General Relativity Turns 100

E ditorial
General Relativity T urns 100
he period of history bookended by Copernicus’s
On the Revolutions o f the Heavenly Spheres in
1543 and Newton’s Mathematical Principles o f
Natural Philosophy in 1687 is known as the
Scientific Revolution, and for good reason. In addition to
the revolutionary achievements of these and a wealth of
other natural philosophers, as they were known at the
time,1 the foundations of scientific inquiry we now know
as the scientific method were strengthened, extended and
popularized by many of the great names of the time, such
as Galileo, Francis Bacon and Descartes.
T
But a later revolution in science is perhaps unmatched in
history, in that our understanding of nature was totally
revolutionized with three great developments in the span
of about 30 years in the early 20th century: special
relativity, general relativity and quantum mechanics. one
individual, Albert Einstein, was by far the dominant
figure in the first two, and his work on the photoelectric
effect[2] was a cornerstone of the third.
In November 1915, Einstein gave four lectures to the
Prussian Academy wherein he presented the field equa­
tions of general relativity (GR) and also showed that it
correctly accounted for the perihelion advance of Mer­
cury, a major unsolved problem of the time [3]. This work
represented the culmination of almost a decade of work
by Einstein, the patent office clerk turned professor of
physics - and soon-to-be international celebrity. Repeat­
ing a feat that he had achieved with special relativity,
Einstein once again turned our understanding of space­
time completely asunder: rather than being flat, space­
time was curved by matter, Riemannian geometry being
the mathematical framework to describe this curvature. In
turn, matter moving in straight lines (geodesics) in curved
geometry appeared to be under the influence of a force
(that of gravity).
What better occasion than its centenary to reflect back on
the discovery and implications of GR?
The seeds of the theory were perhaps sown in 1905, when
Einstein combined the equivalence of all inertial reference
frames (the special principle of relativity) and the
invariance of the speed of light and came up with special
relativity[4] and the equivalence of mass and energy[5].2
Two years later, he had what he later described as his
“happiest thought” [7]: that the principle of relativity can
be extended to gravitational fields. In a paper published
in December, 1907[8], he argued that free fall is in fact
inertial motion, so that special relativity should apply. In
1911, he devised one of his classic thought experiments,
arguing that an observer in a box would not be able to
distinguish between uniform acceleration and a constant
gravitational field (the general principle of relativity)[9].
This gave rise to two of the nascent GR’s most important
predictions: that a gravitational field affects the rate of
passage of time (gravitational time dilation) and that
light is bent by a gravitational field. Curiously, the 1911
prediction of the latter did not in fact provide a test of GR,
since it agreed with an earlier prediction of the bending
of light in Newtonian gravity[10]. However, Einstein redid
the calculation in 1915 once GR had been fully for­
mulated (third paper of Ref. [3]) and found that GR
predicted a deflection twice as large, thus giving a means
to test the theory.
A prediction is of course far more compelling than the
explanation of a previously-observed phenomenon, and it
was soon realized that a solar eclipse might provide an
opportunity to determine whether or not stars’ apparent
positions were altered by the Sun’s gravitational field, a
clear sign of the bending of light. A scientific expedition
to the island of Principe off the west coast of Africa led
by Sir Arthur Eddington measured the bending of light
during the total solar eclipse of 29 May, 1919[11]; the
measurement confirmed the prediction of GR, a success
that immediately caused scientists to take GR seriously.
As a side-effect, it brought international celebrity to
Einstein, who in fact viewed the observation as something
of an anti-climax. The sheer elegance of GR was enough
The contents of this journal, including the views expressed above, do not necessarily represent the views or policies of the Canadian Association of
Physicists.
Le contenu de cette revue, ainsi que les opinions exprimées ci-dessus, ne représentent pas nécessairement les opinions ou les politiques de l'Association
canadienne des physiciens et physiciennes.
Richard Mackenzie
is a Professor of
Physics at the
University of
Montreal, and has
been a member of
the Editorial Board
of Physics in
Canada since 2012.
1. According to Sydney Ross [1], the term “scientist” dates back to 1833, when it was coined by the scientist and philosopher Willliam Whewell.
