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Cosmology Slides
Inhomogeneous cosmologies George Ellis, University of Cape Town 27th Texas Symposium on Relativistic Astrophyiscs Dallas, Texas Thursday 12th December 9h00-9h45 • The universe is inhomogeneous on all scales except the largest • This conclusion has often been resisted by theorists who have said it could not be so (e.g. walls and large scale motions) • Most of the universe is almost empty space, punctuated by very small very high density objects (e.g. solar system) • Very non-linear: / = 1030 in this room. Models in cosmology • Static: Einstein (1917), de Sitter (1917) • Spatially homogeneous and isotropic, evolving: - Friedmann (1922), Lemaitre (1927), Robertson-Walker, Tolman, Guth • Spatially homogeneous anisotropic (Bianchi/ Kantowski-Sachs) models: - Gödel, Schücking, Thorne, Misner, Collins and Hawking,Wainwright, … • Perturbed FLRW: Lifschitz, Hawking, Sachs and Wolfe, Peebles, Bardeen, Ellis and Bruni: structure formation (linear), CMB anisotropies, lensing Spherically symmetric inhomogeneous: • LTB: Lemaître, Tolman, Bondi, Silk, Krasinski, Celerier , Bolejko,…, • Szekeres (no symmetries): Sussman, Hellaby, Ishak, … • Swiss cheese: Einstein and Strauss, Schücking, Kantowski, Dyer,… • Lindquist and Wheeler: Perreira, Clifton, … • Black holes: Schwarzschild, Kerr The key observational point is that we can only observe on the past light cone (Hoyle, Schücking, Sachs) See the diagrams of our past light cone by Mark Whittle (Virginia) 5 Expand the spatial distances to see the causal structure: light cones at ±45o. Observable Geo Data Start of universe Particle Horizon (Rindler) Spacelike singularity (Penrose). 6 The cosmological principle The CP is the foundational assumption that the Universe obeys a cosmological law: It is necessarily spatially homogeneous and isotropic (Milne 1935, Bondi 1960) Thus a priori: geometry is Robertson-Walker Weaker form: the Copernican Principle: We do not live in a special place (Weinberg 1973). -
The Big Bang
The Big Bang • Review of Hubble expansion • Assumptions in cosmology • The Big Bang • Cosmic microwave background Hubble expansion v = H0d What would be the recession speed of a galaxy at a distance of 7 Mpc? A) 0.1 km/s B) 10 km/s C) 250 km/s D) 500 km/s E) 1000 km/s Speed = H0 distance H0 = 71 km/s/Mpc Receding galaxy 8 Speed = 500 km/s = 0.5 Mpc/Gyr 6 4 2 Distance (Mpc) 0 -2 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 Time (Gyr) When was this galaxy in the same place as the Milky Way? time = distance / velocity = 7 Mpc/(0.5 Mpc/Gyr) = 14 Gyr ago If the Hubble constant were doubled, what would be the recession speed of a galaxy at a distance of 7 Mpc? A) 0.1 km/s B) 10 km/s C) 250 km/s D) 500 km/s E) 1000 km/s Speed = H distance H = 271 km/s/Mpc 0 0 Receding galaxy 8 Speed = 1000 km/s = 1.0 Mpc/Gyr 6 4 2 0 Distance (Mpc) -2 -4 -12 -10 -8 -6 -4 -2 0 Time (Gyr) When was this galaxy in the same place as the Milky Way? time = distance / velocity = 7 Mpc/(1.0 Mpc/Gyr) = 7 Gyr ago If Hubble's constant were twice as large as we now think it is, our estimate of the age of the universe would A) be unchanged B) increase by a factor of 2 C) increase by a factor of 4 D) decrease by a factor of 2 E) decrease by a factor of 4 Quasars are receding from us at high velocities because A) matter in black hole jets moves at close to the speed of light B) matter moves rapidly when close to a black hole C) quasars are at large distances D) we smell bad The variety of different active galaxies can be explained as due to A) different orientations of the accretion disk B) different forms of matter being accreted C) different shapes of black holes D) different velocities of black holes Assumptions in Cosmology Copernican principle: – We do not occupy a special place. -
A Democratic Cosmos? Arxiv:1910.00481V1 [Physics.Hist-Ph] 1 Oct 2019
