Centennial event

One-hundred years ago this month, in Berlin on Thursday, November 25, 1915 as World War I was raging fiercely all across Europe, the global community witnessed a seminal scientific breakthrough: Albert Einstein (1879–1955), in addressing the Prussian Academy of Sciences, presented his relativistic field equations of gravitation

thus ending a 10-year conceptual struggle full of heavily exhausting emotional ups and downs. (“Relativistic” in this context means, foremost, independent of an observer’s frame of reference, i.e., the same for all observers.)

Paradigm shift

Einstein’s proposal meant nothing less than a profound paradigm shift in theoretical physical thinking. Up to then, the Newtonian theory had pronounced that physical interactions between material objects unfold on a passive stage built rigidly from absolute space and absolute time. Now a scenario was proposed in which the geometry of the spacetime continuum (technically: manifold), as represented by a metric g determining physical distances and proper time intervals between events, actively influences the motion of matter, and in turn is itself being influenced by matter. In consequence, one abandoned the view that a gravitational force (“gravity”) was responsible for the deflection of a small mass when moving in the vicinity of a big mass, in favour of the interpretation that very large matter distributions generate curvature in the geometry of the spacetime continuum wherein freely falling massive objects and light rays follow the straightest paths possible (“geodesics”). This state of affairs was later famously subsumed by the eminent US-American theoretical physicist John Wheeler (1911–2008) (Misner et al 1973: 408) under the catch phrase

“Geometry tells matter how to move, and matter tells geometry how to curve.”

At its very core, this statement characterises gravitation as an inherently non-linear physical phenomenon.

Gravitation is by far the weakest of the four empirically known fundamental physical interactions in Nature. It becomes a dominating dynamical influence only when astronomically large (huge!) masses are involved, triggering, e.g., the gravitational collapse of gigantic clouds of hydrogen gas in the Universe to form stars, galaxies, and clusters thereof.

Empirical basis and early predictions

At the time of its inception in 1915, the general theory of relativity (as it is referred to since then) had no proper empirical foundation. It was scientifically compelling to experts only to the extent that it succeeded in explaining the advance of the perihelion (point of closest approach) of planet Mercury’s orbit around the Sun, a peculiar effect known to astronomers since 1859.

Einstein was well aware of the fact that only strong gravitational field settings had the potential of revealing differences in measurements of effects between the old Newtonian theory and his new relativistic scenario. His immediate predictions during World War I in this respect were the existence of

1. a gravitational redshift of light emitted by large compact objects such as stars or galaxies,
2. a deflection of light rays passing near massive compact objects like the Sun, providing the conceptual basis for the phenomenon of gravitational lensing,
3. gravitational waves propagating at the speed of light, which are generated when large mass distributions are engaged in asymmetrical acceleration (e.g., when two neutron stars (which were not known at the time) perform binary orbital motion).

The observation of the second effect was soon recognised to be technically the most feasible. The driving-force for empirically testing it was the British astrophysicist Arthur Eddington (1882–1944), a deeply respected person of his time, with strong Quaker beliefs. In the years following November 1915, he had acquainted the Anglo–American scientific community with Einstein’s revolutionary ideas. Besides advocating gestures of reconciliation towards the “enemy,” he managed to convince British government officials of the need to financially support experimental attempts at making sense of this (Newtonian ideas) challenging physical theory that was lately put forward by a scientist active in Germany. Soon afterwards, Eddington was put in charge of an expedition for observing the proposed deflection effect for stars appearing close to the rim of the Sun during the upcoming total solar eclipse on Thursday, May 29, 1919 from the island of Principe in the Atlantic Ocean, off the coast of West Africa. To increase chances for obtaining good quality observational data, a second expedition, led by the then director of the Royal Greenwich Observatory Andrew Crommelin (1865–1939), was sent to Sobral in the Brazilian jungle. Unfortunately, with the sky at Principe mainly overcast on the decisive day, not as much data could be collected by the teams as desired. Nevertheless, following months of meticulous statistical data analysis, the results of the measurements taken by the two expeditions were finally communicated to the public at a joint meeting of the Royal Society and the Royal Astronomical Society in London on Thursday, November 6, 1919. In consequence of the stunning results reported by the organisers of the expeditions, Einstein instantaneously became the first worldwide celebrity in the history of science. (As Peter Coles points out in his 2001 review of the 1919 solar eclipse expeditions, this glorification of the person Einstein, by the international media in particular, had rather detrimental effects on scientists’ obligatory efforts to bridge the gulf between the general public’s perception of fundamental research and their own actual activities therein, with repercussions well into the present time.)

