Category Archives: Astronomy

40 Years of Black Hole Imaging (3): from Kerr black holes to EHT

Sequel of the previous post 40 Years of Black Hole Imaging (2)

Generalizations to Kerr Black Holes

Unfortunately Marck’s simulations of black hole accretion disks remained mostly ignored from the professional community, due to the fact that they were not published in peer-reviewed journals and, after their author prematurely died in May 2000, nobody could find the trace of his computer program…

Then, unaware of Marck’s results, several researchers of the 1990’s were involved in the program of calculating black hole gravitational lensing effects in various situations. Stuckey (1993) studied photon trajectories which circle a static black hole one or two times and terminate at their emission points (« boomerang photons »), producing a sequence of ring-shaped mirror images. Nemiroff (1993) described the visual distortion effects to an observer traveling around and descending to the surface of a neutron star and a black hole, discussing multiple imaging, red- and blue-shifting, the photon sphere and multiple Einstein rings. He displayed computer-generated illustrations highlighting the distortion effects on a background stellar field but no accretion disk, and made a short movie now available on the internet (Nemiroff 2018), two snapshots of which are shown in figure 1.

Figure 1. Trip to a black hole by Robert Nemiroff, 1993.

The first simulations of the shape of accretion disks around Kerr black holes were performed by Viergutz (1993). He treated slightly thick disks and produced colored contours, including the disk’s secondary image which wraps under the black hole (figure 2). The result is a colored generalization of the picture by Cunningham and Bardeen (1973) shown in 40 Years of Black Hole Imaging (1).

Figure 2. Primary and secondary images of a simple accretion disk model around a Kerr black hole, seen by a faraway observer. Colors indicate combined gravitational and Doppler shifts (from Viergutz 1993).

More elaborate views of a geometrically thin and optically thick accretion disk around a Kerr black hole were obtained by Fanton et al. (1997). They developed a new program of ray tracing in Kerr metric, and added false colors to encode the degree of spectral shift and temperature maps (figure 3). Zhang et al. (2002) used the same code to produce black-and-white images of standard thin accretion disks around black holes with different spins, viewing angles and energy bands (figure 4).

Figure 3. False color contour maps showing how the monochromatic radiation emitted by a Keplerian accretion disk would be seen at infinity for various values of the inclination angle to the plane of the disk (top to bottom : 5°, 45°, 85°). The left column refers to a non-rotating black hole, the right one to a rapidly rotating black hole with a=0.998 M. The white zones stand for the regions with zero redshift. Left-hand side of the disk is approaching the observer and blueshifted (from Fanton et al. 1997).
Figure 4. Disk images of accretion disks extending up to 20 Schwarzschild radii for different spins of Kerr black holes, viewed in different energy ranges and inclination angles (from Zhang et al. 2002).

Ben Bromley et al. (1997) calculated integrated line profiles from a geometrically thin disk about a Schwarzschild and an extreme Kerr black hole, in order to get an observational signature of the frame-dragging effect (Figure 5).

Figure 5. Image of a geometrically thin disk around an extreme Kerr (maximally rotating) black hole seen at an inclination of 75°. The inner and outer radii of the Keplerian (circularly rotating) disk are at 1.24 M and 6 M. The colors encode the apparent light frequency, the white strip divides redshifted and blueshifted regions. The asymmetric appearance of the inner disk edge results from the frame-dragging effect of black hole rotation (from Bromley et al. 1997).

In 1998 Andrew Hamilton started to develop for a student project at the University of Colorado a “Black Hole Flight Simulator”, with film clips that have been shown at planetariums, also available on the Internet. The first depictions were very schematic, but the website was constantly implemented. It now offers journeys into a Schwarzschild or a Reissner-Nordström (i.e. electrically charged) black hole with effects of gravitational lensing on a stellar background field, as well as animated visualizations of magneto-hydrodynamic simulations of a disk and jet around a non-rotating black hole (Hamilton 2018).


Journey into and through an electrically charged (non realistic)  Reissner-Nordström black hole, from Andrew Hamilton, 2010

From Idea to Reality

A turning point in the history of black hole imaging came when the possibility of viewing in practice the shadow of SgrA* with VLBI radio astronomy techniques was first discussed (Falcke et al. 2000, Doeleman et al. 2001). Heino Falcke, Fulvio Melia and Eric Agol (who curiously did not quote my 1979 article) developed a general relativistic ray-tracing code that allowed them to simulate observed images of Sgr A* for various combinations of black hole spin, inclination angle, and morphology of the emission region directly surrounding the black hole (figure 6).

Figure 6. Images of an optically thin emission region surrounding the galactic black hole SgrA*. The black hole is maximally rotating (a = 0.998) in the top row and non-rotating in the bottom row. The emitting gas is assumed to be in free fall (top) or on Keplerian shells (bottom) with a viewing angle 45°. The left column shows the ray-tracing calculations in general relativity, the other columns are the images seen by an idealized VLBI array at 0.6 mm and 1.3 mm wavelengths, taking account of the interstellar scattering (from Falcke et al. 2000).

In 2001, Ben Bromley, Fulvio Melia and Siming Liu provided maps of the polarized emission of a Keplerian disk to illustrate how the images of polarized intensity from the vicinity of SgrA* would appear in future VLBI observations (Figure 7).

Figure 7. Polarization maps at three wavelengths (1.5 mm, 1 mm, 0.67 mm from top row to bottom row) calculated for the galactic black hole candidate SgrA*. The left most column shows how the radio maps might look seen from a close observer, the other columns show how the map might look from Earth with our vision blurred by gas in interstellar space (from Bromley et al. 2001)

Indeed, in parallel with but rather independently from the theoretical simulations reviewed here, the work to image SgrA* by VLBI experiments had begun also back in the 1970’s, after the discovery of the compact radio source Sgr A* at the center of the Milky Way and its identification as the likely emission of gas falling onto a supermassive black hole (Balick and Brown 1974). And as soon as it was realized that the shadow of SgrA* could really be photographed in the forthcoming years, the program of imaging black holes with or without accretion disks and/or stellar background field developed at a much accelerated rate. Several dozens of papers with more or less elaborate visualizations bloomed out, so many that I’ll stop my illustrated history of black hole imaging at this turning point.

As already suspected a long time ago, the gravitational dynamics of stars orbiting the Galactic Center SgrA, as observed for more than 20 years, give a good estimate for the centeal black hole mass : 4.4 millions solar masses. Credit : Keck Observatory.

