Lecture%20Three

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Lecture Three
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Michelson-Morley Experiment
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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.

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same

• means
• invariant under a certain transformation

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Newtonian Relativity

• Laws of mechanics are the same in all inertial
  frames of reference.
• namely
• Laws of mechanics are invariant under the
  Galilean transformation.

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Eisteinian Relativity

• Laws of mechanics are the same in all inertial
  frames of reference.
• namely
• Laws of mechanics are invariant under the Lorentz
  transformation.

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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.

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Example 3 Invariance of Momentum Conservation

• In S
• P m1u1 m2u2 m1U1 m2U2
• In S'
• P ' m1u1 ' m2u2 ' m1U1 ' m2U2 '

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Example 4Invariance of Equation of Motion
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ElectromagnetismandNewtonian Relativity
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Maxwells Equationsare not invariantunderGalile
an transformation.
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Maxwells Electrodynamical Laws are not the same
in all inertial frames of reference.
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Ether frame

• the inertial frame of reference in which the
  measured speed of light is exactly
• c (?0?0)-½ 299792458 m/sec

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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
cv.
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Newtonian relativity holds for Newtonian
mechanics but not for Maxwells laws of
electromagnetism.
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Three possibilities or alternatives
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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

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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

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G N
M G N
M ' G '
N ' M
preferred ether frame
No other alternatives
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• 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.

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Alternative 1

• Both Newtonian mechanics and Maxwells
  electrodynamics are correct.

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Alternative 1

• Then since Newtonian relativity holds for
• Newtonian mechanics but not for Maxwells
  electromagnetism ,

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Alternative 1

• there must be a preferred absolute ether frame
  for electrodynamics.

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Alternative 2

• Newtonian relativity holds for both mechanics and
  electrodynamics.

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Alternative 2

• But then electromagnetism is not correct in the
  Maxwell formulation.

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Alternative 3

• Relativity Principle holds for both mechanics and
  Maxwells electrodynamics.

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Alternative 3

• But then the Relativity Principle is not
  Newtonian, the transformation is not Galilean,

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Alternative 3

• and the mechanics in the Newtonian form needs
  modification.

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Alternatives 1 and 2 was ruled out by experiments
of Michelson and Morley.
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Alternative 3 was realized by Einsteins Special
Relativity. (Next lecture)
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Michelson-MorleyExperiment
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Premises

• Both Newtonian mechanics and Maxwell
  electrodynamics are correct.
• Newtonian relativity under Galilean
  transformation holds for Newtonian mechanics but
  not for Maxwell electrodynamics.

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Implication

• A preferred absolute inertial ether frame
  exists in electrodynamics.

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The most famous attempt to locate the ether frame
was the experiment performed by Michelson in 1881
and by Michelson and Morley in 1887.
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A. A. Michelson
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E. W. Morley
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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.

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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 earths orbital speed about the
  sum.
• v/c ? 10 - 4

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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)

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Second-order Experiments

• accurate to second order
• (v/c) 2 ? 10-8
• Michelson (1881)
• Nobel Prize in 1907

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Michelson-Morley Experiment
in apparatus frame
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Michelson-Morley Experiment
in ether frame
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Michelson-Morley Experiment
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Michelson-Morley Experiment

• optical path difference
• fringe system
• nothing to do with relativity
• rotation
• shift in the fringe pattern
• test of relativity

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Michelson-Morley Experiment
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Michelson-Morley Experiment
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Michelson-Morley Experiment
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Michelson-Morley Experiment
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Michelson-Morley Experiment
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Michelson-Morley Experiment
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Null experiment