Transcript The Speed of Light - HRSBSTAFF Home Page

MODERN PHYSICS:
AN INTRODUCTION
Physics 12
QUOTE AND CLIP OF THE DAY:
 http://www.youtube.com/watch?v=ajhFNcUTJI0
CLASSICAL PHYSICS
 Bodies and forces, especially
Newton's laws of motion and
the principles of mechanics
based on them
 Physics that does not make
use of quantum mechanics or
the theory of relativity.
 But many theories in classical
physics break down when
applied to extremely small
objects such as atoms or to
objects moving near the speed
of light.
 At the end of the 19th century
it looked as if Physics was
pretty well “wrapped up”!?
MODERN PHYSICS:
Since roughly 1900, new discoveries have
caused significant paradigm shifts
Includes the advent of quantum mechanics
(QM) and of Einsteinian relativity (ER).
Physics that incorporates elements of either
QM or ER (or both) is said to be modern
physics.
MODERN PHYSICS:
Modern physics is often encountered when
dealing with extreme conditions.
 Quantum mechanical effects tend to appear when
dealing with "lows" (low temperatures, small
distances)
 Relativistic effects tend to appear when dealing with
"highs" (high velocities, large distances)
 The "middles" being classical behaviour.
MAJOR MODERN PHYSICS THEORIES
 Special Theory of Relativity
 General Theory of Relativity
 Quantum Theory
EINSTEIN
A PRACTICAL APPLICATION:
 Perimeter Institute
 Everyday Einstein: GPS and Relativity
 Complete WS # 3 and 4
KEY CONCEPT: FRAMES OF REFERENCE
 are just a way of saying that sometimes dif ferent people will
say dif ferent things about the motion of the same object
 http://www.amnh.org/learn/pd/physical_science/week2/fra
me_reference.html
 There are two types of frames of reference often referred to in
physics:
 Inertial and Non Inertial
(Inertia: resistance of an object to change its state of motion)
INERTIAL FRAME OF REFERENCE
 Non accelerating
 Newton’s 1st law and other laws of physics are valid
 For example:
 Inside a bus moving at constant velocity with a ball inside
NON-INERTIAL FRAME OF REFERENCE
 Accelerating
 Newton’s 1st law does not hold
 For example:
 If you are in the bus when it starts to slow down (accelerating
backward) the ball seems to be accelerating forward inside the bus.
No external force has acted on the ball so how can it be accelerating ?
 There appears to be an external force because we see it from an
accelerated frame of reference inside the bus (non inertial frame).
SPECIAL THEORY OF RELATIVIT Y
 Einstein
 Physical theory of space and time developed based on the
postulates that all the laws of physics are equally valid in all
frames of reference moving at a uniform velocity and that
the speed of light from a uniformly moving source is always
the same, regardless of how fast or slow the source or its
observer is moving.
 Introduced a new way to view:
 Space
 Time
 Simultaneity
FIRST A BIT OF BACKGROUND:
 Once upon a time……
MAXWELL’S EQUATIONS:
 Maxwell demonstrated that electric and
magnetic fields travel through space in the
form of waves at the speed of light in 1865
 When scientists (other than Maxwell) were
originally looking at electric and magnetic
fields generated by charges (in a vacuum),
they came up with some equations to
predict the strength and direction of these
fields. It turned out that some constants
were required in the equations to get the
field strengths right.
 Maxwell came along and (in addition to
fixing one equation), he put them together
and realized that combining the equations
resulted in two "wave equation" which
predicted that the electric and magnetic
fields were waves.
Maxwell continued….
 The important idea is that
the speed of light is
independent of the velocity
of the sources of light!
MICHELSON-MORLEY EXPERIMENT
 Prior to experiments by Michelson and Morley, it was
assumed that light needed a medium to propagate through
 This medium was called the “ luminiferous ether” and
Michelson and Morely set out to test for the presence of this
ether
 They used an interferometer, which is a device designed to
measure wavelengths of light
INTERFEROMETER
 Prevailing theories held that ether formed
an absolute reference frame with respect
to which the rest of the universe was
stationar y.
 It would therefore follow that it should
appear to be moving from the per spective
of an obser ver on the sun -orbiting Ear th.
 As a result, light would sometimes travel
in the same direction of the ether, and
others times in the opposite direction.
 The inter ferometer consists of a:
 Light source
 Beam splitter (half silvered mirror)
 Mirrors (one fixed, one adjustable)
 Screen
 The goal was to obser ve inter ference
patterns between light waves
MICHELSON-MORLEY RESULTS
 Michelson and Morley set the apparatus so that one beam was
travelling parallel to the ether and the other was travelling
perpendicular to the ether
 They then rotated the apparatus and attempted to measure
changes in the interference patterns
 Unfortunately, they were unable to observe a change in
interference patterns that they expected due to the motion of
the earth
 Michelson and Morley’s results remained a mystery until
Einstein published his special theory of relativity
ENTER EINSTEIN: 1905
 In 1905 Albert Einstein proposed that we accept the fact that
the speed of light was the same in all reference systems
 Einstein’s theory of special relativity requires giving up some
long held “common sense” ideas about space and time that
we have held over the centuries.
 But it had the advantage that it embodies both theory
(Maxwell) and experimental results (Michelson and Morley) in
rejecting an absolute reference frame.
THE SPECIAL THEORY OF RELATIVIT Y