On the observational side, successive radio imaging observations progressively reduced the size of emission region if SgrA*. A breakthrough was to extend VLBI to 1mm wavelength, where the scattering effects are greatly reduced and angular resolution is matched to the shadow of the galactic black hole. Then the collective effort was named the “Event Horizon Telescope” as the natural convergence of many historical and parallel works done by several independent teams in the world (Doeleman et al. 2009). The later measurement of the size of the 6 billion solar mass black hole in M87 gave a second source suitable for shadow imaging (Doeleman et al. 2012).

Optical image of the giant elliptical galaxy M87 taken by the Hubble Space Telescope. Its core emits an enormous jet of relativistic plasma. At its very center, M87 harbours the second-largest black hole as seen from Earth, M87*, with a mass of 6.6 billion Suns but over 2000 times farther away than Sagittarius A*.

Now the Event Horizon Telescope Consortium involves 20 universities, observatories, research institutions, government agencies and more than a hundred scientists who hope to make black hole imaging a reality as soon as 2019. The first telescopic image of M87* was delivered on April 10th, 2019.

Sheperd Doeleman, director of the Event Hoziron Telescope, at the press conference of April 10th 2019 in which the first telescopic image of black hole M87* was shown.

The path from idea to reality can take very a long time. Imaging black holes, first with computers, now with telescopes, is a fantastic adventure. Forty years ago I couldn’t hope that a real image would be reachable in my lifetime and that, thanks to contributions by so many dedicated colleagues, my dream would become true.

In May 2019 I was invited to give the keynote talk at the 3rd Black Hole Initiative Conference at Harvard University and I could warmly congratulate the EHT team. The young commputer scientist Katie Bouman led the development of one of the various algorithms for imaging black holes. We were glad to meet each other, the young and the old !

With Katie Bouman on 21 May 2019 at the Black Hole Initiative Conference, Harvard University

Here is the video of my talk :

Technical References for the 3 posts

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Balick, B., Brown, R.L. : Intense sub-arcsecond structure in the galactic center, Astrophys. J. 194, 265-270 (1974).

Bardeen, J. M. 1973, Timelike and null geodesics in the Kerr metric, in Black Holes (Les Astres Occlus), ed. C. Dewitt & B. S. Dewitt, New York: Gordon and Breach, pp.215–239.

Bromley, B., Chen, K., Miller,W. : Line Emission from an Accretion Disk around a Rotating Black Hole: Toward a Measurement of Frame Dragging, Astrophys.J. 475, 57 (1997).

Bromley, B., Melia, F., Liu, S. : Polarimetric Imaging of the Massive Black Hole at the Galactic Center, Astrophys.J. 555, L83-86 (2001).

Carter B. : Axisymmetric Black Hole Has Only Two Degrees of Freedom, Physical Review Letters 26, 331 (1971).

Carter B. , Luminet, J.-P. : Les Trous Noirs, Maelströms cosmiques, La Recherche 94, 944 (1978).

Carter B. , Luminet, J.-P. : Pancake Detonation of Stars by Black Holes in Galactic Nuclei, Nature 296, 211 (1982).

Chatzopoulos, S., Fritz, T. K., Gerhard, Gillessen, O., S. , Wegg, C. , Genzel, R. , Pfuhl, O. : The old nuclear star cluster in the Milky Way: dynamics, mass, statistical parallax, and black hole mass, MNRAS, 447, 948 (2015)

Cunningham, C. T. : The effects of redshifts and focusing on the spectrum of an accretion disk around a Kerr black hole, Astrophys. J., 202, 788 (1975)

Cunningham, C.T., Bardeen J.M. : The optical appearance of a star orbiting an extreme Kerr black hole, Astrophys. J.173 L137-142 (1972).

Cunningham, C.T., Bardeen J.M. : The optical appearance of a star orbiting an extreme Kerr black hole, 1973, Astrophys. J., 183, 237

Davelaar, J., Bronzwaer, T., Kok, D., Younsi, Z., Moscibrodzka, M., Falcke, H.: Observing supermassive black holes in virtual reality, Computational Astrophysics and Cosmology 5,1 (2018). https://doi.org/10.1186/s40668-018-0023-7

Delesalle, L. , Lachièze-Rey, M. , Luminet, J.-P. : Infiniment Courbe, TV documentary, 52 mn, France: CNRS/Arte, 1994.

Doeleman, S.S., et al. : Structure of Sagittarius A* at 86 GHz using VLBI closure quantities, Astron. J., 121, 2610-2617 (2001).

Doeleman, S.S., et al. : Event-horizon-scale structure in the supermassive black hole candidate at the Galactic Centre, Nature, 455, 78 (2008).

Doeleman, S.S., et al. : Imaging an Event Horizon : submm-VLBI of Super massive Black Hole, The Astronomy and Astrophysics Decadal Survey, Science White Papers, no. 68 (2009).

Doeleman, S.S., et al. : Jet-Launching Structure Resolved Near the Supermassive Black Hole in M87, Science 338 (6105), 355 (2012).

Doeleman, S.S. : Seeing the unseeable, Nature Astronomy 1, 646 (2017)

Falcke, H. : Imaging black holes : past, present and future, Journal of Physics : Conf. Series 942, 012001 (2017)

Falcke, H., Melia, F., Agol, E. : Viewing the Shadow of the Black Hole at the Galactic Center, Astrophys. J. Lett. 528, L13–L16 (2000).

Fanton C., Calvani M., de Felice F., Cadez A. : Detecting Accretion Disks in Active Galactic Nuclei, Publ. Astron. Soc. Japan 49, 159-169 (1997).

Fukue, J., Yokoyama, T. : Color Photographs of an Accretion Disk around a Black Hole, Publications of the Astronomical Society of Japan 40, 15–24 (1988).

Goddi, C., Falcke, H., et al.: BlackHoleCam: fundamental physics of the galactic center. Int. J. Mod. Phys. D 26, 1730001-239 (2017).

Hamilton, A.: Falling into a black hole. http://jila.colorado.edu/~ajsh/insidebh/intro.html (1998-2018). Accessed 2019-02-26.

Hills, J.G. : Possible power source of Seyfert galaxies and QSOs, Nature 254, 295 (1975).

James, O., von Tunzelmann, E., Franklin, P., Thorne, K.S.: Gravitational lensing by spinning black holes in astrophysics, and in the movie Interstellar. Class. Quantum Gravity 32(6), 065001 (2015).

Johnson, M. D. , Bouman, K. L., Blackburn, L. L. , Chael, A. A., Rosen, J. , Shiokawa, H. , Roelofs, F. , Akiyama, K. , Fish, V. L. , Doeleman S. S. : Dynamical Imaging with Interferometry, Astrophys. J., 850(2), 172 (2017).

Kerr, R.P. : Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics, Physical Review Letters 11, 237 (1963).

