Transcript Lesson 18 - Oblers Paradox

THE UNIVERSE ACCORDING TO
ERIC IDLE (Monty Python,
Meaning of Life)
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Galaxy.mp3
Olbers Paradox – Heinrich Olbers
(Germany early 1800’s)
• In most early mythological and religious accounts
the universe was created by a divine being at
some date in the fairly recent past.
• Therefore the church embraced the idea that the
Earth was at the center of the solar system and
hence the entire universe. This view was
embraced by most until the middle of the 17th
century.
• Others such as Plato and Aristotle did not like the
idea that a Devine Being would meddle in the
affairs of the world. Hence the universe always
has been and always will be, FOREVER.
Olbers Paradox – Heinrich Olbers
(Germany early 1800’s)
• In the 1600’s, Copernicus (and followed by support
by Galileo) proposes the Heliocentric Model of the
Universe. This model implies that the stars must
be a very far distance away in order the remain
“stationary” as Earth revolves.
• It can be further postulated that the stars are
evenly distributed throughout the universe.
• PROBLEM – in 1687, Newton published his law on
gravitation. So why don’t all the stars gravitate
towards each other and meet at a single point?
Olbers Paradox – Heinrich Olbers
(Germany early 1800’s)
• Newton suggests the universe is infinite such that
the net force on every star is zero meaning the
stars would therefore be static.
• Newton assumed an infinite, uniform and static
universe.
• However, this assumption leads to a profound
contradiction.
• WHY IS THE SKY DARK AT NIGHT?
Olbers Paradox – Heinrich Olbers
(Germany early 1800’s)
• Imagine looking out into space.
• IF the universe is indeed static, infinite and
uniform.
• Then if you look along any line of sight will
eventually you will see a star.
• The sky should be as bright as an average star,
even at night!
Olbers Paradox – Solutions??
• In 1905, Einstein publishes on Relativity.
– Due to gravitational effects, clocks run
at various rates depending on how
close they are to massive objects (such
as planets or stars)
– So how could the universe be static?
In fact Einstein could not get the math
to predict a static universe, but instead a
universe that is either expanding or
contracting.
• Einstein then made what he called the
“greatest blunder of my life”.
Albert Einstein
Olbers Paradox – Solutions??
• To satisfy the deeply held belief
of most people, Einstein
created a cosmological
constant () that allowed for
the math to work out so that the
universe would be static.
(Hydrostatic equilibrium
between “pressure” out and
gravitational attraction “in”)
• Instead of simply publishing
that the universe is expanding,
Einstein simply sat on the idea
while Edwin Hubble stole the
show 10 years later.
• A bad day for Einstein
Repulsive force
Slice through 2D,
model universe on
surface of sphere.
Gravity
A static universe requires repulsive force
to exactly offset the gravitational attraction
which attempts to contract space.
Olbers Paradox – Hubble Solution
• Edwin Hubble is usually credited with discovering that
we live in a expanding universe.
• There is a cosmic speed-limit, the speed of light.
• So if Earth was inside this balloon, would we see all
the light all at once?
• NO
Consider that the universe is expanding,
but light can only go so fast.
Therefore, we only “see” a portion of the
universe.
Boundary of our visible
universe defined by
age of universe.
The concentration of stars in our
universe is low because most of
them are simply outside our
cosmic particle horizon. It
therefore can be dark at night.
As time goes on, the
cosmic particle horizon
grows
Inverse Square Law of Luminosity
d=1
B=1
d=2
B=1/4
d=3
B=1/9
Olbers Paradox – Inverse Square Law
of Luminosity Solution
d
R
• Consider this shell of thickness d
• To an observer at the origin, the
shell would have star density ()
• The density of a thin shell can be
calculated (not required)
• Therefore the number of stars in
the shell can be determined.
4 R d = 
2
Olbers Paradox – Inverse Square Law
of Luminosity Solution
d
R
• If R increases, so does the
volume AND therefore more
stars will be in the shell.
• However…
1
luminosity of light 
R2
4 R d = 
2
• Implying…the universe should
be equally bright in all
directions. (luminosity only
depends on density
distribution of the stars.)
Olbers Paradox – Inverse Square Law
of Luminosity Solution
d
R
1
luminosity of light  2
R
4 R d = 
2
• The only logical conclusion is
that the following must be
true…
• The universe is not infinite in
size or number of stars (rule
out the net force argument)
• The universe is expanding
(Einstein’s general relativity
argument AND Hubble
evidence)
• The universe is not
homogeneous, but rather the
stars are distributed nonuniformly. (present argument)
Solution 3 to Olbers Paradox – Dark Sky? No
Problem in Expanding Universe Model
• Universe has a finite age
–Observable universe
finite, even in infinite
universe.
–If universe is 13 billion
years old, then we cannot
see light emitted by
objects farther away than
13 billion light years.
Radius
Observable Region of Universe
Infinite Universe That We Cannot Observe Yet
Solution 3 to Olbers Paradox – Dark Sky? No
Problem in Expanding Universe Model
• Expanding universe
redshifts light
–light emitted in the visible
portion of the spectrum is
shifted to longer wavelengths.
–more distant sources = greater
shifts.
–As the universe expands, light
gets redshifted into the IR or
longer wavelength EM
radiation.
Radius
Observable Region of Universe
Infinite Universe That We Cannot Observe Yet