As to the third of Einstein’s predictions, indirect evidence for the existence of gravitational waves was obtained from the annual inspiraling rate due to orbital energy loss of the binary pulsar that was first observed in 1974, for which their discoverers, the US-American physicists Russell Hulse (born 1950) and Joseph Taylor Jr. (born 1941), were awarded the 1993 Nobel Prize in Physics. The direct measurement of gravitational waves still awaits its confirmation, resting in particular on the performance of very carefully designed laser interferometer detectors built on planet Earth during the last 20 years. These aim for a sensitivity that is such that incident gravitational waves of an expected relative amplitude at peak size of the extremely tiny order of magnitude of 10E-21 will cause an unambiguous signal.

Subsequent predictions

Two particularly prominent predictions of the general theory of relativity were derived and promoted during the decades following the year 1915, though not by its originator Einstein:

1. the overall expansion of the Universe,
2. the formation of black holes in the gravitational collapse of supermassive stars at the end of their lifetimes, or during merging processes in groups and clusters of galaxies.

Einstein had added to his field equations a term containing a so-called cosmological constant Lambda only in 1917. Back then he had considered this a conceptual necessity so that his prejudice in favour of a static Universe, a belief heavily influenced by the zeitgeist of his time, could be manifestly captured by his own theory. He had realised that otherwise cosmological solutions to his field equations would exhibit dynamic characters.

Fewer philosophical inhibitions rested with the Russian mathematician Aleksandr Friedmann (1888–1925) and with the Belgian priest Georges Lemaître (1894–1966), who, in 1922 respectively in 1927, independently pointed out the possibility of a dynamic Universe as a solution to Einstein’s field equations, wherein the Universe originated from a primeval explosion. Their forecasts, however, went unheard for quite some time.

While Einstein was struggling with the development of his theoretical framework to describe gravitation in quantitative terms, important advances were made in astronomical technology and methodology. The US-American astronomer Vesto Slipher (1875–1969) pioneered in 1912 the measurement of the recessional speeds of nearby galaxies by means of the Doppler shift that the wavelengths of the light they emit experience. A decade later, beginning in 1923, the leading US-American astronomer Edwin Hubble (1889–1953) and the US-American astronomical photographer Milton Humason (1891–1972) employed this technique to embark on a project of systematic observation of the redshifts of galaxies in the vicinity of our own Milky Way galaxy. Later, in 1929, following years of dedicated work that yielded overwhelming evidence for the large majority of galaxies to be “fleeing” from the Milky Way galaxy, they put forward the ground-breaking proposition that the empty space in-between galaxies was continually expanding, and, hence, so was the Universe as a whole. (As we now know, gravitationally bound, ultra-massive galaxy clusters such as Abell 1689 in the Virgo constellation have dropped out of this expansion process due to their mutual interactions.)

The 1929 results of Hubble and Humason convinced Einstein of the reality of an expanding Universe, and he discarded his own static model in consequence. The foundation for a big bang model of the Universe had been laid, but it needed many more decades of detailed observational and theoretical work to fully establish its current status in cosmology.

The term “big bang,” by the way, was created by the British astrophysicist Fred Hoyle (1915–2001) in the context of his 1950 series of public lecture radio broadcasts on the BBC for the purpose of pouring insult on a theory that was strongly competing with his own proposal of a Universe in a steady state, a philosophical preference that had a number of prominent followers at the time. The ultimate clincher of the debate was the serendipitous discovery in 1965 by the US-American radio astronomers Arno Penzias (born 1933) and Robert Wilson (born 1936) of a thermal cosmic microwave background (CMB) radiation at 2.72 K, the most compelling interpretation of which was that it constitutes the afterglow of an ultra-hot big bang phase in the early life of the Universe. Ironically, these two researchers were awarded a share of the 1978 Nobel Prize in Physics for their unplanned findings, even though the existence of the CMB had been predicted at nearly the right temperature (and properly published) already much earlier in 1948 by the US-American cosmologists Ralph Alpher (1921–2007), George Gamov (1904–1968) and Robert Herman (1914–1997). (It seems unthinkable that professional researchers did not duly consult the scientific literature for reference in their investigative projects.)