Kormendy, J., Ho, L. : Supermassive Black Holes in Inactive Galaxies, Encyclopedia of Astronomy and Astrophysics, ed. P.Murdin, article id. 2635. Bristol : Institute of Physics Publishing (2001).

Luminet J.-P.: Seeing Black Holes : from the Computer to the Telescope, Universe 4(8), 86 (2018) [arXiv :1804.03909].

Luminet, J.-P. : Black Holes, Cambridge University Press, 1992.

Luminet, J.-P. : Interstellar Science, International Review of Science vol.1 n°2 (march 2015) [arXiv : 1503.08305].

Luminet, J.-P.: Image of a Spherical Black Hole with Thin Accretion Disk, Astron.Astrophys. 75, 228 (1979).

Marck J.-A., Luminet, J.-P. : Plongeon dans un trou noir, Pour la Science Hors-Série Les trous noirs (July 1997) 50–56.

Marck, J.-A. : Color animation of a black hole with accretion disk, https://www.youtube.com/watch?v=5Oqop50ltrM (1991) (put online in 2011 by J.-P. Luminet).

Marck, J.-A. : Colored images of a black hole accretion disk for various angles of view, unpublished (1989).

Marck, J.-A. : Flight into a Black Hole, videocassette 11 mn, Meudon : CNRS Images (1994).

Marck, J.-A. : Short-Cut Method of Solution of Geodesic Equations for Schwarzschild Black Hole, Classical and Quantum Gravity 13(3) 393–402 (1996).

Marrone, D. P., Moran, J. M., Zhao, J.-H., Rao, R. : An Unambiguous Detection of Faraday Rotation in Sagittarius A*, Astrophys. J. Lett. 654, L57 (2007).

Nemiroff, R. : Visual distortions near a neutron star and black hole, Am. J. Phys. 61, 619 (1993) [astro-ph/9312003].

Nemiroff, R. Trip to a Black Hole https://www.youtube.com/watch?v=ehoOkyHtBXw (2018)

Nerval, G. de : Le Christ aux Oliviers, in Les Chimères, Paris, 1854. Free translation by J.-P. Luminet.

Ohanian, H. C. : The Black Hole as a Gravitational ‘Lens’, Am. J. Phys. 55, 428-432 (1987).

Page, D.N., Thorne, K.S. : Disk Accretion onto a Black Hole. I. Time-Averaged Structure of Accretion Disk, Astrophys. J. 191, 499-506 (1974).

Palmer L., Pryce M. & Unruh W. : Simulation of starlight lensed by a camera orbiting a Schwarzschild black hole, unpublished (1978).

Pounds, K. A. et al. : An ultra-fast inflow in the luminous Seyfert PG1211+143, Monthly Notices of the Royal Astronomical Society 481(2), 1832-1838 (2018).

Pringle, J. E., Rees, M. J. : Accretion Disc Models dor Compact X-ray Sources, Astron. Astrophys. 21 , 1 (1972).

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Sargent, W. L., Young, P. J., Lynds, C. R., et al. : Dynamical evidence for a central mass concentration in the galaxy M87, Astrophys. J. 221, 731–744 (1978).

Schastok, J. , Soffel, M. , Ruder, H., Schneider, M. : Stellar Sky as Seen From the Vicinity of a Black Hole, Am. J. Phys., 55, 336-341 (1987).

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Shakura, N.I., Sunyaev, R. A. : Black holes in binary systems. Observational appearance. Astro. Astrophys. 24, 337-355 (1973)

Stuckey, W. M. : The Schwarzschild Black Hole as a Gravitational Mirror, Am. J. Phys. 61(5), 448-456 (1993).

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40 Years of Black Hole Imaging (2): Colors and movies, 1989-1993

Sequel of the previous post 40 Years of Black Hole Imaging (1)

First Flight into a Black Hole

In 1989-1990, while I spent one year as a research visitor at the University of California, Berkeley, my former collaborator at Paris-Meudon Observatory, Jean-Alain Marck, both an expert in general relativity and computer programming, started to extend my simulation of 1979. The fast improvement of computers and visualization software (he used a DEC-VAX 8600 machine) allowed him to add colors and motions. To reduce the computing time, Marck developed a new method for calculating the  geodesics in Schwarzschild space-time, published only several years later (Marck 1996). In a first step Marck started from my model of 1979 and calculated static images of an accretion disk around a Schwarzschild black hole according to various angles of view, see Figure 1 below.

Figure  1. False-Coloured images of a black hole accretion disk for various angles of view by J.-A.
Marck &  J.-P. Luminet , 1989 (unpublished).

In 1991, when I went back to Paris Observatory, I started the project for the French-German TV channel Arte of a full-length, pedagogical movie about general relativity (Delesalle et al. 1994). As the final sequence dealt with black holes, I asked Marck to introduce motion of the observer with the camera moving around close to the disk, as well as to include higher-order lensed images and background stellar skies in order to make the pictures as realistic as possible. The calculation was done along an elliptic trajectory around a Schwarzschild black hole crossing several times the plane of a thin accretion disk and suffering a strong relativistic precession effect (i.e. rotation of its great axis), see figure 2 below.

Compared to my static, black-and-white simulation of 1979, the snapshot reproduced in Figure 3 below shows spectacular improvements:

Figure 3. Colored image of a black hole accretion disk as seen by a moving observer at 7°
above the disk’s plane. The observer uses a camera equipped with filters to convert into
optical radiation the emitted electromagnetic radiation. The arbitrary coloring encodes the
apparent luminosity of the disk, the brightest and warmest parts being colored yellow, the
colder parts red. The transparency of the disk was enhanced in order to show the secondary
image through the primary, as well as some background stars. Compared with figure 8 there
are additional distortions and asymmetries due to the Doppler effect induced by the motion of
the observer himself. As a result the region of maximum luminosity has no more the shape of a
crescent (from Marck 1991)

The full movie is  available on my youtube channel :

Continue reading

40 Years of Black Hole Imaging (1): Early work 1972-1988

Introduction

Black holes are to many the most mysterious objects in space. According to the laws of General Relativity, they are by themselves invisible. Contrarily to non-collapsed celestial bodies, their surface is neither solid nor gaseous ; it is an immaterial border called the event horizon, beyond which gravity is so strong that nothing can escape, not even light.

Seen in projection on a sky background, the event horizon would have the aspect of a perfectly circular black disk if the black hole is static (the so-called Schwarzschild solution) or of a slightly distorted one if it is in rotation (the Kerr solution). Due to strong gravitational lensing, such a « bare » black hole could leave an observable imprint on a starry background. However, in typical astrophysical conditions, whatever its size and mass (ranging from stellar to galactic scales) a black hole is rarely bare but is dressed in gaseous material. Swirling in a spiral motion, the gas forms a hot accretion disk within which it emits a characteristic spectrum of electromagnetic radiation. Giant black holes, such as those currently lurking at the centers of galaxies, can be also surrounded by a stellar cluster, whose orbital dynamics is strongly influenced. As a matter of fact, , if a black hole remains by itself invisible, it “switches on” in its characteristic way the materials it attracts, and distorts the background starry field by gravitational lensing.

