Transcript ModPhysII W2014 Lecture 1

University of San Francisco
Modern Physics for Frommies II
The Universe of Schrödinger’s Cat
Lecture 1
8 January 2014
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Agenda
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Administrative matters
Physics and the Scientific Method
Notation and Units
Mass vs. Weight
Some History
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Administrative Matters
• Lecture Location and Time: Fromm Hall
Wednesdays 1 PM – 2:40 PM
Prompt start.
• Lecturer: Terrence A. Mulera – HR 112
• Office Hours: TBA and by appointment
• Contact Information:
– e-mail: [email protected]
– Phone: (415) 422-5701
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Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
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210 L13
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210 L11
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1545
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101 L13
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1545
Modern
Physics II
Fromm
Institute1
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101 L16
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8 January – 26 February only
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Administrative Matters 2
• Class Wikis
– http://modphysfromm2.wiki.usfca.edu/ or link from
Fromm web site.
• .pdf notes, 4/page posted hopefully night before class.
These may change by time of lecture.
– Hard copies. How many do we need?
• Power Point® slides posted immediately following
lecture. Will include any changes to .pdf notes
– Material from preceding class (Albert Einstein’s
Universe) still available at
http://modernphysicsfrommies.wiki.usfca.edu/
Unfortunately, no Physics Colloq. S2014
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Please turn off or silence cell phones and
pagers.
Thanks for the cartoon to Moose’s, 1652 Stockton St.,
San Francisco, CA
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Physics and the Scientific Method
•Physics
is a science
-Limited to that which is testable
•Concerned with how rather than why
•Best defined in terms of the “Scientific Method”
•Formulated in the 17th century
•Other concerns reserved to Philosophy,
Metaphysics and Theology.
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Example: Newtonian Gravitation
Observations: Things fall, planets orbit in ellipses etc.
Empirical Law: There is an attractive force
between objects which have mass.
Theory: Newton’s Law of Gravitation
m1m2
F  G 2 rˆ
r
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Testing: Good agreement with experiment and
observation.
Measurement of falling objects
Celestial mechanics pre-1900
Refinement of Theory and Further Testing:
1905 – 1920
Einstein’s theory of general relativity
Eddington’s observation of bending light
Precession of Mercury’s orbit
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Future Refinement and Testing: Quantum gravity?
CAVEAT: A scientific theory can never be proved,
it can only be shown to be not incorrect to the
limit of our ability to test it.
Alternatively, if you cannot devise an experiment
which will disprove your conjecture, your
conjecture is not science.
- Karl Popper (1902-1994)
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Helen Quinn, What is Science, Physics Today (July 2009)
Posted on Wiki
http://modphysfromm2.wiki.usfca.edu
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Scientific Notation
Very large and very small numbers with many zeros
before or after the decimal point are inconvenient in
calculations.
For convenience we write them as
a 10b
e.g.
1.0  1.0 10
.
0
0.1  1.0 10 1
10.0  1.0 10
( Anything )0  1
.
1
0.01  1.0 10
2
10
n
1
 n
10
100.0  1.0 10 2
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Results usually presented as 1 digit to left of decimal with
exponent adjusted accordingly,
i.e. 20 102  2.0  103.
Multiplication:
b1
b2
b1  b2
a

10
a

10

a
a

10
1
 2
 12
 a 10
Division:
 a 10   a
 a 10  a
b1
1
1
b2
2
10b1 b2
 a 2  102b
b
b2
a

