Why do
scientists
believe that?
An inquiry into scientific method
Preliminaries
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My name is Julian Noble, Professor Emeritus
of Physics, UVa
Next meeting dates:
19 September
 26 September
 03 October
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Attendees with hearing difficulties please use
front-row seats—I will use a mike if necessary.
Questions are welcome—don’t be shy about
interrupting!
Things (most) scientists
believe
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The Earth and planets circle the Sun
The Solar system is insignificantly small
Blood circulates in the body; the heart is a pump
The Earth is a magnet (among other things)
Darwinian evolution
Germs cause (most) diseases
Everything is made of atoms; matter is mostly empty
space
Light is waves—oops, particles—oops!! ???
Matter is particles—oops, waves—oops!! ???
Things (most) scientists
disbelieve
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Material objects can travel faster than light
Homeopathic medicine
Astrology
ESP and the paranormal
Crystals have mysterious powers
A “life force” that distinguishes living from dead
Literal interpretation of the Bible
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Special creation
Age of Earth about 6000 years
Miracles
Cold fusion (“…that would be a miracle”)
Magnetic fields from power lines cause cancer (“…that
would be a miracle, too”)
Things you (may) believe
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The Earth is a sphere 8000 miles in diameter
The Earth rotates on its axis once in 24 hours
The Moon orbits the Earth at a distance of 240,000
miles, once every 28 days
The Sun is 92,000,000 miles away
Light travels 186,000 miles/second
The nearest star is 5 light-years away
The Solar System is 5,000,000,000 years old
Electricity is a flow of electrons
But, how do you
What about
science?
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The aims of science—reductionism
Is science “special”?
The prestige of the label scientific.
 Is there a “scientific method”?
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 Bacon,
et al.
 Modern scientists’ ideas.
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A capsule history of science
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 Why is science difficult? 
Reading: R.P. Feynman, Cargo Cult Science
Causality and
Gnosis
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Cause and effect
Volition leads to animism
 Invisible and intangible causes
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 Leads
to superstition and religion
 Signs, omens and portents become important
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Greek idea: Natural law governs events
Gnosis: knowledge gained directly from a
god or guiding spirit
Technology and
Magic
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What is technology?
How to pound a nail
 How to make a samurai sword
 What is magic?
 “Laws” of magic
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 How
to make rain
 How to make a voodoo doll
Magical thinking
 A critique of pure magic
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Science
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Ideal science
Honesty
“No entry without mathematics”
Ex: Law of
Pythagoras:
c  a b
2
2
2
Math (continued)
1 
c   b  a   4   ab 
2 
 b2  2ab  a2  2ab
 b2  a2
2
2
La Geste de Pythagoras
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Proof of Pythagorean theorem (?)
Discovered relation between musical intervals
and rational numbers (for strings!)
Proved the irrationality of  —invented the
“proof by contradiction”.
Had some (religious) ideas about the
“perfection” of the circle and sphere that
influenced natural philosophy through the 17th
Century AD.
Geometry 
Geography
How big is the Earth? Eratosthenes’ method
 to Sun
If the Earth is
spherical, then
we can use
geometry to
measure its
size.
How high the
Moon?
(Aristarchos of Samos)
s
D
 
