Transcript Relativity - University of Dayton

Relativity
Twinkle, twinkle little star
How I wonder where you are
“1.75 seconds of arc from where I seem to be
For
ds2
“
=(1-
2GM
R
)
dt2
– (1 +
2GM
) dr2 – r2 d2 – r2 sin2 d2
R
Source Unknown
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.
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.
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.
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.
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
!!
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.
General Relativity
Thought experiment
a = 9.8 m/sec2
g = 9.8 m/sec2
Scale reads 170 lb
Scale reads 170 lb
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.
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
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
Einstein
wrong
Apparent
Position
Einstein
right
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
Relativity
Twinkle, twinkle little star
How I wonder where you are
“1.75 seconds of arc from where I seem to be
For
ds2
“
=(1-
2GM
R
)
dt2
– (1 +
2GM
) dr2 – r2 d2 – r2 sin2 d2
R
Source Unknown