Special Relativity

1
Special Relativity
VCE Physics Unit 3 Topic 3

• The World at the Speed of Light.
• Einsteins Contribution.

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Unit Outline

• To achieve the outcome the student should
  demonstrate the knowledge and skills to
• describe Maxwells prediction that the speed of
  light depends only on the electrical and magnetic
  properties of the medium it is passing through
  and not on the speed of the source or the speed
  of the medium
• contrast Maxwells prediction with the
  principles of Galilean relativity (no absolute
  frame of reference, all velocity measurements are
  relative to the frame of reference)
• interpret the results of the Michelson Morley
  experiment in terms of the postulates of
  Einsteins special theory of relativity
• the laws of physics are the same in all inertial
  frames of reference
• the speed of light has a constant value for all
  observers
• compare Einsteins postulates and the postulates
  of the Newtonian model
• use simple thought experiments to show that
• the elapse of time occurs at different rates
  depending on the motion of the observer relative
  to the event
• spatial measurements are different when measured
  in different frames of reference
• explain the concepts of proper time and proper
  length as quantities that are measured in the
  frame of reference in which the objects are at
  rest
• explain movement at speeds approaching the speed
  of light in terms of the postulates of Einsteins
  special theory of relativity
• model mathematically time dilation, length
  contraction and mass increase with respectively
  the equations t to?, L Lo/?, m mo? where ?
  1/(1-v2/c2)1/2
• explain the relation between the relativistic
  mass of a body and the energy equivalent
  according to Einsteins equation E mc2
• explain the equivalence of work done to increased
  mass energy according to Einsteins equation E
  mc2
• compare special relativistic and non relativistic
  values for time, length and mass for a range of
  situations.

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Galilean Relativity
One of the earliest of the great minds to ponder
motion, both on Earth and in the heavens, was
Galileo Galilei. He developed the principle of
Galilean Relativity. This is best shown with a
simple example
Imagine an observer in a house by the sea shore
and another in the windowless hull of a ship.
Neither will be able to determine that the ship
is moving at constant velocity by comparing the
results of experiments done inside the house or
on the ship. In order to determine motion these
observers must look at each other.

• FRAMES OF REFERENCE
• Frames of reference can be of 2 types
• Inertial Frames. These are systems (or groups of
  objects) which are either at rest or moving with
  constant velocity.
• Non Inertial Frames. These are systems which are
  accelerating.

Generalizing these observations Galileo
postulated his relativity hypothesis any two
observers in inertial frames of reference with
respect to one another will obtain the same
results for all mechanical experiments.
There is no absolute inertial frame of reference
all velocity measurements are relative to the
frame of reference.
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Galilean Motion

• In Galileos world, the idea of relative motion
  is clearly understood.
• This can be shown with a simple example.

A train carriage is travelling to the right at a
constant velocity of 25.0 ms-1.
A boy standing in the carriage throws a ball to
the right at a constant velocity of 5.0 ms-1.
The boy in the carriage sees the ball travel away
from him at 5.0 ms-1
But, an observer standing beside the track, sees
the ball moving to the right at 30.0 ms-1.
So what is the balls correct speed ? 5.0 ms-1
or 30.0 ms-1?
Remember, according to Galileo, there is no
absolute inertial frame of reference all
velocity measurements are relative to the frame
of reference.
BOTH answers are CORRECT. There is no single
correct answer. The speed of an object depends
on where the observer is when the speed was
measured.
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Isaac Newton
The next great mind to influence mankinds
understanding of the operation of the universe
was Isaac Newton (1642 1727), when he developed
his 3 laws, first mentioned in his 1687 book
Philosophiae naturalis principia mathematica (or
just Principia).
Law 1 (The Law of Inertia) A body will remain
at rest, or in a state of uniform motion,
unless acted upon by a net external force.
Law 2 The acceleration of a body is directly
proportional to net force applied and inversely
proportional to its mass. Mathematically, a
F/m more commonly written as F ma
These Laws explained Galilean relativity and
using Newton's laws, physicists in the 18th and
19th century were able to predict the motions of
the planets, moons, comets, cannon balls, etc.
Law 3 (Action Reaction Law) For every action
there is an equal and opposite reaction.
In classical Newtonian mechanics, time was
universal and absolute.
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The Clouds Gather
For more than two centuries after its inception
(in about the 1680s), the Newtonian view of the
world ruled supreme, to the point that scientists
developed an almost blind faith in this theory.
And for good reason there were very few
problems which could not be accounted for using
this approach.
Nonetheless, by the end of the 19th century, new
experimental evidence, difficult to explain using
the Newtonian theory, began to accumulate, and
the novel theories required to explain this data
would soon replace Newtonian physics.
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19th Century Clouds

