the top takes longer to receive than the clock on the bottom sends signal

Simultaneous
is relative, you have to specify your coordinate system

Slope of
light always bisects space and time

Twins
in space

Worked
out special relativity and general relativity

Red shift

Mercury

Bending
of light (light from distant galaxies get bent/gravitation al lensing and it magnifies)

Time
delay

GPS has
to take general relativity into account

In
understanding of the universe

Dark
energy/ Dark Matter

72% Dark
energy

23% Dark
matter

3% other
matter

2%
ordinary matter (earth stuff)