Transcript natsciGR

Fundamental Principles of General Relativity
general principle: laws of physics must be the same
for all observers (accelerated or not)
general covariance: laws of physics must take the
same form in all coordinate systems
local Lorentz invariance: laws of special relativity
apply locally for all inertial observers
inertial motion is geodesic motion: world lines of
particles unaffected by physical forces are timelike or
null geodesics of spacetime
spacetime is curved:gravitational effects such as
free fall can be described as a form of inertial motion
•The presence of matter changes the geometry of spacetime,
this geometry being interpreted as gravity
2-D visualization of space-time distortion. The white lines do not
represent the curvature of space.
Here, spacetime is treated as a 4-D Lorentzian manifold which is
curved by the presence of mass, energy, and momentum (or stressenergy) within it.
The presence of mass causes a curvature of spacetime in the
vicinity of the mass and this curvature dictates the spacetime
path that all freely moving objects must follow.
Consequence: light ray passing near the Sun should be
deflected by some angle (about 1.75 degrees from
Einstein’s calculations). This was confirmed by Eddington
as bending of starlight during a total solar eclipse in 1919.
Apparent direction to star
) 1.75
Sun
Earth
The Sun acted like a gravitational lens.
Actual direction to star
Defining feature of GR
- gravitational ‘force’ is replaced by geometry. In GR,
phenomena that in classical mechanics are ascribed to the
action of the force of gravity, e.g free fall, orbital motion,
and spacecraft trajectories, are taken to represent inertial
motion in a curved spacetime. People standing on Earth
perceive the ‘force of gravity as a result of their undergoing
a continuous physical acceleration caused by the mechanical
resistance of the surface in which they are standing.
-An object is responsible for the field unlike in Newton’s
field force where gravitational force is an action-at a distance
Justification of GR: the Principle of Equivalence
-freely falling observers are the ones in inertial motion.
Inertial observers can accelerate with respect to each other.
-in the vicinity of any given point, a gravitational field is
equivalent to an accelerated frame of reference in the
absence of gravitational effects.
-gravitational mass and inertial mass are completely identical
and equivalent.
Newton vs. Einstein
-both make essentially identical predictions as long as the
strength of the gravitational field is weak. Some divergence:
1. The orientation of Mercury's orbit is found to precess
in space over time.This is commonly called the
"precession of the perihelion", because it causes the
position of the perihelion to move. Only part of this
can be accounted for by perturbations in Newton's
theory. There is an extra 43 seconds of arc per century
in this precession that is predicted by the Theory of
General Relativity and observed to occur (a second of
arc is 1/3600 of an angular degree). This effect is
extremely small, but the measurements are very
precise and can detect such small effects very well.
2. Einstein's theory predicts that the direction of
light propagation should be changed in a
gravitational field, contrary to the Newtonian
predictions. Precise observations indicate that
Einstein is right, both about the effect and its
magnitude. A striking consequence is
gravitational lensing.
3. The General Theory of Relativity predicts
that light coming from a strong gravitational
field should have its wavelength shifted to
larger values (what astronomers call a "red
shift"), again contrary to Newton's theory.
Once again, detailed observations indicate
such a red shift, and that its magnitude is
correctly given by Einstein's theory.
4. The electromagnetic field can have waves in it
that carry energy and that we call light. Likewise,
the gravitational field can have waves that carry
energy and are called gravitational waves. These
may be thought of as ripples in the curvature of
spacetime that travel at the speed of light.
Just as accelerating charges can emit
electromagnetic waves, accelerating masses can
emit gravitational waves. However gravitational
waves are difficult to detect because they are very
weak and no conclusive evidence has yet been
reported for their direct observation. They have
been observed indirectly in the binary pulsar.
Because the arrival time of pulses from the pulsar
can be measured very precisely, it can be
determined that the period of the binary system is
gradually decreasing. It is found that the rate of
period change (about 75 millionths of a second
each year) is what would be expected for energy
being lost to gravitational radiation, as predicted
by the Theory of General Relativity.
Experimental tests of GR
1. Slight bending of light in the gravitational field of the sun
a) Eddington’s observations
b) work of Irwin Shapiro and collaborators at NIT
c) space probes to Mars
d) discovery of gravitational lens in 1979
2. Advance of the perihelion
3. Clocks running slower in a gravitational field; stronger
the force of gravity, slower the time flows
Other Implications of the Theory of GR
1. Existence of gravity waves
2. Basis of cosmology
3. Changing universe