Tag Archives: Cosmology

Astronomy, History of Science & Epistemology, My books & articles

Alexander Friedmann and the Big Bang : A scientific revolution

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The following is an excerpt from Chapter 4 and 5 of the book  The Big Bang Revolutionaries: The Untold Story of Three Scientists Who Reenchanted Cosmology, by Jean-Pierre Luminet.

The book has received rave reviews including from three Nobel Prize winners.

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In 1922, Alexander Friedmann took the step that Albert Einstein had not been ready to take: if one abandons the hypothesis of a static universe, the relativistic cosmological problem comprises an infinite number of solutions in which the metric varies as a function of time. Friedmann wrote:

Thus begins this founding notice of non-static cosmology. Received on June 29, 1922, by the German journal Zeitschrift für Physik, it was published shortly afterwards.

Ahead of Its Time

Friedmann’s article was ahead of its time, as one can also see from the fact that anybody studying modern cosmology can immediately recognize its main equations. While the formulations of the various metrics (de Sitter’s as well as Friedmann’s) would later change to the unified form of Howard Robertson and Arthur Walker, the differential equations that govern the time development of a space of constant positive curvature have not changed one iota.

With his 1922 article, Friedmann introduced a scientific revolution of the same magnitude as the Copernican revolution. In pre-Copernican cosmology, space was centered on a very particular place, the Earth. In pre-Friedmannian cosmology, the universe was static, in the sense of not evolving. Friedmannian cosmology introduces the historicity of the universe as space-time, as well as the idea of a beginning.

His second major cosmological article appeared in 1924. In 1925, he was appointed director of the Leningrad Geophysical Institute. In the summer of 1925, in the company of the aviator P. F. Fedosenko, he beat the altitude record in a stratospheric balloon, rising to 7,400 meters.

Friedmann died suddenly in Leningrad on September 16, 1925, from typhoid fever, at the age of thirty-seven. In 1931, he was posthumously awarded the Lenin Prize for his outstanding scientific work.

In Search of a Lost Tomb

Friedmann is buried in his hometown. An instructive anecdote is worth telling. The location of the Russian scientist’s grave was quickly forgotten, especially since the Stalinist regime that followed was hardly inclined to perpetuate the memory of this renowned “creationist” scientist. In 1988, the Alexander Friedmann Laboratory of the University of St. Petersburg (then called Leningrad State University) decided to organize the first “A. Friedmann International Seminar in Cosmology” to honor the centenary of the scientist’s birth. The director of the Friedmann Institute, my friend Andrey Grib, had the idea of a search for Friedmann’s tomb, planning a small commemorative ceremony in which admirers from various countries would participate. A venerable professor at the Institute of Physics and Technology in St. Petersburg and a former PhD student of Friedmann, Georgy Grinberg, remembered having attended the funeral of the scientist at the Smolenskoye Cemetery, and that the cosmologist’s grave was close to that of the great mathematician Leonhard Euler.

Grib therefore asked one of his students, Mihail Rosenberg, to go to the cemetery to locate the tomb — even hinting that this task would be recognized as part of his thesis work. When Rosenberg went to the cemetery and asked to consult the register of all the people buried here, the authorities replied that they had no information from prior to World War II. Rosenberg then asked to see the tomb of Leonhard Euler. After the war, he was told, Euler’s remains were transferred to another cemetery. There remained at least the old location, which the authorities indicated to him. Rosenberg explored the surroundings but found no evidence of Friedmann’s presence. He then began to quarrel with the authorities: How can the records have disappeared? At this point, an attendant approached and inquired about the dispute. The director of the cemetery replied that the student was looking for a certain “Friedmann.” “Which Friedmann,” asked the employee, “the one who discovered the non-static cosmological solution to Einstein’s equations?”

“Yes, yes,” exclaimed the student.

“Well, come with me, I’ll show you!”

This is how the cosmologist’s grave was discovered. The cemetery employee was none other than a former physicist who’d had to leave his research institute for lack of funds.

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Jean-Pierre Luminet, a French astrophysicist specializing in black holes and cosmology, is emeritus research director at the French National Centre for Scientific Research. He is a member of the Laboratoire d’Astrophysique de Marseille (LAM) and Laboratoire Univers et Théories (LUTH) of the Paris-Meudon Observatory. Luminet has been awarded several prizes. These include the Georges Lemaître Prize (1999) for his work in cosmology, the UNESCO Kalinga Prize (2021), and the Einstein medal for the Popularization of Science (2021). He has published more than twenty science books, eight historical novels, and eight poetry collections. The asteroid 5523 Luminet was named in his honor.

History of Science & Epistemology, My books & articles, Sciences

The Big Bang Revolutionaries

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The Big Bang Revolutionaries  : The Untold Story of Three Scientists Who Reenchanted Cosmology

by Jean-Pierre Luminet

Many widely read scientific writers of our day mistakenly attribute the concepts of the expanding universe and the Big Bang to Edwin Hubble and Albert Einstein. Hubble did provide evidence of an expanding universe, but he neither discovered such evidence nor accepted the radical idea that space itself was expanding. As for Einstein, he held out against the idea of an expanding universe for more than a decade, and ceased working in the field as soon as he had to amend his view. The real heroes of the Big Bang revolution are the Russian Alexander Friedmann and Belgian priest Georges Lemaître. That they are virtually unknown to the general public is one thing. That their contribution is underestimated by astrophysicists and cosmologists is another, for the concepts they promulgated are among the most remarkable achievements of twentieth-century science. The Big Bang Revolutionaries amends the record, telling the remarkable story of how these two men, joined by the mischievous George Gamow and in the face of conventional scientific wisdom, offered a compelling view of a singular creation of the universe in what Lemaître termed a “primeval atom.”

Publisher : Discovery Institute Press
Published : April 23, 2024
ISBN : 978-1-63712-040-8
Pages : 254
Retail Price : $18.95

Jean-Pierre Luminet, a French astrophysicist specializing in black holes and cosmology, is emeritus research director at the French National Centre for Scientific Research. He is a member of the Laboratoire d’Astrophysique de Marseille (LAM) and Laboratoire Univers et Théories (LUTH) of the Paris-Meudon Observatory. Luminet has been awarded several prizes. These include the Georges Lemaître Prize (1999) for his work in cosmology, the UNESCO Kalinga Prize (2021), and the Einstein medal for the Popularization of Science (2021). He has published more than twenty science books, eight historical novels, and eight poetry collections. The asteroid 5523 Luminet was named in his honor.

Advance Praise

This excellent and well-illustrated book convincingly puts into a clear focus the key original contributions of Friedmann and Lemaître in the early twentieth-century revolution in our understanding of the large-scale physical universe.

Roger Penrose, Emeritus Rouse Ball Professor of Mathematics at the Mathematical Institute of the University of Oxford, Emeritus Fellow of Wadham College at Oxford, fellow of the Royal Society, and recipient of the Wolf Prize (1988) and the Nobel Prize in Physics (2020)

The author brings together many aspects of thinking about the large-scale nature of our world from the points of view of concepts, theory, observation, and culture. The account starts with Albert Einstein’s thought that a philosophically satisfactory universe has no boundary, a bold conjecture that proved to fit well with Einstein’s new gravity theory and now agrees with the observational evidence. You will find fascinating details of the evolution of ideas, evidence, and the cultural situation between that time and the early steps by which George Gamow’s brilliant intuition took him to the realization that an even better picture of our universe is that it expanded from a hot dense state.