A democratic Cosmos? Guilherme Franzmann1 and Yigit Yargic2 1Department of Physics, McGill University, Montréal, QC, H3A 2T8, Canada 2Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo ON, N2L 2Y5, Canada Abstract Despite the success of our best models in Theoretical Physics, especially concerning Cosmology and Particle Physics, we still face persistent challenges. Among them we have the cosmological singularity problem, understanding the late-time acceleration of the Universe, and comprehending the fundamental na- ture of time. We believe relevant new insights to tackle each of these issues may be found in the Philosophy of Cosmology. We elaborate on three philosophical principles that shall guide us on how to improve our current theories. They are the Copernican Principle for Scales, the Cosmological Heterarchical Principle and the Cosmological Principle of Irreversibility. Following these principles, and using some of our current physical theories as a proxy to implement them, we consider a new assessment of each of these challenges, and show how they may be either explained away, hinting towards new physics, or summarized in a new philosophical principle. Essay written for the 2019 Essay Prize in Philosophy of Cosmology1. arXiv:1910.00481v1 [physics.hist-ph] 1 Oct 2019 1http://www.rotman.uwo.ca/2019-essay-prize-in-philosophy-of-cosmology/ 1 Contents 1 The Cosmic Pnyka 3 2 The Copernican Principle for Scales 5 3 The Cosmological Heterarchical Principle 8 4 The landscape of scales 10 5 The Very Early Universe 12 5.1 T-duality . 12 6 Λ-theory: GR’s unknown heir in the deep IR 15 6.1 Inspirations from MOND . -
Living in a Void: Testing the Copernican Principle with Distant Supernovae
Living in a Void: Testing the Copernican Principle with Distant Supernovae Timothy Clifton,∗ Pedro G. Ferreira, and Kate Land Oxford Astrophysics, Physics, DWB, Keble Road, Oxford, OX1 3RH, UK A fundamental presupposition of modern cosmology is the Copernican Principle; that we are not in a central, or otherwise special region of the Universe. Studies of Type Ia supernovae, together with the Copernican Principle, have led to the inference that the Universe is accelerating in its expansion. The usual explanation for this is that there must exist a ‘Dark Energy’, to drive the acceleration. Alternatively, it could be the case that the Copernican Principle is invalid, and that the data has been interpreted within an inappropriate theoretical frame-work. If we were to live in a special place in the Universe, near the centre of a void where the local matter density is low, then the supernovae observations could be accounted for without the addition of dark energy. We show that the local redshift dependence of the luminosity distance can be used as a clear discriminant between these two paradigms. Future surveys of Type Ia supernovae that focus on a redshift range of ∼ 0.1 − 0.4 will be ideally suited to test this hypothesis, and hence to observationally determine the validity of the Copernican Principle on new scales, as well as probing the degree to which dark energy must be considered a necessary ingredient in the Universe. The concordance model of the Universe combines two An alternative to admitting the existence of dark en- fundamental assumptions. The first is that space-time ergy is to review the postulates that necessitate its intro- is dynamical, obeying Einstein’s Equations. -
Nicolaus Copernicus: the Loss of Centrality
I Nicolaus Copernicus: The Loss of Centrality The mathematician who studies the motions of the stars is surely like a blind man who, with only a staff to guide him, must make a great, endless, hazardous journey that winds through innumerable desolate places. [Rheticus, Narratio Prima (1540), 163] 1 Ptolemy and Copernicus The German playwright Bertold Brecht wrote his play Life of Galileo in exile in 1938–9. It was first performed in Zurich in 1943. In Brecht’s play two worldviews collide. There is the geocentric worldview, which holds that the Earth is at the center of a closed universe. Among its many proponents were Aristotle (384–322 BC), Ptolemy (AD 85–165), and Martin Luther (1483–1546). Opposed to geocentrism is the heliocentric worldview. Heliocentrism teaches that the sun occupies the center of an open universe. Among its many proponents were Copernicus (1473–1543), Kepler (1571–1630), Galileo (1564–1642), and Newton (1643–1727). In Act One the Italian mathematician and physicist Galileo Galilei shows his assistant Andrea a model of the Ptolemaic system. In the middle sits the Earth, sur- rounded by eight rings. The rings represent the crystal spheres, which carry the planets and the fixed stars. Galileo scowls at this model. “Yes, walls and spheres and immobility,” he complains. “For two thousand years people have believed that the sun and all the stars of heaven rotate around mankind.” And everybody believed that “they were sitting motionless inside this crystal sphere.” The Earth was motionless, everything else rotated around it. “But now we are breaking out of it,” Galileo assures his assistant. -
