Transcript Tom on Stephen Hawking

Stephen Hawking
Math 305 Tom Kreitinger 11/18/2009
Stephen Hawking
Commercial Overview:
Part I – The shoulders of giants: Newton,
Einstein, Schwarzschild, Friedmann, Lemaitre
and Oppenheimer.
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Part II – Two of Stephen Hawking's major
contributions:
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1.
Big Bang Theory
2.
Black Hole Radiation
Isaac Newton 1643-1727
”If I have seen further it
is by standing on the
shoulders of giants.”
World famous ”Principia”
(1687) - Laws of motion
and gravitation
Applies to all motion in the
solar system
Yes, actually, it is rocket
science!
Isaac Newton's
Law of Universal Gravity
F(force) = G [ (m1 * m2) / R² ]
Example:
G = 6.67e-11 Newtons-metres² / kilograms²
m1 = gravitational mass 1 - A person 60 kg
m2 = gravitational mass 2 - Earth 5.98e24 kg
R² = radius - Earth 6.37e6 metres
F(force) = Weight = 590 Newtons = 132 lb
Isaac Newton's
Law of Universal Gravity
F = G [ (m1 * m2) / R² ]
Gravitational attraction is
weak - The attraction
between two sumo
wreslers is 10,000
times less than the pull
necessary to pick up a
square of toilet tissue
Isaac Newton's
Second Law of Motion
Second Law of Motion:
F(force) = m * a (acceleration)
or
a (acceleration) = F(force) / m
Newton's Law of Gravitation:
F(force) = G [ (m1 * m2) / R² ]
Is there any difference between ”inertial mass”
and ”gravitational mass”?
Albert Einstein 1879-1955
Spooky Action at a Distance
According to Newton if
the Sun disappeared in
an instant, so would its
gravitational field at the
Earth, millions of miles
away; yet light from the
Sun, with its finite
speed, would continue
for another 8 minutes this troubled Einstein.
Albert Einstein
Not a force but space itself ?
Maybe it is not a force
at all. Since the motion
of a freely falling object
does not depend on
the object’s mass or
composition (as Galileo
discovered) gravitation
might be due to certain
properties of the
medium it's falling in -that is, space itself.
Albert Einstein's
Happiest Thought - 1907
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An observer falling
freely from the roof of a
house will not feel his
own weight. If that
person drops other
bodies while falling,
then these remain in a
state of rest relative to
him.
Gravitational mass is
the same as inertial
mass, gravity equals
acceleration
Albert Einstein's
Relativity - Field Equations
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Produces a set of 20
extremely difficult
simultaneous equations
with 10 unknown
quantities.
Matter tells space how to
curve and then space tells
matter how to move.
This becomes "the
mountain” for others to
visit.
Karl Schwarzschild 1873-1916
Provides exact solution
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Visits the mountain...
Provides an exact
solution to Einstein's
Field Equations
System of ten
equations connecting
twenty quantities,
resulting in hundreds
of terms
A math super hero
Karl Schwarzschild - 1915
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The math showed
how the space
curvature around a
mass varies with
distance
Schwarzschild
Radius - the critical
point at which
curvature is so strong
that matter can no
longer escape
R = 2GM / c
G- gravitational constant
c- speed of light
What about Stephen Hawking?
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Several solutions to the
field equations were
fundamental to Stephen
Hawking's work
It is currently 1915 and
Hawking will not even be
born for another 27
years!
On the right we see (or
don't see?) a black hole.
Alexander Friedmann 1888-1925
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Einstein introduced an artificial
term (lambda) in his Field
Equations, essentially to ”stop
the expansion of the Universe”;
at the time astronomers were
telling him the Universe was
static.
Friedmann dropped the
lambda constant and got an
expanding universe.
Alexander Friedmann 1888-1925
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By 1929 Edwin Hubble,
using a 100-inch
telescope, had confirmed
that the universe is, in
fact, expanding.
Einstein later called his
``cosmological constant”
(lambda) the biggest
mistake of his life.
Abbe Lemaitre 1894-1966
Precursor to Big Bang
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First to use Friedmanntype solutions to
formulate a model for the
beginning of the
Universe which he called
the Primordial Atom or
Cosmic Egg.
Abbe Lemaitre - 1931
Precursor to Big Bang
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He thought that the
universe at one time
existed in a very small
space, before the
expansion took place
several billion years
ago, and that it is still
expanding today
Gave a seminar on
his model Universe to
Hubble and Einstein
Singularity – In Mathematics
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A point at which a
function cannot be
defined, diverges to
infinitely large values
y=1/x has x=0 as a
point of singularity
Small change in x
from +0.0000001 to 0.0000001results in y
changing from +1
million to -1 million
Singularity – In Relativity
In general relativity
singularity is a region
of space-time in
which the curvature
becomes so strong
that the laws of
general relativity
break down and the
laws of quantum
gravity take over.
Robert Oppenheimer 1904-1939
Gravitational Collapse – 1939
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The third solution of
Einstein's equations &
important to Hawking
Stars may eventually
burn out and begin to
collapse under
gravitational contraction.
