Lecture Three
Michelson-Morley
Experiment
Principle of Relativity
• Laws of mechanics are the same
in all inertial frames of reference.
namely
• Laws of mechanics are invariant
under a certain transformation.
same
means:
invariant under a certain
transformation
Newtonian Relativity
• Laws of mechanics are the same
in all inertial frames of reference.
namely
• Laws of mechanics are invariant
under the Galilean transformation.
Eisteinian Relativity
• Laws of mechanics are the same
in all inertial frames of reference.
namely
• Laws of mechanics are invariant
under the Lorentz transformation.
Consequences of Relativity
whether Newtonian or Einsteinian
• No mechanical experiments carried out
entirely in one inertial frame can tell the
observer what the motion of that frame is
with respect to any other inertial frame.
• There is no way at all of determining the
absolute velocity of an inertial frame.
• No inertial frame is preferred over any other.
Example 3
Invariance of Momentum Conservation
• In S:
P = m1u1 + m2u2 = m1U1 + m2U2
• In S':
P ' = m1u1 ' + m2u2 ' = m1U1 ' + m2U2 '
Example 4
Invariance of Equation of Motion
Electromagnetism
and
Newtonian Relativity
Maxwell’s Equations
are not invariant
under
Galilean transformation.
Maxwell’s
Electrodynamical
Laws are not the
same in all inertial
frames of reference.
“Ether” frame
the inertial frame of reference in
which the measured speed of
light is exactly
-½
c = (00) = 299792458 m/sec
In a frame of reference
moving at a constant speed
v with respect to the “ether”
frame, the measured speed
of light would range from
c－v to c＋v.
Newtonian relativity
holds for Newtonian
mechanics but not for
Maxwell’s laws of
electromagnetism.
Three possibilities
or alternatives
Arguments following
Panofsky and Phillips
• Insisting the existence of Relativity
Principle
• Fact: Incompatibility of Maxwell
electrodynamics and Newtonian relativity
• Two choices of Relativity: Newtonian or a
new one
• Then there are only three alternatives:
Diagrammatic
N: Newtonian mechanics
N' : new mechanics
M: Maxwell electrodynamics
M' : new electrodynamics
G: relativity under Galilean transformation
G' : new relativity principle
: compatible
: incompatible, preferred frame
G
preferred ether frame
N
M
G
N
M'
G'
N'
No other alternatives
M
• First alternative: without any modification
and sacrifice the relativity of
electrodynamics.
• Second alternative: maintain Newtonian
mechanics and insist Newtonian relativity
of electrodynamics but give up Maxwell
theory.
• Third alternative: maintain Maxwell
electrodynamics and relativity but give up
Newtonian mechanics and relativity.
Alternative 1
Both Newtonian mechanics
and Maxwell’s
electrodynamics are correct.
Alternative 1
Then since Newtonian
relativity holds for
Newtonian mechanics
but not for Maxwell’s
electromagnetism ,
Alternative 1
there must be a preferred
absolute “ether” frame for
electrodynamics.
Alternative 2
Newtonian relativity
holds for both mechanics
and electrodynamics.
Alternative 2
But then electromagnetism
is not correct in the
Maxwell formulation.
Alternative 3
Relativity Principle holds
for both mechanics and
Maxwell’s electrodynamics.
Alternative 3
But then the Relativity
Principle is not Newtonian,
the transformation is not
Galilean,
Alternative 3
and the mechanics in the
Newtonian form needs
modification.
Alternatives 1 and 2
was ruled out by
experiments of
Michelson and Morley.
Alternative 3 was
realized by
Einstein’s Special
Relativity. (Next lecture)
Michelson-Morley
Experiment
Premises
• Both Newtonian mechanics and
Maxwell electrodynamics are
correct.
• Newtonian relativity under
Galilean transformation holds for
Newtonian mechanics but not for
Maxwell electrodynamics.
Implication
•A preferred absolute
inertial “ether” frame
exists in electrodynamics.
The most famous attempt
to locate the ether frame
was the experiment
performed by Michelson in
1881 and by Michelson
and Morley in 1887.
A. A. Michelson
E. W. Morley
Ether
• The medium of propagation of
light was assumed to fill all space.
• An observer moving through the
ether with velocity v would
measure a velocity c' for a light
beam, where
c' = c + v.
Assume ether exists
• Spinning and rotating earth
should be moving through it.
• An observer on earth would sense
an “ether wind” with velocity v.
• Take v to be the earth’s orbital
speed about the sum.
4
v/c  10
First-order Experiments
• accurate to first order in v/c
• unable to detect the absolute
ether frame
• can be interpreted in terms
of an ether theory (Fresnel,
Lorentz)
Second-order Experiments
•accurate to second order
2
-8
(v/c)  10
•Michelson (1881)
•Nobel Prize in 1907
Michelson-Morley Experiment
in apparatus frame
Michelson-Morley Experiment
in ether frame
Michelson-Morley Experiment
Michelson-Morley Experiment
• optical path difference
fringe system
nothing to do with relativity
• rotation
shift in the fringe pattern
test of relativity
Michelson-Morley Experiment
Michelson-Morley Experiment
Michelson-Morley Experiment
Michelson-Morley Experiment
Michelson-Morley Experiment
Michelson-Morley Experiment
Null experiment