2. Although it is in the second o f these papers in spirit, Einstein did not write down his celebrated equation E — mc2 until 1907 [6].
La P hysique au Canada / Vol. 71, No. 3 (2015) ·
125
E ditorial
for him to be convinced of its validity, to the extent that when
asked how he would have reacted had the observation
disagreed with GR, he reportedly replied: “I would have felt
sorry for the Lord. The theory is correct.”
model, based on GR, describes the evolution of the universe
spectacularly well from a tiny fraction of a second on.
Understanding cosmology without GR would be like trying
to understand chemistry without quantum mechanics.
By the end of 1915, the first nontrivial exact solution of the
GR field equations had been found, for space-time outside
a spherically symmetric distribution of matter, by Karl
Schwarzchild[12]. His eponymous solution, for a sufficiently
dense distribution of matter, gives rise to black holes, perhaps
physics’ most important contribution to popular culture other
than Einstein himself.
One prediction of GR which has yet to be observed is
gravitational waves, which are created by moving masses,
just as moving charges create electromagnetic waves. The
effects are so minuscule that only extreme conditions such as
merging neutron stars could give rise to directly measurable
effects. indirect evidence of gravitational waves comes from
binary pulsars [17], but direct evidence may be right around the
corner, with gravitational wave interferometers Advance LIGO
and Virgo taking data now or in the very near future, and
space-based gravitational wave interferometers in the works.
Gravitational time dilation was observed and found to agree
with GR by comparing atomic clocks on airplanes with clocks
on the ground in 1971[13]; more recently, and far more
incredibly, it was observed in clocks differing in height by
33 cm, for which the higher clock gains about a billionth of a
second per year compared to the lower one [14]. On a more
practical (and commercially important!) level, gravitational
time dilation has an effect on the clocks on Global Positioning
System satellites, and GR effects must be taken into account
in order for your smart phone or car’s GPS to tell you where
you are.
By now, a plethora of other observations have been made of
subtle phenomena for which GR makes slightly different
predictions than Newtonian gravity. These include gravita­
tional red shift (the change of wavelength as light escapes
a gravitational field)[15] and gravitational lensing[16], a con­
sequence of the bending of light. Gravitational lensing results
in multiple images of a distant astronomical object due to the
gravitational effect of a closer object in line with it; its
observation is one of the main pieces of direct evidence for
dark matter in the universe.
Furthermore, it is difficult to even imagine modern cosmology
without the pervasive influence of GR. The Λ-CDM/Big Bang
Although perhaps in the shadow of the International Year of
Light, celebrations of the centenary of Einstein’s achievement
have brought GR into the limelight around the world. In
Canada, the 2015 Atlantic General Relativity Conference held
at the University of New Brunswick in Fredericton celebrated
GR’s birthday, and the Fields Institute for Research in
Mathematical Sciences held a Focus Program on 100 Years
of General Relativity in May-June 2015. And of course the
Herzberg Memorial Lecture by Miguel Alcubierre given at this
year’s CAP Congress discussed a peculiarity of GR that allows
for faster-than-light motion.
After 100 years, GR has become an undeniable pillar of
fundamental physics; may the next 100 years of research be
equally fruitful. Happy birthday general relativity!
Richard MacKenzie
Universite de Montreal
Member, PiC Editorial Board
Comments o f readers on this editorial are more than welcome.
REFERENCES
1. S. Ross, “Scientist: The Story of a Word”, Annals o f Science, 18, 65-85 (1962).
2. A. Einstein, “On a Heuristic Point of View Concerning the Production and Transformation of Light”, Annalen der Physik (ser. 4), 17,
132148 (1905).
3. A. Einstein, “On the General Theory of Relativity”, Preussische Akademie der Wissenschaften, Sitzungsberichte 1915 (part 2), 778-786,
799-801 (1915); “Explanation of the Perihelion Motion of Mercury from the General Theory of Relativity”, ibid., 831-839 (1915);
“The Field Equations of Gravitation,” ibid., 844-847 (1915).