s  d
Rr R

d

D
r
r
 1   
Ds


r
  2.5
D  8000 miles
  36 min  0.01 rad
8000
r
 229,000 mi
0.01  1+ 2.5
How far the Sun?
(also Aristarchos)!)
Earth-Moon and EarthSun distances depend on
the assumed geometrical
relationships!
The angle  is very small—way too small for
the Greeks to measure. The best they could
do was to set a lower bound on the EarthSun distance,  15 million miles.
Does the Sun go around
the Earth, or vice versa?
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If the Sun is > 15,000,000 miles away,
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and if the Earth goes around it in a year,
then we are traveling > 11,000 mi/hr.
Riding in a chariot at only 15 mi/hr is very hard to
take, therefore we should all be dead from the
effects of this terrible speed! (Reductio ad
absurdum)
Therefore the Greeks (mostly Archimedes)
concluded the Earth is the center, and everything
goes around it.
Ptolemy vs.
Copernicus
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Ptolemy modeled the universe
and Solar System with complex
motions called cycles and
epicycles, to explain retrograde
motion.
Copernicus reinstated the earlier
picture (due to Aristarchos) of the
Sun at the center.
Both described the motions of the
heavenly bodies “adequately”.
How would you prove either
model?
Which is preferable, and why?
Would you submit to torture and
excommunication to defend your
preference?
Ptolemaic
Kepler (15711630)
Associated with Tycho Brahe at Prague
Galileo (15641642)
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Showed Aristotle was
wrong about motion.
Explained (more-orless) the difference
between acceleration
and uniform linear
motion (we cannot
perceive the latter).
This explained how
we could be moving
swiftly in orbit without
dying.
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Invented the
telescope.
Discovered the
Lunar mountains.
Discovered the
moons of Jupiter.
Discovered that
Venus has phases
like the Moon.
Distance to
the Sun (II)
Transit of
Venus
http://www.venus-transit.de/
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Universal
Gravitation
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Kepler’s 3 “Laws”
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Equal areas swept in equal times:
Period-radius relation: T 2  R3
Orbits are ellipses, not circles
Newton (1642–1727) showed that
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Equal area law  force is central
Period-radius relation  F  1 R2
Same force law predicts elliptical
(bound) orbits.
What is so universal aboutF  G m A mB
Universal Gravitation?
R 2A B
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Relates lunar orbit to fall of
objects at Earth’s surface
Cavendish experiment
Same law applies
to binary stars,
globular star
clusters and to
galaxies and
galactic clusters
Atoms and quanta
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Demokritos of Abdera proposed atomic
theory of matter about 500 BCE, but there
was no way to test it until development of
modern chemistry.
Boyle’s Law (pV = RT) explained by atomic
theory in 1738 (Daniel Bernouilli).
Avogadro (early 19th C) showed that gases
at STP
in3 integral
ratios
3H 2 combine
 1N 2  2NH
Suggests
thatof
discrete
 objects are being revolumes.
Thus
2H  1O  2H O
2
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2
2

shuffled.
But nobody had ever seen an atom!
The nature of
light
Above the red, and below the violet are colors
invisible to the naked eye. They were first
“seen” by letting them fall on the blackened
bulb of a thermometer.
The wavelength of monochromatic light was
first measured using diffraction gratings.
Blackbody radiation
In 1900 Max Planck
proposed an empirical
formula that fit all the
data on “black body”
radiation. He then
proposed a “derivation”
(that he himself didn’t
believe) in which EM
radiation came in
discrete Echunks:
 hf  hc 
But Planck never dared to
say that the EM radiation
was made of particles.
Photoelectric effect (Hertz,
1887)
E  hf  hc   eV  
This was explained by Einstein in 1905 (it’s what he
got the Nobel Prize for). He suggested light was
made of particles (that he called “photons”)—that is,
he took Planck’s quantum hypothesis seriously.
Demo of Photoelectric
effect
X-rays (Roentgen,
1895)
Bremmstrahlung
Discoveries required:
1) Electrical discharges
2) Photography
Duane-Hunt
Sharp
lines
What do the photoelectric effect
and
X-rays have to do with quantum
mechanics?
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The photoelectric effect is the result
of one “photon” knocking one
electron loose from a metal surface.
X-rays (short-wavelength photons)
are produced when energetic
electrons are stopped in matter.
(Inverse photo-electric effect.)
The Compton effect proves that
photons act like particles with
energy and momentum. When they
scatter from electrons in matter they
lose energy in a particular way,
related to the angle of scattering.
For radio waves and even visible
light the effect is too small to notice.
For X-rays it can be detected easily.
Particles are waves
(??)
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We saw that electrons
exhibit wavelike properties.
Thus only certain atomic
orbits (with definite
energies) are possible.
This means atoms and
molecules—especially
DNA—are very stable.
Schrödinger suggested
this is the basis of life!
Modern
genetics
Oswald T. Avery shows DNA is the chemical basis of
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heredity (1944).
Erwin Schrödinger writes What is Life?.
Salvador Luria and Max Delbrück create the “Phage
Group” (1940-1950), hoping to discover the “hydrogen
atom” of biology in the form of bacterial viruses.
Erwin Chargaff discovers that A=T and C=G in DNA
samples.
James Watson and Francis Crick propose a new and
revolutionary molecular structure for DNA that
explains Chargaff’s rules, explains DNA’s ability to
replicate itself exactly, and agrees with all available
data.
Reading: J.D. Watson, The Double Helix
The Universe and Dr.
Einstein
Einstein began with the wish to reformulate all the laws of
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physics in a way that was independent of the coordinates
used to describe space and time. The result was a new
theoretical picture of gravitation, and an explanation of
Galileo’s experiments.
E’s theory differed from that of Newton, and made 3 specific
predictions:
 Light rays bend in gravitational fields, twice as much as
Newtonian gravity predicts.
 Light shifts in color from blue to red as it rises out of a
gravitational field (and vice versa, as it falls). This has
been tested by the Pound-Rebka experiment.
 The planetary orbits are no longer simple ellipses that
remain fixed in space, as Newton predicted, but the
ellipses slowly rotate, or precess.
More about Einstein
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Three more recent tests of General
Relativity:
Time delay of radar bounce from Venus.
 Gravitational lensing.
 “Frame dragging” (precession of a
gyroscope).
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New cosmological results:
Age of the Universe
 Acceleration and “dark energy”
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Probability: Bayes’s
theorem
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Whenever we compare a theory to experiments we use
p  A | E  p  A  p  E| A 
Bayes’s theorem:

