13 January 2010Modern Physics II Lecture 11 University of San Francisco Modern Physics for Frommies II The Universe of Schrödinger’s Cat Lecture 1

13 January 2010 Modern Physics II Lecture 1 1

University of San Francisco

Modern Physics for Frommies II

The Universe of Schrödinger’s Cat

Lecture 1


Agenda• Administrative matters• Physics and the Scientific Method• Notation and Units• Mass vs. Weight• Some History


Administrative Matters

• Lecture Location and Time: Fromm Hall Wednesdays 1 PM – 2:40 PM Prompt start.

• Lecturer: Terrence A. Mulera – HR 102• Office Hours: TBA and by appointment• Contact Information:

– e-mail: [email protected]– Phone: (415) 422-5701

mailto:[email protected]


Monday Tuesday Wednesday Thursday Friday Saturday Sunday 0800

0900 0940 121 Lab 11

1000 1030 120 Lab 13

1030 121 Lab 13

1100 1135 120 Lab 11

1125

1200

1215

1215

1300 1320 1330 120 Lab

1330 210 Lab

1300 Mod. Phys. II Fromm Inst.1

1330 121 Lab 14

1400

1440

1500 1515

1515

1600 1615

1600 Colloquium

1700

1800

1900

2000

1 13 January to 6 March only


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/

http://modphysfromm2.wiki.usfca.edu/

http://modernphysicsfrommies.wiki.usfca.edu/


Administrative Matters 3

• USF Physics and Astronomy Colloquia– Open to the public– Wednesday afternoons 4 -5 PM in HR 127

• Light refreshments at 3:30 PM

– First colloquium will be sometime after start of regular USF spring semester.

• Schedule of colloquia will be provided as soon as it is available. Will also be posted in Fromm Hall.


Thanks for the cartoon to Moose’s, 1652 Stockton St., San Francisco, CA

Please turn off or silence cell phones and pagers.


Physics and the Scientific MethodPhysics 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.



Example: Newtonian GravitationExample: 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

1 22

ˆm m

F G rr


Testing: Good agreement with experiment and observation.

Measurement of falling objectsCelestial mechanics pre-1900

Refinement of Theory and Further Testing: 1905 – 1920

Einstein’s theory of general relativityEddington’s observation of bending lightPrecession of Mercury’s orbit


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)



Helen Quinn, What is Science, Physics Today (July 2009)

Posted on Wiki

http://modphysfromm2.wiki.usfca.edu

http://modphysfromm2.wiki.usfca.edu/


Scientific NotationScientific NotationVery large and very small numbers with many zeros before or after the decimal point are inconvenient in calculations.

For convenience we write them as

.

10ba0

1

1

2

2

e.g. 1.0 1.0 10

0.1 1.0 10

10.0 1.0 10

0.01 1.0 10

100.0 1.0 10

.

0( ) 1

110

10n

n

Anything


Results usually presented as 1 digit to left of decimal with exponent adjusted accordingly, i.e.

Multiplication:

Division:

Exponents add and/or subtract

2 320 10 2.0 10 .

1 2 1 21 2 1 210 10 10b b b ba a a a

1

1 2

2

1 1

22

1010

10

b

b b

b

a a

aa

2 2 2

2

10 10

10 10

b b

b b

a a

a a

010 101 10

10 10

n n

n n


UnitsUnitsMostly 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


Mass vs. WeightMass vs. WeightMass (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


Weight is a force on an object due to gravity.

2

On Earth's surface

9.8 m/secW F mg g

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


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


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?


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.


Socrates → Plato → Aristotle

Earth and its place in the universe: geocentricComplex 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 typesAlteration: Chemical reactionNatural local motion: Weight falling, smoke risingHorizontal or violent motion: Pushing, pulling, throwing

Celestial motion: Involves the interlocking spheres mentioned above.

Ptolemaic model.


Archimedes of Syracuse (287 – 212 BC)

Archimedes Thoughtful by Fetti (1620)

Killed by a Roman soldier at the siege of Syracuse (2nd Punic war)


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


Mathematics:

Infinitesimals. Calculus?

Value of

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).


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 zeroAlgebraAnatomyStar chartsPre-Copernican heliocentric theories

Black Death strikes Europe, 1347 AD, third of population dies


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


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


Tycho Brahe (1546 – 1601)

Greatest of the early observational astronomers.

Naked eye, telescope was invented shortly after his death.1

1 arcminute degree60


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.


Convinced planets orbit Sun

No stellar parallax Earth stationary. Sun orbits Earth

Few took this model seriously


Johanes Kepler (1571 – 1630)

Tycho’s assistant. Inherited data base upon Tycho’s death.

Elliptical orbits


Speculated that some force (like magnetism) originating from the Sun was responsible for planetary motion.

3

2

aM

T

T =


Galileo Galilei (1564 -1642)

1608: 1st working refracting telescopes

Hans Lippershey, Zacharias Janssen, Jacob Metius in the Netherlands

Galileo greatly improved design in 1609


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


Final nails in the coffin:

The moons of Jupiter, a miniature Solar System

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

CLEA exercise

See wiki


Sir Isaac Newton (1642-1726)


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

i i f fm v m v

Action - Reaction

There are rotational extensions to these laws:

e.g. N I


Newton’s Law of Gravitation

1 22

ˆm m

F G rr

2

1Applying the 3 laws of motion with a force

allowed Newton to derive Kepler's Laws.r

Angular momentum, L mvr

This must also be conserved. Careful, it’s a vector so direction as well as magnitude is conserved

i fL L

L r mv


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)


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.


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”


About 100 years later Charles Du Fay showed that there are 2 forms ofelectrification.

attractionIf 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 arbtrary. Consistent use of a sign convention allows a very concise mathematical formulation of experimental facts.


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. 1900Discovered the electron. Its charge under the Franklin convention is (-)


Coulomb’s Law

1 2

1 22

0

Force between 2 charges, and , separated by a distance

1

4

q q r

q qF

r

William Gilbert (1544-1603)

Charles du Fay (1698-1739)

Benjamin Franklin (1706-1790)

Charles de Coulomb (1736-1806)


Magnetism:

“The nation that controls magnetism controls the universe. ”

-Diet Smith in Chester Gould’s Dick Tracy, New York Daily News Syndicate (1962)


Magnetism

Historical:

Interactions between ferromagnetic materials (Fe, Ni, Co)Forces of attraction and repulsionResemble 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.


James Clerk Maxwell (1831-1879)


Maxwell’s Equations (differential form)

t

t

0

000

0

EB

BE

B

E

j

E. M. wave equation2

20 0 2

0t

E

E

where

m/sec10x31 8

00

c

2

2

2

2

2

22

zyx

2

In traveling wave equation

1this is

v


Triumphs:

Electrical Engineering, Electric power and communication

Wireless communication

Radar

Modern optics

First electronic computers


The Deterministic UniverseDeterminism 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

viI

Fi(t)

xiF

viF


“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

Kelvin, Lord William Thomson (1824-1907)


Lord Kelvin


Wilhelm Röntgen

1845 - 1923

Mrs. Röntgen né Anna Ludwig

1872 - 1919


Orville Wright

1871 - 1948Wilbur Wright

1867 - 1912

Documents

13 January 2010Modern Physics II Lecture 11 University of San Francisco Modern Physics for Frommies II The Universe of Schrödinger’s Cat Lecture 1