• In 1884 Lord Kelvin (of temperature scale fame)
  in a lecture delivered in Baltimore, Maryland,
  mentioned the presence of Nineteenth Century
  Clouds'' over the physics of the time, referring
  to certain problems that had resisted explanation
  using the Newtonian approach.
• Among the problems of the time were
• Light had been recognized as a wave, but the
  properties (and the very existence!) of the
  medium that conveys light appeared inconsistent.
• The equations describing electricity and
  magnetism were inconsistent with Newton's
  description of space and time.
• The orbit of Mercury, which could be predicted
  very accurately using Newton's equations,
  presented a small but disturbingly unexplained
  discrepancy between the observations and the
  calculations.
• Materials at very low temperatures do not behave
  according to the predictions of Newtonian
  physics.
• Newtonian physics predicted that an oven at a
  stable constant temperature has infinite energy.

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The Revolution
The first quarter of the 20th century witnessed
the creation of the revolutionary theories which
explained these phenomena. They also completely
changed the way we understand Nature.
The first two problems concerning the nature of
light and electricity and magnetism required the
introduction of the Special Theory of Relativity.
The third item concerning Mercurys orbit
required the introduction of the General Theory
of Relativity. The last two items low
temperature materials and infinite energy ovens
can be understood only through the introduction
of a completely new mechanics quantum mechanics.
The new theories that superseded Newton's had the
virtue of explaining everything Newtonian
mechanics did (with even greater accuracy) while
extending our understanding to an even wider
range of phenomena.
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Maxwells Contribution
One interesting consequence of Maxwells
unification is that you can calculate the
velocity of electromagnetic waves based
on properties of capacitors and inductors.
Throughout 1700s and 1800s, many individual
laws about electricity and magnetism had been
discovered, such as Coulombs law
of electrostatic force.
c Speed of EM Waves µ0 Permeability of free
space e0 Susceptibility of free space
In Maxwells own words This velocity is so
nearly that of light, that it seems we have
strong reasons to conclude that light itself
(including radiant heat, and other radiations if
any) is an electromagnetic disturbance in the
form of waves propagated through the
electromagnetic field according to
electromagnetic laws.
James Clerk Maxwell (1831-1879) had, by 1855,
unified some laws and finally by 1873 had found
that all of these laws could be summarised by
four partial differential equations. A triumph
of unification! (Which of course is the holy
grail of Physics)
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19th Century Physics

• Around this time, Physicists were trying to find
  a way to measure the ABSOLUTE VELOCITY of an
  object relative to some fixed point which was
  COMPLETELY AT REST.
• But what, in our universe, is completely at rest
  ?

Certainly not the Earth, which as well as
spinning on its axis at 500 ms-1 (1800 kmh-1),
travels around the sun at 30 kms-1 (108,000
kmh-1). The sun, of course, is in orbit around
the centre of our galaxy at 250 kms-1 (900,000
kmh-1). And our galaxy is in some kind of orbit
amongst the other galaxies (velocity
unknown). SO MUCH FOR USING THE EARTH AS A
STATIONARY LABORATORY.
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The Ether
By the 1880s scientists knew that waves
transferred energy from one place to another and
their movement depended upon them travelling
through a MEDIUM (water waves in water, sound
waves in air and other materials).
This led them to believe that ALL waves required
a medium for travel, and so to development of the
concept of the luminiferous ether, (or aether)
which was the name given to the medium through
which light supposedly travelled from the sun to
earth.
The ether was a hypothetical medium in which it
was believed that electromagnetic waves (visible
light, infrared radiation, ultraviolet radiation,
radio waves, X-rays), would propagate.
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The Speed of Light

• In 1887, Albert A. Michelson and Edward W.
  Morley working at the Case School in Cleveland,
  Ohio, tried to measure the speed of the ether,
  (or more precisely the speed of the Earth through
  the ether).
• They expected to find the speed of light
  (symbol, c) differed depending on its direction
  with respect to the ether wind. This result
  would accord with Galilean relativity.