Thus, as soon as the basics of  black holes astrophysics developed in the 1970’s,  the scientists logically wondered what could look like a black hole. Many of you certainly saw didactic or artistic representations of a black hole in popular science magazines, in the form of a black sphere floating in the middle of a circular whirlwind of brilliant gas. So striking they are, these images fail to report the astrophysical reality. This one can be correctly described by means of numerical simulations, taking into account the complex distortions that the strong gravitational field prints in spacetime and light rays trajectories.

Since the first numerical simulations performed 40 years ago, tantalizing progress has been done to detect black holes through electromagnetic radiation from infalling matter or gravitational waves. The first telescopic image by the Event Horizon Telescope of the nearest giant black hole SgrA*, lurking at he center of our Milky Way galaxy, is expected for 2018.

The aim of this series of posts is to retrace the rich history of black hole imaging.

Preliminary steps

Black hole imaging started in 1972 at a Summer school in Les Houches (France). James Bardeen, building on earlier analytical work of Brandon Carter, initiated research on gravitational lensing by spinning black holes. Bardeen gave a thorough analysis of null geodesics (light-ray propagation) around a Kerr black hole. The Kerr solution had been discovered in 1962 by the New Zealand physicist Roy Kerr and since then focused the attention of many searchers in General Relativity, because it represents the most general state of equilibitum of an astrophysical black hole.

The Kerr spacetime’s metric depends on two parameters : the black hole mass M and its normalized angular momentum a. An important difference with usual stars, which are in differential rotation, is that Kerr black holes are rotating with perfect rigidity : all the points on their event horizon move with the same angular velocity. There is however a critical angular momentum, given by  a = M (in units where G=c=1) above which the event horizon would « break up » : this limit corresponds to the horizon having a spin velocity equal to the speed of light. For such a black hole, called « extreme », the gravitational field at the event horizon would cancel, because the inward pull of gravity would be compensated by huge repulsive centrifugal forces.

James Bardeen computed how the black hole’s rotation would affect the shape of the shadow that the event horizon casts on light from a background star field. For a black hole spinning close to the maximum angular momentum, the result is a D-shaped shadow.

Apparent shape of an extreme Kerr black hole as seen by a distant observer in the equatorial plane, if the black hole is in front of a source of illumination with an angular size larger than that of the black hole. The shadow bulges out on the side of the hole moving away from the observer (at right) and squeezes inward and flattens on the side moving toward the observer (at left).

The reference is Bardeen, J. M. 1973, Timelike and null geodesics in the Kerr metric, in Black Holes (Les Astres Occlus), ed. C. Dewitt & B. S. Dewitt, (New York: Gordon and Breach) p.215–239

At the time, C.T. Cunningham was preparing a PhD thesis at the University of Washington in Seattle, under the supervision of Bardeen. He began to calculate the optical appearance of a star in circular orbit in the equatorial plane of an extreme Kerr black hole, taking account of the Doppler effect due to relativistic motion of the star, and pointed out the corresponding amplification of the star’s luminosity. He gave formulas but did not produced any image.
The reference is Cunningham, C.T. and Bardeen J.M., The optical appearance of a star orbiting an extreme Kerr black hole, ApJ 173 L137-142 (1972).

One year later Cunningham and Bardeen published a more complete article with the same title. For the first time a picture was shown of the primary and secundary images of a point source moving in a circular orbit in the equatorial plane of an extreme Kerr  black hole. They calculated as functions of time the apparent position and the energy flux of the point source as seen by distant observers.

Apparent positions of the two brightest images as functions of time for two orbital radii and an observer art a polar angle 84°.024. The small, dashed circle in each plot gives the scale of the plot in units of M. The direct image moves along the solid line, the secundary image along the dashed line. Ticks mark the positions of the images at 10 equally spaced times.

In the upper diagram showing the distorted image of a circle of radius  20M, we clearly see that, whatever the observer’s inclination angle, the black hole cannot mask any part of the circle behind. We also see that the black hole’s spin hardly affects the symmetry of the primary image (although the asymmetry is stronger for the secundary image).
The exact reference is Cunningham, C.T. and Bardeen J.M., The optical appearance of a star orbiting an extreme Kerr black hole, 1973, ApJ, 183, 237. The article can be uploaded here.

In 1975, Cunningham calculated the effects of redshifts and focusing on the spectrum of an accretion disk around a Kerr black hole. He gave formulas and drawed graphics but no image.
The reference is  Cunningham, C. T., The effects of redshifts and focusing on the spectrum of an accretion disk around a Kerr black hole, ApJ, 202, 788 (1975)

In 1978 Leigh Palmer, Maurice Pryce and William Unruh carried out,  for pedagogical purpose, a simulation of starlight lensed by a camera orbiting a Schwarzschild black hole, using an Edwards and Sutherland Vector graphics display at Simon Fraser University. They showed a film clip in a number of lectures in that period, but unfortunately they did not publish their simulation, so that I can’t reproduce here any image.

First calculations for a black hole accretion disk

The same year and quite independently, as a young researcher at Paris-Meudon Observatory specialized in the mathematics of General Relativity, I wondered what could be the aspect of a Schwarzschild black hole surrounded by a luminous accretion disk. Continue reading

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

 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

The Rate of Expansion

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

Galaxies in Flight

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

TOTAL SOLAR ECLIPSE 2017 : THE ROLE OF SOLAR ECLIPSES IN ASTROPHYSICS

In view of the total solar eclipse of 2017 Aug 21 through the United States, this is a reminder of the role of solar eclipses in the developments of astronomy and astrophysics.
It is taken from a chapter of my book Glorious Eclipses, presented elsewhere in this blog.

Summary

Eclipses of the Sun and Moon have never ceased to provide us with a host of lessons about the nature of the universe around us. The first of these lessons concerned the celestial bodies directly involved in eclipses: namely the Earth, Moon, and Sun. Indeed, back in antiquity, the proof that the Earth was round, and the first measurements of the respective sizes and distances of the Moon and Sun were deduced from the observation of eclipses. In the 19th century, it was the normally invisible atmosphere of the Sun that was revealed thanks to eclipses. Far from being the perfectly round, and sharply defined ball of hot gas that it appears to the eye – appropriately protected by suitable filters, of course – the Sun is found to be a sprawling giant, overflowing with energy, plasma, and particles, that extends its influence throughout the whole Solar System. Eclipses also provoked the discovery of helium, the second most abundant element in the Sun, and in the universe as a whole. In a more surprising manner, in the 20th century, Einstein’s General Relativity, a fundamental theory about space, was tested experimentally for the first time, thanks to an eclipse. It is on this new vision of the universe, which explains gravitation in terms of the ‘curvature of space-time’, that all our current knowledge of the origin, the structure, and the evolution of the universe, depends, by way of the fascinating concepts of an expanding universe, the Big Bang, and black holes.

