# Lecture Three. Michelson-Morley Experiment Principle of Relativity Laws of mechanics are the same in all inertial frames of reference. namely Laws of.

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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 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. whether Newtonian or Einsteinian

Example 3 Invariance of Momentum Conservation In S: P = m 1 u 1 + m 2 u 2 = m 1 U 1 + m 2 U 2 In S': P ' = m 1 u 1 ' + m 2 u 2 ' = m 1 U 1 ' + m 2 U 2 '

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 c = (  0  0 ) -½ = 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 N M G N M ' G ' N ' M preferred ether frame No other alternatives

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. v/c  10 - 4

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 (v/c) 2  10 -8 Michelson (1881) Nobel Prize in 1907

Michelson-Morley Experiment in apparatus frame

Michelson-Morley Experiment in ether frame

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

Null experiment

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