The Copernican Revolution: Observational Tests
The Copernican Revolution: Observational Tests The Trigonometric (Geometric) Parallax Aristotle’s missing Stellar Parallax: The Earth has moved! Parallactic ellipse has (angular) semi major axis p = a/d (radians) ... where a is the Earth’s orbital “radius” and d is the distance to the star. For d in parsecs (pc), and p in arc-seconds (“): (pc) = 1/p(“) aEarth = 1 au = 1.50 x 108 km and 1 pc = 206,265 au First Measurement of a Stellar Parallax by Bessel (1838) ... 61 Cygni, also know as “Piazzi’s Flying Star”, with p = 0.287”, d = 3.48 pc (The largest stellar parallax is that of α Centauri with p = 0.75”) There are 206,265 arc-seconds (“) in a radian: 180°= π radians; 1°= 60’= 3,600” One astronomical unit is 23,455 Earth radii. The Aberration of Starlight The Earth is moving! The Earth’s orbital speed is v = 30 km s-1 The speed of light is c = 3 x 105 km s-1 Therefore, the maximum aberration angle is v/c = 10-4 radian = 21” (Note that the semi major axes of all annual aberration ellipses are 21”) History Roemer (1675) measures the velocity of light Observations of eclipses of the satellites of Jupiter. (Io, P = 1.76d) (His value for the speed of light was about 75% of the true value.) Note: Light travels 1 astronomical unit in about 500 seconds. Picard (1680) observes “puzzling parallax” of Polaris (~20”) d (parsecs) = 1/p(“) .... but the motion was in the wrong direction for parallactic motion! ... and was seen with the same amplitude in all directions on the sky! Bradley (1728) explains the phemomenon (and provides observations of γ Draconis) Note that this was over a century before Bessel successfully measured the trigonometric parallax of 61 Cygni in 1838. -
Lecture 2: Our Place in Space Copernican Principle Multiwavelength Astronomy
Lecture 2: Our Place in Space •It is now clear that Earth is not central or special in its general properties (mass, distance from central star, etc.) •The Sun is an average star •The Milky Way is a typical spiral galaxy •This leads to the “principle of mediocrity” or “Copernican principle” Copernican Principle •The “principle of mediocrity” or “Copernican principle” states that physical laws are the same throughout the Universe •This principle can be tested using the scientific method! •So far, it seems to agree with observations perfectly •One of the key ideas is that we can use light from distant objects to understand conditions there, using the work of Isaac Newton Multiwavelength Astronomy •The color and energy of light are related to the Wavelength… •Different wavelengths of radiation tell us about objects with different temperatures… 1 Multiwavelength Astronomy Multiwavelength Astronomy •Using Newton’s techniques, combined with our knowledge of atomic structure, we can use light to study distant objects… X-ray optical composition of matter temperature of matter Scientific Method and Observation •Transformed the search for meaning into a quest for objective truth •We can deduce the properties of distant objects using observations •The scientific method originated in the renaissance, and is still used today: hypo thesi n s io tti iic d e r y p y p r r o o e o truth e truth h b h t s t e rr v a tt ii o n test 2 Copernican Principle •The validity of the “Copernican principle” is great news for science, because it means that we can -
The Copernican Revolution Setting Both the Earth and Society in Motion
