Relativity

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Relativity
Twinkle, twinkle little star How I wonder where
you are 1.75 seconds of arc from where I seem to
be For
2GM
2GM
ds2 ( 1 - ) dt2 (1 )
dr2 r2 d?2 r2 sin2? d?2
R
R
Source Unknown
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Relativity
Frame of Reference - A set of coordinate axes in
terms of which position or movement may be
specified or with reference to which physical
laws may be mathematically stated. Also called
reference frame. Relativity the study of the
laws of physics in reference frames which are
moving with respect to one another.
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Relativity
Relativity the study of the laws of physics in
reference frames which are moving with respect to
one another. Two cases Case 1 (special case)
reference frames move at a constant velocity with
respect to each other. Case 2 (general case)
reference frames accelerate with respect to each
other.
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Special Relativity Introduced in 1905 by A.
Einstein
Special Relativity the study of the laws of
physics in the special case of reference frames
moving at a constant velocity with respect to
each other. Inertial Reference Frame a
reference frame that moves at a constant
velocity.
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Special Relativity The Postulates of Special
Relativity
First postulate Observation of physical
phenomena by more than one inertial observer must
result in agreement between the observers as to
the nature of reality. Or, the nature of the
universe must not change for an observer if their
inertial state changes. Every physical theory
should look the same mathematically to every
inertial observer. To state that simply, no
property of the universe will change if the
observer is in motion. The laws of the universe
are the same regardless of inertial frame of
reference. Second postulate (invariance of
c) The speed of light in vacuum, commonly
denoted c, is the same to all inertial observers,
is the same in all directions, and does not
depend on the velocity of the object emitting the
light. When combined with the First Postulate,
this Second Postulate is equivalent to stating
that light does not require any medium (such as
"aether") in which to propagate.
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Special Relativity The Postulates of Special
Relativity
As a result of the second postulate, once the
distance to a celestial object is know, one can
determine how far in the past the event
occurred. Given the speed of light and the
distance to the Large Magellanic Cloud, Supernova
1987a actually occurred 160,000 years before the
observation, in about 158,000 BC !!
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General Relativity Introduced in 1916 by A.
Einstein
General Relativity the study of the laws of
physics in the general case of reference frames
accelerating with respect to each
other. Non-Inertial Reference Frame a
reference frame that accelertes.
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General Relativity
Thought experiment
a 9.8 m/sec2
g 9.8 m/sec2
Scale reads 170 lb
Scale reads 170 lb
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General Relativity
Principle of Equivalency - Experiments performed
in a uniformly accelerating reference frame with
acceleration a are indistinguishable from the
same experiments performed in a non-accelerating
reference frame which is situated in a
gravitational field where the acceleration of
gravity g -a intensity of gravity field.
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General Relativity
Implication of the Principle of Equivalency
photons should experience a gravitational force
just like all other particles. The deflection
is not observed under normal (ie, earth)
gravitational fields because the photons move to
fast. In order to observe the deflection of a
photon, a large gravitational field is
required. Because of the Principle of
Equivalency, General Relativity is often referred
to as the study of gravity
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General Relativity
Experimental test Einstein proposed that the
deflection of light from a star could be measured
during a solar eclipse for a star near the edge
of the sun during an eclipse.
True Position
Apparent Position
Einstein right
Einstein wrong
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General Relativity
It is common wisdom now that the determination of
the defelction of light from a star during the
solar eclipse in 1919 by Arthur Eddington and his
group was the second observational confirmation
of General Relativity and the basis of Einstein's
huge popularity starting in the 1920s. (The first
one had been the explanation of Mercury's
perihelion shift.) Recently, the value predicted
by Einstein was confirmed to an accuracy better
than 0.02 104. The position of the star was
off by 1.75 seconds of arc
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Relativity
Twinkle, twinkle little star How I wonder where
you are 1.75 seconds of arc from where I seem to
be For
2GM
2GM
ds2 ( 1 - ) dt2 (1 )
dr2 r2 d?2 r2 sin2? d?2
R
R
Source Unknown