Michelson explained his experiment to his
children this way two swimmers race one
struggles upstream and back while the other swims
the same distance across and back. The second
swimmer will always win, if there is any current
in the river.
The result of the Michelson-Morley experiment was
that the speed of the Earth through the ether (or
the speed of the ether wind) was zero.
Therefore, they also showed that there is no need
for any ether at all, and it appeared that the
speed of light (in a vacuum) was independent of
the velocity of the observer!
Expected result
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Michelson Morley in Detail
The experiment was set up using a monochromatic
(single colour) light source split into two beams.
Using an interferometer floating on a pool of
mercury, they tried to determine the existence of
an ether wind by observing interference patterns
between the two light beams. One beam travelling
with the "ether wind" as the earth orbited the
sun, and the other at 90º to the ether wind.
The interference fringes produced by the two
reflected beams were observed in the telescope.
It was found that these fringes did not shift
when the table was rotated. That is, the time
required to travel one leg of the interferometer
never varied with the time required to travel its
normal counterpart. They NEVER got a changing
interference pattern.
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Michelson Morley in Detail 2
The travel times for the two beams were compared
in a very sensitive manner. If the travel times
were different the two beams, when combined,
would have produced an interference pattern.
This is the same as the pattern produced when a
monochromatic beam of light is allowed to pass
through two narrow slits.
NO CHANGE IN THE PATTERN COULD EVER BE DETECTED
WHEN THE EQUIPMENT TURNED THROUGH 900
Michelson and Morley repeated their experiment
many times up until 1929, but always with the
same results and conclusions.
Michelson won the Nobel Prize in Physics in 1907.
Probably the only prize ever awarded for a failed
experiment.
The result proved to be an extremely perplexing
and frustrating to the physicists of the day who
firmly believed in the ether theory. The result
proved, beyond doubt, that the speed of light is
CONSTANT, no matter how fast an observer was
travelling when measuring it. In other words, it
led to the death of the ether concept and, more
importantly, the death of Galilean Relativity
It took nearly 20 years to develop the theory to
match this experimental result.
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Newton versus Maxwell
Under Galileo and Newton, the speed of light
would vary depending the inertial frame of
reference.
No, its c - 1000
The Speed of Light (c) is 3 x 108 ms-1
No, its c - 100
No, its c - 10
Whilst under Maxwell, the speed of light is
constant no matter what the inertial frame of
reference.
I agree its c
100 ms-1
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Einsteins Insight
It was Einstein who finally found an answer to
the seemingly unbelievable result that the
speed of light in inertial frames of reference is
always the same. The answer was to change the
understanding of the term simultaneity.
Two physical events that occur simultaneously in
one inertial frame are only simultaneous in any
other inertial frame if they occur at the same
time and at the same place. This means TIME IS
RELATIVE!
The figures to the left, seen from two different
inertial frames, help clarify the concept of
simultaneity Fig 1In the inertial frame of the
wagon, the lamps are switched on simultaneously
and the two light impulses reach the girl at the
same time.
Fig 2In the inertial frame of the observer
outside the wagon, it seems that the left lamp is
switched on first, although for the girl in the
wagon the lamps are switched on simultaneously.
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Introducing Relativity
Special Relativity deals with large velocity
differences between frames of reference (Inertial
Frames). General Relativity deals with large
acceleration differences between frames of
reference (Non inertial Frames)
Einstein developed the theory of Special
Relativity in 1905 and the more comprehensive and
far more complex theory of General Relativity
about 10 years later.
At low speeds, Newtons laws are adequate to
explain motion. But the relativity theories need
to be applied to objects travelling at or near c,
the speed of light.
Newtons Laws Plus Fake Forces
Very much less than c
Newtons Laws
Close to c
Special Relativity
General Relativity
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Special Relativity

• The theory of Special Relativity was developed by
  Einstein in 1905 when, as a 26 year old, he was
  working as a clerk in the Swiss Government
  Patents Office.
• Basically the theory states
• 1. The laws of physics are identical for all
  observers, provided they are moving at constant
  velocity with respect to one another, i.e., they
  are all in inertial frames of reference.
• 2. The SPEED OF LIGHT is CONSTANT. This is true
  no matter how fast the observer is travelling
  relative to the source of light.
• This theory was completely at odds with the
  classical physics of Aristotle, Galileo and
  Newton.

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Einsteins Early History

• An only child, Albert Einstein was born in Ulm,
  Germany, on the 14th of March 1879.
• His parents - Herman, an electrical engineer,
  and Pauline, were worried their son may be
  retarded, as he did not speak his first words
  until after his 3rd birthday.

