Chapter 29
Physics of the
Atom
A Brief Overview of Modern
Physics

20th Century revolution
• 1900 Max Planck

Basic ideas leading to Quantum theory
• 1905 Einstein


Special Theory of Relativity
21st Century
• Story is still incomplete
Basic Problems


The speed of every particle in the
universe always remains less than
the speed of light
Newtonian Mechanics is a limited
theory
• It places no upper limit on speed
• It is contrary to modern experimental
results
• Newtonian Mechanics becomes a specialized
case of Einstein’s Theory of Special
Relativity

When speeds are much less than the speed of
light
Galilean Relativity

Choose a frame of reference
• Necessary to describe a physical event

According to Galilean Relativity, the
laws of mechanics are the same in all
inertial frames of reference
• An inertial frame of reference is one in
which Newton’s Laws are valid
• Objects subjected to no forces will move
in straight lines
Galilean Relativity – Example

A passenger in an
airplane throws a
ball straight up
• It appears to move
in a vertical path
• The law of gravity
and equations of
motion under
uniform
acceleration are
obeyed
Galilean Relativity – Example,
cont

There is a
stationary observer
on the ground
• Views the path of
the ball thrown to
be a parabola
• The ball has a
velocity to the right
equal to the
velocity of the
plane
Galilean Relativity – Example,
conclusion




The two observers disagree on the shape
of the ball’s path
Both agree that the motion obeys the law
of gravity and Newton’s laws of motion
Both agree on how long the ball was in the
air
Conclusion: There is no preferred frame of
reference for describing the laws of
mechanics
Galilean Relativity – Limitations


Galilean Relativity does not apply to experiments
in electricity, magnetism, optics, and other areas
Results do not agree with experiments
• The observer should measure the speed of the pulse as
v+c
• Actually measures the speed as c
Newtonian Mechanics
1. In the absence of forces, a body moves with uniform speed
in a straight line.
2. In the presence of force, the body changes its state of motion
in such a way that
 (mv )
F
t


Ft  p
Based on the premise of Absolute Space and Absolute Time.
Newton wrote “Absolute space in its own nature, without relation
to any external, remains always similar and immovable.”
“But because the parts of space cannot be seen, or distinguished
from one another by our senses, therefore in their stead we use
sensible measures of them. For from the positions and distances
of things from any body considered as immovable, we define all
places; and then with respect to such places, we estimate all motions,
considering bodies are transferred from some of those places
into others. And so, instead of absolute places and motions, we use
relative ones; and without any inconvenience in common affairs.
- Isaac Newton -
However, Newton himself recognized that there is an ambiguity
in his argument.
Newton’s law of mechanics holds true in any inertial frames.
platforms moving with a uniform speed
Relative to a platform
z
z’
r = (x,y,z)
x
x’
vt
y
y’
r = (x’,y’,z’)
x’ = x – vt
y’ = y
z’ = z
vx’ = vx – v
vy’ = vy
vz’ = vz
Luminiferous Ether

19th Century physicists compared
electromagnetic waves to mechanical
waves
• Mechanical waves need a medium to support
the disturbance

The luminiferous ether was proposed as
the medium required (and present) for
light waves to propagate
• Present everywhere, even in space
• Massless, but rigid medium
• Could have no effect on the motion of planets
or other objects
Verifying the
Luminiferous Ether



Associated with an ether was
an absolute frame where the
laws of e & m take on their
simplest form
Since the earth moves
through the ether, there
should be an “ether wind”
blowing
If v is the speed of the ether
relative to the earth, the
speed of light should have
minimum or maximum
values depending on its
orientation to the “wind”
Michelson-Morley Experiment



First performed in 1881 by Michelson
Repeated under various conditions
by Michelson and Morley
Designed to detect small changes in
the speed of light
• By determining the velocity of the earth
relative to the ether
Michelson-Morley Equipment




Used the Michelson
Interferometer
Arm 2 is aligned along
the direction of the
earth’s motion through
space
The interference pattern
was observed while the
interferometer was
rotated through 90°
The effect should have
been to show small, but
measurable, shifts in the
fringe pattern
Michelson-Morley Results