Jim Peebles, the Albert Einstein Professor in Science, emeritus, Princeton University, and recipient of the 2019 Nobel Prize in Physics

It is rare to find an internationally distinguished astrophysicist who is also a searching and meticulous historian. It is rarer still to find such a person who is also a gifted prose stylist. Jean-Pierre Luminet is such a man. The Big Bang Revolutionaries is invaluable reading for anyone fascinated by the history of the big ideas that have shaped and reshaped Western science and civilization, and for anyone who wants a front row seat to witness the all-too-common character of scientific revolution—messy, full of unexpected twists and turns, and not without its casualties. In the present case and as Luminet dramatically shows, the revolution occurred in the face of sustained prejudice from some of the finest minds in physics and astronomy. As for the wider implications of the Big Bang revolution, Luminet leaves those for the reader to contemplate.

Stephen C. Meyer, Director of the Center for Science and Culture and author of Signature in the Cell, named a Book of the Year by the Times (of London) Literary Supplement, Return of the God Hypothesis, and the New York Times bestseller Darwin’s Doubt

The twentieth century represents an exceptional period in the study of the cosmos. But this century will be remembered above all as the one in which physics, for the first time, made it possible to study the universe and its evolution. Jean-Pierre Luminet, an eminent cosmologist, takes the role of historian in this analysis of the emergence of ideas, and pays tribute to the physicists who contributed to this dizzying scientific adventure.

Michael Mayor, Swiss astrophysicist and professor emeritus at the University of Geneva; a recipient of the Viktor Ambartsumian International Prize (2010), the Kyoto Prize (2015), and the Nobel Prize in Physics (2019)

An inspiring overview of the history and physics of our modern view of the universe by the brilliant scientist Jean-Pierre Luminet, who was first to simulate black hole silhouettes. The reader is introduced to the scientific insights that revolutionized the perception of our cosmic roots and future. A fascinating read!

Abraham (Avi) Loeb, Frank B. Baird Jr. Professor of Science and Director of the Institute for Theory & Computation, Harvard University, and director for the Breakthrough Initiatives of the Breakthrough Prize Foundation

This book is a very careful discussion of the work of three less-known key figures who laid the foundations of modern cosmology—Alexander Friedmann, Georges Lemaître, and George Gamow. It does a great service in detailing the contributions that each of them made to the topic. I particularly appreciate the discussion of the pioneering work and personality of Lemaître, who can justly be called the father of scientific cosmology. With its discussion also of cosmic topology, the book is a unique contribution to the history of cosmology.

George Ellis, emeritus distinguished professor, University of Cape Town, co-author with Stephen Hawking of The Large Scale Structure of Space-Time, former president of the International Society on General Relativity and Gravitation, fellow of the Royal Society, recipient of the Templeton Prize and the Georges Lemaître International Prize

The Big Bang Revolutionaries is one terrific book. And one, I might add, of historical importance inasmuch as it restores to their rightful place two fascinating figures whom the standard history of physics in the twentieth century has shamefully neglected. Lucid? Of course it is lucid. Luminet is a fine astrophysicist. Moving? Very much so, not only for what it says about Friedmann and Lemaître, but for what it reveals about the author’s sensitive intelligence on encountering the story of men whose position of prominence was denied them. It is, all in all, a splendid restoration—something very French, I might add, in that it describes men who should have been monarchs reacquiring their thrones.

David Berlinski, Senior Fellow of the Center for Science and Culture, and author of A Tour of the Calculus, The Advent of the Algorithm, Newton’s Gift, The Devil’s Delusion: Atheism and Its Scientific Pretensions, and Science After Babel

Finally a book that brings the credit of the great cosmological revolution of the twentieth century to where it is properly due: the Russian Alexander Friedmann and the Belgian priest Georges Lemaître.

Carlo Rovelli, founder of the quantum gravity group of the Centre de Physique Théorique (CPT), Aix-Marseille University, and author of the bestselling Seven Brief Lessons on Physics

Big Bang theory has become a popular topic, but who knows the scientists who first proposed the outrageous concept that our entire universe started as an ultra-dense fireball? Theoretical physicist Jean-Pierre Luminet, well-known for his pioneering work on the visualization of black holes, takes the reader through a pedagogical, and historically accurate, tour of the conceptual vistas opened by the inventors of Big Bang theory, namely: the Russian mathematician (and meteorologist) Alexander Friedmann, the Belgian cosmologist (and priest) Georges Lemaître, and, last but not least, the eclectic genius physicist George Gamow. A must-read for any person eager to understand one of the major scientific breakthroughs of twentieth-century physics.

Thibault Damour, Institut des Hautes Études Scientifiques, recipient of the Einstein medal, the Galileo Galilei medal, and the Balzan prize

Essays, My books & articles, Sciences

My books (4) : The Wraparound Universe

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Until now I published as an author 30 books in my native language (French), including 14 science essays, 7 historical novels  and 9 poetry collections (for the interested reader, visit my French blog  here.
Although my various books have been translated in 14 languages (including Chinese, Korean, Bengali…), only 4 of my essays have been translated in English.

The fourth one was :

The Wraparound Universe

316 pages – AK Peters Ltd, 2008 – ISBN 978 1 56881 309 7 – ISBN 0 521 40906 3 (paperback)

WraparoundWhat shape is the universe? Is it curved and closed in on itself? Is it expanding? Where is it headed? Could space be wrapped around itself in a formation that produces ghost images of faraway galaxies? Such are the questions posed by Jean-Pierre Luminet, which he then addresses in clear and accessible language. An expert in black holes and the big bang, he leads us on a voyage through the surprising byways of space-time, where possible topologies of the universe, explorations of the infinite, and cosmic mirages combine their mysterious traits and unlock the imagination.

Praise for The Wraparound Universe

– “Luminet’s deep understanding of the history of cosmology combines with his scientific knowledge and expository skills to produce a delightful introduction to the much-debated question of the shape of the universe. Directed at an intelligent layperson, The Wraparound Universe combines geometrical insights with astronomical observations leading to the idea of a universe that is finite yet has no boundary.” (Jeff Weeks, author of The Shape of Space)
– “This book is well written and nicely illustrated, giving a clear exposition of the mathematical and astronomical ideas involved as well as the various ways of observationally testing this possibility.” (George Ellis, Cape Town University, Templeton Prize)

Available on amazon : click here

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PRESS REVIEWS

New Scientist, CERN Courier, etc : Click here

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Astronomy, Essays, History of Science & Epistemology

Geometry and the Cosmos (2) : From the Pre-Socratic Universe to Aristotle’s Two Worlds

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 Sequel of the previous post Geometry and the Cosmos (1): Kepler, from polyedra to ellipses 

The Pre-Socratic Universe

Since He [Zeus] himself hath fixed in heaven these signs,
The Stars dividing; and throughout the year
Stars he provides to indicate to men
The seasons’ course, that all things may duly grow.
Aratus, Phaenomena, I, 18.

