Why do scientists believe that?

An inquiry into scientific method

Preliminaries My name is Julian Noble, Professor Emeritus

of Physics, UVa Next meeting dates:

19 September 26 September 03 October

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

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 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

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 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 know?

The aims of science—reductionism Is science “special”?

The prestige of the label scientific. Is there a “scientific method”?

Bacon, et al. Modern scientists’ ideas.

A capsule history of science Why is science difficult?

What about science?

Reading: R.P. Feynman, Cargo Cult Science

Causality and Gnosis Cause and effect

Volition leads to animism Invisible and intangible causes

Leads to superstition and religion Signs, omens and portents become important

Greek idea: Natural law governs events Gnosis: knowledge gained directly from a

god or guiding spirit

Technology and Magic What is technology?

How to pound a nail How to make a samurai sword What is magic? “Laws” of magic

How to make rain How to make a voodoo doll

Magical thinking A critique of pure magic

Science Ideal science Honesty “No entry without mathematics”

22 2c ba

Ex: Law of Pythagoras:

Math (continued)

22

2 2

2 2

14

2

2 2

c b a ab

b ab a ab

b a

La Geste de Pythagoras

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

If the Earth is spherical, then we can use geometry to measure its size.

to Sun

How high the Moon?

s DR r R

dr

D sr

1

s d

Dr

2.5

8000miles

36min 0.01rad

8000229,000mi

0.01 1+2.5

D

r

(Aristarchos of Samos)

How far the Sun?

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 Earth-Sun distance, 15 million miles.

(also Aristarchos)!)

Earth-Moon and Earth-Sun distances depend on the assumed geometrical relationships!

Does the Sun go around the Earth, or vice versa? If the Sun is > 15,000,000 miles away,

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

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 (1571-1630)

Associated with Tycho Brahe at Prague

Galileo (1564-1642) Showed Aristotle was

wrong about motion. Explained (more-or-

less) 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.

Invented the telescope.

Discovered the Lunar mountains.

Discovered the moons of Jupiter.

Discovered that Venus has phases like the Moon.

29Why do scientists believe that?04/19/23

Distance to the Sun (II) Transit of Venus http://www.venus-transit.de/

30Why do scientists believe that?04/19/23

Universal Gravitation Kepler’s 3 “Laws”

Equal areas swept in equal times: Period-radius relation: Orbits are ellipses, not circles

Newton (1642–1727) showed that Equal area law force is central Period-radius relation Same force law predicts elliptical

(bound) orbits.

2 3T R

21F R

32Why do scientists believe that?04/19/23

What is so universal about Universal Gravitation?

Relates lunar orbit to fall of objects at Earth’s surface

Cavendish experiment

2A B

AB

m mF G

R

Same law applies to binary stars, globular star clusters and to galaxies and galactic clusters

37Why do scientists believe that?04/19/23

Atoms and quanta

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 combine in integral ratios of volumes. Thus

But nobody had ever seen an atom!

2 2 3

2 2 2

3H 1N 2NH

2H 1O 2H O

Suggests that discrete objects are being re-shuffled.

38Why do scientists believe that?04/19/23

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.

40Why do scientists believe that?04/19/23

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 chunks:

E hf hc

But Planck never dared to say that the EM radiation was made of particles.

41Why do scientists believe that?04/19/23

Photoelectric effect (Hertz, 1887)

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.

E hf hc eV

Demo of Photoelectric effect

43Why do scientists believe that?04/19/23

X-rays (Roentgen, 1895)

Discoveries required:

1) Electrical discharges

2) Photography

Duane-Hunt limit

Sharp lines

Bremmstrahlung

45Why do scientists believe that?04/19/23

What do the photoelectric effect andX-rays have to do with quantum mechanics?

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.

46Why do scientists believe that?04/19/23

Particles are waves (??) 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

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 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 Three more recent tests of General

Relativity: Time delay of radar bounce from Venus. Gravitational lensing. “Frame dragging” (precession of a

gyroscope). New cosmological results:

Age of the Universe Acceleration and “dark energy”

60Why do scientists believe that?04/19/23

Probability: Bayes’s theorem Whenever we compare a theory to experiments we use

Bayes’s theorem:

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 to pick, should we choose that drawer?)

| |

| |

p A E p A p E A

p B E p B p E B

Solution:

1E probof goldon sttry

| 0p C E

| | | | | 1p A E p B E p C E p A E p B E

13

1 13 2

| | 12

| |

p A E p A p E A

p B E p B p E B

| 2 | || , 3 | 1p A E p Bp A EE p B E p B E

1 23 3| , |p B E p A E

Probability and Ockham’s Razor

-20 0 20 40 60

Prob

ability

Fudged NewtonEinstein theory

Observed: 41.6 2 sec/century

What is science about? 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. 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 Biology

Summary (p. 2) 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. 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.

Summary (p. 3) We are thus confident in extrapolating the diffraction of X-rays, electrons and neutrons to learn the geometrical 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. 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 vice versa.

Summary (p. 4) Scientists choose one theory over another based

on probabilities: 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.