During a total eclipse, the Sun’s invisible empire appears : eruptions and prominences rise above the level of the photosphere, and colour the Sun’s inner atmosphere, known as the chromosphere.
The Earth is round
According to Aristotle, lunar eclipses prove that the Earth is round. Indeed, if the Earth were square, or triangular, its shadow projected onto the disk of the Moon at the time of an eclipse would not appear circular. Aristotle’s geometrical argument is shown in several ancient astronomy texts, including Cosmographia, by Petrus Apianus and Gemma Frisius, 1581.

The first demonstration of an astrophysical nature resulting from eclipses is the one given by Aristotle concerning the fact that the Earth is round. The astronomical views of this Greek philosopher are well-known to us, thanks to his two works, known to us as Meteorology and On the Heavens, dating from the 4th century BC. Like other thinkers of his day, Aristotle believed that all heavenly bodies were spherical, because to him heavenly bodies were a reflection of divine perfection, and the sphere is the most outstandingly perfect geometrical figure. But this argument was not a physical demonstration, because, naturally, Aristotle did not have any experimental means of confirming the spherical nature of the planets and stars.
As far as the Moon was concerned, the philosopher adopted an explanation attributed to the Pythagoreans, namely that the observed appearance of the Moon throughout its various phases corresponded to a spherical body, half of which is illuminated by the Sun. As for the spherical nature of the Earth, the proof given by Aristotle is quite original: he notes that an eclipse of the Moon is caused by the shadow of the Earth, and that the circular shape to the edge of the shadow seen on the Moon’s surface implies that our world is spherical

Sizes and distances of the Moon and Sun

The golden age of Greek astronomy flourished at Alexandria. Since its foundation under the reign of Ptolemy Soter (3rd century BC), the Alexandrian school brought together brilliant mathematicians and geometers, such as Euclid, Archimedes, and Apollonius. Similarly, the greatest ancient astronomers Aristachus of Samos, Eratosthenes, and Hipparchus, as well as Ptolemy (2nd century BC), all worked there.

Aristarchus (310-230 BC) is nowadays known for having been the first to voice the heliocentric theory, i.e., that it is the Sun that reigns at the centre of the world system, not the Earth as was believed at the time. His statement does not appear in any known work, but it was reported by Archimedes and by Plutarch. The only work of Aristarchus that has come down to us relates to the sizes and distances of the Sun and the Moon.
The Alexandrian astronomer completely reopened this question, which had been discussed since the 4th century BC. The Pythagoreans had positioned the heights of the celestial bodies according to musical intervals. Eudoxus, the brilliant disciple of Plato, had estimated the diameter of the Sun as nine times that of the Moon. As for Aristarchus, he devised an ingenious geometrical method of calculating the distance ratios of the Sun and Moon.

On the Sizes and Distances of the Sun and the Moon is the only surviving work usually attributed to Aristarchus.

 

Aristarchus of Samos tried to calculate the relative diameter of the moon and sun, as deduced from the line subtending the arc that divides the light and dark portions of the moon during an eclipse.

 He found that the Sun lay at a distance between 18 and 20 times that of the Moon. (In fact, it is 400 times as far.) By an argument based on the observation of eclipses, he determined the diameter of the Moon as one third of that of the Earth, which is very close to the actual value. He also announced that the diameter of the Sun is seven times that of the Earth. Even though Aristarchus considerably underestimated the size of the Sun, because it is actually 109 times as large as the Earth, he had grasped the essential fact that the daytime star was much larger than the Earth. It was precisely this result that led him to the heliocentric hypothesis. He did, in fact, argue that under these circumstances, it was logical to believe that the Earth and the other celestial bodies revolved around the Sun, rather than the reverse. Aristachus was before his time. The world had to wait until 1543 and the work by Copernicus, before the heliocentric theory was again put forward, this time with success.

A century after Aristachus, and again at Alexandria, Hipparchus developed a complete theory of the Moon.   He defined the   lengths of the synodic month (or lunation, the period in which the Moon returns to the same position relative to   the   Sun);   the   draconitic month   (the period for the Moon to return to the same position   relative to the nodes of its   orbit);   and   the anomalistic month (the period for the Moon to return to perigee or apogee). The immense improvements that   Hipparchus brought to theories of the apparent motion of the Moon and Sun enabled him to have far more success than his predecessors in dealing with the problem of predicting eclipses, which had always   been   of   immense   interest.

Hipparchus   considerably   extended Aristarchus’ method: by observing the angular diameter of the shadow of the Earth at the Moon’s distance during a lunar eclipse, and comparing it with the known apparent diameters of the Sun and Moon (about half a degree), he obtained the ratio of the Earth-Moon and   Earth-Sun distances, giving one when   the   other   is   known.   Pappus, another famous   astronomer of the Alexandrian   school,   recounts   that Hipparchus     made     the     following observation of: “An eclipse of the Sun, which in the area of the Hellespont was precisely an exact eclipse of the whole Sun; such that none of it was visible,   but at Alexandria,   in   Egypt, about 4/5 of its diameter were hidden. By means of the foregoing arguments, [Hipparchus] showed that,   measured in   units   where   the   radius   of   the Earth has the value of 1, the smallest distance to the Moon is 71, and the larger 83. Whence the average of 77.

The total solar eclipse mentioned is that of 20 November 129 BC. The actual value of the Earth-Moon distance is 60,4 terrestrial radii.

During a total eclipse of the Sun, the electrified plasma hugs the lines of the sun’s magnetic field, just as iron filings follow those of a magnet. The corona displays narrow filaments over the poles, and extends in a more homogeneous manner in the equatorial regions.
The empire of the Sun

Continue reading

A brief history of space (4/4)

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

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

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

A Brief History of Space (2/4) : from Ptolemy to Galileo

Sequel of the preceding post A Brief History of Space (1/4).