Although Kepler was the first to determine the motion of the planets by mathematical laws, his search for a rational explanation to the universe was anticipated by numerous earlier thinkers. Even before the time of Socrates a number of philosophers had broken away from accepted mythology and postulated the idea of universal harmony. From the sixth century BC increasingly rational and mathematical ideologies based on the laws of physics began to compete with the traditional belief that the world was controlled by gods with supernatural powers. Most of these thinkers attempted to describe natural phenomena in mechanical terms, with reference to the elements of water, earth and fire. The Ionian philosophers in particular developed new ideas about the heavens, whose signs were used by many of their compatriots to navigate between the islands. Their fundamental notion was that the universe was governed by mechanical laws, by natural principles which could be studied, understood and predicted.

It was Thales of Miletus who propounded one of the first rational explanations of the world, according to which the earth was separate from the sky. Anaximander and Anaximenes, both also natives of Miletus on the coast of Asia Minor, put forward different ideas, which nevertheless derived from the same rationale: they proposed the existence of cosmological systems, explained natural phenomena in terms of a small number of “elements”, and invented new concepts – Anaximander’s “equilibrium” and Anaximenes’ “compression” – which can be regarded as the first recognition of the force of gravity.

The Expanding Universe. According to Empedocles of Acragas (now Agrigento, in Sicily), the universe was held in balance by forces of harmony and conflict, the attractive force of love and the repulsive force of hate alternatively prevailing. This idea of balance can be seen as a mythical precursor of modern astronomical theories whereby the tendency for structures to become compressed by their own gravitational forces is offset by the expansion of the universe, which constantly dilutes all matter.
In Lemaître’s so-called “hesitating universe”, a cosmological model he devised in 1931 from Einstein’s field equations, the evolution of the cosmos is divided into three disctinct phases : two periods of rapid expansion are separated by a period of “stagnation”, representing a sort of equilibrium between the forces of gravitational contraction and expansion.

According to Heraclitus of Ephesus, the day was caused by exhalations from the sun, while the night was the result of dark emissions from the earth. The stars and the planets were bowls of fire which, when turned over, gave rise to eclipses and the phases of the moon. The moon itself, pale and cold, moved in the rarefied air above the earth, whereas the sun, our nearest star, was bright and hot.

Meanwhile, the Greeks were amassing measurements which would enable them to plot the stars more accurately. This required specialised instruments – gnomons to measure the sun’s shadow, compasses to fix the positions of the stars in the sky, etc. – as well as a system of notation which anyone could understand (previously the study of astronomy had been restricted to priests): how many fingers’ width above the horizon was such and such a star; where was due north, and so on. As well as mining the extensive archive of observations made by the Egyptians and Babylonians, the Greeks developed their own system of records. The pre-Socratic thinkers refined and analysed the basic ideas of their predecessors from Miletus with the result that the mechanistic view of the world gradually lost currency and a belief in underlying harmony became de rigueur. As early as 450 BC Anaxagoras of Clazomenae was accused of impiety for referring to the sun as a mass of hot metal, to the moon as a second earth and to the stars as burning stones – views no longer considered seemly. Continue reading →

History of Science & Epistemology, Literature

Geometry and the Cosmos (1) : Kepler, from polyhedra to ellipses

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Introduction

The regularity of so much celestial activity has led many cultures to base their models of the universe on concepts of order and harmony. Around the Mediterranean it was the Pythagoreans who first expressed the idea that the universe is characterised by proportion, rhythm and numerical patterns. Plato’s hypothesis was of an organised cosmos whose laws could be deciphered, explained in geometric terms.

The history of physics is nothing other than the story of man’s desire to uncover the hidden order and harmony of things. The most ambitious physicists have attempted to unify apparently discrete phenomena: Galileo with terrestrial and celestial laws; Newton with gravity and the movement of celestial bodies; Maxwell with magnetism and electricity; Einstein with space and time; today’s physists with gravitation and microphysics.

But, as Heraclitus said as long ago as 500 BC, “Nature loves to hide.” Indeed advances in geometry and mathematics have led to new theories of the cosmos which we are unable to comprehend. They provide only abstract images, which do not allow us to visualise the structure of atoms or the dynamics of space-time or the topology of the universe in any direct sense.

It is this fundamental belief in celestial harmony – for which successive generations have found various elaborate expressions: just proportion, equation of the part and the whole, symmetry, constancy, resonance, group theory, strings -that has underlain the development of physics for the past 2,500 years.

Melancholy, or the Spirit of Man in Search of the Secret of the Universe. This etching, dating from 1514 according to the numbers in the square in the top right corner, depicts man contemplating the nature of the world in a state of melancholy, which in medieval times was associated with black bile and with the planet Saturn. The winged man prefigures Johannes Kepler’s interrogations as he calculates how to express the underlying harmony of the cosmos using spheres and polyhedra. The bright light in the sky is the great comet that was observed in the winter of 1513-14. As it shines on the scales (depicting the astronomical sign Libra) it symbolises the end of an earthly cycle, if not the end of time itself. The ladder with seven rungs represents the belief held by the Byzantines that the world would not exist for more than seven thousand years. It is the end of the Middle Ages; Diirer (1471-1528) is to be one of the prime movers of the Renaissance.

 

Geometry and the Cosmos

“Geometry, which before the origin of things was coeternal with the divine mind and is God himself […], supplied God with patterns for the creation of the world.”
Johannes Kepler, The Harmony of the World, 1619.

The 17th century German astronomer Johannes Kepler was undoubtedly the first to integrate man’s fascination with harmony into an overall vision of the world which can properly be called scientific. For Kepler, as for the natural philosophers of ancient Greece, the cosmos was an organised system comprising the earth and the visible stars. His avowed intention was to investigate the reasons for the number and sizes of the planets and why they moved as they did. He believed that those reasons, and consequently the secret of universal order, could be found in geometry. Kepler wanted to do more than create a simple model or describe the results of his experiments and observations; he wanted to explain the causes of what he saw. This makes him one of the greatest innovators in the history of science and it led him in particular to formulate laws of planetary motion which are still valid today.

Despite his innovative methods, Kepler wrote two studies of the cosmos in the style of the ancient Greeks: Mysterium Cosmographicum (The Secret of the Cosmos) in 1596 and Harmonices Mundi (The Harmony of the World) in 1619. At this turning point between ancient and modern thinking Kepler was steeped in a tradition which connected cosmology explicitly with the notion of divine harmony. But what Kepler sought to express was not the numerical mysticism of the Pythagoreans; his starting point was geometric patterns, which he saw as “logical elements”. His profound desire to devise a rational explanation for the cosmos led him to establish procedures which resembled those of modern science. Continue reading →

Astronomy

The Rate of Expansion

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There, where worlds seem, with slow steps,
Like an immense and well-behaved herd,
To calmly graze on the ether’s flower.
Giovanni Pascoli, Il Ciocco

A question often asked by the general public interested in cosmology about the expansion of the Universe is the distance scales on which it effectively acts. Before commenting on this, let me recall first some historical facts.