Einstein refused to
accept that relativity
could describe collapsed
stars (e.g. Black holes)
Robert Oppenheimer 1904-1939
Gravitational Collapse – 1939
1) Massive star exhausts
nuclear fuel
2) Star implodes to point of
no return, as defined by
the Schwarzschild
Radius (R=2GM/c)
3) Then cuts itself off from
the rest of the universe
(i.e. singularity).
Hitler's troops invade Poland
triggering second World War
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The threat of Nazi rule postponed work on
cosmology. In 1942 physicist began to focus
on other projects (e.g. The Manhattan
project)
Einstein had opposed all the radical
cosmological predictions of his own
equations as developed by Schwarzschid,
Friedmann and Oppenheimer.
It would be 20 years before this work was
resumed and the consequences of these
solutions appreciated.
Stephen Hawking 1942
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In 1962 Hawking found it
difficult to tie his shoelace: he
had contracted ALS - Lou
Gehrig's Disease.
Doctors gave him only 2
years to live.
Yet he came to Cambridge
University from Oxford to
study cosmology, and
married Jane Wilde at
Cambridge in July 1965.
Stephen Hawking
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Hawking called his doctoral
thesis ”Properties of Expanding
Universes”
The steady state model
proposed that matter is
continuously being created as
the universe expands in utter
disagreement with the big bang
notion of an infinitely dense
initial state
In the 60's steady state was
more accepted than big bang
Stephen Hawking
Big Bang
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Roger Penrose determined that a
singularity exists when a giant
star collapses to form a black
hole.
Hawking adapted Penrose’s
results to the expanding universe,
as a giant collapsing star in
reverse.
Hawking showed that if general
relativity is correct there must
have been a singularity in the
past which was the beginning of
time.
Stephen Hawking
Big Bang
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Today everyone assumes the
Universe started with a Big
Bang (background micro).
This is Hawkings major world
wide contribution to Big Bang
cosmology.
Thus by 1970, five years after
receving his PhD. Hawkings
was an internationally known
cosmologist
Stephen Hawking
A new way of thinking
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By the early 1970s Hawking's hands
were largely paralyzed: he could not
draw pictures or write down equations.
His research has to be done in his
head. Because the loss of his faculties
was so gradual, he has trained his mind
to think in new types of intuitive mental
pictures and equations which replaced
written work – an astounding
adaptation.
Stephen Hawking
Black hole - Eureka Moment
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Hawking has used his mental pictures
to gain insight into the study of the
surface areas of black holes.
He was getting ready for bed one night
and he saw in a flash that the surface
area of a black hole can never
decrease.
He concluded that the combined area of
two black holes must always be greater
than or equal to the sum of the two
areas.
Stephen Hawking
Black Holes
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Hawking explores the
boundary between the
black hole and the
vacuum of inter-stellar
space, and envisions
how the intense
gravity at the surface
might affect any
particles that might
appear there, whether
real or virtual.
Uncertainty Principle & Virtual
Particles
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The uncertainty principle states that there are
limits on how accurately we can observe
certain physical quantities (e.g. position,
energy and time).
The limit is not related to our instruments, but
an inherent characteristic of the Universe,
which does not reveal any quantity with
absolute precision.
Black Holes Emit Radiation
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Hawking has in effect
combined quantum
mechanics and
general relativity in a
single calculation to
show that Black Holes
have temperature,
entropy, and produce
radiation just like any
other thermodynamic
body.
Hawking Recognition
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He has received Britain's highest
academic honour: Fellow of The Royal
Society.
He received the Pope Pius XI Medal –
Why? Because the Big Bang model
appeals to the church as a creation
event! We’ve come a long way since
Galileo....
Hawking Summary
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Using general relativity (and standing on the
shoulders of other giants) Hawking showed that
the classical concept of time must have begun
with a singularity at the Big Bang, and thus the
Universe existed at one time in a hot dense state.
Hawking discovered that Black Holes radiate like
thermodynamic bodies (now called Hawking
Radiation) and possess a temperature and an
entropy.
He has written books that make these complex
subjects easier to understand.
The End
“We are just an advanced
breed of monkeys on a
minor planet of a very
average star. But we
can understand the
Universe. That makes
us something very
special.”
- Stephen Hawking
Sources
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A Brief History of Time & The Universe in a Nutshell – Stephen Hawking
ISBN 978-0-307-29117-2
Introducing Stephen Hawking by J.P McEvoy and Oscar Zarate ISBN 184046-096-2
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http://en.wikipedia.org/wiki/J._Robert_Oppenheimer
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http://en.wikipedia.org/wiki/Georges_Lemaitre
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http://en.wikipedia.org/wiki/Alexander_Friedmann
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http://en.wikipedia.org/wiki/Karl_Schwarzschild
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http://en.wikipedia.org/wiki/Isaac_Newton
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http://en.wikipedia.org/wiki/Albert_Einstein
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http://en.wikipedia.org/wiki/Black_holes
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http://en.wikipedia.org/wiki/Stephen_Hawking