The cosmology of Aristotle, as perfected by Ptolemy and reintroduced thanks to arabic translations and commentaries, was adapted to satisfy the demands of the theologians. Notably, that which is situated beyond the last material sphere of the world acquired the status of, if not physical, at least ethereal or spiritual space. Baptized “Empyrean”, it was considered to be the residence of God, the angels and the saints. The medieval cosmos was not only finite, but quite small: the distance from the Earth to the sphere of the fixed stars was estimated to be 20,000 terrestrial radii, because of which Paradise, at its edge, was reasonably accessible to the souls of the deceased. The Christian naturally found his place at the center of this construction.

In this medieval system of the world designed by Apianus in 1520, the whole universe is finite, bounded by a spherical layer containing the fixed stars, beyond which lies the Empyreum, the house of God and Saints.
In this medieval system of the world designed by Apianus in 1520, the whole universe is finite, bounded by a spherical layer containing the fixed stars, beyond which lies the Empyreum, the house of God and Saints.

A Hierachical universe according to Dante's Divine Comedy
A Hierarchical universe according to Dante’s Divine Comedy

 

Nicholas of Cusa
Nicholas of Cusa

This model of the universe imposed itself until the seventeenth century, without nevertheless impeding the resurgence of atomist ideas. After the rediscovery of the manuscript of Lucretius De rerum natura, the German cardinal Nicholas of Cusa (1401-1464) argued in favor of an infinite Universe, of a plurality of inhabited worlds, and of an Earth in motion. However, his arguments remained primarily metaphysical: the universe is infinite because it is the work of God, who could not possibly be limited in His works.

When the Polish canon Nicolaus Copernicus (1473-1543) proposed his heliocentric system, in which the Sun is at the geometric center of the world while the Earth turns around it and around itself, he kept the idea of a closed cosmos, surrounded by the sphere of fixed stars. Even if this is two thousand times further away than in the Ptolemeian model, the universe nevertheless remained bounded.

A romantic depiction of Copernicus
A romantic depiction of Copernicus and his new model of the universe

We must wait several decades more for the first cracks to appear in the Aristotelian edifice. In 1572, a new star was observed by the Dane Tycho Brahe (1546-1601), who showed that it was situated in the sphere of fixed stars, that is to say in the celestial region until then presumed to be immovable. In 1576, the Englishman Thomas Digges (1545-1595), a staunch Copernican, maintained that the stars were not distributed on a thin layer, at the surface of the eighth and last sphere of the world, but extended endlessly upwards. Digges nevertheless was not proposing a physical conception of infinite space: for him, the sky and the stars remained Empyrean, God’s realm, and in this regard did not truly belong to our world.

copernicus-diag Syst-Digges

An epistemological rupture[1] was triggered by two Italian philosophers. In 1587, Francesco Patrizi (1529-1597) produced Of Physical and Mathematical Space[2], where he put forth the revolutionary idea that the true object of geometry was space in itself, and not figures, as had been believed since Euclid. Patrizi inaugurated a new understanding of infinite physical space, in which it obeyed mathematical laws and was therefore accessible to understanding. But it is above all his contemporary Giordano Bruno (1548-1600) who is attributed with the true paternity of infinite cosmology. brunoThe first book of his De immenso is entirely dedicated to a logical definition of infinite space. Bruno argued from physical, and no longer exclusively theological, basics. His cosmological thought was inspired by the atomism of Lucretius, the reasoning of Nicholas of Cusa, and the Copernican hypothesis. From the latter, Bruno retained heliocentrism and the ordering of the solar system, but rejected the cosmological finitism. A precursor to Kepler and Newton, he also refuted the cult of sphericity and of uniform circular motion for describing celestial motion. His bold and original writings were not understood by his contemporaries, most notably Galileo. Above all they were firmly opposed by the Church. In fact, the true philosophical subversion of the end of the sixteenth century did not reside so much in the heliocentric affirmation of Copernicus as in that of the infinite multiplicity of worlds. Camped at the front ranks of the anti-Aristotelian battle, Bruno, carried away by his passion for infinity, refused to abjure and was burned at the stake in Rome.

Johannes Kepler (1571-1630), another great artisan of the astronomical revolution, tried at first to construct a universal model founded on the use of particular geometric figures: the regular polyhedra. He failed at this attempt; the ordering of planetary orbits as calculated did not correspond to the new experimental data collected by Tycho Brahe. After discovering the elliptical nature of the planetary trajectories, Kepler overturned the Aristotelian dogma of circular and uniform motion as the ultimate explanation of celestial movement. He nevertheless refused to follow Bruno in his arguments for the infinitude of the universe. He considered this notion to be purely metaphysical and, since it was not founded on Kepler_Epitomeexperiment, denuded of scientific meaning: “In truth, an infinite body cannot be understood by thought. In fact the concepts of the mind on the subject of the infinite refer themselves either to the meaning of the word `infinite,’ or indeed to something which exceeds any conceivable numeric, visual or tactile measurement; that is to say to something which is not infinite in action, seeing that an infinite measurement is not conceivable.”[3] Kepler supported his argument by expressing for the first time an astronomical paradox that seemed to be an obstacle to the concept of infinite space, and which would be extensively discussed: the “paradox of the dark night.” Just like the edge paradox, this problem would not be satisfactorily resolved until the middle of the nineteenth century, although by completely different arguments.

Starting in 1609, the telescope observations of Galileo (1564-1642) furnished the first direct indications of the universality of the laws of nature. On the question of spatial infinity, however, Galileo, like Kepler, adopted the prudent attitude of the physicist: “Don’t you know that it is as yet undecided (and I believe that it will ever be so for human knowledge) whether the Universe is finite or, on the contrary, infinite?” [4]

systemegalilee001

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[1] See Alexander Koyre, From the Closed World to the Infinite Universe, New York: Harper Torchbook, 1958.

[2] De spacio physico et mathematico ; See R. Brickman, “On Physical Space, Francesco Patrizi”, Journal of the History of Ideas, vol.4, 224 (1943).

[3] De stella nova, 1606. Unfortunately there is no English translation for this masterpiece.

[4] Letter to Ingoli, quoted in A. Koyré, From the Close World to the Infinite Universe, The John Hopkins Press 1957, p. 97.

A Brief History of Space (1/4)

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.

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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

Cosmogenesis (10) : A Modern Account

Sequel of the preceding post Cosmogenesis (9) : The Big Bang Discovery and End of the Cosmogenesis Series.

According to modern physics the universe has undergone a gradual process of expansion and cooling ever since the big bang; at the same time increasingly complex physical structures have evolved. The history of the universe can conveniently be divided into two main periods: the first million years (infancy) and the remaining 15 billion years (maturity).