Georges Lemaître in 1927

In 1927, Georges Lemaître published a revolutionary article in the Annales de la Société scientifique de Bruxelles entitled “Un univers homogène de masse constante et de rayon croissant, rendant compte de la vitesse radiale des nébuleuses extragalactiques” (“A homogeneous universe of constant mass and increasing radius, accounting for the radial velocity of extragalactic nebulae.” As the title suggests, Lemaître showed that a relativistic cosmological model of finite volume, in which the Universe is in perpetual expansion, naturally explains the redshifts of galaxies, which at that point were not understood. In particular, the article contained a paragraph establishing that forty-two nearby galaxies, whose spectral shifts had been measured, were moving away at speeds proportional to their distances.

Lemaître gave the numerical value of this proportionality factor: 625 km/s per megaparsec, which means that two galaxies separated by 1 megaparsec (or 3,26 million light-years) moved away from each other at an apparent speed of 625 km/s, and that two galaxies separated by 10 megaparsecs moved apart at a speed ten times greater.

The paragraph of Lemaître’s paper in which he derives the law of proportionality between recession velocity and distance, later called the Hubble law.

This unit of measurement, the kilometer per second per megaparsec, shows clearly that the speed of recession depends on the scale. In 1377, in his Book of the Heavens and the World, the scholar Nicole Oresme had noted that, at dawn, one would not notice anything if the world and all living creatures had grown by the same proportion during the night. In Lemaître’s theory, on the contrary, the recession velocity between two points in space grows faster with greater separation, which renders it perceptible.

Eddington and Lemaître

Lemaître’s article, published in French, passed unnoticed until 1931, when it was finally read by Arthur Eddington, who published an English translation. Unfortunately, this version omits the paragraph in which Lemaître established his law of proportionality, see this article for all the details. Meanwhile, in 1929 the great American astronomer Edwin Hubble had published the experimental results he obtained with his collaborators and described a general law, according to which the speed of recession of a galaxy is proportional to its distance. This law, identical to Lemaître’s, with the same proportionality factor, would from now on carry the name of “Hubble’s law.” It forms the experimental basis for the theory of the expansion of the Universe, of which the big bang models are the fruit. Continue reading →

Astronomy, My books & articles, Sciences

Galaxies in Flight

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This post is an adaptation of a chapter of my book  “The Wraparound Universe” with many more  illustrations.

 

Galaxies in Flight

                     The spawning galaxy in flight is a rainbow trout which goes
back against the flow of time towards the lowest waters, towards the dark retreats of duration.
Charles Dobzynski (1963)

Since the time of Newton, we have known that white light, passing through a prism, is decomposed into a spectrum of all colors. Violet and blue correspond to the shortest wavelengths or, equivalently, to the largest frequencies; red corresponds to the largest wavelengths and to low frequencies. In 1814, the German optician Joseph von Fraunhofer discovered that the light spectrum from stars is streaked with thin dark lines, while that from candlelight has bright stripes. These phenomena remained puzzling until 1859. It was then that the chemist Robert Bunsen and the physicist Gustav Kirchhoff analyzed the light created from the combustion of different chemical compounds (burned with the now-famous Bunsen burner) and saw that each of them emitted light with its own characteristic spectrum.

Fraunhofer lines in the solar spectrum

At nearly the same time, Christian Doppler discovered in 1842 that moving the source of a sound produced shifts in the frequency of sound waves, a phenomenon experienced by anyone listening to the siren of an ambulance passing by. The French physicist Armand Fizeau noticed the same phenomenon with light waves: depending on whether a source of light was moving closer or farther away, the received frequencies are either raised or lowered with respect to the emitted frequencies. The shift becomes larger as the speed of displacement is increased. If the source is getting closer, the frequency grows, and the light becomes more “blue”; if it moves away, the frequency lowers and the wavelengths stretch out, becoming more “red,” with respect to the spectrum of visible light. Since this shift affects the whole spectrum by the same amount, it is easily quantified by looking at the dark or bright stripes, which are shifted together, either towards the blue or towards the red, and it furnishes an incomparable means of measuring the speed of approach or retreat for light sources.

Shortly after this discovery, astronomers began an ambitious program of spectroscopy, with the aim of measuring the speed of the planets and stars by using their spectral shifts. Continue reading →

My books & articles, Sciences

Expansion and the Infinite

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This post is an adaptation of a chapter of my book  “The Wraparound Universe” with many more  illustrations.

Expansion and the Infinite

Space alike to itself
that it grows or denies itself
Stéphane Mallarmé

The Universe is expanding. What does this really mean? Most people imagine an original huge explosion, as the term “big bang” suggests, and the metaphor is constantly used in popular accounts. Some speakers even have the tendency to mime a gesture of expansion with their hands, as if they were holding a piece of space or an immaterial balloon in the process of inflating. The public imagines some matter ejected at prodigious speeds from some center, and tell themselves that it would be better not to be there at the moment of explosion, so as not to be riddled through with particles.

A misleading view of the expanding universe commonly used in popular science

None of all this is accurate. At the big bang, no point in the Universe participated in any explosion. Put simply, if one considers any point whatsoever, we notice that neighboring points are moving away from it. Is this to say that these points are animated by movement, given a speed? No, they are absolutely fixed, and nevertheless they grow apart.

To unravel this paradox, it is necessary to make more precise what one exactly means when speaking of a fixed point. The position of a point is fixed by coordinates: one number for a line (the miles along a highway), two numbers for a surface (latitude and longitude), and three for space in general (length, width, and height). A point is said to be fixed if its coordinates do not change over the course of time. In an arbitrary space, curved or not, the distance between two points is given by the so-called metric formula, which depends on the coordinates and generalizes the Pythagorean theorem. In principle, therefore, the distance between two points does not vary. In an expanding space, on the other hand, this distance grows, while the points do not move, even by a millimeter, meaning that they strictly conserve the same coordinates. These fixed coordinates are known as “comoving” coordinates. In relativistic cosmology, galaxies remain fixed at comoving positions in space. They may dance slight arabesques around these positions, under the influence of local gravitational fields, but the motion which moves them apart from each other resides in the literal expansion of the space which separates them. Continue reading →

History of Science & Epistemology, Sciences

The Edge Paradox

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The world has no outside, no beyond, since it contains and embraces everything
Guillaume d’Auvergne (De Universo, 1231)

If the Universe is finite, it seems necessary for it to have a center and a frontier. The center poses hardly any conceptual difficulty: it suffices to place the Earth there, like the geocentric systems of Antiquity (appearances lead one in this direction), or the Sun, as Copernicus did in his heliocentric system. The notion of an “edge” of the Universe is on the other hand more problematic.

Archytas, born in 428 BC in Tarentum (Italy) and died in 347, was a philosopher, mathematician, astronomer, statesman, and strategist. He belonged to the Pythagorean school and was famous for his scientific abilities.

