Lecture Two. Historical Background of Special Relativity.
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Transcript of Lecture Two. Historical Background of Special Relativity.
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Lecture Two
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Historical Background
ofSpecial Relativity
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Principle of Relativity in Classical Mechanics
•Galilean transformation
•Newtonian Relativity
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Galilean transformation
x' = x – v ty' = yz' = zt' = t
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Measurement of length
EA = (tA, xA, yA, zA) marking of the left end A
EB = (tB, xB, yB, zB) marking of the right end B
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Measurement of length
simultaneous measurement
tA = tB
length = xB - xA
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tA = tB
Simultaneity is crucial in length measurement of
a moving rod.
Otherwise …
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Under Galilean transformation
t'A = tA
t'B = tB
x'A = xA – v tA
x'B = xB – v tB
time is absolute
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x'B - x'A= (xB – v tB) – (xA – v tA)
= xB - xA - v (tB – tA)
= 0
= xB - xA
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Measurement of length
length = xB - xA
= x'B - x'ALength is invariant.
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So much about measurement process
Now physics:
• kinematics
• dynamics
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Notationv : relative velocity between inertial frames of reference
u : velocity of object
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kinematics
u' = u - v(classical velocity addition theorem)
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kinematics
a' = a
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dynamics•mass is unaffected by the motion of the reference frame
F = m a = m a ' = F '
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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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samemeans:
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
• 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
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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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Electromagnetismand
Newtonian Relativity
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Maxwell’s Equationsare not invariant
underGalilean transformation.
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Maxwell’s 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 = (00)-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 c+ v.
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Newtonian relativity holds for Newtonian mechanics but not for Maxwell’s 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 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 1Both Newtonian mechanics and Maxwell’s electrodynamics are correct.
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Alternative 1
Then since Newtonian relativity holds for
Newtonian mechanics but not for Maxwell’s 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 Maxwell’s 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. (Next lecture)
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Alternative 3 was realized by Einstein’s Special Relativity. (Fourth lecture)
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The End
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http://www.scu.edu.tw/physics/teacher/rency/