The Principle
of Equivalence
|
FIRST: Whereas
Einstein's Special Theory describes motion in an inertial
(non-accelerating frame), his General Theory references a non-inertial
(accelerating) frame.
|
SECOND:
Any and all physics experiments conducted in
a uniform gravitational field yield exactly the same results
as the same experiments conducted in a uniformly accelerated reference
frame. There is no physical way to distinguish between the results
in the two situations. This is the Principle
of Equivalence!
|
THIRD: In
a non-accelerating elevator, a physics student shines a beam of light
toward the opposite wall. The student observes that the
light travels in a straight line to the opposite wall. Note: The elevator
may be moving as long as the speed and direction of the elevator remain
unchanged or the elevator may be at "rest". See below!
|
FOURTH: The
same student shines the beam as the elevator accelerates upward. The
wall accelerates at a non-zero pace whereas the light beam is in the
space in the elevator with no force creating an upward acceleration
on it. In this case the light beam bends downward in the frame of the
elevator. See below!
|
|
|
|
5. Einstein reasoned that
a beam of light must bend downward in the accelerating elevator just
as it should bend in a uniform gravitation field. In both cases, the
path should be parabolic. He reasoned that according to the Principle
of Equivalence, gravity must bend light! In 1919, Sir
Arthur Eddington conducted experiments on an expedition to Africa
which proved that our sun did indeed bend light.
|
Gravitational
Lensing
According to
the Special Theory of Relativity, gravity bends light and the more powerful
the gravitational force, the greater the bending of light. When a large
galaxy lies between us and more distant objects, the intermediate galaxy
produces much bending of light. This creates multiple images of the
distant object. Such images may form arcs of multiple images around
the center of the nearer galaxy. This is referred to as a cross. See
the picture above.
Massive objects
bend or bend the space around them as shown above. Einstein envisioned
a universe where space curved as gravity distorted it. Regions far from
a massive object would appear flat. In such regions, light travels in
a straight line. In areas where space is "dented" by gravity,
light travels in a curved path. All of this is a result of the General
Theory of Relativity.
The next phase
of this view of gravity is to attempt to detect "gravity waves".
The LIGO
( Laser Interferometer Gravitational
Wave Observatory) just started up with a few runs in 2005. It is
designed to detect gravity waves. Doing so will open a new world to
physicists to explore! See
how LIGO works!
|
Black Holes
Black holes
are invisible as they do not allow light to escape due to their immense
gravitational field. The gravitational field is so strong that it traps
light. This occurs when a star collapses to such a small size that it
can bend light back inside the source of light because of such a large
gravitational field. Since Black Holes cannot be observed (no light
is emitted), they are detected by the intense radiation emitted by ionized
matter as it is captured by the Black Hole.
From mechanics
we learned the equation for the velocity an object must obtain to escape
a given mass M. The escape velocity equation is given by
To escape a
Black Hole the escape velocity must equal c.
If we replace
v with c and solve for R in the escape velocity equation above we obtain
what is known as the Schwarzschild Radius. The R below defines the
Event Horizon: that is, any event within a sphere of this radius is
invisible to any observer outside the Black Hole (since light cannot
escape).
|