In the fifth century BCE, the Pythagorean Archytas of Tarentum described a paradox that aimed to demonstrate the absurdity of having a material edge to the Universe. His argument would have a considerable career in all future debates on space: if I were at the extremity of the sky, could I extend my hand or stick out a staff? It is absurd to think that I could not; and if I could, that which is found beyond is either a material body, or space. I could therefore move beyond this once again, and so on. If there is always a new space towards which I can extend my hand, this clearly implies an expanse without limits. There is therefore a paradox: if the Universe is finite, it has an edge, but this edge can be passed through indefinitely.

This line of reasoning was taken up by the atomists, such as Lucretius, who gave the image of a spear thrown to the edge of the Universe, and afterwards by all the partisans of an infinite Universe, such as Nicholas of Cusa and Giordano Bruno. Continue reading →

Astronomy, History of Science & Epistemology, My books & articles

A brief history of space (4/4)

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Sequel of the preceding post A Brief History of Space (3/4) : From Descartes to Schwarzschild

Cosmology developed rapidly after the completion of general relativity by Albert Einstein, in 1915. In this theory, the Universe does not reduce to a space and a time which are absolute and separate; it is made up of the union of space and time into a four dimensional geometry, which is curved by the presence of matter.

Albert Einstein (here in 1910) developed the theory of relativity and was awarded the 1921 Nobel prize for physics. Image by © Hulton-Deutsch, Collection/CORBIS

It is in fact the curvature of space-time as a whole which allows one to correctly model gravity, and not only the curvature of space, such as Clifford had hoped. The non-Euclidean character of the Universe appeared from then on not as a strangeness, but on the contrary as a physical necessity for taking account of gravitational effects. The curvature is connected to the density of matter. In 1917, Einstein presented the first relativistic model for the universe. Like Riemann, he wanted a closed universe (one whose volume and circumference were perfectly finite and measurable) without a boundary; he also chose the hypersphere to model the spatial part of the Universe.

Einstein static universe in a space-time diagram.

At any rate, Einstein’s model made the hypothesis of a static Universe, with the radius of the hypersphere remaining invariable over the course of time. In truth, the cosmological solutions of relativity allow complete freedom for one to imagine a space which expands or contracts over the course of time: this was demonstrated by the Russian theorist Alexander Friedmann, between 1922 and 1924.

At the same time, the installment of the large telescope at Mount Wilson, in the United States, allowed for a radical change in the cosmic landscape. In 1924, the observations of Edwin Hubble proved that the nebula NGC 6822 was situated far beyond our galaxy. Very rapidly, Hubble and his collaborators showed that this was the case for all of the spiral nebulae, including our famous neighbor, the Andromeda nebula: these are galaxies in their own right, and the Universe is made up of the ensemble of these galaxies. The “island-universes” already envisaged by Thomas Wright, Kant and Johann Heinrich Lambert were legitimized by experiment, and the physical Universe seemed suddenly to be immensely enlarged, passing from a few thousand to several dozen million light-years at the minimum. Beyond this spatial enlargement, the second major discovery concerned the time evolution of the Universe. In 1925, indications accumulated which tended to lead one to believe that other galaxies were systematically moving away from ours, with speeds which were proportional to their distance. Continue reading →

Astronomy, History of Science & Epistemology, My books & articles

A brief history of space (3/4) : from Descartes to Schwarzschild

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Sequel of the preceding post A Brief History of Space (2/4) : From Ptolemy to Galileo

At the beginning of XVIIth century, the way was open for new cosmologies, constructed on the basis of infinite space. Until then, the notion of space was conceived in the cosmological and physical order of nature, and not as the “background” of the figures and geometric constructions of Euclid. In other terms, physical space was not mathematicized. It became so thanks to René Descartes (1596 – 1650), who had the idea of specifying each point by three real numbers: its coordinates. The introduction of a universal system of coordinates which entirely criss-crossed space and allowed for the measurement of distances was a reflection of the fact that, for Descartes, the unification and uniformization of the universe in its physical content and its geometric laws was a given. Space is a substance in the same class as material bodies, an infinite ether agitated by vortices without number, at the centers of which were held the stars and their planetary systems.

A portrait of René Descartes

This new conception of the cosmos upset philosophical thought and led it far from the initial enthusiasm of the atomists and Giordano Bruno: “The absolute space which inspired the hexameters of Lucretius, the absolute space which that had been a liberation for Bruno, was a labyrinth and an abyss for Pascal.”[5] As for the scholars, they did not allow themselves to be discouraged by these moods and irresistibly moved towards the infinite universe.

The Descartes system of the world using vortices

The tendency toward the radical geometrization of an infinite space, initiated by Descartes, was consummated by the Englishman Isaac Newton (1642-1727). Newton postulated an absolute space, encompassing not only the background space of mathematics and the physical space of astronomy, but also that of metaphysics, since space was the “sensorium of God.” Physical space, finally identified with geometrical space, was necessarily Euclidean (the only one known at the epoch), without curvature, amorphous and infinite in every direction. At the heart of this immobile framework, Newton explained celestial mechanics in terms of the law of universal attraction, from now on considered responsible for gravitation and the large scale structure of the Universe. With Newton, cosmology took root for more than two centuries in the framework of an infinite Euclidean space and an eternal time.

Newton around 1700

All the problems are not resolved in Newtonian cosmology, far from it. On the question of the distribution of stars in space, for example, Newton believed that they must occupy a finite volume since, he argued, if they occupied an infinite space, they would be infinite in number, the force of gravitation would be infinite, and the universe would be unstable. Newton moreover supposed that the stars were uniformly spread within a finite mass|like a galaxy, for example. But a problem of instability remained: since each celestial body is attracted by every other one, at the least movement, at the least mechanical perturbation, all the bodies in the universe would fall towards a unique center, and the universe would collapse. Newton’s universe is therefore only viable if it does not admit motion on the large scale: its space is rigid and its time immobile. Continue reading →

Astronomy, History of Science & Epistemology, My books & articles

A Brief History of Space (1/4)

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This post is based on a chapter of my book  “The Wraparound Universe” but is much more illustrated.  The chapter is divided into 4 parts, here is the first one.

*************

That which keeps quiet beyond everything, is this in fact simply what I name Space? . . . Space! An idea! A word! A breath!
Jean Tardieu

There is no space or time given a priori; to each moment in human history, to each degree of perfection of our physical theories of the Universe, there corresponds a conception of those fundamental categories of thought known as space, time, and matter. To each new conception, our mental image of the Universe must adapt itself, and we must accept that “common sense” was found lacking. For example, if space is limited by a boundary, what is there beyond it? Nothing? It is difficult to imagine that, by voyaging sufficiently far in a given direction, one could reach a point beyond which nothing more exists, not even space. It is just as troubling to think of an infinitely large Universe. What would be the meaning of any measurable, that is to say finite, thing with respect to the infinite?

A possible representation of Anaximander learning Pythagoras on his left, detail of Raphael's famous painting The School of Athens.
A possible representation of Anaximander learning Pythagoras on his left, detail of Raphael’s famous painting The School of Athens.