In 1894, as a 15 year old, he was expelled from
Catholic College for disruptive behaviour. In
1896, he managed to talk himself into a place at
the Swiss Federal Polytechnic Academy in Zurich,
graduating in 1900 (at age 21), as a secondary
school teacher of Maths and Physics. At age 23
he married his university sweetheart Mileva Maric
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From Student to Professor
Einstein did not take up a teaching position
immediately, but in 1902 obtained a position as a
Patents Clerk at the Swiss Patents Office in
Bern where he worked until 1909. During his time
there he completed an astonishing number of
papers on theoretical physics, mostly completed
in his spare time. He submitted one of his papers
to the University of Zurich for which he obtained
his PhD degree in 1905.
In 1908, he submitted a further paper to the
University of Bern leading to an offer of
employment as a lecturer. In 1909 he received an
offer of an associate professorship in physics at
the University of Zurich. He jumped into various
university professorships throughout German
speaking Europe, finally landing Europes most
prestigious post as physics professor at
Kaiser-Wilhelm Gesellschaft in Berlin.
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Special Relativity

• After studying the results of the Michelson -
  Morley experiments, Einstein proposed the
  following
• THE SPEED OF LIGHT IS ALWAYS THE SAME, REGARDLESS
  OF WHO MEASURES IT AND HOW FAST THEY ARE GOING
  RELATIVE TO THE LIGHT SOURCE.
• From this simple statement a number of startling
  consequences arise

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Time Dilation
The first of these consequences is known as Time
Dilation

• It requires that, depending on the motion of an
  observer, time must pass at different rates.
• Two observers, one stationary, the other moving
  near the speed of light, observe the same event.
• In order for each to get the same speed for the
  event, each must see it occur during different
  time intervals.
• The faster the observer travels the slower the
  rate at which his time appears to pass to
  stationary observer.

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Time Dilation
Mirror
In order to demonstrate this change in the rate
at which time passes, let us produce a simple
clock.
A photon of light (travelling at c) is bouncing
backwards and forwards between two parallel
mirrors. One back and forth motion of the photon
represents one tick of the clock.
Mirror
An observer, stationary in space with respect to
the Sun, sees the Earth (with its attached
clock), go zooming past on its orbit around the
sun.
1 Tick
In the time, we (standing on Earth), see the
photon bounce back and forth once, the space
observer sees the Earth move a little way along
its orbit path.
Hence, if the photon is to strike the mirrors,
the space observer requires it to travel on a
diagonal path, as shown.
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Time Dilation
Clock as seen by Earth bound observer
Clock as seen by Space observer
Since the photon MUST travel at the Speed of
Light, c, the only logical outcome for the space
observer is to conclude that the photon on Earth
takes a LONGER TIME to cover the APPARENTLY
LONGER DISTANCE it needs to travel.
The space observer thus concludes the Earth clock
runs slow compared to his clock.
This same argument holds true for the earth bound
observer, who would see the space observers
clock running slow.
Remember, Speed distance time
Thus, MOVING CLOCKS RUN SLOW.
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Time Dilation
The mathematical representation of Time Dilation
is shown in the formula t ?to
where t moving observers time as
measured by the stationary observer. to
time measured by
stationary observers clock. (proper time)
v speed of moving observer. c
Speed of Light.
? is called the Lorentz Factor

• The formula has a number of consequences
• If v ltlt c, the term v2/c2 approaches zero and the
  square root term approaches 1.
• Thus t to and no change in time (the rate at
  which time passes) is observed.
• As v approaches c (say v 0.9c), the stationary
  observer sees the moving observers clock tick
  over only 0.4 sec for every 1 second on his own
  clock.
• If v c, the term v2/c2 1 and the square root
  term becomes zero. Dividing a number by zero
  equals infinity.
• Thus, when v c the time interval becomes
  infinite. In other words, time stops passing.

