SPU-22: The Unity of Science from the Big Bang to the Brontosaurus and Beyond

1. SPU-22: The Unity of Science from the Big Bang to the Brontosaurus and Beyond Lecture 9 26 February 2014 Science Center Lecture Hall A

2. Banishing A Blemish Need to EMPHASIZE that dark matter and dark energy, individually and collectively, set severe challenges for astronomers and physicists. Resolution could have truly profound effect on our understanding of Nature

3. Today’s Talkathon(Outline Of Lecture 9) Terra Firma: - Origin (“Hand-waving” scenario) - Shape - Size - Age (Detective story extraordinaire) - Innards (next week or so)

4. Earth From Nothing: Current Scenario Big bang – fluctuations – matter – stars & galaxies – second generation stars – discs – collisions − growth − planet − differentiation (melting) − water: VoilàEarth Assessment of story: Lot of progress;no where near complete and reliable model

5. Basic Questions About Earth Of perhaps infinite number could ask (if had infinite time), restrict to four for the nonce; given our historical approach, ask about earth: What shape? How big? How old? What innards?

6. Shape Of Earth Determined in “antiquity” from: - shape of shadow of earth on moon during eclipse - ships disappear over horizon from top down Yet “Flat Earth Society,” as noted, is alive and well (last admittedly question of definition)

7. How Big Is Earth? First known attempt at measurement of earth’s circumference: Eratosthenes in 3rd century BCE in Egypt How done? Measure arc of known length and relevant angle: see next slide Fortuitous happening: Existence of well supposedly due south of Alexandria, in which sun shown directly overhead at noon on 21 June each year (sunlight then went all way to well bottom). Measurement of angle from directly overhead to direction of sun at noon on same day in Alexandria yields desired angle (see above and slide)

8. Circumference Of Earth: Principle Of Measurement(Drawing NOT To Scale)

9. Solving Equation Thus, equation yields for earth’s circumference, C: C = D x 360/θ(deg)

10. How Long The Arc? Three questions arise: • How were measurements made? • What units were used? 3. What was relation between those units and modern ones, needed to allow us, e.g., to assess accuracy achieved?

11. Arclength “Measured” Three answers: 1. No one knows how D measured; speculation runs from speed of camels and temporal extent of trip from Syene to Alexandria, through collation of land surveys over this route, to “educated” guess • Units used were stade. One stadion was apparently perimeter of olympic stadium - long gone - used in original olympics 3. Enormous scholarly energy has yielded: 1 stade= 175 ± 20 m (my estimate of value and error, based on assessment of published papers on conversion of stade to meters)

12. Eratosthenes’ Result Re-interpreted C = [Measured arclength][360/Measured angle (deg)] = [5,000± 1,000][360/7.2] = 250,000 ± 50,000 stade = 44,000 ± ≈ 9,000 km = 40,000 km (modern value; approx.) Percent error: ≈ 10%, within estimated error of ≈ 20% Remarkably accurate result for that era with that technology (given that our interpretation of conversion is reliable!)

13. More Modern Results For Earth Size Jean Picard measured in 1669 -70 one degree of latitude with improved instrumentation and techniques of triangulation. Result: 6,329 km, yielding Earth’s polar circumference: ≈ 40,000 km. According to one legend, this new result, ~10% smaller than previously accepted value, demonstrated harmony between acceleration of gravity at surface of earth and acceleration of moon in its orbit, thus prompting Newton, when he learned of new result, to proceed with publication of his theory of gravity in Principia (1687).

14. Space-Age Results For Size Of Earth Earth’s surface very uneven as casual inspection discloses Overall shape differs substantially from spherical: equatorial radius about 20 km larger than polar radius. Why? (See demonstration.) Detailed surface shape measured with centimeter accuracy from satellites, using radar-type techniques; shape changes rapidly on this and much larger scales due to both natural and human causes. Nonetheless, measurements made with this incredible accuracy, worldwide. Surface resolution far less accurate, at nearlymeter level

15. Introduction To Solving Mystery Of Age Of Earth There are few problems more fascinating than those that are bound up with the bold question: How old is the Earth? With insatiable curiosity men (sic!) have been trying for thousands of years to penetrate the carefully guarded secret. Arthur Holmes, 1927 (after solution in hand)

16. Age Of Earth: Before 20th Century No one had a clue - was truly vexing problem: obvious “handles” were missing Ancient Greeks, to my knowledge, left no evidence on this point, other than belief that world always was (Aristotle supposedly held this view) Biblical story of Genesis provides a religious answer

17. Estimates Of Age Of Earth Bishop of Ussher (c. 1650 & 1654) analyzed Bible’s “begats” and other data, and concluded that Earth was created in the evening on 23 October 4004 BCE (Julian calendar). That specific origin, though, apparently traces back to St. Basil the Great, c.370. Creation date still believed by many Scientific approach by Benoit de Maillet to use changes in sea level to estimate earth’s age (see next slide) Edmund Halley, of comet fame, described clever method to estimate earth’s age based on salinity of oceans (see next slide plus one) Experimental attempts began in earnest in 18th century with Comte de Buffon; earlier comments made by Newton and Leibniz (see next slide plus two and plus three)