Measurements failed to show any change
in the fringe pattern
• No fringe shift of the magnitude required was
ever observed

Light is now understood to be an
electromagnetic wave, which requires no
medium for its propagation
• The idea of an ether was discarded

The laws of electricity and magnetism are
the same in all inertial frames
Einstein’s Principle of Relativity


Resolves the contradiction between
Galilean relativity and the fact that the
speed of light is the same for all observers
Postulates
• The Principle of Relativity: All the laws of
physics are the same in all inertial frames
• The constancy of the speed of light: the speed
of light in a vacuum has the same value in all
inertial reference frames, regardless of the
velocity of the observer or the velocity of the
source emitting the light
The Principle of Relativity




This is a sweeping generalization of the
principle of Galilean relativity, which refers
only to the laws of mechanics
The results of any kind of experiment
performed in a laboratory at rest must be
the same as when performed in a
laboratory moving at a constant speed
past the first one.
No preferred inertial reference frame
exists
It is impossible to detect absolute motion
The Constancy of the Speed of
Light

Been confirmed experimentally in many
ways
• A direct demonstration involves measuring the
speed of photons emitted by particles traveling
near the speed of light
• Confirms the speed of light to five significant
figures


Explains the null result of the MichelsonMorley experiment
Relative motion is unimportant when
measuring the speed of light
• We must alter our common-sense notions of
space and time
Consequences of Special
Relativity


Restricting the discussion to concepts of
length, time, and simultaneity
In relativistic mechanics
• There is no such thing as absolute length
• There is no such thing as absolute time
• Events at different locations that are observed
to occur simultaneously in one frame are not
observed to be simultaneous in another frame
moving uniformly past the first
L
tout  tin  L / c
ttotal  2 L / c
In 19th century, physicists believed in luminiferous ether and that
Light travels with the speed of light,c relative to this light medium.
Now, let’s consider the effect that we are making this measurement
on the surface of earth which is moving through the ether with a speed
v, close to 18 miles/s
Moving with v
L
L
ctout  L  vtout
ctin  L  vtin
tout  L /( c  v)
tin  L /( c  v)
L
L
2L
1
ttotal  tout  tin 


2
2
cv cv
c (1  v / c )
However, Michelson-Morley’s experiment showed with a high precision
ttotal = 2L/c
Accurate measurements of speed of light give the value
c = 2.998 x 108 m/s no matter how the light source or/and
the measurer are moving!!
Serious conflict with then current understanding based on
Newtonian world.
Albert Einstein (1879 – 1955)
In 1905, He provided a new view on
space-time,and proposed a new theory of
mechanics which is consistent with
Newtonian mechanics in the limit of low
speed.
1921 Nobel Prize in Physics
“for his services to Theoretical Physics, and
especially for his discovery of the law of
the photoelectric effect"
In his 1905 paper, Einstein proposes:
… the same law of electrodynamics and optics will be valid for
all frames of reference for which the equation of mechanics hold
good. We will raise this conjecture (the purport of which will
hereafter be called the “Principle of Relativity”) to the status of
a postulate….
a fundamental physical constant
+ the experimental observation that the speed of light is c regardless
Of the reference frame where the light source or the observer resides.
1. Neither an object nor any form of energy can be accelerated to a speed
as fast as or faster than c.
2. The mass of an object increases when its speed increases.
3. Mass is a form of energy in the sense that mass and energy can be
interchanged.
4. An observer observes that the clock moving with a speed relative to
the observer is clicking slower than his.
5. When a long object is moving fast in its length direction passing by an
observer, the observer will measure the length of the object is shorter
than that at rest relative to the observer.
Time Dilation
Einstein Clock
L
1 round trip time = 2L/c
is longer than
Time interval from the
point of view of the
stationary observer
=
Time interval from the
point of view of the
observer moving with
The clock
1
1 v2 / c2
Time Dilation, Summary


The time interval Δt between two events
measured by an observer moving with
respect to a clock is longer than the time
interval Δtp between the same two events
measured by an observer at rest with
respect to the clock
A clock moving past an observer at speed
v runs more slowly than an identical clock
at rest with respect to the observer by a
factor of 1  v 2 / c 2