p  B| E 
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p  B  p  E| B 
It is less well known that B’s theorem can be used to
assess whether one or another competing theory is
more probable, given a certain measurement or
observation.
I illustrate with a problem: Suppose we have drawers A,
B and C containing two gold, one gold and one silver,
and two silver coins, respectively. If we pick a drawer at
random, reach inside and take a coin (without looking at
the coin remaining inside), what is the probability that, if
the coin we picked is gold, the coin remaining in that
drawer is also gold? (That is, if we had a second chance
Solution:
E  prob of gold on 1st try
p C | E   0
p A | E  p B| E  p C | E  p A | E  p B| E   1
p A | E 
p B| E 

p  A  p  E| A 
p  B  p  E| B 

1
1
3
3
1
1
2
2
p A | E  2 p B| E , p A | E  p B| E  3 p B| E  1
 p B| E  1 3 , p A | E  2 3
Probability and Ockham’s
Razor
Fudged Newton
Einstein theory
Probabilit y
Observed: 41.6 2 sec/cent ury
-20
0
20

40
60
What is science about?
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Math is used to make precise statements. If it isn’t
precise enough we can’t tell the difference between
different ideas. So it is the essential language of
science.
As the precision of measurements increases, so
does our ability to learn new things. Ex: Tycho
Brahe’s observations and Kepler’s discovery that the
orbits are elliptical, with the Sun at a focus.
Science builds on previous discoveries. This is why
we teach our courses in a prescribed order.
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The English Department would think nothing of
teaching Keats before Shakespeare, or Chaucer
before Beowulf.
Physics, however, must teach mechanics and
Newton’s Laws before electricity and magnetism.
Similar strictures hold in Astronomy, Chemistry and
Summary (p. 2)
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Science extrapolates beyond the range of our
senses. This is why logical positivism (“We can’t
believe in atoms until we can see an atom”) runs into
trouble.
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Telescopes and photography let us see stars and
galaxies too faint for the naked eye.
Microscopes let us see things too small for the eye to
resolve. This is why we extrapolate to molecules,
atoms and electrons which are smaller still.
Diffraction of wave-like entities (sound, radio, light,
etc.) from macroscopic structures lets us reconstruct
the geometry of these structures.
We are thus confident in extrapolating the diffraction of
Summary
(p. 3)
X-rays, electrons and neutrons to learn the geometrical
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arrangement of atoms in crystals and complex
molecules (such as hæmoglobin or DNA).
Similarly, we think we know what we are doing when we
extrapolate these ideas to distances the size of the
atomic nucleus and even smaller (the proton and
neutron), and thereby make confident statements about
their geometries.
Science is not merely a social compact, i.e. an
agreement about what to believe this week. There is
an underlying objective reality to it, that forces itself
on us no matter what we want to believe. Ex:
Rutherford’s discovery of the structure of the atom.
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He—and everyone else—believed in the Thomson
“plum-pudding” model, for what seemed to be
irrefutable reasons.
But when he checked by scattering energetic particles from gold foils he found something very
different. In other words, data changes our ideas, not
Summary (p. 4)
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Scientists choose one theory over another based
on probabilities:
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Ockham’s Razor was based on an intuition that the
simpler theory was somehow more probable.
Today we know how to make that a quantitative
statement, and can determine just how much more
(or less) probable a given experimental result or new
observation makes a given theory, relative to others.
Scientists are always aware of their own frailties.
This is why good experiments have controls and—
if there is any psychological component—are
designed to be “double-blind”.
Scientists who forget these things—perhaps for
political reasons—are no longer scientists. Ex:
Lysenko.