Please pick up problem set #3. Median score = 87. Recitation session: Today, 4:30 – 5:30 pm. 4054 McPherson (Prof subbing for
Transcript
Slide 1
Please pick up problem set #3. Median score = 87. Recitation
session: Today, 4:30 5:30 pm. 4054 McPherson (Prof subbing for
TA)
Slide 2
Is the Universe Infinite? Monday, October 27 Next Planetarium
Show: Thurs, Nov 6
Slide 3
Newtons Newtons view of space: rectilinear & rigid (not
expanding or contracting) Think of a bug crawling over stiff graph
paper.
Slide 4
Einsteins Einsteins view of space: curved & wavy (can also
expand or contract) Think of a bug crawling over a rumpled rubber
sheet.
Slide 5
Einsteins view of space is mathematically complicated. However,
it gives better results when gravity is strong (close to massive
objects). Einsteins triumphs: Gravitational lensing by the Sun
Orbit of Mercury (closest planet to Sun)
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massenergy Space is curved by the presence of mass and
energy.
Slide 7
General rule: high density (of either mass or energy) leads to
highly curved space. Black holes Black holes cause extreme
curvature.
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Whats a black hole? escape velocity Newton: a black hole is an
object whose escape velocity is greater than the speed of light.
Earth: escape velocity = 11 kilometers/sec Sun: escape velocity =
600 km/sec black hole: escape velocity > 300,000 km/sec
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Whats a black hole? event horizon Einstein: a black hole is an
object smaller than its event horizon. Whats an event horizon?
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inside outside Event horizon = a mathematically defined surface
around a black hole. Photons (& other particles) inside the
event horizon cant ever move outside. What happens inside the event
horizon stays inside the event horizon.
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Black hole as lobster trap: once an object enters the event
horizon, it cant exit. mass Size of event horizon is proportional
to mass of black hole: for Suns mass, its 3 kilometers (about 2
miles).
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If black holes are compact and (by definition) black, how do we
see them against the blackness of the sky? We can detect their
gravitational influence on glow-in-the-dark matter like stars.
Slide 13
Stars near the Galactic Center (8000 parsecs away) orbit a
massive, compact, dark object. Mass = 2 million times the Suns
mass
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simplest The simplest explanation of the massive object at our
galaxys center is that it is a supermassive black hole (SMBH).
Other galaxies have supermassive black holes, too. quasiar As gas
falls toward the black hole, it heats up & emits light. Quasars
(quasi-stellar objects) are black holes that accrete lots of
gas.
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Locally, dense knots of mass (& energy), such as black
holes, cause strong curvature. average average Globally, the
average density of mass & energy in the universe causes an
average curvature. On large scales, the homogeneous, isotropic
distribution of mass (& energy) causes homogeneous, isotropic
curvature.
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There are 3 possible examples of homogeneous, isotropic
curvature: (Asserted without proof: find a 4 th case, win a Nobel
Prize) (flat)
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Is the universe infinite? positively finite If space is
positively curved, space is finite, but without a boundary.
negatively flat infinite If space is negatively curved or flat,
space is infinite (unless a boundary or edge is imposed).
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Measuring curvature is easy, in principle. Flat: angles of
triangle add to 180 >180 Positive: angles add to >180
Parallax (negative curvature) October April p p p > 1/d As d
infinity, p1/R radius of curvature
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Bright idea: The smallest parallax you measure puts a lower
limit on the radius of curvature of negatively curved space. at
least Hipparcos measured p as small as 0.001 arcsec; radius of
curvature is at least 1000 parsecs.
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Bigger We need Bigger triangles to measure the curvature
accurately! L d =L/d (flat) >L/d (positive)
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Positively magnifying large Positively curved universe: curved
space is a magnifying lens; distant galaxies appear anomalously
large. Negatively demagnifying small Negatively curved universe:
curved space is a demagnifying lens; distant galaxies appear
anomalously small. magnifying demagnifying
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And the answer is Distant galaxies are neither absurdly small
in angle nor absurdly large. If If the universe is curved, radius
of curvature is bigger than the Hubble distance (c/H 0 = 4300
Mpc).
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Horizons horizon The Earth has a horizon: we cant see beyond it
because of the Earths curved surface. event horizon A black hole
has an event horizon: we cant see into it because photons cant
escape.
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The Ultimate Horizon cosmological horizon The universe has a
cosmological horizon: we cant see beyond it because photons from
beyond havent had time to reach us. Distance to cosmological
horizon is approximately equal to the Hubble distance (c/H 0 = 4300
Mpc).
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Suggestion:positively Suggestion: space is positively curved,
but with a radius of curvature much larger than the Hubble distance
(4300 Mpc). finite This gives the universe a huge (but finite)
volume. The part I can see looks flat!
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Wednesdays Lecture: Reading: Chapter 7 Dark Energy Problem Set
#4 due.