4. A. Einstein, “On the Electrodynamics of Moving Bodies”, Annalen der Physik (ser. 4), 17, 891-921 (1905).
5. A. Einstein, “Does the Inertia of a Body Depend upon its Energy Content?”, Annalen der Physik (ser. 4), 18, 639-641 (1905).
6. A. Einstein, “On the Inertia of Energy Required by the Relativity Principle”, Annalen der Physik (ser. 4), 23, 371-384 (1907).
7. A. Pais, Subtle is the Lord: The Science and the Life o f Albert Einstein, p. 178, Oxford University Press, 1982.
8. A. Einstein, “On the Relativity Principle and the Conclusions Drawn from It”, Jahrbuch der Radioaktivitt, 4, 411-462 (1907).
9. A. Einstein, “On the Influence of Gravitation on the Propagation of Light”, Annalen der Physik (ser. 4), 35, 898-908 (1911).
10. J.G.V. Soldner, “On the defl of a light ray from its rectilinear motion, by the attraction of a celestial body at which it nearly passes by”,
Berliner Astronomisches Jahrbuch, 161-172 (1804).
126 ·
Physics in Canada / V ol. 71, No. 3 (2015 )
E ditorial
11. F.W. Dyson, A.S. Eddington, C.R. Davidson, “A determination of the defl of light by the Sun’s gravitational fi from observations
made at the Solar eclipse of May 29, 1919”, Phil. Trans. Roy. Soc. A, 220, 291-333 (1920).
12. A. Schwarzchild, “On the gravitational fi of a mass point according to Einstein’s theory”, Sitzungsber. Preuss. Akad. Wiss. Berlin
(Math. Phys.), 1916, 189-196 (1916).
13. J.C. Hafele, R.E. Keating, “Around-the-World Atomic Clocks: Predicted Relativistic Time Gains”, Science, 177, 166-168 (1972);
“Around-the-World Atomic Clocks: Observed Relativistic Time Gains”, ibid., 168-170 (1972).
14. C.W. Chou, et al., “Optical Clocks and Relativity”, Science, 329, 1630-1633 (2010).
15. R.V. Pound, G.A. Rebka Jr, “Gravitational Red-Shift in Nuclear Resonance”, Phys. Rev. Lett., 3, 439-441 (1959).
16. D. Walsh, R.F. Carswell, R.J. Weymann, “0957 + 561 A, B: twin quasistellar objects or gravitational lens?”, Nature, 279, 381-384
(1979).
17. J.H. Taylor, L.A. Fowler, P.M. McCulloch, “Measurements of general relativistic effects in the binary pulsar PSR1913 + 16”, Nature,
277, 437-440 (1979).
La RELATIVITE GÉNÉRALE A CENT ANS
a période d ’histoire encadrée par les documents Des
revolutions des spheres celestes ecrit par Copernic
en 1543, et Principes mathematiques de philosophie
naturelle, elaborés par Newton en 1687, est connue
sous le nom de revolution scientifique, et avec raison. Outre les
realisations revolutionnaires de ces hommes et d ’une foule
d’autres philosophes naturalistes, ainsi appeles a l’epoque1,
de nombreux grands noms d ’alors tels Galilee, Francis Bacon
et Descartes, ont consolide, elargi et vulgarise les fondements
de l’enquete scientifique, aujourd’hui appeles la methode
scientifique.
L
Mais une revolution scientifique ulterieure est peut-etre
inegalee dans l’histoire, du fait que trois grands evenements
survenus en l ’espace d’environ 30 ans au debut du 20e siecle
ont completement révolutionne notre comprehension de la
nature: la relativite restreinte, la relativite generale et la
mecanique quantique. Albert Einstein a de loin ete la figure
dominante dans les deux premiers cas, et ses travaux sur l’effet
photoelectrique [2] ont ete la pierre angulaire du troisieme.