The Infant Universe

The Bubble Theory of Cosmogenesis. According to some models constructed according to the laws of quantum physics, the observable universe is merely one of a multitude of ephemeral "bubbles" created by spontaneous fluctuations in the quantum vacuum. The universe as a whole is like a rapidly expanding foam, each "baby universe" giving birth to more "baby universes" and so on in an eternally self-reproducing system. Artistic view by S. Numazawa.
The Bubble Theory of Cosmogenesis. According to some models constructed according to the laws of quantum physics, the observable universe is merely one of a multitude of ephemeral “bubbles” created by spontaneous fluctuations in the quantum vacuum. The universe as a whole is like a rapidly expanding foam, each “baby universe” giving birth to more “baby universes” and so on in an eternally self-reproducing system.
Artistic view by S. Numazawa.

During the Planck era, time and the dimensions of space as we know them were so intimately linked as to be practically indistinguishable. Various speculative theories of “quantum cosmogenesis”, as yet in their infancy, attempt to explain how our universe emerged at the end of the Planck era. Some physicists refer to its “spontaneous emergence”, others to an infinite number of separate “cosmic bubbles” arising from the quantum vacuum like foam from the surface of the sea.

Between 10-43 and 10-32 seconds after the big bang the infant universe consisted of elementary particles bound by a primeval superforce. A few billiseconds later gravity separated itself from the surviving electrostrong force, which in turn, as the temperature fell to 1027 degrees, divided into the strong force and the electroweak force. Recent experiments in high energy physics suggest that these “symmetry breakdowns” had spectacular consequences: the appearance of strange objects; “topological defects” such as “cosmic strings”; even the onset of “inflation” – a very short period during which the universe grew immeasurably. The fundamental constituents of matter – quarks, electrons and neutrinos – also appeared at this time.

10-11 seconds after the big bang the temperature of the universe had dropped to 1015 degrees and the electroweak force split into an electromagnetic and a weak force, thus establishing the four fundamental forces  and fixing the physical conditions for the formation of complex structures.

10-6 seconds after the big bang all quarks were “linked” in threes by the strong force to form the first nucleons, i.e. protons and neutrons. By this time the temperature had fallen to a billion degrees as the universe continued to expand. As particles became more widely spaced, they collided less frequently but one hundred seconds or so later the crucial process of nucleosynthesis began. Neutrons and protons combined to form the simplest atomic nuclei: hydrogen, helium and lithium (in various isotopes). Most of the universe, however, remained as isolated protons, i.e. as hydrogen nuclei.

Nucleosynthesis took place only for a very short time: the universe was cooling so rapidly that there was only time for the lightest elements to form. These therefore constitute 99 per cent of the visible matter in the universe today (75% hydrogen and 24% helium). The remaining one per cent, consisting of heavier elements like carbon, nitrogen and oxygen, would not be created until billions of years later, when the stars were formed.

Nucleosynthesis. Scientists at the particle accelerator near Caen in France (known as GANIL — Grand Accélérateur National d'lons Lourds) have managed to fuse heavy ions by making them collide at high speed. These computer-generated images show the fusion of a lanthanum nucleus with a copper nucleus. Such experiments help scientists to understand the process of nucleosynthesis which, during the first few seconds after the big bang, caused the fusion of hydrogen ions and helium ions, creating the first lightweight elements. Nucleosynthesis is one way of testing big bang theory, whose predictions as to the quantity of each element in the universe can be compared with experimental results. Indeed they are remarkably similar: the universe does in fact comprise 75% hydrogen (in mass) and between 24 and 25% helium (in mass). There is an equally close correlation between the predicted and observed prevalence of deuterium and tritium. Other experimental results are valuable in limiting the possibilities open to those refining big bang theory. Montage by Philippe Chomaz (GANIL)
Nucleosynthesis. Scientists at the particle accelerator near Caen in France (known as GANIL — Grand Accélérateur National d’lons Lourds) have managed to fuse heavy ions by making them collide at high speed. These computer-generated images show the fusion of a lanthanum nucleus with a copper nucleus. Such experiments help scientists to understand the process of nucleosynthesis which, during the first few seconds after the big bang, caused the fusion of hydrogen ions and helium ions, creating the first lightweight elements. Nucleosynthesis is one way of testing big bang theory, whose predictions as to the quantity of each element in the universe can be compared with experimental results. Indeed they are remarkably similar: the universe does in fact comprise 75% hydrogen (in mass) and between 24 and 25% helium (in mass). There is an equally close correlation between the predicted and observed prevalence of deuterium and tritium. Other experimental results are valuable in limiting the possibilities open to those refining big bang theory.
Montage by Philippe Chomaz (GANIL)

Until it was 300,000 years old the universe remained opaque; in other words it emitted no radiation: the density of electrons prevented photons from moving freely. But the universe, consisting of a “soup” of particles and radiation, continued to cool and expand until, at 3,000 degrees, it became transparent and emitted its first electromagnetic signal in the form of what we now detect as cosmic background radiation.

A million years after the big bang the first atoms were formed, when electrons were captured by hydrogen and helium nuclei, and these atoms combined into molecules to create vast clouds of hydrogen, out of which stars would later emerge. Continue reading

Cosmogenesis (9) : The Big Bang Discovery

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

Cosmogenesis (8) : The Nebular Hypothesis

Sequel of the preceding post Cosmogenesis (7) : The Date of the Creation

The Nebular Hypothesis

The ancient Babylonians had a different idea of how the world began. They believed that it had evolved rather than being created instantaneously. Assyrian inscriptions have been found which suggest that the cosmos evolved after the Great Flood and that the animal kingdom originated from earth and water. This idea was at least partially incorporated into a monotheist doctrine and found its way into the sacred texts of the Jews, neighbors and disciples of the Babylonians. It was also taken up by the early Ionian philosophers, including Anaximander and Anaximenes, and by the Stoics and atomists.

A portrait of Democritus (460-370 BC), the founder of atomistic theory.
A portrait of Democritus (460-370 BC), the founder of atomistic theory.

Democritus developed a theory that the world had originated from the void, a vast region in which atoms were swirling in a whirlpool or vortex. The heaviest matter was sucked into the center of the vortex and condensed to form the earth. The lightest matter was thrown to the outside where it revolved so rapidly that it eventually ignited to form the stars and planets. These celestial bodies, as well as the earth itself, were kept in position by centrifugal force. This concept admitted the possibility that the universe contained an infinite number of objects. It also anticipated the 19th century theory of the origin of the solar system, known as the nebular hypothesis, according to which a “primitive nebula” condensed to form the sun and planets.

The idea of universal evolution had a strong influence on classical thought and developed in various directions during Greek and Roman times. In the first century BC Lucretius extended the theories of atomism and evolution to cover every natural phenomenon[i] and argued that all living things originated from earth. Two centuries later, in his medical treatise On the Use of the Parts of the Body[ii], the Greek physician Galen (Claudius Galenus) expressed the essentially Stoic view that matter is eternal and that even God is subject to the laws of nature: contrary to the literal interpretation of the Genesis story, he could not have “formed man from the dust of the ground”; he could only have shaped the dust according to the laws governing the behaviour of matter. The Church Fathers, who insisted that the Creation was instantaneous, rejected any sort of evolutionary theory; to them the ideas of the Stoics and atomists were heretical.