My Clock
My observation of the moving clock
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The Twins Paradox
Twins, Adam and Eve, are thinking how they will
age if one of them goes on a space journey,
travelling at say 0.866c. Will Eve be younger,
older, or remain the same age as her brother if
she does a round trip of some years duration
? Assume that Adam and Eves clocks are
synchronized before Eve leaves. At 0.866c, Adam
will see Eves time pass at exactly half the
rate his time passes. So when Eve returns, she
will have aged by 1 year for every 2 years Adam
has aged. Thus, Eve is younger than Adam.
However, can you turn the discussion around and
say that Eve has been at rest in her space-ship
while Adam has been on a "space journey" with
planet Earth? In that case, Adam must be younger
than Eve at the reunion! Adam is at rest all the
time on Earth, i.e., he is in the same inertial
frame all the time, but Eve is not - she will
have felt forces when her space-ship accelerates
and retards, and Adam will not feel such forces.
So the argument is not an interchangeable one.
The travelling twin is the younger upon their
reunion.   P.S. Eve's space-ship has to consume
fuel, which means that it costs to keep yourself
young!
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Length Contraction
The 2nd consequence of light having a constant
speed is Length Contraction.
An observer sees two set squares, one stationary
in his inertial frame,
the other in an inertial
frame moving near the speed of light.
Remember Speed distance time
How does the speed difference affect the apparent
size of the set square ?
Remember the stationary observer sees the moving
frames clock running slow. To get the same
value for c in each frame, he must measure the
length of the set square (in the direction of
travel) to be shorter than his own stationary
ruler.
IMPORTANT NOTE The length contraction only
occurs in the direction of travel (x direction)
and measurements at right angles to that
direction are unaffected ! (no contraction in the
y direction)
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Length Contraction
Land available on Mars and its free !
The Martians send an advertising rocket to fly
past Earth.
What is the best speed for the rocket so
stationary Earthlings can read the sign ?
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Length Contraction
The mathematical representation of Length
Contraction is shown in the formula.
L Lo/?
Where L Length of moving object as
measured by stationary observer. Lo
Length of stationary object measured by
stationary observer.
(Proper Length) v speed of moving
object. c Speed of Light.

• The formula has a number of consequences
• 1. If the v ltlt c, the square root term approaches
  1 and the length is unaffected, ie. L Lo
• 2. As v approaches c, v2/c2 approaches 1 and the
  square root term approaches 0. Thus, the length
  approaches 0 ie. L 0.

So, a photon of light travelling at c from the
Sun to the Earth makes the journey in no time and
travels no distance !!!!!!
The moving observers view of the length
contracted world
The stationary observers view of the length
contracted Superman
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Mass Dilation
The third effect of the invariance of the speed
of light is mass dilation. As the speed of an
object increases so too does its mass !!!!!!
Under Einstein mass is whatever we measure it to
be. We must use an operational definition for
mass. He showed that the mass of an object
depends on how fast the object is moving relative
to a stationary observer.
Under Newton, mass is an absolute quantity for
each object and it is conserved, never changing
for each object. This invariance of mass is the
basis of Newtons 2nd Law (F ma), and our own
every day experience seems to verify that mass is
absolute.
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Mass Newton v Einstein
Einsteins relativity deals with faster speeds.
Newtonian physics gives good results at speeds
less than 10 of the speed of light.
The mass of an object does not change with speed,
it changes only if we cut off or add a piece to
the object .
As an object moves faster its mass increases. (As
measured by a stationary observer).
F ma means that to accelerate a mass requires a
force, by supplying sufficient force you can make
an object go as fast as you like.
Mass approaches infinity as speed approaches c.
To reach c would require infinite force.
Since mass changes with speed, a change in K.E.
must involve both a change in speed and a change
in mass. At speeds close to c most of the change
occurs to the mass.
Kinetic Energy ½mv2, since mass does not change
an increase in KE means an increase in speed.
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Mass - How Fast, How Heavy ?
The mass of an object at rest is called its rest
mass (m0)
At low velocities the increase in mass is small.
An object travelling at 20 of the speed of light
(60,000 kms-1) has an apparent mass only 2
greater than its rest mass (m0).
As speed increases, apparent mass increases
rapidly.
Mathematically m ?mo
where m Apparent Mass of the
object m0 Rest Mass of the object
v speed of object. c
Speed of Light.
1. When v ltlt c, the square root term approaches
1, and m m0 2. As v approaches c, the square
root term approaches 0, and m approaches infinity.
There is insufficient energy in the universe to
accelerate even the smallest particle up to the
speed of light !!!!!!!!!!
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Energy Mass
Increasing the speed of a mass requires energy.
The truth of this is best seen in interactions
between elementary particles. For example, if a
positron and an electron collide at low speed (so
there is very little kinetic energy) they both
disappear in a flash of electromagnetic
radiation.
The fact that feeding energy into a body
increases its mass suggests that the rest mass
m0 of a body, multiplied by c2, can be considered
as a quantity of energy.
Einstein recognised the fundamental importance of
the interchangeability of mass and energy which
is summarised in his famous equation
E mc2
This EM radiation can be detected and its energy
measured. It turns out to be 2m0c2 where m0 is
the mass of the electron (and the positron). So
each particle must have possessed so called rest
energy of m0c2
where m is the Apparent Mass. Remember,
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Rest Energy
If an object is at rest it possesses rest mass
energy or more simply rest energy
A Hiroshima sized atomic bomb releases about 1014
Joules, (100,000 billion joules). How much mass
has been converted ?
Einsteins equation is then written as E m0c2
E m0c2 Thus m0 (1014)/(3 x
108)2 1.1 x 10-3 kg 1.1 g
Where E Energy (joules) m0 Rest
Mass (kg) c 3 x 108 ms-1
As can be seen a tiny mass converts to a huge
amount of energy
How much energy does 1 kg of mass, at rest,
represent ? E m0c2 (1)(3 x 108)2 9 x
1016 Joules This represents the average annual
output of a medium sized Power Station
35
Moving Mass
As a mass begins to move it possesses BOTH rest
mass energy AND energy of motion (Kinetic Energy).
This is essentially defining the kinetic energy
of an object as the excess of the objects energy
over its rest mass energy. For low velocities
this expression approaches the non-relativistic
kinetic energy expression.
Expressing Einsteins equation as E
mc2 Includes both rest mass and kinetic energy
The Kinetic Energy of a fast moving particle can
be calculated from K.E. mc2 m0c2
For v/c ltlt 1, KE mc2 m0c2 ½ m0v2
As an objects speed increases more and more of
the energy goes into increasing mass and less and
less into increasing velocity.
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The Speed of Light. A Limit ?

