Gravity a Fictious Force

1
Gravity a Fictious Force?
Equivalence Principle The physics of a free
falling frame is the same as an inertial frame.
You can go to a new reference frame (the free
falling one) that does have gravity!
Gravity is a result of a choice of reference
frames
Einstein Relativistic gravity is the result of
a curved space time gravity is geometry!
2
Curved Surfaces
Gausss problem How do you determine if your
space is curved or flat without going outside it?
Answer Measure a triangle and see if it obeys
Pythagorean theorem.
Answer Measure circumference of a circle and
compare it to 2pR.
Curvature definition (2D)
Flat space
Sphere
Curvature definition (N-D)
Different curvatures
Curvature is related to metric (Riemann geometry)
3
Lorentz Transformations
Invariant space interval
Proper time
Moving Lorentz frame
4
The Metric Tensor
Flat Space
Metric Tensor
5
Rotating Coordinates
Rotating coordinate system
Synchronization term
Time dilation
6
Simultaneity Revisited
S
v
S
x
7
Rotating Coordinates (continued)
8
Rotational Metric Revisited
Transverse Doppler Effect
9
Revisit Gravitational Red Shift
Lower to higher gravitational fields
Clocks run slower in lower gravitational
potentials
Metric for position stationary in gravitational
field must link time and position.
10
Schwarzschild MetricGravitational Field of a
Spherically Symmetric Mass
Small deviations
Exact metric