Transcript PHY 108 – Atoms to Galaxies

PHY 102 – Atoms to Galaxies
PHY 102 – Atoms to Galaxies
Our early human ancestors most
certainly looked at the night sky,
and wondered.
Light: Particle or Wave?
• Newton’s corpuscular theory
of light had a few difficulties,
such as explaining refraction.
• Newton discovered that white light
is composed of the same system of
colors that can be seen in the
rainbow (refraction).
Diffraction: Thomas Young, 1803.
Light: Particle or Wave?
• From the
diffraction
experiment with
light there is good
evidence that
light is a wave.
Chapters 13 & 14
•
Quantum Mechanics
Quantum Physics
Unlike mechanics (Newton), or
electrodynamics (Maxwell), or
relativity (Einstein),
quantum mechanics was not
developed by one individual.
It was rather the result of the
work of several scientists in
conjunction with a few
unexpected experimental
measurements.
Quantum Physics
Even though it was born about a century
ago, there is no general consensus as to
what its fundamental principles are.
It still is “work in progress.”
“If you are you are not confused by
quantum physics then you haven’t really
understood it.”
Niels Bohr
“I think I can safely say that nobody
understands quantum mechanics.”
Richard Feynman
Blackbody Radiation
Blackbody (radiation):
Theoretical object that
absorbs 100% of the
radiation that hits it;
perfect emitter too
(carbon-graphite: 97%).
Ultraviolet catastrophe:
the theoretical
prediction of early
1900s physics was
that an ideal
blackbody would emit
radiation with
infinite power. This was
in total contrast with
experimental results.
Quantum Physics: December of 1900
Max Planck
• proposed that oscillating electrons emitted radiation
according to Maxwell’s laws of E & M
• proposed that the energy must increase in discrete
amounts (quantized) because the frequencies of the
oscillating electrons could only take certain values
(digital versus analog).
Quantum Physics
Planck’s approach
produced a
theory with
results that
matched
experimental
measurements.
Quantum Physics
Planck’s approach
produced a
theory with
results that
matched
experimental
measurements.
Max Planck, 1918 Physics Nobel Prize
”in recognition of the
services he rendered
to the advancement of
Physics by his discovery
of energy quanta”
Quantization of Light
Quantum Physics
Revisit the double slit experiment with light.
Quantization of Light
Revisit the double slit experiment with
light, this time using extremely dim light.
Quantum Physics
What is coming through the slits? We expect it to be
waves, but then how can we explain the particle-like
impacts of light on the screen?
For example, take yellow
light with a frequency of
We may expect it to be
14 Hz. The EM field
5
x
10
disturbances in the
allowed to carry this light is
electromagnetic field
allowed to have energies
(light wave), but, as we
understand it today, it is
0J
zero
a “quantized” magnetic
-19 J
3.2
x
10
1E
field.
6.4 x 10-19 J
2E
9.6 x 10-19 J
3 E etc.
Quantum Physics
Consider a typical 100 watt light bulb. About 10% of
this energy (10 watt = 10 joule/second) emerges as
visible light.
Assuming this light to be yellow, in 1 second
10 J / 3.2 x 10-19 J = 3 x 1019 photons
are emitted. These are 30 million trillion quanta of
energy. So, the amount of energy in 1 photon is really,
really, really, really small.
We do not notice quantization in our everyday lives.
Quantum Physics
When carrying radiation of frequency f ,
an EM field is allowed to have only the
following particular values of total
energy:
Etotal = 0, hf , 2hf , 3hf , etc.,
where h = 6.6 x 10-34 J s.
Quantum Physics
So, Planck’s equation E = nhf indicates that
electromagnetic waves carry only well defined
discrete amounts of energy.
When this particle-like waves hit the screen they
produce a dot which corresponds to a specific
amount of energy.
The quantized particle-like waves are called photons.
They are energy quanta that act like particles.
Note that each individual photon “knows”
about the interference pattern
regardless of the other photons.
The precise impact point of each photon is
unpredictable, but the emerging
statistical pattern is predictable.
Like dice throws, individual outcomes are
unpredictable but overall statistics are
predictable. Unpredictability, or
uncertainty, is characteristic of
quantum mechanics.
Photoelectric Effect
The most dramatic prediction of Maxwell’s theory
of electromagnetism (1865) was the existence
of electromagnetic waves moving at the speed
of light. Light itself was just such a wave.
Experimentalists then came up with experimental
setups to test the theory.
Photoelectric Effect
First reported in 1839 by Becquerel. Hertz
observed it in 1887 but did not explain the
phenomenon:
An electric current is produced
when a metallic surface is exposed
to electromagnetic radiation (visible
light or x-rays, for example)
In fact, electrons are emitted from the
metallic surface due to absorption of the
electromagnetic radiation.
Quantum Physics
Photoelectric Effect
Quantum Physics
Photoelectric Effect
Quantum Physics
Photoelectric Effect
The photoelectric effect was successfully
explained by Albert Einstein who assumed
quantization of energy.
hf =  + K.E.electron
hf = e.m. radiation energy
 = work function
K.E.electron = electron kinetic energy
Albert Einstein, 1921 Physics Nobel Prize
"for his services to
Theoretical Physics, and
especially for his
discovery of the law of
the photoelectric effect"
Waviness of Matter
In 1923, Louis de Broglie proposed that matter should possess
wave properties, as much as waves displayed particle
characteristics.
Even though there was no experimental evidence, he considered
energy = m v v = p  f = h f   = h / p
Compute the wavelength associated with a 1 kg ball moving at a
speed of 1 m/s:
=h/p
= 6.6 x 10-34 J s / (1 kg 1 m/s)
= 6.6 x 10-34 m
Louis de Broglie, 1929 Nobel Prize
“for his discovery of the
wave nature of electrons”
How do we know that
matter has wave properties?
Use electrons, not light, in the
double slit experiment. What
do we get?
Compare with the output using
light.
The Wave Theory of Matter
Every material particle has wave properties with a
wavelength  equal to h/mv where m is the particle’s
mass and v is its speed.
• http://video.google.com/videoplay?docid=390849738419231822
The Wave Theory of Matter
Electrons are not tiny particles that follow a specific
path from the electron source through the slits to the
screen. Instead, electrons are quanta, increments of
the energy of a spread-out field, just as photons are
quanta.
The Wave Theory of Matter
Range of visible light: ~ 4 to 7 x 10-7 m
Size of the atom: ~ 10-10 m
Nature: Nonlocal and Uncertain
Nonlocality: This is one of the most exotic behaviors of
microscopic objects such as electrons and photons.
A microscopic object knows what happens to
another instantaneously, regardless of how far apart
they happen to be.
In the double-slit experiment with light and with
matter, the entire EM field or matter field changed
its character instantaneously when an impact
appeared on the screen.
Nature: Nonlocal and Uncertain
Uncertainty: It is impossible to know exactly both
position and momentum of a particle. The more
accuracy applied to the measurement of one of
them, the less precision is obtained with the other:
x p ≈ h
(Heisenberg uncertainty principle)
Werner Heisenberg, 1932 Physics Nobel Prize
"for the creation of
quantum
mechanics, the
application of which
has, inter alia, led to
the discovery of the
allotropic forms of
hydrogen"
Niels Bohr, in 1913, proposed a partially quantized
version of the planetary atom.
He postulated that the
electron would follow
specific trajectories
around the nucleus
of the atom,
performing quantum
jumps from one
trajectory to the
other depending on
its amount energy.
Niels Bohr, 1922 Physics Nobel Prize
"for his services in the
investigation of the
structure of the atom
and the radiation
emanating from them”
In the 1920s, Bohr
along with Max
Born, Werner
Eisenberg and
others, developed
a view of what
quantum theory
means.
Max Born proposed
that the wave
patterns observed
in experiments on
microscopic
particles were
probability patterns.
Max Born, 1954 Physics Nobel Prize
"for his fundamental
research in quantum
mechanics, especially
for his statistical
interpretation of the
wavefunction"
In 1926, Erwin
Schroedinger’s
Schroedinger
equation is
developed an
consistent with the
equation for studying
energy quantum
the motion of matter
levels and the
waves.
probability character
of the wave
function.
Schrödinger Equation