10

a

10


2
Exponents add and/or subtract
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
b 2
n
10n
10
0

1

10
 n
n
10
10
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Units
Mostly rationalized mks units, i.e. distance in meters,
mass in kilograms, time in seconds.
Occasional use of cgs units, i.e. centimeters, grams,
seconds and of “English” units, i.e. ft., slugs, seconds
Special units. e.g. light years, parsecs, fermis, barns
introduced as needed
Mass vs. Weight
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Mass vs. Weight
Mass (if non zero) is a measure of the quantity of matter
present.
e.g. 1 kg of say air corresponds to n molecules of air
2 kg corresponds to 2n molecules
Mass is independent of the gravitational environment of
the matter.
1 kg on Earth = 1 kg on Mars = 1 kg in interstellar space
etc.
Alternatively, mass is a measure of an object’s resistance to
acceleration.
F  ma
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Weight is a force on an object due to gravity.
On Earth's surface
W  F  mg
g  9.8 m/sec2
Units: kg m/sec2  Newton (N)
Weight is dependent on the gravitational environment of the
object.
Weight on Earth  3 x weight on Mars  6 x weight on moon.
Common usage: Weights quoted in kg with environment
understood to be surface of Earth.
Further confusion: lbs. are units of weight, mass units are slugs.
1 slug x (32 ft/sec2) = 1 lb
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A Brief History of Views of the Universe
Arbitrary definition of “Modern Physics”
Post 1900 CE
Two major foundations
Relativity
Quantum Mechanics
Where were we? Where are we?
Maybe we can ask: Where are we going?
“It’s difficult to make predictions, especially
about the future.”
- Yogi Berra
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The Ancients (mostly Greeks):
Physics from the Greek physika meaning “natural things” or the
study of nature.
All of the ancient civilizations tried to understand their worlds in
terms of myths.
Anthromorphizication of natural forces
e.g. Egyptian sun god, Ra
Greek mythology: Zeus, Athena, Aphrodite, Aeres etc.
Ca. 600 BC the Pre-Socratics began to apply reason to the
comprehension of nature
What is the underlying order that is hidden in nature?
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What is the most basic substance in the universe?
Is the structure of nature based on mathematics, processes or
substances?
Some of the Players
Thales (600 BC): H2O is the primary and simplest element
Anaximander: World composed of interacting, aggressive opposites
Anaximenes: Like Thales only air rather than H2O
Empedocles: Earth, air, fire and water
Paramendes: Processes. Matter is conserved.
Pythagoras: Defined the world in terms of mathematics. Coined the
term philosopher.
Leucippus and Democritus: Elementary particles. Coined the term
atom.
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Socrates → Plato → Aristotle
Earth and its place in the universe: geocentric
Complex system of interlocking spheres with names like
prime mover, cycles and epicycles.
Aside: A heliocentric theory was proposed as early as the 6th
century BC by non other than Pythagoras.
.
Physical phenomena: 4 elements. Properties and motions of
objects could be described in terms of the chemical reaction
properties of these elements.
Motion: 4 basic types
Alteration: Chemical reaction
Natural local motion: Weight falling, smoke rising
Horizontal or violent motion: Pushing, pulling, throwing
Celestial.motion: Involves the interlocking spheres mentioned above.
Ptolemaic model.
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Archimedes of Syracuse (287 – 212 BC)
Archimedes Thoughtful by Fetti (1620)
Killed by a Roman soldier at the siege of Syracuse (2nd Punic war)
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Discoveries and Inventions Credited to Archimedes
Hydrostatics: Archimedes principle
Principle of levers: “Give me a place to stand on, and I will
move the Earth.”
Block and tackle systems
Archimedes screw
Military weapons:
Archimedes claw
Death ray (mirrors focusing the Sun on enemy ships)
Possibly apocryphal but principle verified by MIT
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Mathematics:
Infinitesimals. Calculus?
Value of p
Area under the arc of a parabola
Attempted to calculate the number of sand grains which the
universe could contain. Lead to his devising a system of
dealing with extremely large numbers using powers of
myriads (10,000 in Greek).
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Interregnum: Aristotle - Renaissance
Not much happening in physics but lots going on in history
Rome dominates the classical world
Rome falls ca. 450 AD
Dark ages in Europe ca. 450 – 750 AD
Light of classical civilization preserved in Islamic countries.
Returned to the West in the Middle ages, 750 – 1350 AD.
Concept of the zero
Algebra
Anatomy
Star charts
Pre-Copernican heliocentric theories
Black Death strikes Europe, 1347 AD, third of population dies
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Renaissance: Ca. 1400- 1600 AD
The Copernican Revolution
Observation → Tables of planetary motion
Geocentric (Ptolemaic) model noticeably inaccurate and
difficult to calculate.
“ If I had been present at the creation, I would have
recommended a simpler design for the universe”
- Alphonso X (1221 – 1284)
King of Spain
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Nicholas Copernicus (1473-1543)
Tried a heliocentric model much like that proposed by Aristarchus
1700 years earlier.
Model was successful but not overly so.
Assumed orbits were perfect circles, required reintroduction of
complexity
Few converts over 50 years
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Tycho Brahe (1546 – 1601)
Greatest of the early observational astronomers.
Naked eye, telescope was invented shortly after his death.
1
1 arcminute 
degree
60
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Observed a “new star” or nova.
Observed the 1563 alignment of Jupiter and Saturn.
Noted that it occurred two days later than predicted by the
Copernicus model
Spent the next 30 years compiling stellar and planetary
measurements.
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Convinced planets orbit
Sun
No stellar parallax
 Earth stationary.
Sun orbits Earth
Few took this
model seriously
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Johanes Kepler (1571 – 1630)
Tycho’s assistant. Inherited data base upon Tycho’s death.
Elliptical orbits
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T=
a3
M  2
T
Speculated that some force (like magnetism) originating from
the Sun was responsible for planetary motion.
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Galileo Galilei (1564 -1642)
1608: 1st working refracting telescopes
Hans Lippershey, Zacharias Janssen, Jacob Metius
in the Netherlands
Galileo greatly improved design in 1609
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Three objections to Kepler’s heliocentric theories:
(1) The Earth cannot move because birds, falling stones etc,
would be left behind.
Inertia later Newton’s 1st law. Galilean relativity
(2) Non circular orbits are contradictory to the non changing
perfection of the heavens.
Novae, supernovae, comets already observed
Telescopes allowed observation of sunspots, mountains on Moon
(3) No stellar parallax observed.
Telescope  stars are much farther away than Tycho thought
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Final nails in the coffin:
The moons of Jupiter, a miniature Solar System
CLEA exercise
See wiki
Observation of the phases of Venus can only be
explained in terms of a heliocentric model.
Observation of the transit of Mercury across the face of
the Sun
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Sir Isaac Newton (1642-1726)
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Newtonian Mechanics (translational)
Three laws of motion:
1) A body at rest or in constant rectilinear motion
remains at rest or in motion unless acted upon by
an outside force.
2)
F  ma
3) Momentum is conserved
mi vi  m f v f
Action - Reaction
There are rotational extensions to these laws:
e.g.
N  I
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Angular momentum, L  mvr
 L  r  mv 
This must also be conserved. Careful, it’s a vector so direction
as well as magnitude is conserved
Li  L f
Newton’s Law of Gravitation
F  G
m1m2
rˆ
2
r
1
Applying the 3 laws of motion with a 2 force
r
allowed Newton to derive Kepler's Laws.
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Leonhard Euler
(1736-1783)
Jean Le Rond d’Alembert
(1717-1783)
Joseph Louis Lagrange
a.k.a. Giusseppe Lodovico
Lagrangia
(1736-1813)
William Rowan Hamilton
(1805-1865)
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Triumphs:
Celestial mechanics, planetary orbits
Navigation
Mechanical Engineering and the Industrial Revolution
The above Classical Mechanics was accompanied by the 2nd great
triumph of pre-20th century physics, Classical Electromagnetic
Theory, a.k.a. Classical Electricity and Magnetism, a.k.a. Classical
Electrodynamics.
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Electrical charge
Ancient Greece, ca. 600 B. C.
Rub a rod of amber or hard rubber with a cloth.
After rubbing, rod is able to attract small bits of paper or other
light material.
No real advance in understanding until ca. 1600 A. D.
William Gilbert (court physician to Elizabeth I) studied
materials that act like amber.
“electric” (elektron is Greek for amber)
Electric: modern term is “insulator”
Non-electric: “conductor”
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About 100 years later Charles Du Fay showed that there are 2 forms of
electrification.
attraction
If you rub various insulators →
repulsion
Postulate: There are 2 types of electrical charges
like charges repel
unlike charges attract
Benjamin Franklin: Assign (+) charge to one type and (-) charge
to the other.
Which is ± is arbitrary. Consistent use of a sign convention
allows a very concise mathematical formulation of experimental
facts.
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Franklin’s arbitrary choice: rubbing glass rod w/silk → (+)
rubbing amber or hard rubber → (-)
Hindsight: Picking signs opposite to Franklin’s choice →
more “sensible” conceptual picture.
“Hindsight is always 20-20” - .Anonymous
  