4/21/2014 The Copernican Revolution Setting both the Earth and Society in Motion David Linton EIU Physics Department November 5, 2013 Drawing an ellipse The Modern Picture of the Solar System . A planet moves in an ellipse with the Sun at one focus. A planet moves fastest when closest to the Sun, slowest when furthest. A planet would travel in a straight line were there not a force to hold it to the Sun – this force is supplied by “Gravity” – an attraction Focus Focus between masses, and weakens with increasing distance. A planet’s axis is “fixed’ in space. (Orbital Period)2 = (Semimajor Axis)3 (This derives from the Law of Gravitation and Newton’s 3 Laws of Motion) 1 4/21/2014 Drawing an ellipse Drawing an ellipse Focus Focus Sun For a planetary orbit, one focus is unoccupied. For a planetary orbit, one focus is unoccupied. 2 4/21/2014 Some Other Things We Now Know . Every planet beyond Earth has more than one moon. Both planets closer to the Sun than Earth have no moons. Comets orbit the Sun also. They are dirty icebergs (or icy dirtballs) orbiting along extremely stretched-out (meaning, highly eccentric) ellipses. Many of the comets we see as they pass near the Sun take many thousands of years to orbit one time. Retrograde Motion – the Heliocentric View Astronomy at Copernicus Birth (1473) . Ancient Greek Philosophers held that Earth was the center of Creation, that everything in the sky must wheel in circles about us. Circles were considered the perfect geometric form, and the Greeks had felt the Heavens to be perfect. -
The Scientific Revolution
13/01/2017 the Scientific Revolution: the Cosmos Mechanized • 1543 Nicolaus Copernicus ‐ publishes heliocentric universe in De Revolutionibus Orbium Coelestium ‐ implicit introduction Copernican principle: Earth/Sun is not special • 1609‐1632 Galileo Galilei ‐ by means of (telescopic) observations, proves the validity of the heliocentric Universe. • 1609/1619 Johannes Kepler ‐ the 3 Kepler laws, describing the elliptical orbits of the planets around the Sun • 1687 Isaac Newton ‐ discovers Gravitational Force as agent behind cosmic motions ‐ publishes his Principia (Philosophiae Naturalis Principia Mathematica), which establishes the natural laws of motion and gravity (the latter only to be replaced by Einstein’s theory of GR) • 1755 Immanuel Kant ‐ asserts that nebulae are really galaxies separate from and outside from the Milky Way, ‐ calling these Island Universes • 1785 William Herschel ‐ proposes theory that our Sun is at or near the center of ou Galaxy (Milky Way) 1 13/01/2017 Birthhouse Copernicus, Nicolaus Copernicus Torun 1473 –born in Torun (Poland) 1491‐1495 ‐ study Univ. Krakow 1496‐1501 ‐ 3 years Univ. Bologna ‐ canon law 1503‐‐Warmia 1514 ‐ Frombork Languages: Latin , German 1514 ‐ Commentariolus Nicolai Copernici de hypothesibus motuum coelestium a se constitutis commentariolus + theoretical treatise on heliocentric mechanism + 40 pages, 7 basic assumptions Tower (living) Copernicus, Frombork Frombork Cathedral 2 13/01/2017 1. There is no one center of all the celestial circles or spheres. 2. The center of the earth is not the center of the universe, but only of gravity and of the lunar sphere. 3. All the spheres revolve about the sun as their midpoint, and therefore the sun is the center of the universe. -
The (Likely) Last Edition of Copernicus's Libri Revolutionum
Variants The Journal of the European Society for Textual Scholarship 14 | 2019 Varia The (likely) Last Edition of Copernicus’s Libri revolutionum André Goddu Electronic version URL: http://journals.openedition.org/variants/908 DOI: 10.4000/variants.908 ISSN: 1879-6095 Publisher European Society for Textual Scholarship Printed version Number of pages: 159-178 ISSN: 1573-3084 Electronic reference André Goddu, « The (likely) Last Edition of Copernicus’s Libri revolutionum », Variants [Online], 14 | 2019, Online since 10 July 2019, connection on 12 July 2019. URL : http://journals.openedition.org/ variants/908 ; DOI : 10.4000/variants.908 The authors The (likely) Last Edition of Copernicus’ Libri revolutionum André Goddu Review essay of Nicolas Copernic, De revolutionibus orbium coelestium, Des revolu- tions des orbes célestes. 3 volumes. Science et Humanisme, Collection published under the patronage of the Association Guillaume Budé (Paris: Les Belles Lettres, 2015). Vol. I: Introduction by Michel-Pierre Lerner and Alain-Philippe Segonds with the collaboration of Concetta Luna, Isabelle Pantin, and Denis Savoie, xxviii + 859 pp. Vol. II: Critical Edition and translation by Lerner, Segonds, and Jean-Pierre Verdet with the collaboration of Concetta Luna, viii + 537 pp. with French and Latin on facing pages and with the same page numbers. Vol. III: Notes, appendices, iconographic dossier, and general index by Lerner, Segonds, and Verdet with the collaboration of Luna, Savoie, and Michel Toulmonde, xviii + 783 pp. and 34 plates. T C’ , probably the last for the foresee- able future, represents the culmination of efforts that can be traced back to 1973. The two fundamental sources of De revolutionibus are Copernicus’s auto- graph copy which survived by sheer luck and the first edition published in Nuremberg in 1543. -