2
i

   V
t
2m
2
Erwin Schrödinger, 1933 Physics Nobel Prize
"for the discovery of new
productive forms of
atomic theory”
Paul Dirac, 1933 Physics Nobel Prize
"for the discovery of new
productive forms of
atomic theory”
Chaos Theory
Late 1800s: The N-body Problem
Old and famous: find exact solutions to N
point masses moving under their mutual
(Newtonian) gravitational forces.
N = 2, straightforward solutions, known for
a long time.
N = 3, chaos breaks loose, literally.
Oscar II, King of Sweden and Norway
1887 Prize for the
solution of the three
body problem (solar
system stability).
Henri Poincaré won the competition
Mathematical error
found in the
manuscript.
In fixing the mistake
Poincaré discovered
sensitive dependence
on initial conditions.
“If we knew exactly the laws of nature and the situation of
the universe at the initial moment, we could predict
exactly the situation of that same universe at a
succeeding moment. But even if it were the case that
the natural laws had no longer any secret for us, we
could still only know the initial situation approximately.”
“If that enabled us to predict the succeeding situation with
the same approximation, that is all we require, and we
should say that the phenomenon had been predicted,
that it is governed by laws. But it is not always so;
it may happen that small differences in the initial
conditions produce very great ones in the final
phenomena. A small error in the former will produce an
enormous error in the latter. Prediction becomes
impossible, and we have the fortuitous phenomenon.”
The Königsberg Problem
Early 1960s
Lorenz in 1963 published a
paper titled “Deterministic
non-periodic flows” that
went mostly unnoticed
until the mid 1970s.
It contained a set of
differential equations
meant to represent the
behavior of the
atmosphere.