En novembre 1915, Einstein a donne a l’academie prussienne
quatre conferences exposant les equations de champ de la
relativite generale (RG) et montrant qu’il avait bien tenu
compte de l’avance du perihelie de Mercure, grand probleme
non résolu a l’epoque [3]. Ces travaux ont ete l’aboutissement
de près d ’une decennie d’efforts de la part d ’Einstein, agent du
bureau des brevets et devenu professeur de physique - sur le
point d ’etre une celebrite internationale. Repetant un exploit
realise grace a la relativite restreinte, Einstein a encore une fois
transforme de fond en comble notre comprehension de
l’espace-temps. L ’espace-temps n ’est pas plat, du fait que
la matiere le fait courber, la geometrie de Riemann etant le
cadre mathematique qui decrit cette courbure. En revanche,
la matiere se deplacant en lignes droites (geodesiques) en
geometrie courbe semblait etre sous l’influence d ’une force
(celle de la gravite).
Y a-t-il meilleure occasion que le centenaire de la RG pour
reflechir a sa decouverte et a ses implications?
Les graines de la theorie ont peut-etre ete semees en 1905,
annee oh Einstein combinait l’equivalence de tous les cadres de
reference inertiels (le principe restreint de la relativite) à
l’invariance de la vitesse de la lumiere et trouvait la relativite
restreinte [4] et l’equivalence masse-energie [5].2 Deux ans plus
tard, est ne ce qu’il a par la suite appele « sa pensee la plus
heureuse » [7]: soit que le principe de la relativite peut etre
etendu aux champs gravitationnels. Dans un document publie
en decembre 1907[8], il a avance que la chute libre etait en fait
un mouvement d ’inertie, de sorte que la relativite restreinte
devrait s’appliquer. En 1911, il a concocte l’une de ses
experiences classiques de pensee, affirmant qu’un observateur
dans une boîte ne saurait distinguer l ’acceleration uniforme
d ’un champ gravitationnel constant (principe general de la
relativite) [9]. Cela a donne lieu a deux des plus importantes
previsions de la RG naissante: soit qu’un champ gravitationnel
influe sur le rythme de passage du temps (la dilatation du
temps gravitationnel) et qu’il fait courber la lumiere. Curieuse­
ment, cette derniere prevision de 1911 n ’a pas permis de
verifier la RG, en fait, car elle etait conforme a une prevision
anterieure de la courbure de la lumiere sous la gravite
newtonienne [10]. Einstein a toutefois repris ses calculs en
1915 apres avoir enonce globalement la RG (troisieme
document du Ref. [3]) et avoir trouve que celle-ci prévoyait
un braquage deux fois plus grand, fournissant ainsi un moyen
de verifier la theorie.
1. Selon Sydney Ross [1], le terme « scientifique » remonte a 1833, annee de son invention par le scientifique et philosophe Willliam Whewell.
2. Bien que ce soit dans l’esprit du second de ces documents, Einstein n ’a ecrit qu’en 1907 sa fameuse equation: E — mc2[6].
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Bien sûr, une prévision est beaucoup plus contraignante que
l’explication d’un phenomene deja observe et l’on s’est vite
rendu compte qu’une eclipse solaire peut permettre de
determiner si le champ gravitationnel du Soleil modifie ou
non la position apparente des etoiles, indice eloquent de la
courbure de la lumiere. Une expedition scientifique, menee a
l’île de Principe au large de la cote ouest de l’Afrique par Sir
Arthur Eddington, a permis de mesurer la courbure de la
lumiere durant l’eclipse solaire totale du 29 mai 1919 [11]; sa
mesure a confirme la prevision de la RG, succes qui a tout de
suite amene les scientifiques a prendre la RG au serieux. A titre
secondaire, elle a valu la celebrite internationale a Einstein
pour qui cette observation equivalait, en fait, a accoucher d ’une
souris. A son avis, l’elegance sobre de la RG suffisait a le
convaincre de sa validite, à tel point que, lorsqu’on lui a
demande quelle aurait ete sa reaction si l’observation avait
ecarte la RG, il aurait répondu: « J’aurais ete peine pour son
auteur: la theorie est bonne.»
