Fromm Institute for Lifelong Learning
University of San Francisco
Agenda
Modern Physics for Frommies IV
The Universe - Small to Large
Lecture 1
13 January 2016
Modern Physics IV Lecture 1
48 slides
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Administrative Matters
Administrative Matters
Physics and the Scientific Method
Notation and Units
Mass vs. Weight
Some History; Premodern Physics
13 January 2016
Monday
Modern Physics IV Lecture 1
48 slides
Tuesday
• Lecture Location and Time: Fromm Hall,
Broad Room, Wednesdays 1 PM – 2:40 PM
Prompt start.
• Lecturer: Terrence A. Mulera – HR 114
• Office Hours: TBA and by appointment
• Contact Information:
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Modern Physics IV
Fromm Institute1
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– e-mail: [email protected]
– Phone: (415) 422-5701
Modern Physics IV Lecture 1
48 slides
Thursday
0800
0900
13 January 2016
Wednesday
2
1900
1
11 January to 7 March only
Preliminary, Updates TBA
3
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1
Administrative Matters 2
http://modphysicsfrommiies.wiki.usfca.edu/
• Class Wikis
– http://modphysfromm4-2016.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
http://modphysfromm2.wiki.usfca.edu
http://modphysfromm3.wiki.usfca.edu
Please turn off or silence cell phones and
pagers.
– Material from preceding classes (Albert Einstein’s
Universe, The Universe of Schrödinger’s Cat and A
Universe of Leptons, Quarks and Bosons) still
available at:
13 January 2016
Modern Physics IV Lecture 1
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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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2
Example: Newtonian Gravitation
Observations: Things fall, planets orbit in ellipses etc.
Testing: Good agreement with experiment and
observation.
Measurement of falling objects
Celestial mechanics pre-1900
Empirical Law: There is an attractive force
between objects which have mass.
Refinement of Theory and Further Testing:
1905 – 1920
Theory: Newton’s Law of Gravitation
mm
F = −G 1 2 2 rˆ
r
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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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3
Scientific Notation
Helen Quinn, What is Science, Physics Today (July 2009)
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
Posted on Wiki
http://modphysfromm2.wiki.usfca.edu
a × 10b
1.0 = 1.0 × 100
e.g.
Small to Large:
0.1 = 1.0 × 10
Planck Length: 0.00000000000000000000000000000000001 m
.
10.0 = 1.0 × 101
Cosmological Horizon: 150,000,000,000,000,000,000,000,000.0 m
( Anything )0 = 1
−1
0.01 = 1.0 × 10 −2
.
10
−n
=
1
10 n
100.0 = 1.0 ×102
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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.
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Small to Large:
Planck Length: 1 x 10-35 m
Multiplication:
( a ×10 )( a
b1
1
2
Cosmological Horizon: 1.5 x 1026 m
× 10b2 ) = a1a2 ×10b1 +b2
( a ×10 ) = a
( a ×10 ) =
b 2
Division:
( a ×10 ) = a
( a ×10 ) a
b
b1
1
1
b2
2
× 10
b1 −b2
×102 b
a ×10b 2
Cosmological Horizon [units of Planck Lengths (PL)]
=
2
Exponents add and/or subtract
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1.5 ×10 26 m
= 1.5 × 1061 PL
1× 10−35 m/PL
10n
10− n
= 1 = 100 = − n
n
10
10
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4
Mass vs. Weight
Units
Mass (if non zero) is a measure of the quantity of matter
present.
Mostly rationalized mks units, i.e. distance in meters,
mass in kilograms, time in seconds.
e.g. 1 kg of say air corresponds to n molecules of air
2 kg corresponds to 2n molecules
Occasional use of cgs units, i.e. centimeters, grams,
seconds and of “English” units, i.e. ft., slugs, seconds
Mass is independent of the gravitational environment of
the matter.
1 kg on Earth = 1 kg on Mars = 1 kg in interstellar space
etc.
Special units. e.g. light years, parsecs, fermis, barns
introduced as needed
Alternatively, mass is a measure of an object’s resistance to
acceleration.
Mass vs. Weight
F = ma
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On Earth's surface
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Arbitrary definition of “Modern Physics”
g = 9.8 m/sec 2
Post 1900 CE
Units: kg m/sec2 ≡ Newton (N)
Two major foundations
Relativity
Weight is dependent on the gravitational environment of the
object.
Weight on Earth ≈ 3 x weight on Mars ≈ 6 x weight on moon.
Quantum Mechanics
Where were we? Where are we?
Maybe we can ask: Where are we going?
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
Weight is a force on an object due to gravity.
W = F = mg
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“It’s difficult to make predictions, especially
about the future.”
- Yogi Berra
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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.
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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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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Renaissance: Ca. 1400- 1600 AD
The Copernican Revolution
Interregnum: Aristotle - Renaissance
Not much happening in physics but lots going on in history
Observation → Tables of planetary motion
Rome dominates the classical world
Geocentric (Ptolemaic) model noticeably inaccurate and
difficult to calculate.