These types of questions were formulated in the sixth century BCE, in ancient Greece, where they rapidly became the object of controversy. The first schools of scholars and philosophers, called “presocratic” (although they were spread over two centuries and were quite different from each other), each attempted in their way to rationally explain the “world,” meaning the ensemble formed by the Earth and the stars, conceived as an organized system. For Anaximander, from the school of Miletus, the world where observable phenomena take place was necessarily finite. Nevertheless, it was plunged within a surrounding medium, the apeiron, corresponding to what we today consider as space. This term signifies both infinite (unlimited, eternal) and indefinite (undetermined). For his contemporary, Thales, the universal medium was made of water, and the world was a hemispheric bubble floating in the middle of this infinite liquid mass.

We meet up again with this intuitive conception of a finite material world bathing in an infinite receptacle space with other thinkers: Heraclitus, Empedocles, and especially the Stoics, who added the idea of a world in pulsation, passing through periodic phases of explosions and deflagrations.

Atomism, founded in the fifth century by Leucippus and Democritus, advocated a completely different version of cosmic infinity. It maintained that the Universe was constructed from two primordial elements: atoms and the void. Indivisible and elementary, (atomos means “that which cannot be divided”), atoms exist for all eternity, only differing in their size and shape. They are infinite in number. All bodies result from the coalescence of atoms in motion; the number of combinations being infinite, it follows that the celestial bodies are themselves infinite in number: this is the thesis of the plurality of worlds. The formation of these worlds is produced within a receptacle without bounds: the void (kenon). This “space” has no other property than being infinite and accordingly matter has no influence on it: it is absolute, given a priori.

Part of a fresco in the portico of the National University of Athens representing Anaxagoras.
Part of a fresco in the portico of the National University of Athens representing Anaxagoras.

The atomist philosophy was strongly criticized by Socrates, Plato, and Aristotle. Moreover, by affirming that the universe is not governed by gods, but by elementary matter and the void, it inevitably entered into conflict with the religious authorities. In the fourth century BCE, Anaxagoras of Clazomenae was the first scholar in history to be accused of impiety; however, defended by powerful friends, he was acquitted and was able to flee far from the hostility of Athens. Thanks to its two most illustrious spokesmen, Epicurus (341-270 BCE), who founded the first school that allowed female students and Lucretius (first century BCE), author of a magnificent cosmological poem, On the Nature of Things, atomism continued to flourish until the advent of Christianity. It was however marginalized over the course of the first centuries of the christian era, and would not again be part of mainstream science until the seventeenth century. Continue reading →

Astronomy, History of Science & Epistemology, My books & articles, Sciences

Cosmogenesis (9) : The Big Bang Discovery

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Sequel of the preceding post Cosmogenesis (8) : The Nebular Hypothesis

Star Clusters and Nebulae. This page from "Telescopic views of Nebulae and Clusters by the Earl of Rosse and Sir J. Herschel" (1875) includes a variety of drawings of nebulosities by different observers. There are star clusters and gaseous nebulae (now known to belong to our own galaxy) as well as other galaxies. Observational techniques of the time were unable to distinguish between these very different types of objects.
Star Clusters and Nebulae. This page from “Telescopic views of Nebulae and Clusters by the Earl of Rosse and Sir J. Herschel” (1875) includes a variety of drawings of nebulosities by different observers. There are star clusters and gaseous nebulae (now known to belong to our own galaxy) as well as other galaxies. Observational techniques of the time were unable to distinguish between these very different types of objects.

In the first quarter of the 20th century cosmology became a distinct scientific discipline, thanks in part to the theoretical advance made in 1915 by Einstein with his theory of general relativity and in part to the revolution in observational techniques which revealed the true extent of the universe. Having at last been able to measure the distance of certain spiral nebulae, Edwin Hubble could confirm in 1925 that there existed other galaxies like our own.

His colleague Vesto Slipher had previously discovered that the radiation from these galaxies was constantly shifting towards the red end of the optical spectrum, which suggested that they were moving away from us at great speed. This movement was not understood until scientists came to accept an idea based on the theory of general relativity and first proposed by Alexandre Friedmann in 1922 and independently Georges Lemaître in 1927: that space was constantly expanding and consequently increasing the distance between galaxies. This idea proved to be one of the most significant discoveries of the century[i].

Alexander Friedmann in 1922
Alexander Friedmann in 1922

In an article which appeared in 1922, entitled “On the Curvature of Space“, Friedmann took the step which Einstein had balked at: he abandoned the theory of a static universe, proposing a “dynamic” alternative in which space varied with time. For the first time the problem of the beginning and the end of the universe was couched in purely scientific terms. Friedmann suggested that the universe was several tens of billions of years old, much older than the earth (then estimated to be about one billion years old) or the oldest known celestial objects. It was a remarkable prediction, the most recent estimate for the age of the universe being between 10 and 20 billion years.

In 1927, in a seminal article entitled “A Homogeneous Universe of Constant Mass and Increasing Radius Accounting for the Radial Velocity of Extra-Galactic Nebulae“, Lemaître explained the observations of Hubble and Slipher by interpreting them, within the context of general relativity, as manifestations of the expansion of the universe. This expansion was taking place uniformly across the entire universe (which might be finite or infinite), not outwards from a particular point (in this sense the often quoted analogy of a balloon being inflated is misleading). It was not a case of matter moving within a fixed geometric framework, but of the framework itself dilating, of the very “fabric” of space-time stretching. Continue reading →

Essays, History of Science & Epistemology, Literature

Cosmogenesis (1) : From Myth to Myth

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Introduction

Every society has a story, rooted in its most ancient traditions, of how the earth and sky originated. Most of these stories attribute the origin of all things to a Creator -whether god, element or idea.

In the Western world all discussions of the origin of the world were dominated until the 18th century by the story of Genesis, which describes the Creation as an ordered process that took seven days. The development of mechanistic theories in the 18th century meant that the idea of an organized Creation gave way to the concept of evolution, and in the 19th century astrophysicists discovered that stars had their origin in clouds of gas. Big bang theory, conceived at the beginning of the 20th century, was subsequently developed into a more or less complete account of the history of the cosmos, from the birth of space, time and matter out of the quantum vacuum until the emergence of life.

Today sophisticated telescopes show us how the first galaxies were formed, how clouds of hydrogen gave birth to stars and how the planets emerged from swirling dust. We now know that creation is still going on in our universe but the origin of life remains an enigma. How did life forms appear? The universe’s best kept secret continues to baffle scientists.

From Myth to Myth

What are the origins of the universe, of the sky, of the earth, of life, of man? These questions have given rise to many different myths and legends and continue to be the subject of intensive research by astrophysicists, biologists and anthropologists. What were once fanciful stories are now scientific models but, whatever form they take, ideas about the origins of the universe both reflect and enrich the imagination of the people who generate them. Every society has developed its own stories to explain the creation of the world; most of them are ancient myths rooted in religion.

Whereas in monotheistic religions God is believed to have existed before the Creation, in most other kinds of religion the gods themselves are thought to originate from a creative element such as Desire, the Tree of the Universe, the Mundane Egg, Water, Chaos or the Void.