A la fin de 1915, Karl Schwarzchild avait trouve la premiere
solution exacte non negligeable aux equations de champ de la
RG pour l’espace-temps hors d’une distribution spherique
symetrique de la matiere [12]. La solution qui porte son nom,
pour une distribution de matiere suffisamment dense, est a
l’origine des trous noirs, ce qui est peut-etre l’apport le plus
important de la physique a la culture populaire, mis a part celui
d ’Einstein lui-meme.
Apres avoir observe la dilatation du temps gravitationnel, on
l’a trouvee conforme a la RG en comparant des horloges
atomiques aeroportees avec d ’autres a terre, en 1971[13]; tout
dernierement, ce qui est beaucoup plus incroyable, on l’a
observee dans des horloges dont la hauteur variait de 33 cm et
dont la plus elevee gagnait environ un milliardieme de seconde
par annee par rapport a la moins elevee [14]. Sur un plan plus
pratique (d’ordre commercial important!), la dilatation du
temps gravitationnel influe sur les horloges des satellites du
systeme mondial de localisation (GPS) et il faut tenir compte
des effets de la RG pour que votre telephone intelligent ou le
GPS de votre voiture indique l ’endroit ou vous etes.
De nos jours, on a observe une foule d ’autres phenomenes
subtils pour lesquels la RG donne des previsions legerement
differentes de celles de la gravite newtonienne. Cela comprend
le decalage gravitationnel vers le rouge (modification de la
longueur d ’onde a mesure que la lumiere echappe a un champ
gravitationnel) [15] et l’effet lenticulaire gravitationnel[16], qui
decoule de la courbure de la lumiere. L ’effet lenticulaire
gravitationnel donne de multiples images d ’un objet astrono­
mique eloigne en raison de l’effet gravitationnel d ’un objet plus
rapproche, en ligne droite avec lui; son observation est l’une
des principales preuves directes de la matiere noire dans
l’univers.
En outre, il est difficile d ’imaginer la cosmologie moderne sans
la profonde influence de la RG. Le modele Λ-CDM/Big Bang,
fonde sur la RG, decrit bien de facon spectaculaire r evolution
de l’univers depuis une minime fraction de seconde de son
existence. Comprendre la cosmologie sans la RG s’apparente­
rait a essayer de comprendre la chimie sans la mecanique
quantique.
Les ondes gravitationnelles, que créent les masses en mouve­
ment tout comme les charges en mouvement suscitent les
ondes electromagnetiques, sont une prevision de la RG qui n ’a
pas encore ete observee. Les effets sont tellement minimes que
seules les conditions extremes des etoiles a neutrons en fusion
pourraient susciter des effets directement mesurables. Des
preuves indirectes des ondes gravitationnelles emanent des
pulsars binaires [17], mais des preuves directes pourraient etre a
portee de main, et la date de demarrage des interferometres a
ondes gravitationnelles Advance LIGO et Virgo est arrivee ou
arrivera très bientôt, et l’on entrevoit les interferometres a
ondes gravitationnelles bases dans l’espace.
Les celebrations du centenaire de l’œuvre d ’Einstein, peut-etre
dans l’ombre de l ’Annee internationale de la lumiere, ont mis
la RG en exergue aux quatre coins du monde. Au Canada, la
Conference de l’Atlantique sur la relativite generale de 2015,
tenue a l’Université du Nouveau-Brunswick de Fredericton, a
celebre l’anniversaire de la RG et le Fields Institute for
Research in Mathematical Sciences avait un programme axeé
sur les cent ans de la theéorie de la relativiteé geéneérale en mai
et juin 2015. Et, bien sûr, a la conference commemorative
Herzberg donnée au Congrès de l’ACP de cette année, Miguel
Alcubierre a exposeé une particulariteé de la RG, qui permet de
depasser la vitesse de la lumiere.
Apres cent ans, la relativite generale est devenue un pilier
incontournable de la physique fondamentale; puissent les 100
prochaines annees de recherche etre tout aussi fructueuses. Bon
anniversaire a la relativite generale!
Richard MacKenzie
Universiteé de Montreéal
Membre, Comiteé de reédaction de la PaC
Les commentaires des lecteurs sur cet éditorial sont toujours
les bienvenus.
