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Unformatted text preview: PHYSICS 222
Introduction to Classical Physics II
Prof. Ruslan Prozorov
Iowa State University
Fall 2011 LECTURES 34
Relativity relativity theories
• Special relativity  formulated by Albert Einstein in
1905 based on works of Henri Poincaré and
Hendrik Lorentz
o is the physical theory of measurement in an inertial
frame of reference • General relativity  Einstein's theory of gravitation
o the geometric theory of gravitation published by
Albert Einstein in 1916. PHYS222  Lecture 34  Prof. Ruslan Prozorov  Iowa State University 14 November 2011 2 The Twin Paradox One of the twin sisters travels 3 light years from Earth at a speed of
0.6c and returns back home to see her twin sister.
On Earth, 1o years have passed, whereas the travelling twin calendar
only showed 8 years. How can this be? PHYS222  Lecture 34  Prof. Ruslan Prozorov  Iowa State University 14 November 2011 3 The Ladder Paradox
let a long ladder fly lengthwise at great
velocity past a normal garage. The proper
length of the ladder is more than the length
of the garage. Due to the length contraction
of special relativity, the passing ladder can
for an instant (or two) fit into the garage, as
observed by the garage owner. However, for an observer riding on the
ladder, it is the garage that moves at high
speed and is length contracted. For the
ladder observer there is no way that the
ladder can fit into the garage, even for the
briefest of moments. Hence, the whole
idea seems paradoxical.
http://en.wikipedia.org/wiki/Ladder_paradox
PHYS222  Lecture 34  Prof. Ruslan Prozorov  Iowa State University 14 November 2011 4 Albert Einstein’s solution
• “The insight fundamental for the special
theory of relativity is this: The
assumptions of relativity and light speed
invariance are compatible if relations of a
new type ("Lorentz transformation") are
postulated for the conversion of
coordinates and times of events... “
• “The universal principle of the special
theory of relativity is contained in the
postulate: The laws of physics are
invariant with respect to Lorentz
transformations (for the transition from
one inertial system to any other arbitrarily
chosen inertial system). This is a
restricting principle for natural laws...”
A. Einstein, Autobiographical Notes, 1949.
PHYS222  Lecture 34  Prof. Ruslan Prozorov  Iowa State University 14 November 2011 5 Einstein’s First Postulate o The laws of physics apply in the
same fashion everywhere.
Newton’s Laws work no matter
what your point of view.
o A magnet moving in a coil of wire
will induce a current, but … who’s
to say if the coil is moving over the
magnet or if the magnet is moving
through the coil. PHYS222  Lecture 34  Prof. Ruslan Prozorov  Iowa State University 14 November 2011 6 Einstein’s Second Postulate
The speed of light is always the same. It matters not how
fast you are going or in which direction you travel, the
speed of light is always the same. PHYS222  Lecture 34  Prof. Ruslan Prozorov  Iowa State University 14 November 2011 7 information – causality!
information (signal)
cannot be relayed
between any two
objects in any
reference frame with a
speed greater than the
speed of light, c PHYS222  Lecture 34  Prof. Ruslan Prozorov  Iowa State University 14 November 2011 8 information – causality!
