USC2001 Energy Lecture 4 Special Relativity

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USC2001 Energy Lecture 4 Special Relativity

• Wayne M. Lawton
• Department of Mathematics
• National University of Singapore
• 2 Science Drive 2
• Singapore 117543

Email matwml_at_nus.edu.sg Tel [phone]
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VELOCITY OF LIGHT
Wave velocity velocity of the wave relative to
the medium velocity of observer relative to
medium.
1887 experiment by Albert Michelson and Edward
Morley, using the Michelson Interferometer,
showed that the velocity of light is independent
of the velocity of the observer (there is no
ether medium for light)
Bullet velocity velocity of the source relative
to the observer velocity of the bullet relative
to the source.
1964 experiment at CERN (European
particle-physics laboratory) showed that
velocity of light emitted from neutral pions
travelling at 0.99975c was the same as the
velocity of light emitted by stationary neutral
pions
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ALBERT EINSTEINS POSTULATES
1905 Albert Einstein, an employee at the patent
office in Bern, Switzerland, published his
Special Theory of Relativity. His theory asserted
The Relativity Postulate The laws of physics
are the same for observers in all inertial
frames.
The Speed of Light Postulate The speed of light
in vacum has the same value c in all directions
and in all inertial frames (c 299792458 m/s).
He courageously worked out the mind boggling
logical consequences of these simple assumptions.
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MEASURING EVENTS
An event is something that happens to which an
observer can assign three space coordinates and
one time. Examples include turning on a small
lightbulb, collision of two particles, passage
of a pulse of light through a specified point in
space, an explosion, the coincidence of the hand
of a clock with a marker on the rim of a clock.
In any inertial frame space coordinates can be
measured by setting up a three dimensional grid
of rulers and time coordinates can be measured
by a grid of clocks synchronized by transmitting
a single light pulse from one clock to all the
other clocks using the Speed of Light Postulate.
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TIME SIMULTANEITY
Speeding Sally
Stationary Sam
Speeding Sally
Stationary Sam
In Sams frame light emitted simultaneously from
A and B will meet at his middle C, but to the
left of the Sallys middle C so she measures
that the light left A after it left B so
simultaneity depends on the frame
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RELATIVITY OF TIME
mirror
mirror
Stationary Sam
Speeding Sally
Sally sends a light pulse to a mirror located
distance D above her train and measures time
Sam measured time must satisfy the
equations
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RELATIVISTIC MANNERS
mirror
mirror
Stationary Sam
Speeding Sally
When two events occur at the same location in an
inertial frame, the time interval between them,
measured in that frame, is called the proper
time
Sams improper time
Lorentz factor
Sallys proper time
Speed parameter
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RELATIVITY OF LENGTH
The length of an object measured in the rest
frame of the object is called its proper length.
The length measured in any frame that is in
relative motion parallel to the length is always
less than the proper length.
Sally measures proper time for platform to
traverse the front end of her train
Stationary Sam measures
Speeding Sally
Stationary Platform
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DERIVATION OF THE LORENTZ TRANSFORMATION
We need 4 equations to compute the 4 matrix
entries
Since light moving right, left has velocity c, -c
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DERIVATION OF THE LORENTZ TRANSFORMATION
We need 2 additional equations to compute
Since the primed frame is moving with velocity v
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DERIVATION OF THE LORENTZ TRANSFORMATION
The Relativity Postulate implies that
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DERIVATION OF THE LORENTZ TRANSFORMATION
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CONSERVATION OF MOMENTUM
The law of conservation of classical momentum
does not hold in moving frames, but it does hold
for the modified momentum
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EQUIVALENCE OF MASS AND ENERGY
The mass and energy added to an object of rest
mass
accelerated to velocity
is
and this led Einsteins to his famous formula
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TUTORIAL 4
1. What time elapses on Stationary Sams watch
when he observes Speeding Sallys watch advance
by one Minute? Does he think that her watch runs
too fast or too slow. What does she think about
his measurements does she feel inclined to buy
a new watch ? What does she say about Sams
watch ?
2. An elementary particle known as a positive
kaon has on the average a lifetime of 0.1237
microseconds. Compute the average distance it
moves in a laboratory reference frame if its
speed relative to the laboratory is 0.990c.
Hint the particles internal clock runs at a
different speed than the laboratory clock