Modern Physics

1
Modern Physics

• Newtonian Mechanics
• Heat and Thermodynamics
• Electricity and Magnetism
• Waves and Vibrations
• Odds and Ends Remain but all is almost well

2
Modern Physics

• The nagging problems turned out to cause a
  revolution
• All we have studied so far is called classical
  physics
• Now we enter the modern era
• Theory of Relativity
• Quantum Mechanics

3
Relativity in Classical Physics

• Galileo and Newton dealt with the issue of
  relativity
• The issue deals with observing nature in
  different reference frames, that is, with
  different coordinate systems
• We have always tried to pick a coordinate system
  to ease calculations

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Relativity and Classical Physics

• We defined something called an inertial reference
  frame
• This was a coordinate system in which Newtons
  First Law was valid
• An object, not subjected to forces, moves at
  constant velocity (constant speed in a straight
  line) or sits still

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Relativity and Classical Physics

• Coordinate systems that rotate or accelerate are
  NOT inertial reference frames
• A coordinate system that moves at constant
  velocity with respect to an inertial reference
  frame is also an inertial reference frame

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Moving Reference Frames

• While the motion of a dropped coin looks
  different in the two systems, the laws of physics
  remain the same!

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Classical Relativity

• The relativity principle is that the basic laws
  of physics are the same in all inertial reference
  frames
• Galilean/Newtonian Relativity rests on certain
  unprovable assumptions
• Rather like Euclids Axioms and Postulates

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Classical Assumptions

• The lengths of objects are the same in all
  inertial reference frames
• Time passes at the same rate in all inertial
  reference frames
• Time and space are absolute and unchanging in all
  inertial reference frames
• Masses and Forces are the same in all inertial
  reference frames

9
Measurements of Variables

• When we measure positions in different inertial
  reference frames, we get different results
• When we measure velocities in different inertial
  reference frames, we get different results
• When we measure accelerations in different
  inertial reference frames, we get the SAME
  results
• The change in velocity and the change in time are
  identical

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Classical Relativity

• Since accelerations and forces and time are the
  same in all inertial reference frames, we say
  that Newtons Second Law, F ma satisfies the
  relativity principle
• All inertial reference frames are equivalent for
  the description of mechanical phenomena

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Classical Relativity

• Think of the constant acceleration situation

Changing to a new moving coordinate system means
we just need to change the initial values. We
make a coordinate transformation.
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The Problem!!!

• Maxwells Equations predict the velocity of light
  to be 3 x 108 m/s
• The question is, In what coordinate system do we
  measure it?
• If you fly in an airplane at 500 mph and have a
  200 mph tailwind in the jet stream, your ground
  speed is 700 mph
• If something emitting light is moving at 1 x 108
  m/s, does this means that that particular light
  moves at 4 x 108 m/s?

13
The Problem!!

• Maxwells Equations have no way to account for a
  relative velocity
• They say that
• Waves in water move through a medium, the water
• Same for waves in air
• What medium do EM waves move in?

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The Ether

• It was presumed that the medium in which light
  moved permeated all space and was called the
  ether
• It was also presumed that the velocity of light
  was measured relative to this ether
• Maxwells Equations then would only be true in
  the reference frame where the ether is at rest
  since Maxwells Equations didnt translate to
  other frames

15
The Ether

• Unlike Newtons Laws of Mechanics, Maxwells
  Equations singled out a unique reference frame
• In this frame the ether is absolutely at rest
• So, try an experiment to determine the speed of
  the earth with respect to the ether
• This was the Michelson-Morley Experiment

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Michelson-Morley

• Use an interferometer to measure the speed of
  light at different times of the year
• Since the earth rotates on its axis and revolves
  around the sun, we have all kinds of chances to
  observe different motions of the earth w.r.t. the
  ether

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Michelson-Morley
We get an interference pattern by adding the
horizontal path light to the vertical path
light. If the apparatus moves w.r.t. the ether,
then assume the speed of light in the horizontal
direction is modified. Then rotate the apparatus
and the fringes will shift.
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Michelson-Morley

• Calculation in the text
• Upshot is that no fringe shift was seen so the
  light had the same speed regardless of presumed
  earth motion w.r.t. the ether
• Independently, Fitzgerald and Lorentz proposed
  length contraction in the direction of motion
  through the ether to account for the null result
  of the M-M experiment
• Found a factor that worked
• Scientists call this a kludge

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Einsteins Special Theory

• In 1905 Einstein proposed the solution we accept
  today
• He may not even have known about the M-M result
• He visualized what it would look like riding an
  EM wave at the speed of light
• Concluded that what he imagined violated
  Maxwells Equations
• Something was seriously wrong

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Special Theory of Relativity

• The laws of physics have the same form in all
  inertial reference frames.
• Light propagates through empty space (no ether)
  with a definite speed c independent of the speed
  of the source or observer.
• These postulates are the basis of Einsteins
  Special Theory of Relativity

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Gedanken Experiments

• Simultaneity
• Time Dilation
• Length Contraction (Fitzgerald Lorentz)

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Simultaneity
23
Simultaneity
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Simultaneity

• Time is NOT absolute!!

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Time Dilation
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Time Dilation
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Time Dilation
Clocks moving relative to an observer are
measured by that observer to run more slowly
compared to clocks at rest by an amount
28
Length Contraction

• A moving objects length is measured to be
  shorter in the direction of motion by an amount