Why do scientists believe that? : Why do scientists believe that? An inquiry into scientific method
Preliminaries : 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 : 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 : 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 : 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?
What about science? : 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
Summa : Summa
Einstein at work : Einstein at work
Causality and Gnosis : 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 : 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
samurai sword : samurai sword
voodoo doll : voodoo doll
Science : Science Ideal science
Honesty
“No entry without mathematics” Ex: Law of Pythagoras:
Math (continued) : Math (continued)
La Geste de Pythagoras : 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.
“Proof” of Pythagoras’s Theorem : “Proof” of Pythagoras’s Theorem Copyright Notice: The animation on this page is a copyrighted work of Davis Associates, Inc. Permission is granted to copy and display the animation provided that the following copyright notice is displayed in a clearly legible font in close and obvious proximity to the display of the subject animation:
Copyright © 1998 by Davis Associates, Inc.
All Rights Reserved
Geometry Geography : 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? : How high the Moon? (Aristarchos of Samos)
How far the Sun? : 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? : 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 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
Solar System : Solar System Ptolemy Copernicus
retrograde motion : retrograde motion
Kepler (1571-1630) : Kepler (1571-1630) Associated with Tycho Brahe at Prague
Galileo (1564-1642) : 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.
Lunar mountains : Lunar mountains
Moons of Jupiter : Moons of Jupiter Io Europa Ganymede Callisto
Phases of Venus : Phases of Venus
Distance to the Sun (II) Transit of Venus : Distance to the Sun (II) Transit of Venus http://www.venus-transit.de/
Universal Gravitation : 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.
Equal area law : Equal area law
What is so universal about Universal Gravitation? : What is so universal about Universal Gravitation? 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
Lunar orbit : Lunar orbit
Binary star orbits : Binary star orbits
Globular Cluster M-10 : Globular Cluster M-10
Galaxies and galactic clusters : Galaxies and galactic clusters
Atoms and quanta : 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! Suggests that discrete objects are being re-shuffled.
The nature of light : 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.
Diffraction grating : Diffraction grating
Blackbody radiation : 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: But Planck never dared to say that the EM radiation was made of particles.
Photoelectric effect (Hertz, 1887) : 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.
Demo of Photoelectric effect : Demo of Photoelectric effect
X-rays (Roentgen, 1895) : X-rays (Roentgen, 1895) Discoveries required:
Electrical discharges
Photography Duane-Hunt limit Sharp lines Bremmstrahlung
Duane-Hunt Limit : Duane-Hunt Limit (Inverse photoelectric effect)
What do the photoelectric effect and X-rays have to do with quantum mechanics? : What do the photoelectric effect and X-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.
Particles are waves (??) : 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 : 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
DNA1 : DNA1
DNA2 : DNA2
DNA3 : DNA3
The Universe and Dr. Einstein : 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.
Deflection of light by the Sun : Deflection of light by the Sun
Red shift : Red shift As light rises out of a gravitational field its wavelength gets longer and its color shifts toward the red end of the spectrum. This is equivalent to saying that clocks go slower at the surface of a planet or star than they do far away from the object.
Perihelion precession : Perihelion precession
More about Einstein : 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”
Radar bounce : Radar bounce
Gravitational lensing : Gravitational lensing
Frame dragging : Frame dragging
Cosmology : Cosmology
Probability: Bayes’s theorem : 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?)
Solution: : Solution:
Probability and Ockham’s Razor : Probability and Ockham’s Razor
What is science about? : 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
Tycho Brahe (1546–1601) and his technology : Tycho Brahe (1546–1601) and his technology
Summary (p. 2) : 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) : 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 a-particles from gold foils he found something very different. In other words, data changes our ideas, not vice versa.
Plum-pudding model : Plum-pudding model
Geiger-Marsden data : Geiger-Marsden data Plum-pudding model
Summary (p. 4) : 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.