A theory of Gravitation, explaining the gravitational attraction between masses resulting from their warping of space and time

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A theory of Gravitation, explaining the
gravitational attraction between masses resulting
from their warping of space and time
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Consider two rooms (Einsteins closed elevator
thought experiment). The first one is sitting
quietly on the ground (in a uniform gravitational
field). The other is in deep spaceand is being
towed by a starship that is accelerating at 9.8
m/s2.
Lets try some experiments to see if we can
determine which room we are in
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What would be the apparent weight in each room?
Fma mg
A9.8m/s2
SAME!
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What would each observe if the donut is dropped?
(start with scene on right)
A9.8m/s2
SAME!
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What path would a bullet take in each room?
A9.8m/s2
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The Equivalence Principle
No experiment performed in one place can
distinguish a gravitational field from an
accelerated reference frame.
Albert Einstein
Or there is no way in which gravitational
effects can be distinguished from acceleration
(inertial) effects
Albert Einstein
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Thus

• Gravitational mass is unified with inertial mass
• Inertial mass, mSF / a (the measure of the
  sluggishness of an object to acceleration)
• Gravitational mass, m Weight/g (that which
  attracts one object to another)

The same!
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Consequences of General Relativity (write these
down!)

• Gravitational mass and inertial mass are the
  same

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Consequences of General Relativity (write these
down!)

• Gravitational mass and inertial mass are the
  same
• Speed of light in a grav. Field is the same as
  in any accelerating F.O.R.

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• now back to Homer in the elevator

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What path would a bullet take in each room?
A9.8m/s2
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So what about for light?

• Put on your thinking caps!!!

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The Accelerating Room
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For the accelerating FOR, light BENDs!
A9.8m/s2
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The Equivalence Principle
And since Accelerating FORs gravitational
FORs THEN
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Light also BENDS due to gravitational fields!
A9.8m/s2
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This is a strong statement about the nature
of our universe! Light bending in a
gravitational field is a direct consequence.
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Consequences of General Relativity

• Gravitational mass and inertial mass are the same
• Speed of light in a grav. Field is the same as in
  any accelerating F.O.R.
• Near a massive body
• Light bends toward it

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The Room in a Gravitational Field
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How Much Does Light Bend?
Not much (at least in our ordinary experience)!
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How Much Does Light Bend?
Not much (at least in our ordinary
experience)! Consider a distance of 30 meters ---
light takes time t 30m/3x108 m/s 10-7 sec to
cross the room
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How Much Does Light Bend?
Not much (at least in our ordinary
experience)! Consider a distance of 30 meters ---
light takes time t 30m/3x108 m/s 10-7 sec to
cross the room How far does it fall in this
time? -- The same amount anything falls in that
time d ½ gt2 5x10-14m a very
small distance.
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This is such a small distance, how could you ever
measure the bending of light due to gravity?
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How Much Does Light Bend?
How can we make this bigger?
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How Much Does Light Bend?

• How can we make this bigger?
• Increase the flight path length

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How Much Does Light Bend?

• How can we make this bigger?
• Increase the flight path length
• Increase the gravitational field strength.

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Observed position of the star
Cant see the little star from Earth, right?
Unless my graviational field BENDS the light!
Actual position of the star
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First Experimental Test of General
Relativity GRAVITATIONAL LENSING


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Of course this could only be done during a solar
eclipse.
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As luck would have it, an ideal eclipse for this
test was due to occur fairly soon, in 1919.
Expeditions were organized, and went to
Brazil and Africa to make measurements during the
solar eclipse.
There was great fanfare and anticipation.
This was the first joint scientific expedition of
the countries who had just concluded World War I
the year before.
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Results the change of position was 1.74 arc
seconds, in agreement with Einsteins prediction
of 1.74 arc seconds (3600 arc seconds 1
degree). More recently, more precise measurements
have been made, with these being closer to the
predicted amount.
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Eddingtons telegram to Einstein
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Well of course, I would have been surprised if
it had not been true.
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Albert Einstein and Arthur Eddington the father
of relativity and the man who proved him right.
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More Experimental Evidence
Called Gravitational Lensing (bending of light)
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O.K. So how does gravity bend light?
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Easy, mass warps space, and the light appears to
bend as it travels through warped space.
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Normally, away from all masses, space is flat.
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... like a heavy man sitting in the middle of a
bed...
Mass curves space(and time!)
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Can you see This can explain the orbit of
planets around the sun!
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Matter tells space how to curve, Space tells
matter how to move.
Theory of General Relativity gravity bending
of space by mass, light follows curved space
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Other Cool Stuff. BLACK HOLES
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Black Hole forms when a star (large mass)
collapses into a very small space, such that even
its own light cannot escape)
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A Black Hole looks like
Schwarzchild Radius

• RS 2 G M / c2

Any object (including light!) passing closer to
the center of the black hole than Rs will fall
into the hole
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• 2. Time slows down in the presence of gravity
• Clocks near a massive object run slower than ones
  at higher elevation (the general relativity
  analogue of time dilation)
• ( for further details, see reading packet pg 676
  bottom)

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Consequences of General Relativity

• Gravitational mass and inertial mass are the same
• Speed of light in a grav. Field is the same as in
  any inertial F.O.R.
• Near a massive body
• Light bends toward it
• Time slows down

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Consequences of General Relativity

• Gravitational mass and inertial mass are the same
• Speed of light in a grav. Field is the same as in
  any inertial F.O.R.
• Near a massive body
• Light bends toward it
• Time slows down
• Frequency of a moving photon is higher
  (Gravitational Redshift/Blueshift)
• (show Pound Rebka Experiment OH)

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Summary

• General Relativity Replaces Newtons Theory of
  gravitation
• No need for forces Replaced by curved space
  time coupled to matter.
• Newtons laws still work for everyday problems