 
J. J. Thomson ca. 1900
Discovered the electron. Its charge under the Franklin convention is (-)
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Coulomb’s Law
Force between 2 charges, q1 and q2 , separated by a distance r
q1q2
F
4p 0 r 2
1
William Gilbert
(1544-1603)
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Charles du Fay
(1698-1739)
Benjamin Franklin
(1706-1790)
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Charles de Coulomb
(1736-1806)
45
Magnetism:
“The nation that controls magnetism controls the
universe. ”
-Diet Smith in Chester Gould’s Dick Tracy, New York
Daily News Syndicate (1962)
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Magnetism
Historical:
Interactions between ferromagnetic materials (Fe, Ni, Co)
Forces of attraction and repulsion
Resemble but are quite distinct from electrostatic
Use of permanent magnet in Earth’s magnetic field as compass
for navigation.
In 1819 Ørsted showed connection between electric current and
magnetism.
Faraday and others, culminating in Maxwell’s equations.
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James Clerk Maxwell (1831-1879)
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Maxwell’s Equations (differential form)
 

E 
0
 
B  0



B
E  
t




E
  B   0 j   0 0
t
E. M. wave equation
 2 E  0 0
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 E
0
2
t
In traveling wave equation
1
this is 2
v
1
 0 0
2
where
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 c  3 x 10 8 m/sec
2
2
2



2  2  2  2
x
y
z49
Triumphs:
Electrical Engineering, Electric power and communication
Wireless communication
Radar
Modern optics
First electronic computers
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The Deterministic Universe
Determinism  The future is completely determined by the past.
 The future can be predicted if enough is known
of the past.
What is enough?
Consider a universe whose component objects are labeled
with the index i. Each object has mass mi.
If we know the initial position, xiI, and velocity, viI of each
particle plus the resultant or sum of all the forces acting on it
as a function of time, Fi(t), then we can, in principle, calculate
the final position, xiF, and velocity, viF. ,
xiI
xiF
viI
Fi(t)
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viF
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Kelvin, Lord William Thomson (1824-1907)
“There is nothing new to be discovered in physics now. All that
remains is more and more precise measurement.”
-1900
“Heavier than air flying machines are impossible.”
-1895
“X-rays will prove to be a hoax.”
-1896
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Lord Kelvin
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Wilhelm Röntgen
Mrs. Röntgen né Anna Ludwig
1845 - 1923
1872 - 1919
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Orville Wright
Wilbur Wright
1871 - 1948
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1867 - 1912
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