NOTE: Le genre masculin n'a ete utilise que pour alieger le
texte.
RÉFÉRENCES
1.
128 ·
S. Ross, “Scientist: The Story of a Word”, Annals o f Science, 18, 65-85 (1962).
Physics in Canada / V ol. 71, No. 3 (2015 )
E ditorial
2. A. Einstein, “On a Heuristic Point of View Concerning the Production and Transformation of Light”, Annalen der Physik (série 4), 17,
132148 (1905).
3. A. Einstein, “On the General Theory of Relativity”, Preussische Akademie der Wissenschaften, Sitzungsberichte 1915 (partie 2), 778-786,
799-801 (1915); “Explanation of the Perihelion Motion of Mercury from the General Theory of Relativity”, ibid., 831-839 (1915);
“The Field Equations of Gravitation”, ibid., 844-847 (1915).
4. A. Einstein, “On the Electrodynamics of Moving Bodies”, Annalen der Physik (serie 4), 17, 891-921 (1905).
5. A. Einstein, “Does the Inertia of a Body Depend upon its Energy Content?”, Annalen der Physik (serie 4), 18, 639-641 (1905).
6. A. Einstein, “On the Inertia of Energy Required by the Relativity Principle”, Annalen der Physik (serie 4), 23, 371-384 (1907).
7. A. Pais, Subtle is the Lord: The Science and the Life o f Albert Einstein, p. 178, Oxford University Press, 1982.
8. A. Einstein, “On the Relativity Principle and the Conclusions Drawn from It”, Jahrbuch der Radioaktivitat, 4, 411-462 (1907).
9. A. Einstein, “On the Influence of Gravitation on the Propagation of Light”, Annalen der Physik (serie 4), 35, 898-908 (1911).
10. J.G.V. Soldner, “On the deflection of a light ray from its rectilinear motion, by the attraction of a celestial body at which it nearly
passes by”, Berliner Astronomisches Jahrbuch, 161-172 (1804).
11. F.W. Dyson, A.S. Eddington, C.R. Davidson, “A determination of the deflection of light by the Sun’s gravitational field from
observations made at the Solar eclipse of May 29, 1919”, Phil. Trans. Roy. Soc. A, 220, 291-333 (1920).
12. A. Schwarzchild, “On the gravitational field of a mass point according to Einstein’s theory”, Sitzungsber. Preuss. Akad. Wiss. Berlin
(Math. Phys.), 1916, 189-196 (1916).
13. J.C. Hafele, R.E. Keating, “Around-the-World Atomic Clocks: Predicted Relativistic Time Gains”, Science, 177, 166-168 (1972);
“Around-the-World Atomic Clocks: Ob- served Relativistic Time Gains”, ibid., 168-170 (1972).
14. C.W. Chou, et al., “Optical Clocks and Relativity”, Science, 329, 1630-1633 (2010).
15. R.V. Pound, G.A. Rebka Jr, “Gravitational Red-Shift in Nuclear Resonance”, Phys. Rev. Lett., 3, 439-441 (1959).
16. D. Walsh, R.F. Carswell, R.J. Weymann, “0957 + 561 A, B: twin quasistellar objects or gravitational lens?”, Nature, 279, 381-384
(1979).
17. J.H. Taylor, L.A. Fowler, P.M. McCulloch, “Measurements of general relativistic effects in the binary pulsar PSR1913 + 16”, Nature,
277, 437-440 (1979).
The Editorial Board welcomes arti­
cles from readers suitable for, and
understandable to, any practising or
student physicist. Review papers
and contributions of general interest
of up to four journal pages in length
are particularly welcome. Sugges­
tions for theme topics and guest
editors are also welcome and should
be sent to [email protected].
Le comité de rédaction invite les
lecteurs à soumettre des articles
qui intéresseraient et seraient com­
pris par tout physicien, ou physici­
enne, et étudiant ou étudiante en
physique. Les articles de synthèse
d’une longueur d’au plus quatre
pages de revue sont en particulier
bienvenus. Des suggestions de
sujets pour des revues à thème sont
aussi bienvenues et pourront être
envoyées à [email protected].
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