MatterEnergy Interface

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Matter-Energy Interface

• Welcome to Modern Physics

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Readings

• In Search of Schrödinger's Cat
• by John Gibbin

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• Classical Physics
• Newtonian Mechanics, Maxwells Theory
• 1900
• Modern Physics
• Einstein, Relativity, Quantum Physics

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Einsteins Special Relativitypg 562-584

• The speed of light, c Maxwell (4-equations)
• The Ether - Michelson-Morley experiment
• Simultaneity
• Time Dilation
• The Twin Paradox
• Length Contraction
• Relativistic Momentum
• Mass and Energy E mc2

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Maxwell (1900)

• Through his 4 equations he found that the speed
  of light was c 2.9987 x 108 m/s
• Through his 4 equations he also found that for a
  particle traveling gt 0.1c the relativistic
  momentum, p E/c (confirmed by expt.)
• But what was this speed relative to? Like water
  waves have a speed relative to the water.
• Light must be traveling through a substance
  called the ether.

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Michelson-Morley Experiment

• Light must travel faster if shined with the
  ether than if shined against the ether
• Since the earth is also traveling through this
  ether then light should travel faster in one
  direction greater than in another
• They used the interference of light waves to
  detect any change in speed
• NO CHANGE NO ETHER
• (see OH slide 262)

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Einsteins Special Theory of Relativity

• Educational video tour of relativity
• www.onestick.com/relativity

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Simultaneity

• Einstein in1905 (a junior 28 year old patent
  clerk) proposed
• Not only are Newtonian Laws valid in inertial
  reference fames but ALL Laws of Physics hold
  (including electricity, magnetism, optics)
• c is constant relative to any inertial reference
  frame even if they are traveling at different
  speeds.

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According to Newtonian Physics

• The time scale was universal (regardless of where
  or when you were).
• A 2-second event takes 2 seconds whether you are
  moving or not.

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Einstein says No

• Einstein stood on a train platform in Switzerland
  and observed a platform clock and a train.
• An event that occurs over a time ?t1 in one
  inertial reference frame takes ?t2 in anotherie.
  it takes a different amount of time in each
  reference frame

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Stationary Train
Marks train platform
Marks train platform
Om sees both explosions at same time Os sees both
explosions at same time
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Om measures distance on the train and finds equal
distance to both marks Os measures distance on
the platform and finds equal distance to both
marks
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Om assumes c is constant so both explosions
occurred at the same time and so
D
D
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Os assumes c is constant so both explosions
occurred at the same time and so
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Both Om and Os conclude that the two events were
simultaneous.
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Moving Train close to speed of light
Om sees explosion 2 before explosion 1 Os sees
both explosions simultaneously
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Om measures distance on the train and finds equal
distance to both marks. Os measures distance on
the platform and finds equal distance to both
marks.
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Om assumes c is constant and d1 d2 therefore
time of travel ?t1 ?t2 So either both
explosions occurred at different distances and at
the same time (not since d1 d2 ) or actually at
different times! So
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• Two events that are simultaneous in one frame of
  reference are not necessarily simultaneous in
  another frame, if the two frames are moving
  w.r.t. each other. (even acceleration is not
  necessary)
• Simultaneity is not absolute

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Time Dilation
Speed of Al w.r.t. the rope is the same as the
ropes speed w.r.t. Al. So we just use v for the
speed.
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Time Dilation
Distance light travels in Als frame of reference
Distance light travels in Grandmas frame of
reference
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(No Transcript)
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Time Dilation
Rearrange to get
Proper Time (Als time)
Dilated Time (Grandmas time)
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Example

• Al measures his pulse at 72 beats/minute. What
  is his heart rate according to Grandma with her
  fantastic telescope if his speed is 9.95c?
• v 9.95c meters/second
• ?tAl1/72 minutes/beat1.388x10-2 minutes

Als pulse 1/0.13897 7.19 beats/min According
to Grandma
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The Twin Paradox
Read page 573 It omits the details but basically
its like Doppler Effect having a different
formula for the a sound source approaching you as
opposed to you approaching a sound source (see
grade 11 text).
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Length Contraction

• Al travels the length of the blue line, LOfficer
  , at a speed v w.r.t. Al, or the police officer
  (since they approach each other at the same
  speed).

LOfficer is the proper length since it is
stationary w.r.t. the police officer
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• The Proper Time, ?tAl , is measured on Als watch
  just as before since the event of traveling the
  line all happens in one place, his spaceship.

The Proper Length, LOfficer , is the length of an
object stationary in its frame of reference. Not
as measured by Al since the blue rope is moving
w.r.t. Als spaceship. Al can measure his own
arm length as a proper length since it is
stationary in his frame of reference.
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• The speed of traveling along the blue line
  according to either Al or the Police officer is v
  .
• LAl v ?tAl (blue length according to Al)
• and
• LOfficer v ?tOfficer (blue length according to
  Officer)

Starting with the Time Dilation eqn. then
replacing Grandma with the Officer, and
multiplying both sides by v, we get
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Length Contraction

• aka the Lorentz Contraction
• or Lorentz-Einstein Contraction
• becomes

As Al goes faster, v increases and the
denominator approaches Zero! Indicating that the
length of the blue line shortens, LAl lt LOfficer !
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Example

• Al is traveling at v .95c . The Police Officer
  measured the blue line to be 1 light year long so
  Al only measures it to be only

Length contracts in the direction parallel to the
motion. There is no effect along a perpendicular
axis.
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Additional Resources

• http//galileo.phys.virginia.edu/classes/252/home.
  html

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Paradoxes

• Many physicists in the early 1900s tried to
  envisage situations that would result in a
  contradiction arising from relativity! The most
  famous attempt is called the Twin Paradox
• http//galileo.phys.virginia.edu/classes/252/srel_
  twins.html

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Relativistic Momentum

• This is conserved just as we have done previously
  in class.
• The following equation is derived from Maxwells
  4 equations (seen on the right)

(ie. dont ask)
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Mass and Energy E mc2

• http//galileo.phys.virginia.edu/classes/252/mass_
  and_energy.html
• From we get

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Quantum Theory

• Blackbody Radiation
• Plancks Quantum Hypothesis
• Plancks Constant, h
• Einsteins Photoelectric Effect (his Nobel Prize
  work)
• The Compton Effect
• Photons and Matter
• Wave-Particle Duality
• Matter Waves

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Plancks Constant, h(early 1900s)

• Max Planck found that the ratio of a photons
  energy to its frequency (co lour) was a constant
  
• E 6.63 x 10-34 Js h
• f
• or h E/f
• or E hf
• or E 6.63 x 10-34 x Freq

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Models of Matter (Classical Modern)

• Rutherfords Model of the Atom
• Alpha particles (Helium Nucleii)
• (see www.science.nelson.com for software that can
  simulate alpha scattering)
• The size of the nucleus
• Absorption and Emission Spectra
• Ground state and energy levels
• Fluorescence and Phosphorescence (pg 634-635)
• Bohrs Model of the Atom
• Probability vs. Determinism
• Heisenbergs Uncertainty Principle