Announcements HW10 – missing some?

Reading: Gregory, Chapter 25, pp. 524-end Also note next week’s 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, 7:30am - 9:30am, In-class NPB 1002

Final exam Monday, April 27, 7:30am - 9:30am, 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

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 =h/p• Schroedinger and Heisenberg (1920s) constructed general framework of

quantum mechanics• Born: wave function has probabilistic interpretation: |(x,t)| is probability of finding particle at x,t• Wave-particle duality and role of observer in measurement

Bohr’s atomic model was criticized by classical physicists, who believed

1. protons and electrons both had positive charge

2. atoms did not exist3. the proton should orbit the electron, not vice

versa4. electrons did not exist5. the atom would collapse because the

accelerating electrons would radiate energy

HW10 comments a)How old is each twin at their reunion? Neglect the Earth’s 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 sister’s clocks running slower by this amount. This means that when she arrives, he says that it has taken longer, i.e. 10 years ⋅ = 26 years. He is 47.

5

13

1321

1

1

v1

12

2

2

c

Twin paradox problem

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 astronaut’s watch times her speed, or

5 years (12/13)c = 60/13=4.61 light years.

As seen from Earth, the distance is contracted by a factor , so it is only 4.61 / (13/5) =1.77 light years.

We won’t count this problem because of the ambiguity in “or”

HW10 comments

c) You might worry that from the frame of the astronaut, the homebound twin’s 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 twin’s statement that other twin’s moving clock runs slower is reliable.

HW10 comments a)How old is each twin at their reunion? Neglect the Earth’s 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 sister’s clocks running slower by this amount. This means that when she arrives, he says that it has taken longer, i.e. 10 years ⋅ = 26 years. He is 47.

5

13

1321

1

1

v1

12

2

2

c

Twin paradox problem

Cosmology in 20th century

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

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

E=mc2Mass of fusionproducts lessthan inputs

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?v=h4OnBYrbCjY• Redshift is Doppler shift for light

Hubble’s Discovery• Edwin Hubble’s 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 Hubble’s Law.

http://rst.gsfc.nasa.gov/Sect20/A9.html

Hubble’s 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?

Hubble’s law: data

Hubble’s Constant

• Expansion rate measured using Type 1A Supernovae.

• The age of the universe can be derived from Hubble’s constant by working backwards d0

• T0 = 1 /H0

– Current measurements H0 = 73 km/s*Mpc, then

T0 = 13.4 billion years old (age of universe)

Einstein doesn’t like it.

• All the solutions to E’s equations which give Hubbard’s 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.

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 Einstein’s

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 wouldn’t be realized. His effort resulted in the steady-state model of the Universe, which we’ll describe later.

• Cosmological constant, will come back, though.

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.

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.

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).

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