The Reception of the Copernican Revolution Among Provençal Humanists of the Sixteenth and Seventeenth Centuries*
The Reception of the Copernican Revolution Among Provençal Humanists of the Sixteenth and Seventeenth Centuries* Jean-Pierre Luminet Laboratoire d'Astrophysique de Marseille (LAM) CNRS-UMR 7326 & Centre de Physique Théorique de Marseille (CPT) CNRS-UMR 7332 & Observatoire de Paris (LUTH) CNRS-UMR 8102 France E-mail: [email protected] Abstract We discuss the reception of Copernican astronomy by the Provençal humanists of the XVIth- XVIIth centuries, beginning with Michel de Montaigne who was the first to recognize the potential scientific and philosophical revolution represented by heliocentrism. Then we describe how, after Kepler’s Astronomia Nova of 1609 and the first telescopic observations by Galileo, it was in the south of France that the New Astronomy found its main promotors with humanists and « amateurs écairés », Nicolas-Claude Fabri de Peiresc and Pierre Gassendi. The professional astronomer Jean-Dominique Cassini, also from Provence, would later elevate the field to new heights in Paris. Introduction In the first book I set forth the entire distribution of the spheres together with the motions which I attribute to the earth, so that this book contains, as it were, the general structure of the universe. —Nicolaus Copernicus, Preface to Pope Paul III, On the Revolution of the Heavenly Spheres, 1543.1 Written over the course of many years by the Polish Catholic canon Nicolaus Copernicus (1473–1543) and published following his death, De revolutionibus orbium cœlestium (On the Revolutions of the Heavenly Spheres) is regarded by historians as the origin of the modern vision of the universe.2 The radical new ideas presented by Copernicus in De revolutionibus * Extended version of the article "The Provençal Humanists and Copernicus" published in Inference, vol.2 issue 4 (2017), on line at http://inference-review.com/. -
Full Text - Nicholas Copernicus, "De Revolutionibus (On the Revolutions)," 1543 C.E
Full text - Nicholas Copernicus, "De Revolutionibus (On the Revolutions)," 1543 C.E. The text of: Nicholas Copernicus De Revolutionibus (On the Revolutions), 1543 C.E. Nicholas Copemicus (1473-1543) That Nicholas Copernicus delayed until near death to publish De revolutionibus has been taken as a sign that he was well aware of the possible furor his work might incite; certainly his preface to Pope Paul III anticipates many of the objections it raised. But he could hardly have anticipated that he would eventually become one of the most famous people of all time on the basis of a book that comparatively few have actually read (and fewer still understood) in the 450 years since it was first printed. Copernicus was bom into a well-to-do mercantile family in 1473, at Torun, Poland. After the death of his father, he was sponsored by his uncle, Bishop Watzenrode, who sent him first to the University of Krakow, and then to study in Italy at the universities of Bologna, Padua and Ferrara. His concentrations there were law and medicine, but his lectures on the subject at the University of Rome in 1501 already evidenced his interest in astronomy. Returning to Poland, he spent the rest of his life as a church canon under his uncle, though he also found time to practice medicine and to write on monetary reform, not to mention his work as an astronomer. In 1514, Copernicus privately circulated an outline of his thesis on planetary motion, but actual publication of De revolutionibus orbium coelestium (On the Revolutions of the Heavenly Spheres) containing his mathematical proofs did not occur until 1543, after a supporter named Rheticus had impatiently taken it upon himself to publish a brief description of the Copernican system (Narratio prima) in 1541.