The current understanding is that the evolving spacetime geometry of the Universe came into its state of being nearly 14 billion years ago. So far, the CMB is the prime signal sent by the Universe to wo/man-kind concerning information on its early life. Correspondingly, the properties of the CMB are put under continuing rigorous scrutiny by means of the US-American WMAP and European PLANCK satellites, which have been in orbit around planet Earth since 2001 respectively 2009. Due to the finite speed of light, there exists a cosmological particle horizon for Milky Way galaxy bound observers (and for residents of other galaxies, too), defined by the theoretical maximum distance that light could have travelled from deep space towards us inside of nearly 14 billion years. (Note that by observing any kind of signal propagating at a finite speed one is always looking back into the past!) There are thus parts of the Universe beyond this particle horizon which cannot be observed by wo/man-kind at the present time.

In 1967, at the height of an exceptionally productive period in theoretical research on relativistic gravitational physics, Wheeler had coined the term “black hole” for referring to extremely curved compact regions of the spacetime continuum from which not even light rays can escape out towards infinity. (In the French-speaking community, initially, the corresponding term “trou noire” was considered an obscenity). The compact boundary that separates emission positions in spacetime from which light rays manage to escape outwards from those from which they do not defines a black hole’s event horizon. Incidentally, the very first known exact solution of Einstein’s field equations played a central role in the interpretation of the physical properties of black holes. This solution, which describes the gravitational field generated by a static, spherically symmetrical compact mass distribution, was obtained in early 1916, just a few months after Einstein’s announcement of his field equations, by Karl Schwarzschild (1873–1916), the director of the Potsdam Observatory. At the time, he fought on the battlefields of World War I, but soon died of a rare skin disease which, apparently, he had attracted in the trenches. To date, astronomers have catalogued a wide spectrum of black holes which they have observed by indirect means (remember: black holes cannot emit light), ranging from candidates with just a few solar masses for relics of large dead stars to supermassive black holes at the centres of galaxies worth millions of solar masses.

Time-travel

A topic which has captured the public’s attention on numerous occasions is the idea of time-travel. In the context of the general theory of relativity, this required the existence in the spacetime continuum of causality violating closed timelike curves, for massive objects to move along. Researchers in relativistic gravitation refer to this issue as the “grandmother paradox”: you intend to travel into the past to arrange for your grandmother not to meet your grandfather, so that your own mother could not have been born. (A variant of this idea was used by the screenplay authors of the 1985 Hollywood movie “Back to the Future”, recently featured in a triple night on Wednesday, October 21, 2015 at Karlshochschule). To provide a conceptual basis for time-travel within the general theory of relativity, the possibility of wormholes in the spacetime continuum needed to be accommodated therein. This in turn required in general a non-trivial topology for the spacetime continuum, meaning that it needed to be multiply connected (as opposed to merely simply connected) to itself so that closed timelike curves became possible in principle.

General relativity in everyday life

100 years later, wo/man-kind finds itself in the comfortable position of directly benefitting from a number of applications of effects that have become known (and controllable) thanks to Einstein’s general theory of relativity. Amongst others, there is the accurate navigation in the gravitational field of our rotating planet Earth of the currently 31 satellites that make up the global positioning system (GPS); this includes the synchronisation of their on-board clocks. If it was not for the ability to account for the general relativistic effect of dragging of frames of reference in the vicinity of large rotating massive objects, GPS would be a hopeless endeavour.

Moreover, exploiting gravitational lensing in astronomy to the extent of using galaxies and clusters of galaxies as gigantic “magnifying glasses” aiding the observation of weakly luminous objects out in deep space (some of which are not too far off this side of the cosmological particle horizon) has become a standard practical tool.

Also, nowadays relativistic gravitational physics inspired topics apparently make for some decent entertainment at an intellectually stimulating level. At least this is the impression one gets in view of the commercial successes of the CBS sitcom “The Big Bang Theory” or the recent Hollywood movie “Interstellar”.