• These equations together are called The Lorentz
  Transforms.
• Each Lorentz Transform has a limiting factor.
• If v gt c, then
• t becomes negative, and time runs
  backward !!!!!! (the bullet hits you BEFORE it is
  fired from the gun).
• L becomes negative, and an object has a length
  less than zero!!!!!,
• m becomes negative and objects have a mass less
  than zero!!!!!
• Thus, c (the speed of light) is the limiting
  factor.
• Speeds greater than c are not possible.

37
Relativistic Speed Addition
Imagine that you are standing between two
space-ships moving away from you.
One space-ship moves to the left with a speed of
0.75 c (relative to you) and the other one moves
to the right also with a speed of 0.75 c (again
relative to you). At what speed will each
space-ship see the other moving away? 0.75 c
0.75 c 1.5 c? No, their relative speed will be
0.96 c (according to the relativistic addition of
velocities), and it cannot, of course, be faster
than the speed of light c.
However, in special relativity, the velocities
are added together as
In classical Newtonian mechanics, two different
velocities and are added together by the formula
v v v where v is the sum of
the two velocities.
v v v 1 v.v c2
This formula is called the relativistic addition
of velocities. Note that if v c and/or v c,
then v c, and for small velocities v, v ltlt c,
then the classical formula is regained.
38
Special RelativityExperimental Proofs
Experimental proof of the for each of the areas
of Time Dilation, Length Contraction and Mass
Dilation are available on Earth. These are shown
below.
39
Relativistic Doppler Effect
Suppose a source emits light of frequency f (or
wavelength ?, remember that c f?). Then, an
observer moving with a speed v away from the
source, will observe the frequency
The Doppler Effect Motion towards or away from a
source will cause a change in the observed
frequency f (or wavelength ?) as compared to the
emitted frequency. All wave phenomena (e.g.,
water, sound, and light) behave in this way.
This formula is called the relativistic Doppler
formula. Note that f lt f0 for all 0 lt v lt c,
i.e., the frequency which the observer sees, is
smaller than the "original" frequency in the
inertial frame of the source.
If you are driving towards a red traffic light
(?0 650 nm) at a speed of approximately v
0.17 c, the traffic light will actually appear to
be green (? 550 nm)! (0.17 c is approximately
5.0 x107 ms-1.)
Observers moving away from the source will see a
redshift in the frequency of the light, since
light with lower frequencies are "more red" and
light with higher frequencies are "more blue."
While observers moving towards the source will
see a corresponding blueshift.
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Special RelativityConclusion

• I leave the last word to Einstein himself who,
  when asked to describe Special Relativity in
  laymen's terms, said
• Put your hand on a hot stove for a minute, and
  it seems like an hour.
• Sit with a pretty girl for an hour and it seems
  like a minute.
• Thats relativity

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THE END