Rome falls ca. 450 AD
Dark ages in Europe ca. 450 – 750 AD
“ If I had been present at the creation, I would have
recommended a simpler design for the universe”
Light of classical civilization preserved in Islamic countries.
Returned to the West in the Middle ages, 750 – 1350 AD.
- Alphonso X (1221 – 1284)
Concept of the zero
Algebra
Anatomy
Star charts
Pre-Copernican heliocentric theories
King of Spain
Black Death strikes Europe, 1347 AD, third of population dies
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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.
Johanes Kepler (1571 – 1630)
Tycho’s assistant. Inherited data base upon Tycho’s death.
Assumed orbits were perfect circles, required reintroduction of
complexity
Elliptical orbits
Few converts over 50 years
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T=
Galileo Galilei (1564 -1642)
1608: 1st working refracting telescopes
a3
M⊙ = 2
T
Hans Lippershey, Zacharias Janssen, Jacob Metius
in the Netherlands
Speculated that some force (like magnetism) originating from
the Sun was responsible for planetary motion.
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Galileo greatly improved design in 1609
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Three objections to Kepler’s heliocentric theories:
Final nails in the coffin:
(1) The Earth cannot move because birds, falling stones etc,
would be left behind.
The moons of Jupiter, a miniature Solar System
Inertia later Newton’s 1st law. Galilean relativity
(2) Non circular orbits are contradictory to the non changing
perfection of the heavens.
CLEA exercise
http://modphysfrom
m2.wiki.usfca.edu
Novae, supernovae, comets already observed
Telescopes allowed observation of sunspots, mountains on Moon
Observation of the phases of Venus can only be
explained in terms of a heliocentric model.
(3) No stellar parallax observed.
Telescope ⇒ stars are much farther away than Tycho thought
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Observation of the transit of Mercury across the face of
the Sun
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Newtonian Mechanics (translational)
Three laws of motion:
This image cannot currently be display ed.
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
m i vi = m f v f
Action - Reaction
There are rotational extensions to these laws:
e.g. N = I α
Sir Isaac Newton (1642-1726)
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Angular momentum, L = mvr
Triumphs:
( L = r × mv )
This must also be conserved. Careful, it’s a vector so direction
as well as magnitude is conserved
Li = L f
Celestial mechanics, planetary orbits
Navigation
Mechanical Engineering and the Industrial Revolution
Newton’s Law of Gravitation
mm
F = −G 1 2 2 rˆ
r
Force acting at a distance
1
force
r2
allowed Newton to derive Kepler's Laws.
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.
Applying the 3 laws of motion with a
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Ancient Greece, ca. 600 B. C.
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attraction
Rub a rod of amber or hard rubber with a cloth.
If you rub various insulators →
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.
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.
“electric” (elektron is Greek for amber)
Electric: modern term is “insulator”
Non-electric: “conductor”
Modern Physics IV Lecture 1
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About 100 years later Charles Du Fay showed that there are 2 forms of
electrification.
Electrical charge
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Which is ± is arbtrary. Consistent use of a sign convention allows
a very concise mathematical formulation of experimental facts.
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Coulomb’s Law
Franklin’s arbitrary choice: rubbing glass rod w/silk → (+)
rubbing amber or hard rubber → (-)
Force between 2 charges, q1 and q2 , separated by a distance r
1 q1q2
F=
rˆ Another force at a distance.
4πε 0 r 2
Hindsight: Picking signs opposite to Franklin’s choice →
more “sensible” conceptual picture.
“Hindsight is always 20-20” - .Anonymous
± ↔ ±
a
± →← ∓
J. J. Thomson ca. 1900
Discovered the electron. Its charge under the Franklin convention is (-)
William Gilbert
(1544-1603)
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Magnetism:
Charles du Fay
(1698-1739)
Benjamin Franklin
(1706-1790)
Charles de Coulomb
(1736-1806)
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Magnetism
“The nation that controls magnetism controls the
universe. ”
Historical:
-Diet Smith in Chester Gould’s Dick Tracy, New York
Daily News Syndicate (1962)
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)
Maxwell’s Equations (differential form)
∇ ⋅E =
ρ
ε0
∇ ⋅B = 0
∂B
∇ × E = −
∂t
∇ × B = µ 0 j + µ 0ε
0
∂E
∂t
In traveling wave equation
this is
1
⇒E. M. wave equation
∇ 2 E + µ 0ε 0
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∂ 2E
= 0
2
∂t
µ 0ε 0
where
∇2 =
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v2
= c = 3 x 10 8 m/sec
∂2
∂2
∂2
+
+ 2
∂x 2 ∂y 2 ∂z 42
The Deterministic Universe
Triumphs:
Determinism ⇒ The future is completely determined by the past.
⇒ The future can be predicted if enough is known
of the past.
Electrical Engineering, Electric power and communication
Wireless communication
What is enough?
Consider a universe whose component objects are labeled
with the index i. Each object has mass mi.
Radar
Modern optics
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. ,
First electronic computers
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
Lord Kelvin
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Orville Wright
Wilbur Wright
1871 - 1948
Wilhelm Röntgen
Mrs. Röntgen né Anna Ludwig
1845 - 1923
1872 - 1919
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1867 - 1912
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