General Relativity



1905 Einstein works out theory of relativity

Gravity didnít work in well with his theory


1911 the happiest thought in his life

ďIf I jumped of a barn and I was falling, I would cancel gravityĒ


 Theprinciple of equivalence

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



F=ma (principle of inertia)

qE = matherefore 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 canít 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 doesnít know how to use them yet

But they didnít 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


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)