In the second half of the 16th century the idea of universal evolution began to be incorporated into the new system of scientific thought resulting from the work of Copernicus, Kepler, Galileo, Descartes and Newton. According to Descartes, for example, space consisted of “whirlpools” of matter whose motion was governed by the laws of physics. Newton, with his theory of universal attraction, was accused of having substituted gravitation for providence, for having replaced God’s spiritual influence on the cosmos by a material mechanism[iii]. A new view of the world had nevertheless been established, whereby the workings of the universe were subject not to the whim of the Almighty but to the laws of physics – it was an irreversible step. Continue reading

Cosmogenesis (7) : The Date of the Creation

Sequel of the preceding post Cosmogenesis (6) : The Creation in the Renaissance

The Date of the Creation

None of the traditional myths gives a precise date for the Creation. The very idea of putting dates to the history of the world seems to have been foreign to the mentality of the ancients. For them the origin of the universe was simply a notion which helped them to understand the separation of reality into two regions: formless chaos and cosmic order. It was the Jewish/Christian preoccupation with time as a linear process which prompted the question: when was the Creation? From then on the greatest theologians (from Eusebius of Caesarea in the fourth century to James Ussher, Irish prelate and archbishop of Armagh, in the 17th century) and scientists (from Kepler to Newton) would attempt to provide the answer.

For centuries the only clues were to be found in the Bible, which was thought to be able at least to provide an upper limit to the age of the world. From studying the Bible, the vast majority of scholars put the date of the Creation at around 4000 BC, the most common method of calculation being to count the number of generations between Adam and Jesus. St Luke[i] and other commentators list 75 generations, which at approximately 50 years per generation make 4000 BC a plausible date. This reasoning was accepted until the 18th century, even though Ronsard ended his Hymn to the Sky of 1555 with the words: “Your beauty is such that I simply cannot believe / It is but four or five thousand years since your beginning.

More precise estimates gradually appeared. According to the theologian and historian the Venerable Bede in the eighth century and Vincent de Beauvais in the 13th, the Creation took place in the spring.

Depiction of the Venerable Bede from the Nuremberg Chronicle, 1493
Depiction of the Venerable Bede from the Nuremberg Chronicle, 1493

In his historical treatise Annales Veteris Testamenti, a Prima Mundi Origine Deducti (Annals of the Old Testament, Traced Back to the Origin of the World) of 1650, James Ussher attempted to determine precisely the dates of the great biblical events by checking them against historical facts and astronomical phenomena. According to his calculations the first day of the Creation was 23rd October 4004 BC (beginning at midday) and Adam and Eve were expelled from the Garden of Eden on Monday 19th November, Noah’s Ark went aground on the summit of Mount Ararat on 5th May 1491 BC, and so on.

Similarly, in 1642, the Vice-Chancellor of Cambridge University, John Lightfoot, an eminent Hebrew scholar, stated that “heaven and earth, centre and circumference, were created all together, in the same instant” and that “man was created by the Trinity on October 23, 4004 BC at nine o’clock in the morning.”[ii] Continue reading

Cosmogenesis (5) : The Order of the Creation

Sequel of the preceding post Cosmogenesis (4) : The Creator

The order of the Creation

“Order and Truth are born when Passion is aroused. From them is born Night and from Night the Ocean and its waves. From the Ocean’s waves is born the Year, which apportions Night and Day and governs all that the eye sees. The Creator gave shape first to the Sun and Moon, then to the Sky and the Earth, then to the Air and finally to Light.”
Rig-veda, X, 190.

According to Vedic tradition the Creation took place in a completely different order from that specified by the familiar Jewish/Christian story: on the first day God created matter and light out of chaos; on the second day He,  created the air by separating the sky from the waters; on the third day He divided the earth and the waters; on the fourth day He created the celestial bodies, on the fifth the fish and the birds and on the sixth the animals and man; finally, on the seventh day, God rested and contemplated his work.

According to Genesis the separation of light and darkness took place on the first day, the sun and moon not appearing until the fourth. The light which existed on the first day therefore did not come from the sun. Here the bible is perpetuating an ancient belief that light and darkness are independent of the sun, moon and stars, which exist not to provide light but merely to increase it, to distinguish between day and night, to mark the changing of the seasons, and so on. “We must remember that daylight is one thing and sunlight, moonlight and starlight another – the sun’s purpose is to give daylight additional brilliance,” wrote St Ambrose in his Hexameron.

This idea is clearly illustrated by the mosaics in St Mark’s cathedral in Venice and by the frescos in the baptistery in Florence and the basilica of St Francis at Assisi, all of which show the Creator placing in the sky two discs of equal size distinguished only by their colour or by an inscription.

The Creation of Light. The ceiling of St Mark's cathedral in Venice is adorned with a series of beautiful mosaics illustrating the story of Genesis. The pictures relating to the Creation, in the first cupola, were probably completed around 1220 and are modelled on the Cotton bible, a 5th or 6th century illuminated copy of an -ancient Greek manuscript.
The Creation of Light. The ceiling of St Mark’s cathedral in Venice is adorned with a series of beautiful mosaics illustrating the story of Genesis. The pictures relating to the Creation, in the first cupola, were probably completed around 1220 and are modelled on the Cotton bible, a 5th or 6th century illuminated copy of an -ancient Greek manuscript.

Whereas mythical and religious stories describe the creation of the world (by one or more gods), scientific “accounts” are concerned with the formation and evolution of the universe and its content. There are, however, many parallels between these two approaches.

The Creation of Heaven and Earth. The caption to this bible illustration reads: "The Creation of Heaven and Earth, of Trees, Plants, Stars and all the Animals". The engraving therefore represents the first five days of the Creation. God the Father is seen setting the sun and moon among the clouds and the stars; below are the creatures of the land (left) and the sea (right). Engraving by Jean Cousin, in Figures de la Bible, Paris, 1614.
The Creation of Heaven and Earth. The caption to this bible illustration reads: “The Creation of Heaven and Earth, of Trees, Plants, Stars and all the Animals”. The engraving therefore represents the first five days of the Creation. God the Father is seen setting the sun and moon among the clouds and the stars; below are the creatures of the land (left) and the sea (right). Engraving by Jean Cousin, in Figures de la Bible, Paris, 1614.

 

The Creation of the World According to the Nuremberg Chronicle Continue reading