Announcements

1
Announcements
HW10 missing some? Reading Gregory, Chapter
25, pp. 524-end Also note next weeks
reading! - Gregory, Chapter 27, to p. 576, pp.
581 to end - Erazim Kohak, A Philosophy of
Personalism (coursepack) - Steven Weinberg,
The more comprehensible the universe is
the more pointless it seems (online) Online
evaluations open Final Exam Monday, April 27,
730am - 930am, In-class NPB 1002
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Final exam

• ? Monday, April 27, 730am - 930am, in class
  NPB 1002, aka here
• Comprehensive covers entire course but with
  emphasis on material
• since midterm
• Bring ID, scratch paper (no calculator
  necessary). One cheat sheet
• with formulas allowed, handwritten front
  and back of 1 page
• ? Format 30 mult. choice 40 short answer 30
  essay (choice of 2)
• Review session 2nd part of class Tues next week,
  
• during reading week TBA

3
Last time

• Photoelectric effect minimum energy required for
  1 photon to remove electron from a metal ?
  minimum frequency for photon (Einstein 1905)
• Bohr atom model (1913) accounted for Balmer
  spectrum (set of discrete frequencies) of
  hydrogen gas
• de Broglie a particle is a wave lh/p
• Schroedinger and Heisenberg (1920s) constructed
  general framework of quantum mechanics
• Born wave function y has probabilistic
  interpretation
• y(x,t) is probability of finding particle
  at x,t
• Wave-particle duality and role of observer in
  measurement

4
Bohrs atomic model was criticized by classical
physicists, who believed

1. protons and electrons both had positive charge
2. atoms did not exist
3. the proton should orbit the electron, not vice
   versa
4. electrons did not exist
5. the atom would collapse because the accelerating
   electrons would radiate energy

5
HW10 comments

• How old is each twin at their reunion? Neglect
  the
• Earths orbital motion, i.e. treat it as fixed in
  space.
• The astronaut twin has elapsed 10 years on her
  watch, so
• is 31. To calculate how old her brother is, we
  need to
• calculate the dilation factor
• This means that the brother sees his sisters
  clocks running
• slower by this amount. This means that when she
  arrives,
• he says that it has taken longer, i.e. 10 years
  g 26 years.
• He is 47.

Twin paradox problem
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HW10 comments
b) How far away is the turnaround point, as seen
from Earth or from the traveling spaceship?
Give the distance in light years, the distance
that light travels in a year.   The distance as
seen from the spaceship is just the time on the
astronauts watch times her speed, or 5 years
? (12/13)c 60/134.61 light years. As seen
from Earth, the distance is contracted by a
factor g, so it is only 4.61 / (13/5) 1.77
light years.
We wont count this problem because of the
ambiguity in or
7

HW10 comments
c) You might worry that from the frame of the
astronaut, the homebound twins clocks should be
running slower therefore the astronaut would
say that the homebound twin should be younger
rather than the other way around. You do not
have to explain the twin paradox fully here
simply identify the difference between the
motion of the two twins. Remember the rules of
relativity apply to frames of reference in
uniform motion.   The two twins perspectives are
not equivalent. The astronaut accelerates twice
during her journey, whereas the Earthbound twin
is always in uniform motion. Only the earthbound
twins statement that other twins moving clock
runs slower is reliable.
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HW10 comments

• How old is each twin at their reunion? Neglect
  the
• Earths orbital motion, i.e. treat it as fixed in
  space.
• The astronaut twin has elapsed 10 years on her
  watch, so
• is 31. To calculate how old her brother is, we
  need to
• calculate the dilation factor
• This means that the brother sees his sisters
  clocks running
• slower by this amount. This means that when she
  arrives,
• he says that it has taken longer, i.e. 10 years
  g 26 years.
• He is 47.

Twin paradox problem
9
Cosmology in 20th century
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Measuring large distances

• Henrietta Leavitt In 1908 studied Cepheid
  variables stars that oscillate in brightness.
  She found intrinsic relation between brightness
  and period? compare stars with same period. If
  they are dimmer, then further away because
  brightness ? 1/r2

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Composition of Stars

• Cecelia Payne-Gaposchkin Ph.D thesis (1925)
  showed that spectral lines observed in stars
  showed overwhelmingly evidence for hydrogen and
  helium, unlike Earth
• Hans Bethe 1939 shows energy of sun comes from
  nuclear fusion of hydrogen

Mass of fusion products less than inputs
Emc2
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Doppler shift/ Redshift

• Doppler shift (usually for sound) occurs when
  emmitter is moving with respect to the observer
  change in apparent frequency
• https//www.youtube.com/watch?vh4OnBYrbCjY
• Redshift is Doppler shift for light

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Hubbles Discovery

• Edwin Hubbles observations of remote galaxies,
  and the redshift of their spectral lines (1924).
• Hubble noticed that the further away the galaxy,
  the greater the redshift of its spectral lines.
• This linear relationship is called Hubbles Law.

http//rst.gsfc.nasa.gov/Sect20/A9.html
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Hubbles Law

• v H0d
• v recessional velocity of the galaxy
• H0 Hubble constant
• d distance of galaxy to earth
• Galaxies are getting farther apart as time
  progresses, therefore the universe is expanding.

Note 1/H0 is a time meaning?
15
Hubbles law data
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Hubbles Constant

• Expansion rate measured using Type 1A Supernovae.
• The age of the universe can be derived from
  Hubbles constant by working backwards d?0
• T0 1 /H0
• Current measurements H0 73 km/sMpc, then
• T0 13.4 billion years old (age of universe)

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Einstein doesnt like it.

• All the solutions to Es equations which give
  Hubbards law have singularities
• Einstein thought that singularities such as these
  indicated that there were important physical
  effects not accounted for in his equations. He
  also thought that the right answer would involve
  static behavior large-scale structure should not
  change with time.
• He also saw how he could fix the field equation
  to eliminate singular and dynamic solutions
  introduce an additional constant term, which
  became known as the cosmological constant, to
  represent the missing, unknown, physical effects.

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Einstein gives up.

• The Universe is observed to be expanding it is
  not static.
• Thus the real Universe may be described by one of
  the dynamic solutions to the original Einstein
  field equation.
• Thus there appeared to be no point in Einsteins
  cosmological constant, so he let it drop, calling
  it my greatest blunder.
• Thereafter he began trying to show that the
  singularities in the dynamic solutions simply
  wouldnt be realized. His effort resulted in the
  steady-state model of the Universe, which well
  describe later.
• Cosmological constant, will come back, though.

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How the Universe Expands

• The space between galaxies expands, not the
  galaxies themselves
• Example raisins in a loaf of bread.
• As the dough rises, the overall loaf of bread
  expands the space between raisins increases but
  the raisins themselves do not expand.

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Center of Universe?

• There is NO CENTER to the universe
• Expansion looks the same regardless of where you
  are in the universe.
• Every point appears to be the center of the
  expansion, therefore no point is the center.
• The universe is infinite.

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Evidence for Expansion

• The light from remote galaxies and other objects
  is redshifted.
• This redshift is called cosmological redshift
  because it is caused by the expansion of the
  universe, not by the actual movement of the
  object (Doppler redshift).

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Questions unanswered or unasked

• What was there before the big bang?
• What caused the big bang?
• Is the universe open or closed or marginal?
• What is the meaning of life?
• What is the airspeed of an unladen swallow?

One of these questions will be answed on Tuesday