• signal from can reach
• but NO information can
be exchanged between
and (in any direction)
(what about and ?) PHYS222  Lecture 34  Prof. Ruslan Prozorov  Iowa State University 14 November 2011 9 simultaneity—watching lightning
Perception of one reference frame from another makes it hard to
correctly interpret perceptions of physical events. PHYS222  Lecture 34  Prof. Ruslan Prozorov  Iowa State University 14 November 2011 10 Galilean transformation t't
x ' x ut
y' y
z' z PHYS222  Lecture 34  Prof. Ruslan Prozorov  Iowa State University u 14 November 2011 11 The Lorentz transformation ux t ' t 2 c x ' x ut y' y
z' z 1 u u2
1 2
c Lorentz factor PHYS222  Lecture 34  Prof. Ruslan Prozorov  Iowa State University 14 November 2011 12 same point in two reference frames all reference
frames are equal
and
indistinguishable PHYS222  Lecture 34  Prof. Ruslan Prozorov  Iowa State University 14 November 2011 13 The  factor’s exponential impact PHYS222  Lecture 34  Prof. Ruslan Prozorov  Iowa State University 14 November 2011 14 relativity of time intervals
A “light clock” can be used to gain a graphic understanding of
the gamma term that modifies the size of any quantity modified
by relativistic effects. PHYS222  Lecture 34  Prof. Ruslan Prozorov  Iowa State University 14 November 2011 15 Lengths parallel or perpendicular to motion
o Lengths perpendicular to the relativistic velocities
are not affected. o Lengths parallel are directly involved. PHYS222  Lecture 34  Prof. Ruslan Prozorov  Iowa State University 14 November 2011 16 Contraction examples PHYS222  Lecture 34  Prof. Ruslan Prozorov  Iowa State University 14 November 2011 17 transformation of EM fields PHYS222  Lecture 34  Prof. Ruslan Prozorov  Iowa State University 14 November 2011 18 Appearance of objects in relativistic motion PHYS222  Lecture 34  Prof. Ruslan Prozorov  Iowa State University 14 November 2011 19 the Doppler effect PHYS222  Lecture 34  Prof. Ruslan Prozorov  Iowa State University 14 November 2011 20 The Doppler effect applied to EM waves
The Doppler effect can cause enough change in the velocity of
light to change the wavelength perceived by an observer at a
distance. “RED SHIFT” is used to
measure velocities of
distant galaxies
PHYS222  Lecture 34  Prof. Ruslan Prozorov  Iowa State University 14 November 2011 21 Relativistic mechanics
The energy and momentum of
an object with invariant mass m0
(also called rest mass in the
case of a single particle), moving
with velocity v with respect to a
given frame of reference. What if m0=0?
> massless
particles MUST
move with the
speed of light! E m0 c mc
2 p m0 v 2 m is relativistic mass E pc m0 c
2 2 2 2 E pc 0
2 2 E pc m0 c m0vc
2 vc PHYS222  Lecture 34  Prof. Ruslan Prozorov  Iowa State University 14 November 2011 22 relativistic momentum
• As velocities near the speed of light, the gamma factor would cause
momentum/mass/kinetic energy needed to cause the motion to
approach infinity. It’s simply impossible. PHYS222  Lecture 34  Prof. Ruslan Prozorov  Iowa State University 14 November 2011 23 most famous equation EVER: E = mc2
• when a single massive object is at rest (v = 0, p = 0), there is a nonzero
mass remaining: mrest = E/c2.
• The corresponding energy, which is also the total energy when a single
particle is at rest, is referred to as "rest energy".
• In systems of particles which are seen from a moving inertial frame, total
energy increases and so does momentum.
• However, for single particles the rest mass remains constant, and for systems
of particles the invariant mass remain constant, because in both cases, the
energy and momentum increases subtract from each other, and cancel.
• Thus, the invariant mass of systems of particles is a calculated constant for all
observers, as is the rest mass of single particles. PHYS222  Lecture 34  Prof. Ruslan Prozorov  Iowa State University 14 November 2011 24 Relativistic examples PHYS222  Lecture 34  Prof. Ruslan Prozorov  Iowa State University 14 November 2011 25 nuclear fusion
3.3445 x 1027 kg 5.0083 x 1027 kg m = 3.1375×1029 kg
6.6465 x 1027 kg 1.6749×1027 kg 14.1 + 3.5 = 17.6 MeV = 2.8 X 1012 J PHYS222  Lecture 34  Prof. Ruslan Prozorov  Iowa State University 14 November 2011 26 the Sun & other stars PHYS222  Lecture 34  Prof. Ruslan Prozorov  Iowa State University 14 November 2011 27 General Relativity Einstein’s tensor
(spacetime curvature) energy – momentum tensor 1
8 G
R g R 4 T
2
c
PHYS222  Lecture 34  Prof. Ruslan Prozorov  Iowa State University equation of cosmos 14 November 2011 28 gravitation and acceleration
produce the same effect PHYS222  Lecture 34  Prof. Ruslan Prozorov  Iowa State University 14 November 2011 29 Newtonian mechanics and relativity PHYS222  Lecture 34  Prof. Ruslan Prozorov  Iowa State University 14 November 2011 30 collapsing star PHYS222  Lecture 34  Prof. Ruslan Prozorov  Iowa State University 14 November 2011 31 ...
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This note was uploaded on 11/14/2011 for the course PHYS 5863005 taught by Professor Meyer during the Fall '09 term at Iowa State.
 Fall '09
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