Typhoid Mary, the first healthy carrier of disease ever identified in the United States is put in quarantine for the second time, where she would remain for the rest of her life.
Irish cook who was an asymptomatic carrier of typhoid fever in New York
Mary Mallon (September 23, 1869 – November 11, 1938), also known as Typhoid Mary, was an Irish-born cook believed to have infected 53 people with typhoid fever, three of whom died, and the first person in the United States identified as an asymptomatic carrier of the disease, Salmonella typhi.^{[1]}^{[2]} Because she persisted in working as a cook, by which she exposed others to the disease, she was twice forcibly quarantined by authorities, eventually for the final two decades of her life. Mallon died after a total of nearly 30 years in isolation.^{[3]}^{[4]}
Biography
Early life
Mary Mallon was born in 1869 in Cookstown, County Tyrone, in what is now Northern Ireland. Presumably, she was born with typhoid because her mother was infected during pregnancy.^{[5]}^{[6]}^{[7]} At the age of 15, she immigrated to the United States.^{[6]}^{[8]} She lived with her aunt and uncle for a time and worked as a maid, but eventually became a cook for affluent families.^{[9]}^{[10]}
Career
From 1900 to 1907, Mallon worked as a cook in the New York City area for eight families, seven of whom contracted typhoid.^{[11]}^{[12]} In 1900, she worked in Mamaroneck, New York, where within two weeks of her employment, residents developed typhoid fever. In 1901, she moved to Manhattan, where members of the family for whom she worked developed fevers and diarrhea, and the laundress died. Mallon then went to work for a lawyer and left after seven of the eight people in that household became ill.^{[13]}^{[14]}
In June 1904, she was hired by a prosperous lawyer, Henry Gilsey. Within a week, the laundress was infected with typhoid, and soon four of the seven servants were ill. No members of Gilsey's family were infected, because they resided separately, and the servants lived in their own house. The investigator Dr. R. L. Wilson concluded that the laundress had caused the outbreak, but he failed to prove it. Immediately after the outbreak began, Mallon left and moved to Tuxedo Park,^{[15]} where she was hired by George Kessler. Two weeks later, the laundress in his household was infected and taken to St. Joseph's Regional Medical Center, where her case of typhoid was the first in a long time.^{[10]}
In August 1906, Mallon took a position in Oyster Bay on Long Island with the family of a wealthy New York banker, Charles Henry Warren. Mallon went along with the Warrens when they rented a house in Oyster Bay for the summer of 1906. From August 27 to September 3, six of the 11 people in the family came down with typhoid fever. The disease at that time was "unusual" in Oyster Bay, according to three medical doctors who practiced there. The landlord, understanding that it would be impossible to rent a house with the reputation of typhoid, hired several independent experts to find the source of infection. They took water samples from pipes, faucets, toilets, and the cesspool, all of which were negative for typhoid.^{[16]}^{[17]}^{[18]}
Investigation
In late 1906, Mallon was hired by Walter Bowen, whose family lived on Park Avenue. Their maid got sick on January 23, 1907, and soon Charles Warren's only daughter got typhoid and died. This case helped to identify Mallon as the source of the infections. George Soper, an investigator hired by Warren after the outbreak in Oyster Bay, had been trying to determine the cause of typhoid outbreaks in well-to-do families, when it was known that the disease typically struck in unsanitary environments. He discovered that a female Irish cook, who fit the physical description he had been given, was involved in all of the outbreaks. He was unable to locate her because she generally left after an outbreak began, without giving a forwarding address. Soper then learned of an active outbreak in a penthouse on Park Avenue and discovered Mallon was the cook. Two of the household's servants were hospitalized, and the daughter of the family died of typhoid.^{[13]}
Soper first met Mallon in the kitchen of the Bowens and accused her of spreading the disease. Though Soper himself recollected his behavior "as diplomatic as possible", he infuriated Mallon and she threatened him with a carving fork.^{[13]}^{[19]} When Mallon refused to give samples, Soper decided to compile a five-year history of her employment. He found that of the eight families that had hired Mallon as a cook, members of seven claimed to have contracted typhoid fever.^{[20]} Then Soper found out where Mallon's boyfriend lived and arranged a new meeting there. He took Dr. Raymond Hoobler in an attempt to persuade Mary to give them samples of urine and stool for analysis. Mallon again refused to cooperate, believing that typhoid was everywhere and that the outbreaks had happened because of contaminated food and water. At that time, the concept of healthy carriers was unknown even to healthcare workers.^{[10]}^{[21]}^{[22]}
It was found that the family changed cooks on August 4. This was about three weeks before the typhoid epidemic broke out. The new cook, Mallon, remained in the family only a short time and left about three weeks after the outbreak occurred. Mallon was described as an Irish woman about 40 years of age, tall, heavy, single. She seemed to be in perfect health.^{[24]}
First quarantine (1907–1910)
Mallon (foreground) in a hospital bed
Soper notified the New York City Health Department, whose investigators realized that Mallon was a typhoid carrier. Under sections 1169 and 1170 of the Greater New York Charter, Mallon was arrested as a public health threat. She was forced into an ambulance by five policemen and Dr. Josephine Baker, who at some point had to sit on Mallon to restrain her.^{[21]} Mallon was transported to the Willard Parker Hospital, where she was restrained and forced to give samples. For four days, she was not allowed to get up and use the bathroom on her own.^{[25]} The massive numbers of typhoid bacteria that were discovered in her stool samples indicated that the infection center was in her gallbladder. Under questioning, Mallon admitted that she almost never washed her hands. This was not unusual at the time; the germ theory of disease still was not fully accepted.^{[13]}^{[26]}
On March 19, 1907, Mallon was sentenced to quarantine on North Brother Island. While quarantined, she gave stool and urine samples three times per week. Authorities suggested removing her gallbladder, but she refused because she did not believe she carried the disease. At the time, gallbladder removal was dangerous, and people had died from the procedure.^{[27]} Mallon was also unwilling to stop working as a cook, a job that earned her more money than any other. Having no home of her own, she was always on the verge of poverty.
