By Leiwen Wu. Albert Einstein. The Special and General Theory of Relativity and his Thought Experiments. A Little About Albert Einstein. Born: 14 March 1879 in Ulm, Württemberg, Germany Died: 18 April 1955 in Princeton, New Jersey, USA
its mass, directly proportional to the net force, and in
the same direction as the net force.
F = ma
Newton’s Laws of Motion
I. A body continues at rest or in uniform motion in a
straight line unless acted on by some net force.
III. To every action, there is an equal and opposite reaction.
F = -
Newton’s Law of Gravitation:
where G is the “gravitational constant,”
M is the mass of the larger body,
m is the mass of the smaller body,
r is the separation between them.
The gravitational attraction between the Earth and the Moon causes the Moon to orbit around the Earth rather than moving in a straight line.
Newton's Laws: Gravity and Motion
Cannon ball applet: http://zebu.uoregon.edu/~js/ast122/lectures/lec03.html
Newton showed that objects moving along closed orbits under the influence of gravity follow elliptical paths.
Recall: Kepler’s First Law
Newton also showed that objects in these orbits conserve angular momentum.
Recall: Kepler’s Second Law
An object orbiting in a circle around mass M has speed
The orbital period of this object is the circumference of its orbit divided by its speed :
Recall: Kepler's Third Law
Einstein was 26 when he devised the special theory of relativity
1 year old
Imagine two twin brothers.
One in a space ship and one on the launch pad
Now the spaceship travels at 99.9% of light for 100 years earth time
100 years old
Time to both are very different.
1. Observers cannot detect absolute uniform motion,
only motion relative to other objects
– or –
The laws of physics are the same for all observers.
2. The speed of light is the same for all observers,
independent of their motion relative to the source
of the light.
point before car B! You would see a different event!
absolute speed of light
for all observers:
In his General Theory of Relativity, Einstein explained the force of attraction between massive objects in this way:
“Mass tells space-time how to curve, and the curvature of space-time tells masses how to accelerate.”
Einstein’s general theory of relativity predicted that light paths should be affected by massive objects.
Einstein’s predictions were confirmed when the positions of stars near the sun were observed to be shifted during a 1919 solar eclipse.
Imagine an elevator and a person standing in it.
What would happen to the person if the elevator free-falls?
The person would be floating in the elevator while it is free-falling.
Now Imagine that person in a space ship far away from any gravitational force. He would be floating in the ship.
If the ship the person is in accelerates at the right amount of speed, the person would feel the same as if gravity was pulling on him.
Box stationary in gravity field
in empty space
Box moves through
space at constant velocity
Gravitational field = acceleration
freely falling frames in GR
uniformly moving frames in SR.
Moral: direction of light beam is relative
Now assume boxes are accelerating
Light path is curved
Principle of Equivalence (acceleration = gravity)
Gravity attracts light!
if light has no mass?
Gravity extracts energy from escaping matter
Gravity extracts energy from escaping light
Gravitational redshift, time dilation
Other points of view same result:
BUT: in spacetime, time and space are not separable
=> Both space and time are curved (warped)
This is a bit hard to vizualize (spacetime already 4D…)
not freely falling
not freely falling
=> in freely falling frame, light travels on straight lines
=> Maybe gravity has something to do with…
curvature of space ?
Gravity information propagates at the speed of light
=> gravitational waves
left, right, forward, backward,
but NOT up/down…
=> use ant (let’s call the ant “metric”), count steps it has to take on its way from P1 to P2 (in spacetime, the ant-walk is a bit funny looking, but never mind that)
(the fewest possible ant steps)
i.e., the ant neverhas toturn
move on geodesics in spacetime.
2) Deflection of light
=> Can gravity warp spacetime to the point where even light cannot escape its grip?
That, then, would be a black hole.
space is “stretched” out (circumference < 2R)
If this ratio is small, GR effects are large (i.e., more mass within same region or same mass within smaller region)
space time within and around that mass concentration qualitatively changes. A far away observer would locate this critical surface at a radius
=> Events inside the critical surface can never affect the region outside the critical surface, since no information about them can escape gravity.
=> We call this surface the event horizon
because it shields the outside completely from any events on the inside.
Nothing ever leaves the horizon of a GR black hole.
What happens to matter falling in?
What happens at the center?
Can we observe black holes anyway?
And much, much more…