18. Sea-Level Changes Imply Age of Earth? Benoit de Maillet (1656-1738); scientific approach to age of earth through sea-level changes; first to oppose clerical argument for young earth Resultant estimates up to 2 billion years Great fear of church reaction. Wrote results as conversation with Telliamed Work not published until 10 years after death

19. Salt Of Earth:How Salty Are Oceans? Edmund Halley (of comet fame; early 18th century): Wondered how long for oceans, starting with fresh water, to reach present salinity. How to approach? Consider all rivers that flow into sea and measure how much salt they carry. What are obvious flaws in this clever approach to age of earth? This approach, through chemistry and in particular sodium, taken up in earnest by John Joly in late 19th century Result: 89 million years

20. Cooling Of Spheres Newton and Leibniz, apparently independently, reasoned that could estimate age of earth from time to cool, t. Newton apparently was aware that: t ~ volume/surface area ~ R3/R2 ~ R, i.e., cooling time proportional to radius of object

21. Cooling Of Spheres (concluded) Compte de Buffon (1707-1788) measured cooling times of 10 white-hot iron (and other, supposedly earth-like, materials) spheres; radii ranged from ≈ 1 to ≈ 15 cm, in equal steps. Spheres set up to cool in basement (why?). Found linear relation between cooling time and sphere radius, and scaled up to imitate earth’s cooling from an assumed initial melting temperature of iron. His result? About 75,000 years, quite at variance with Bishop Ussher’s value. Suspicious was too low; later estimated 3 billion years; discovered century after his death

22. Layering Of Earth’s Surface And Age Of Earth By mid 19th century, determining age of earth became more pressing scientific issue (see next six slides plus one) Geologists had extended examinations of surface features around globe. Uncovered many (complicated) layered regions (see next six slides). Inferred relative ages: Assumed layers arranged by age, with top youngest. Why? (Where did “new” material come from?)

23. Geological Layers in Extremadura, Spain

24. Geological Layering In Cafayate, Argentina

25. Geological Layering in Utah

26. Folded Geological Layers

27. Curved Layering In Eastern Canada

28. “Tight” Folding Of Layering

29. Analysis Of Surface Layers Of Earth Correlations between types and thicknesses of layers from different geographical regions enabled reasonable inferences on common epochs Why should anyone care about “absolute” ages? Why weren’t relative ages sufficient for all purposes? One example (Part 3 of this course): Was Earth old enough for there to have been enough time for natural selection to have operated to yield present cornucopia of biological diversity?

30. Geologists’ Views: Internecine Warfare; No Answer On Earth Age Two main schools of thought: Uniformitarianism (main protagonist: Charles Lyell of James Hutton’s late 18th century theory) and catastrophism (undeclared leader: Georges Cuvier of late 18th- early 19th century) Very different conceptions of geologic history. What was behind each? But how old is earth? Neither of above views of geologic history led to quantitative estimate

31. Darwin’s Estimate of Age Of Earth Charles Darwin worried: Enough time for natural selection to “work”? Age of earth via estimate of erosion time for chalk cliffs in southeast England (see next slide). Guessed at erosion rate Result: 306,662,400 years. In first edition of Origin of Species. Disappeared from later editions. Why?

32. Downs Southeast England

33. Enter Forceful Perspective Of Physics Major battleground: Mid-19th century confrontation between geologists and physicist. William Thomson, known now as Lord Kelvin, took on age problem; approach quantitative physics vs. qualitative geology Kelvin took two fundamental approaches, one based on earth other on sun, discussed in that order

34. Cooling Of Earth (Not Of Proxy) Kelvin assumed earth initially melted Used measurements of temperature as function of depth inside mines, and estimates of how well rocks conduct heat Using formulas describing heat flow and above information to estimate rate of flow, computed time from melted state to present earth temperature

35. The Everlasting Sun? Kelvin asked : How old could sun be? To answer, he needed its output of energy and sources of energy to estimate how long could “match” Present luminosity of sun: How determined? What result? ≈4x1033erg/sec What sources of energy “feed” this luminosity? Energy from: - objects that impact sun - exothermic chemical reactions in sun - shrinkage of sun

36. Sun: Burning Brightly For How Long? Magnitude and time variability of various sources of solar energy not well known Lord Kelvin’s calculations, based on “reasonable” estimates of uncertainty, yielded results (see next slide) for age of sun, with dim prospects for long-term future

37. What Were Kelvin’s Results? Unknowns were large resulting in Kelvin’s estimates being different at different times From cooling of earth: About 20 to 100 million years From supplying of energy to sun: Under 100 million years

38. Reaction Of Geologists To Kelvin’s Estimates Geologists little background in physics; didn’t know what to do with results that tumbled from equations Nonetheless, contemporary geologists profoundly skeptical of Kelvin’s results: seemed far too low, despite geologists’ limits falling well short of defensible quantitative realm. Also stinging critiques of Kelvin’s assumptions