Babylonian Gods. An inscription on the back of this stone carving tells us that it was a gift from the Kassite king Melishishu II to his son. The picture shows the symbols representing the gods carved on the front. On the right the principal deities -Anu, god of the sky, and Enlil, god of the atmosphere - are each shown as a sort of tiara standing on a plinth. Next a ram's head above a creature half-goat half-fish represents Ea, god of the Waters of the Abyss. The symbol on the left might be for the goddess Ninhursag. Above these are the three celestial divinities: a crescent for Sin, god of the moon, a star for Ishatar and an image of the sun for Shamash. Stone from Kassite era (1202-1188 BC). Paris, Louvre.
Babylonian Gods. An inscription on the back of this stone carving tells us that it was a gift from the Kassite king Melishishu II to his son. The picture shows the symbols representing the gods carved on the front. On the right the principal deities -Anu, god of the sky, and Enlil, god of the atmosphere – are each shown as a sort of tiara standing on a plinth. Next a ram’s head above a creature half-goat half-fish represents Ea, god of the Waters of the Abyss. The symbol on the left might be for the goddess Ninhursag. Above these are the three celestial divinities: a crescent for Sin, god of the moon, a star for Ishatar and an image of the sun for Shamash.
Stone from Kassite era (1202-1188 BC). Paris, Louvre.
The Chinese giant Pangu
The Chinese giant Pangu

Ideas like these appear in the Rig-veda, one of the four sacred books of the Brahmins and the oldest surviving written record of Indian culture which were compiled between 2000 and 1500 BC. The Tree of the Universe, symbol of the outward growth of the world and of its organic unity, is mentioned in ancient Indian legends as well as in those of the Babylonians and Scandinavians (who call it Yggdrasil). The anthropomorphic symbol of Desire was invoked by the Phoenicians and by the Maoris of New Zealand. The Mundane Egg, from which the Hindu Prajapatis (lords of all living things) emerged, also gave birth to the gods Ogo and Nommo, worshipped by the Dogon of Mali, and the Chinese giant Pan Gu as well as constituting the celestial vault in the legend of Orpheus.

Birth of Gods and Cosmic Egg according to the Upanishad
Birth of Gods and Cosmic Egg according to the Upanishad

A belief in some such primordial element, of which there are traces in every culture, underlies man’s thinking about the history of the cosmos like a primitive universal symbol buried in the collective subconscious. This may explain the vague links which can always be discerned between this or that creation myth and modern scientific descriptions of the origin of the universe – for example, big bang theory. There is therefore nothing mysterious or surprising about these correspondences other than that certain ways of thinking about the world should be so ingrained in the human mind. Continue reading →

History of Science & Epistemology, Sciences

The Rise of Big Bang Models (5) : from Gamow to Today

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Sequel of previous post : Lemaître

In this series of posts about the history of relativistic cosmology, I  provide an epistemological analysis of the developments of the field  from 1917 to 2006, based on the seminal articles by Einstein, de Sitter, Friedmann, Lemaître, Hubble, Gamow and other main historical figures of the field. It appears that most of the ingredients of the present-day standard cosmological model, including the accelation of the expansion due to a repulsive dark energy, the interpretation of the cosmological constant as vacuum energy or the possible non-trivial topology of space, had been anticipated by Lemaître, although his papers remain mostly  unquoted.

First English Edition of The primeval atom
First English Edition of The primeval atom

Lemaître, the "Big bang Man"
Lemaître, the “Big bang Man”
The hot big bang model

By 1950, when Lemaître published a summary, in English, of his theory, entitled The Primeval Atom: An Essay on Cosmogony, it was thoroughly unfashionable. Two years previously the rival theory of a « steady state » universe, supported principally by Thomas Gold in America and by Hermann Bondi and Fred Hoyle in Britain, had met with widespread acclaim. Their argument was that the universe had always been and would always be as it is now, that is was eternal and unchanging. In order to obtain what they wanted, they assumed an infinite Euclidean space, filled with a matter density constant in space and time, and a new « creation field » with negative energy, allowing for particles to appear spontaneously from the void in order to compensate the dilution due to expansion ! Seldom charitable towards his scientific adversaries, Fred Hoyle made fun of Lemaître by calling him « the big bang man ». In fact he used for the first time the expression « big bang » in 1948, during a radio interview.

Thomas Gold, Hermann Bondi and Fred Hoyle, promotors of the steady state theory"
Thomas Gold, Hermann Bondi and Fred Hoyle, promotors of the steady state theory”

The term, isolated from its pejorative context, became part of scientific parlance thanks to a Russian-born American physicist George Gamow, a former student of Alexander Friedmann. Hoyle therefore unwittingly played a major part in popularising a theory he did not believe in; he even brought grist to the mill of big bang theory by helping to resolve the question why the universe contained so many chemical elements. Claiming that all the chemical elements were formed in stellar furnaces, he was contradicted by Gamow and his collaborators Ralph Alpher and Robert Hermann. The latter took advantage of the fact that the early universe should have been very hot. Assuming a primitive mixture of nuclear particles called Ylem, a Hebrew term referring to a primitive substance from which the elements are supposed to have been formed, they were able to explain the genesis of the lightest nuclei (deuterium, helium, and lithium) during the first three minutes of the Universe, at an epoch when the cosmic temperature reached 10 billion degrees. Next they predicted that, at a later epoch, when the Universe had cooled to a few thousand degrees, it suddenly became transparent and allowed light to escape for the first time. Alpher and Hermann calculated that one should today receive an echo of the big bang in the form of « blackbody » radiation at a fossil temperature of about 5 K. Their prediction did not cause any excitement. They refined their calculations several times until 1956, without causing any more interest; no specific attempt at detection was undertaken. Continue reading →

History of Science & Epistemology, Sciences

The Rise of Big Bang Models (4) : Lemaître

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Sequel of previous post : Dynamical solutions

In this series of posts about the history of relativistic cosmology, I  provide an epistemological analysis of the developments of the field  from 1917 to 2006, based on the seminal articles by Einstein, de Sitter, Friedmann, Lemaître, Hubble, Gamow and other main historical figures of the field. It appears that most of the ingredients of the present-day standard cosmological model, including the accelation of the expansion due to a repulsive dark energy, the interpretation of the cosmological constant as vacuum energy or the possible non-trivial topology of space, had been anticipated by Lemaître, although his papers remain mostly  unquoted.

The discovery of expanding space

The 1920’s were precisely the time when the experimental data began to put in question the validity of static cosmological models. For instance, in 1924 the British theorist Arthur Eddington pointed out that, among the 41 spectral shifts of galaxies as measured by Vesto Slipher, 36 were redshifted ; he thus favored the de Sitter cosmological solution while, in 1925, his PhD student, the young Belgian priest Georges Lemaître, proved a linear relation distance-redshift in de Sitter’s solution. The same year 1925, Edwin Hubble proved the extragalactic nature of spiral nebulae. In other words, he confirmed that there existed other galaxies like our own, and the observable Universe was larger than previously expected. More important, the radiation from the faraway galaxies was systematically redshifted, which, interpreted as a Doppler effect, suggested that they were moving away from us at great speed. How was it possible ?