The general theory of relativity has had unprecedented spins-offs, which last well into the present days. For the future of the 21^st Century, researchers anticipate the possibility of conducting gravitational wave astronomy. If successful in its data gathering methodology, this would open up to wo/man-kind a channel worth of information of an entirely new quality on the past life of our Universe and the astrophysical objects contained therein. To date, all the information available to us in this respect was received exclusively via the electromagnetic wave channel (ranging from low-frequency microwaves to ultra-high frequency gamma rays).

Festive activities

Many of the world’s leading relativistic gravitational physicists will be convening at Berlin’s Harnack–Haus from Monday, November 30 to Wednesday, December 2, 2015 to celebrate the centenary of the release of the relativistic field equations of gravitation by Albert Einstein. This scientific meeting has been organised by The International Society on General Relativity and Gravitation and the Albert–Einstein–Institut of the Max Planck Society at Golm, Germany. Expect live-streaming on the internet of the festive lectures given at this event. A recommended appetizer in preparation of the upcoming celebrations is the appealing centennial review written by George Ellis earlier this year.

To conclude our considerations with the words of Einstein:

“The most incomprehensible thing about the world is that it is at all comprehensible.”

Post scriptum for the technically inclined reader: Einstein’s field equations constitute a set of 10 non-linear partial differential equations of the second order for the 10 components of the physical spacetime metric g. In these equations, the Greek indices mu and nu take values in 4 spacetime dimensions, so that mu, nu = 0,1,2,3. Moreover, G denotes Newton’s gravitational coupling constant, while c is the constant speed of light. The Ricci curvature Ric, and its scalar R, are constructed in a non-linear fashion from first and second spacetime derivatives of the spacetime metric g. The energy–momentum of the matter content is condensed in T. As a set of deterministic equations, Einstein’s field equations predict the future development of the geometry of a spacetime continuum and its respective matter content from given initial data, subject to the constraint of conservation of energy–momentum (which is an empirical law). To date, exact solutions are known only for special cases.

Bibliography

1. Ashtekar A, B K Berger, J Isenberg and M MacCallum (eds.) (2015) General Relativity and Gravitation – A Centennial Perspective (Cambridge: Cambridge University Press) ISBN-13: 978-1-107-03731-1
2. Coles P (2001) Einstein, Eddington and the 1919 eclipse arXiv:astro-ph/0102462v1
3. Einstein A (1915) Die Feldgleichungen der Gravitation Sitzungsberichte der Preußischen Akademie der Wissenschaften, Berlin 844-847
4. Ellis G F R (2015) 100 years of general relativity arXiv:1509.01772v1 [gr-qc]
5. Friedman A (1922) Über die Krümmung des Raumes Zeitschrift für Physik 10 377-386
6. Lemaître G (1927) Un univers homogène de masse constante et de rayon croissant rendant compte de la vitesse radiale des nébuleuses extra-galactiques Annales de la Société Scientifique de Bruxelles A47 49-59
7. Misner C W, K S Thorne and J A Wheeler (1973) Gravitation (New York: Freeman and Co.) ISBN-10: 0-7167-0344-0

Related books in Karlshochschule’s library

• Lightman A and R Brawer (1990) Origins – The Lives and Worlds of Modern Cosmologists (Cambridge, MA: Harvard University Press) ISBN-10: 0-674-64471-9 [MA 1 Lig]
• Penrose R (1989) The Emperor’s New Mind – Concerning Computers, Minds, and the Laws of Physics (Oxford: Oxford University Press) ISBN-10: 0-198-51973-3 [MA 1 Pen]
• Penrose R (2004) The Road to Reality – A Complete Guide to the Laws of the Universe (London: Jonathan Cape) ISBN-10: 0-224-04447-8 [MA 1 Pen]
• Sagan C (1980) Cosmos (New York, Ballantine Books) ISBN-10: 0-345-33135-4 [MA 1 Sag]
• Singh S (2004) Big Bang: The Most Important Discovery of All Time and Why You Need to Know About It (London: Fourth Estate) ISBN-13: 978-0-00715-252-0 [MA 1 Sin]
• Wambsganß J (2012) Universum für alle – 70 spannende Fragen und kurzweilige Antworten (Berlin: Springer Spektrum) ISBN-13: 978-3-8274-3053-3 [MA 1 Uni]