Based on his consideration of Maxwell’s lack of a frame of
reference, Einstein proposed his special theory of relativity
based on two postulates:
1.
2.
All physical laws must be equally valid in all inertial (non accelerated) frames of reference
The speed of light through a vacuum will be measured to be the
same in all inertial frames of reference
Time Dilation:
 The term time dilation
applies to situations in
which time intervals appear
dif ferent to observers in
dif ferent inertial frames of
reference.
 It is only when an object
approaches speeds on the
order of 30,000 km/s (1/10
the speed of light) that time
dilation becomes important.
TIME DILATION
As a result, we end
up with two times:
t
 Δt – dilated time
0
(seconds)
 Δt 0 – proper time
2
(seconds)
 v – velocity of moving
2
frame of reference
(m/s)
 c – speed of light
(m/s)time could be thought of it as the “rest time,” where the event is at
The proper
t 
v
1
c
rest, although this term is not generally used. Another way to picture it is as the
“one-point” time, the time for an observer who sees the clock as staying at only
one point.
Example 1:
 A rocket speeds past an asteroid at 0.800 c. If an observer in
the rocket sees 10.0 s pass on her watch, how long would that
time interval be as seen by an observer on the asteroid?
Proper time!
Lorentz Factor:
 Is the factor by which time, length,
and "relativistic mass" change for
an object while that object is
moving
 is of ten written as gamma to SAVE
TIME!!!
 This number is determined by the
object's speed in the following way:

1
2
v
1 2
c
Note: that for small speeds, γ
is approximately 1 thus, no
time dilation
So…..
t  t0
TRY IT :
 Page 819
 Questions 1-3
Another Relativistic Effect: Length
Contraction
 In a way that is similar to
time changes depending on
the frame of reference,
length is also af fected
 An observer at rest
(relative to the moving
object) would observe the
moving object to be shorter
in length.
Length Contraction:
 http://www.physicsclassroom.c
om/mmedia/specrel/lc.cfm
Note: only affects
distances parallel to
motion!
Muon
 is an elementary particle similar to the electron
 On Earth, most naturally occurring muons are created by
cosmic rays, which consist mostly of protons, many arriving
from deep space at very high energy
 About 10,000 muons reach every square meter of the earth's
surface a minute; these charged particles form as by -products
of cosmic rays colliding with molecules in the upper
atmosphere.
 These particles are created about 9000m above the surface of
the Earth and travel at about 0.998c
Example: Muon
 The muon is an unstable
subatomic particle with a mean
lifetime of 2.0 µs (measured from
earth). These particles travel at
about 0.998c. What distance
does the muon travel over its
lifetime?
 According to time dilation, the muon’s
half-life should be 30μs in the muon’s
frame
 As a result, the muon can travel a
.998c for 30μs covering a distance of
9000m
t 
t 
t0
v2
1 2
c
2 s
(.998c) 2
1
c2
t  30s
d  vt
d  .998c(30s )
d  9000m
Example: Muon
 According to length
contraction, the distance
that the muon needs to
move through (measured in
the frame of reference of the
Earth) should be 600m in
the muon’s frame.
 Use the info from the
previous slide to prove this!
 Thus, the Earth rushes towards
the muon at .998c for 2μs
covering a distance of 600m
v 22
L  L00 1  2
cc 2
(.
998
cc))
(.
998
L
L
 9000
9000m
m 11 

cc 22
L
L
 600
600m
m
d  vt
d  .998c(2 s )
d  600m
2
2
Try it 
 Page 824
 Questions 4-6
VIDEOS
 http://www.youtube.com/watch?v=30KfPtHec4s
 http://www.youtube.com/watch?v=G -R8LGy-OVs