PH604 Special Relativity (8 lectures)

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PH604 Special Relativity (8 lectures)

• Newtonian Mechanics and the Aether
• Einsteins special relativity and Lorentz
  transformation and its consequences
• Causality and the interval
• Relativistic Mechanics
• Optics and apparent effects

Books Special Relativity, a first encounter,
Domenico Giulini, Oxford
Introduction to the Relativity Principle,
G.Barton, Wiley many others in
Section QC.6
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Newtonian Mechanics and the Aether

1. Newtonian Mechanics and Newtons law of Inertia
2. The relativity principle of Galileo and Newtonian
3. Questions with regard to Newtonian Mechanics
4. The Aether does it exist?
5. Michelson Morley Experiment

Books Special Relativity, a first encounter,
Domenico Giulini, Oxford
Introduction to the Relativity Principle,
G.Barton, Wiley many others in
Section QC.6
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1.Newtonian Mechanics and Newtons law of Inertia
--Newtons Law m a F Predict the motions
of the planets, moons, comets, cannon balls, etc
--This law is actually not always correct!
(surprised?)
http//www.phys.vt.edu/takeuchi/relativity/notes/
section02.html
--Inertial Frame A frame in which the Newtons
law is correct.
--Any frame that is moving at a constant relative
velocity to the first inertial frame is also an
inertial frame.
--The frames in which Newtons law does NOT hold
that are accelerating with respect to inertial
frames and are called non-inertial frames.
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2. The relativity principle of Galileo and
Newtonian
S
Two inertial reference frames S and S moving
with a constant velocity u relative to each other
S
u
( u is // to x and x)
A moving object is described in
S as (x,y,z,t) and in
S as (x, y, z, t)
Common sense shows the two measurements are
related by
Or in vector form v v - u a a
--This is the Galilean transformation. Note the
universal time, tt
--They would assert that Mechanics only deals
with relative motion and that absolute motion
can never be measured.
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2a. Universal Time
The difference between the -coordinate in the
moving frame and the x -coordinate in the
stationary frame is exactly the distance
travelled by the frame in time t .
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2b. Invariance Simultaneity
A fundamental example of an invariant quantity,
in all forms of relativity, is an event in
space-time. Suppose two events, E1,E2, have the
same space-time coordinates in a particular
inertial frame of reference,. then they will have
the same space-time coordinates in every inertial
frame of reference.
In Galilean relativity, spatial separation
(length) is invariant. In Galilean relativity,
time intervals are invariant.
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2b. Invariance Simultaneity
. and so we can consider simultaneous events,
which are events that occur at the same time, but
not necessarily at the same location. Then, if
two events are simultaneous in one frame, they
will be simultaneous in any other frame. This,
along with time-invariance and spatial separation
itself, gets dropped in special relativity.
Consider a particle trajectory x(t). Neither
position nor velocity are invariant ..but
acceleration is! Why?
Distance ?Force? Mass, all invariants ?
m a F
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3. The finite speed of light
The speed of light was measured from astronomical
phenomena
Io around jupiter, Roemer 1672, Huygens
Stellar aberration
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4. Questions with regard to Newtonian Mechanics
i) phenomena on a very small scale
?we need Quantum Mechanics
ii) Phenomena where the speed of motion is near
the speed of light c
?we need relativity
We shall be concerned with case ii) in this
course.
Modern experiment that shows the limitation of
Newtonian mechanics
T ? Kinetic Energy of electrons (between 0.5-15
MeV)
The V. of electrons can be determined by V D /
time
A relation between V2 vs K.E of the electrons
can be plotted.
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v2
C2
O
K.E.
--N-M prediction is valid at low energy
(velocities).
--Experiment Vmax ? 3?108(ms-1)?C
--The Vmax of the electrons appear to equal the
speed of light in Vacuum.
--Other massless particles such as neutrinos
appear only to move at C as well
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5. Speed of Light existence of Aether ?
Maxwells electromagnetic theory predicted that
light should travel with a constant speed in
vacuum, irrespective of reference frames
How light propagates through a vacuum ?
--All other wave motions known, needed some form
of medium
-- Wave velocity would be relative to the
medium
Suggestion Perharps, even a vacuum contains a
very tenuous medium --- the Aether, then the
constant velocity of light is relative to this
absolute frame, and the speed of light in other
inertial systems would not be C.
if so, can we detect it?
Direct measurement of the relative motion to
aether is difficult, but If it existed in space,
we should be able to measure the motion of the
Earth relative to aether -- Michelson-Morley
(1887).
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Michelson-Morley Experiment Detect the Earth
moving through the Aether??
--In 1887 Michelson and Morley built an
interferometer
To measure the movement of the Earth through the
Aether.
Even though this instrument can be a few meters
in size, it can detect changes in distance of
hundreds of nanometers
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Interferometer Moving Through the Aether
Interferometer, stationary in the Aether
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The time for light to travel along l2 arm (cross
stream)
The time for light to travel along l1 arm and
back (downstream)
travel along l2 arm and back
If the light has frequency of f, the number of
fringes that corresponds with differences, t1-t2
of the light travel in the two arms is
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Since the test was to see if any fringes moved as
the whole apparatus was turned through 90o.Then
the roles of l1 and l2 would be exchanged, and
the new number of fringes would be
So the observed number of fringe shift on
rotation through 90o should be
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Michelson Morley made apparatus long enough to
detect 1/3 of a fringe, with ?500nm, so that l1
l2 17m, ?Nfringe 108v2 /(3c2)
--But they could detect no shift at all (at any
time of year!)
--The only possible conclusion from this series
of very difficult experiments was that the whole
concept of an all-pervading aether was wrong from
the start.