Arthur Eddington (1882-1944)
Arthur Eddington (1882-1944)

Young-Lemaitre
The young Georges Lemaître

It was Lemaître who solved the puzzle. In his 1927 seminal paper Un univers homogène de masse constante et de rayon croissant, rendant compte de la vitesse radiale des nébuleuses extragalactiques, published in French in the Annales de la Société Scientifique de Bruxelles, Lemaître calculated the exact solutions of Einstein’s equations by assuming a positively curved space (with elliptic topology), time varying matter density and pressure, and a non-zero cosmological constant. He obtained a model with perpetual accelerated expansion, in which he adjusted the value of the cosmological constant such as the radius of the hyperspherical space R(t) constantly increased from the radius of the Einstein’s static hypersphere RE at t = – ∞. Therefore there was no past singularity and no « age problem ». The great novelty was that Lemaître provided the first interpretation of cosmological redshifts in terms of space expansion, instead of a real motion of galaxies : space was constantly expanding and consequently increased the apparent separations between galaxies. This idea proved to be one of the most significant discoveries of the century. Continue reading →

History of Science & Epistemology, Sciences

The Rise of Big Bang Models (3) : Friedmann’s Dynamical solutions

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Sequel of previous post : Static Solutions

In this series of posts about the history of relativistic cosmology, I  provide an epistemological analysis of the developments of the field  from 1917 to 2006, based on the seminal articles by Einstein, de Sitter, Friedmann, Lemaître, Hubble, Gamow and other main historical figures of the field. It appears that most of the ingredients of the present-day standard cosmological model, including the accelation of the expansion due to a repulsive dark energy, the interpretation of the cosmological constant as vacuum energy or the possible non-trivial topology of space, had been anticipated by Lemaître, although his papers remain mostly  unquoted.

The Friedmann’s pioneering work

expanding-friedmannIn an article which appeared in 1922, entitled On the Curvature of Space (see Luminet 2004 for reference and translation), the Russian physicist Alexander Friedmann took the step which Einstein had balked at : he abandoned the theory of a static universe, proposing a “dynamic” alternative in which space varied with time. As he stated in the introduction, “the goal of this notice is the proof of the possibility of a universe whose spatial curvature is constant with respect to the three spatial coordinates and depend on time, e.g. on the fourth coordinate.“

friedmann-equation
The Friedmann’s Equation. R is the curvature radius of space, rho the mass density, Lambda the cosmological constant, k the sign of the space curvature, G the gravitational constant, c the speed of light

Thus he assumed a positively curved space (hypersphere), a time variable matter density and a vanishing cosmological contant. He obtained his famous “closed universe model”, with a dynamics of expansion – contraction. Continue reading →

History of Science & Epistemology, Sciences

The Rise of Big Bang Models (2) : Static solutions

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Sequel of previous post :  From Myth to Science

In this series of posts about the history of relativistic cosmology, I  provide an epistemological analysis of the developments of the field  from 1917 to 2006, based on the seminal articles by Einstein, de Sitter, Friedmann, Lemaître, Hubble, Gamow and other main historical figures of the field. It appears that most of the ingredients of the present-day standard cosmological model, including the accelation of the expansion due to a repulsive dark energy, the interpretation of the cosmological constant as vacuum energy or the possible non-trivial topology of space, had been anticipated by Lemaître, although his papers remain mostly  unquoted.

The History of Relativistic Cosmology can be divided into 6 periods :

– the initial one (1917-1927), during which the first relativistic universe models were derived in the absence of any cosmological clue.

– a period of development (1927-1945), during which the cosmological redshifts were discovered and interpreted in the framework of dynamical Friedmann-Lemaître solutions, whose geometrical and mathematical aspects were investigated in more details.

– a period of consolidation (1945-1965), during which primordial nucleosynthesis of light elements and fossil radiation were predicted.

– a period of acceptation (1965-1980), during which the big bang theory triumphed over the « rival » steady state theory.

– a period of enlargement (1980-1998), when high energy physics and quantum effects were introduced for describing the early universe.

– the present period of high precision experimental cosmology, where the fundamental cosmological parameters are now measured with a precision of a few %, and new problematics arise (nature of the dark energy, topology of the universe, new cosmologies in quantum gravity theories, etc.)

Let us follow chonologically the rather hectic evolution of the ideas in the field. Continue reading →

History of Science & Epistemology

The Rise of Big Bang Models (1) : from Myth to Science

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In this series of posts about the history of relativistic cosmology, I’ll  provide an epistemological analysis of the developments of the field  from 1917 to 2006, based on the seminal articles by Einstein, de Sitter, Friedmann, Lemaitre, Hubble, Gamow and other main historical figures of the field. It appears that most of the ingredients of the present-day standard cosmological model, including the accelation of the expansion due to a repulsive dark energy, the interpretation of the cosmological constant as vacuum energy or the possible non-trivial topology of space, had been anticipated by Lemaitre, although his papers remain mostly  unquoted.

 From Myth to Science

What are the origins of the universe, of the stars, of the earth, of life, of man? These questions have given rise to many different myths and legends, and today they are more than ever the subject of intensive research by astrophysicists, biologists and anthropologists. What were once fanciful stories are now scientific models; but whatever form they take, ideas about the origins of the universe both reflect and enrich the imagination of the people who generate them. Every society has developed its own stories to explain the creation of the world; all of them are ancient myths rooted in religion.

Whereas in monotheistic religions God is believed to have existed before the Creation, in most other kinds of religion the gods themselves are thought to originate from a creative element such as Desire, the Tree of the Universe, the Mundane Egg, Water, Chaos or the Void.

Tiamat-Marduk
Marduk slays the chaos dragon, Tiamat, in the Babylonian creation epic (British Museum, London)

A belief in some such primordial element, of which there are traces in every culture, underlies man’s thinking about the history of the cosmos like a primitive universal symbol buried in the collective subconscious. This may explain the vague links that can always be discerned between this or that creation myth and modern scientific descriptions of the origin of the universe –for example, big bang theory. There is therefore nothing mysterious or surprising about these correspondences other than that certain ways of thinking about the world should be so ingrained in the human mind.

An interesting approach, by the scientist and philosopher Wolfgang Smith (published in 2012)
An interesting approach, by the scientist and philosopher Wolfgang Smith (published in 2012)

In fact scientific and mythical explanations of the origins are neither complementary not contradictory; they have different purposes and are subject to different constraints. Mythical stories are a way of preserving collective memories, which can be verified neither by the storyteller nor by the listener. Their function is not to explain what happened at the beginning of the world but to establish the basis of social or religious order, to impart a set of moral values. Myths can also be interpreted in many different ways. Science, on the other hand, aims to discover what really happened in historical terms by means of theories supported by observation. Often considered to be anti-myth, science has in fact created new stories about the origin of the universe: big bang model, the theory of evolution, and the ancestry of mankind. It is therefore hardly surprising that the new creation stories developed by scientists tend to be regarded by the general public as modern myths.

Continue reading →