11 January 2012 Modern Physics IV Lecture 1 1

Modern Physics for Frommies IVThe Universe - Small to Large

Lecture 1

Fromm Institute for Lifelong Learning University of San Francisco

11 January 2012 Modern Physics IV Lecture 1 2

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

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Administrative Matters

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

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

– e-mail: mulera@usfca.edu– Phone: (415) 422-5701

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Monday Tuesday Wednesday Thursday Friday Saturday Sunday 0800

0900 0945_____________ 121 L15

0955___________

120 L12

1000 1025___________ 121 L11

1100

1130 __ _______

1140___ _______

1200 1210_ _ _______

1300 101 L11

210 L11

Modern Physics IV Fromm Institute1

210 L13

1400

1440 ________

1500 _______ _______ 1545

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1600

1700

1800

1900

1 11 January to 7 March only

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Problem with Lecture 2

I am having cataract surgery on Wednesday, 18 January

I will give an extra lecture during the “make up week” (on 7 March)

On 18 January the Fromm staff will show a movie or movies reviewing relativity.

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Administrative Matters 2• Class Wikis

– http://modphysfromm4.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 classes (Albert Einstein’s Universe, The Universe of Schrödinger’s Cat and A Universe of Leptons, Quarks and Bosons) still available at:

11 January 2012 Modern Physics IV Lecture 1 7

http://modernphysicsfrommies.wiki.usfca.edu/http://modphysfromm2.wiki.usfca.eduhttp://modphysfromm3.wiki.usfca.edu

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

Please turn off or silence cell phones and pagers.

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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.

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11 January 2012 Modern Physics IV Lecture 1 10

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

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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

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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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11 January 2012 Modern Physics IV Lecture 1 14

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

Posted on Wiki

http://modphysfromm2.wiki.usfca.edu

Small to Large:

Planck Length: 0.00000000000000000000000000000000001 m

Cosmological Horizon: 150,000,000,000,000,000,000,000,000.0 m

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Scientific NotationScientific 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

.

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

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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

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Small to Large:

Planck Length: 1 x 10-35 m

Cosmological Horizon: 1.5 x 1026 m

2661

35

Cosmological Horizon [units of Planck Lengths (PL)]

1.5 10 m 1.5 10 PL

1 10 m/PL

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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

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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

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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

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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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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.

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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 zeroAlgebraAnatomyStar chartsPre-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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Johanes Kepler (1571 – 1630)

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

Elliptical orbits

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

3

2

aM

T

T =

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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

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 exercisehttp://modphysfromm2.wiki.usfca.edu

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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

i i f fm v m v

Action - Reaction

There are rotational extensions to these laws:

e.g. N I

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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

Force acting at a distance

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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.

11 January 2012 Modern Physics IV Lecture 1 36

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 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.

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

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Coulomb’s Law

1 2

1 22

0

Force between 2 charges, and , separated by a distance

1ˆ

4

q q r

q qF r

r

William Gilbert (1544-1603)

Charles du Fay (1698-1739)

Benjamin Franklin (1706-1790)

Charles de Coulomb (1736-1806)

a

Another force at a distance.

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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 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.

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James Clerk Maxwell (1831-1879)

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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

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Triumphs:

Electrical Engineering, Electric power and communication

Wireless communication

Radar

Modern optics

First electronic computers

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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

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“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)

12 January 2011 Modern Physics III Lecture 1 47

Lord Kelvin

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Wilhelm Röntgen

1845 - 1923

Mrs. Röntgen né Anna Ludwig

1872 - 1919

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Orville Wright

1871 - 1948Wilbur Wright

1867 - 1912