dx
  (y  x)
dt
dy
 x(r  z)  y
dt
dz
 xy  bz
dt
Edward Lorenz, 1963
Back in the 1960s Lorenz
was one of a few
scientists who had a
computer to help with
numerical calculations.
In the course of his
computations Lorenz
“discovered” sensitive
dependence on initial
condition.
“When our results concerning the instability
of non-periodic flow are applied to the
atmosphere, which is ostensibly nonperiodic, they indicate that
prediction of the sufficiently distant future
is impossible by any method,
unless
the present conditions are known exactly.
In view of the inevitable inaccuracy and
incompleteness of weather observations,
precise very-long range forecasting would
seem to be non-existent.”
Imagine a butterfly
flipping its wings in
the middle of the
Amazon forest. The
small perturbation
the wings produce
in the atmosphere
propagates,
enlarges and a few
weeks later evolves
into a big storm in
Japan.
This is one landmark
of chaotic systems:
small variations on
initial conditions
may lead the system
into unpredictable
behavior some time
later.
The Butterfly Effect
The Butterfly Effect: From nearly the
same starting point the trajectories
evolves farther and farther apart.
The Butterfly Effect: From nearly the
same starting point the trajectories
evolves farther and farther apart.
This is the so called sensitivity dependence
on initial conditions of chaotic systems.
http://www.exploratorium.edu/complexity/java/lorenz.html
The Lorenz equations intended as a
model for the weather are similar to the
waterwheel equations as well as laser
equations.
D:\ISU Waterwheel.mov
Another example of sensitive
dependence on initial
conditions: Plasmas
Plasma movie
Poincaré surface of section
xn+1 = r xn (1 - xn)
Set r = 4.0:
n
0
1
2
3
4
5
6
7
8
9
10
11
12
xn
0.499000
0.999996
0.000016
0.000064
0.000256
0.001024
0.004090
0.016295
0.064117
0.240024
0.729649
0.789045
0.665812
Logistic Map & Bifurcation
A Universal Constant
In the mid 1970s
Mitchell Feigenbaum
was working at Los
Alamos Nat Lab when
he attended a lecture
given by Stephen
Smale, about the
period doubling
behavior of quadratic
functions.
Feigenbaum
discovered a
constant value
between ratios of
ranges of periodic
windows, in the
limit when
n∞

rn  rn1
n 
rn1  rn
  4.669202
James Yorke & T.Y. Li (1975), paper
entitled “Period Three Implies Chaos.”
Plasma movie
Fractals
We live in a 3-dimensional world  need 3
numbers to specify the position of a point:
longitude, latitude and altitude, or x y z in
Cartesian coordinates.
Number of dimensions: Space  3
Plane  2
Line  1
Point  0
Cantor (ternary) set: Set of points
lying on a single line segment with
some remarkable properties
(Georg Cantor, 1883)
What is the dimension of this set?
Example: Koch snowflake
What is the
length of the
line?
What is the
size of the
area inside
the line?
Benoit Mandelbrot (late 1960’s) coined
the word “fractal.”
Fractals are fragmented geometric shapes
such that parts are a reduced-size copy of the
whole (self-similarity).
Chapter 15
The Nucleus and
Radioactivity
Size of
atom: ~10-10 m
nucleus: ~10-14 m
subnuclear particles: ~10-19 m
How come that like
electrically charged
nuclear particles,
such as protons (+)
do not get away from
each other? In other
words, how come
that the nucleus of
the atom is stable?
Gravitational forces?
Nuclear Forces
There must exist a third force besides
electric and gravitational forces. This
force must be a strong attractive
force between nuclear particles to
prevent the nucleus from being
blown apart by electrical repulsion.
Strong Forces
Experiments show that this strong
nuclear force, or simply strong force,
has a short range of action, only
10-15 m (about the distance between
adjacent nuclear particles).
Fundamental Forces in Nature
So far to our knowledge, every force
in nature can be reduced to the
action of four fundamental forces:
• gravitational
• electric
• strong
• weak
Radioactive Decay
In 1896, the French physicist Becquerel left
some uranium compound in a drawer
containing an unexposed photographic
plate. To his surprise he notice later that
the film had been exposed, even though it
had been kept in the dark.
Becquerel did some chemical treatment to
the uranium, but the effect persisted.
Notice that the atomic nucleus had not been
discovered yet.
Radioactive Decay
Henri Becquerel, 1903
Physics Nobel Prize,
“in recognition of the
extraordinary services
he has rendered by his
discovery of
spontaneous
radioactivity”
Radioactive Decay
In 1898, the French physicists Marie and
Pierre Curie detected radioactivity in
pitchblende. The surprise was that the
radiation was more intense than the
radiation from pure uranium.
The Curies separated a new radioactive
substance from 8 tons (~16000 pounds)
of pitchblende to get about 0.01 g of the
new substance. They named it radium.
Radioactive Decay
Marie and Pierre Curie,
1903 Physics Nobel
Prize, “in recognition
of the extraordinary
services they have
rendered by their joint
researches on the
radiation phenomena”
Radioactive Decay
Experiments show that radioactive
materials emit three types of
radiation:
• alpha rays
• beta rays
• gamma rays