After the publication of Soper's article in the Journal of the American Medical Association, Mallon attracted extensive media attention and received the nickname "Typhoid Mary".^{[28]} Later, in a textbook that defined typhoid fever, she again was called "Typhoid Mary".^{[29]}
Soper visited Mallon in quarantine, telling her he would write a book and give her part of the royalties.^{[30]} She angrily rejected his proposal and locked herself in the bathroom until he left.^{[31]} She hated the nickname and wrote in a letter to her lawyer:
I wonder how the said Dr. William H. Park would like to be insulted and put in the Journal and call him or his wife Typhoid William Park.^{[28]}
Not all medical experts supported the decision to forcibly quarantine Mallon. For example, Milton J. Rosenau and Charles V. Chapin both argued that she just had to be taught to carefully treat her condition and ensure that she would not transmit the typhoid to others. Both considered isolation to be an unnecessary, overly strict punishment.^{[32]} Mallon suffered from a nervous breakdown after her arrest and forcible transportation to the hospital. In 1909, she tried to sue the New York Health Department, but her complaint was denied and the case closed by the New York Supreme Court.^{[33]} In a letter to her lawyer, she complained that she was treated like a "guinea pig". She was obliged to give samples for analysis three times a week, but for six months was not allowed to visit an eye doctor, even though her eyelid was paralyzed and she had to bandage it at night. Her medical treatment was hectic: she was given urotropin in three-month courses for a year, threatening to destroy her kidneys. That was changed to brewers yeast and hexamethylenamin in increasing doses.^{[34]}^{[28]}^{[35]} She was first told that she had typhoid in her intestinal tract, then in her bowel muscles, then in her gallbladder.^{[28]}
Mallon herself never believed that she was a carrier. With the help of a friend, she sent several samples to an independent New York laboratory. All came back negative for typhoid.^{[32]} On North Brother Island, almost a quarter of her analyses from March 1907 through June 1909 were also negative.^{[25]} After 2 years and 11 months of Mallon's quarantine, Eugene H. Porter, the New York State Commissioner of Health, decided that disease carriers should no longer be kept in isolation and that Mallon could be freed if she agreed to stop working as a cook and take reasonable steps to avoid transmitting typhoid to others. On February 19, 1910, Mallon said she was "prepared to change her occupation (that of a cook), and would give assurance by affidavit that she would upon her release take such hygienic precautions as would protect those with whom she came in contact, from infection."^{[36]} She was released from quarantine and returned to the mainland.^{[35]}^{[37]}^{[38]}
Release and second quarantine (1915–1938)
Poster depiction of "Typhoid Mary"
Upon her release, Mallon was given a job as a laundress, which paid less than cooking—$20 per month instead of $50. At some point, she wounded her arm and the wound became infected, meaning that she could not work at all for six months.^{[39]} After several unsuccessful years, she started cooking again. She used fake surnames like Breshof or Brown, and took jobs as a cook against the explicit instructions of health authorities. No agencies that hired servants for upscale families would offer her employment, so for the next five years, she moved to the mass sector. She worked in a number of kitchens in restaurants, hotels, and spa centers. Almost wherever she worked, there were outbreaks of typhoid.^{[36]} However, she changed jobs frequently, and Soper was unable to find her.^{[13]}
In 1915, Mallon started working at Sloane Hospital for Women in New York City. Soon 25 people were infected, and two died. The head obstetrician, Dr. Edward B. Cragin, called Soper and asked him to help in the investigation. Soper identified Mallon from the servants' verbal descriptions and also by her handwriting.^{[36]}^{[39]}
Mallon again fled, but the police were able to find and arrest her when she took food to a friend on Long Island.^{[13]}^{[37]} Mallon was returned to quarantine on North Brother Island on March 27, 1915.^{[37]}^{[39]}
Little is known about her life during the second quarantine. She remained on North Brother for more than 23 years, and the authorities gave her a private one-story cottage. As of 1918, she was allowed to take day trips to the mainland. In 1925, Dr. Alexandra Plavska came to the island for an internship. She organized a laboratory on the second floor of the chapel and offered Mallon a job as a technician. Mallon washed bottles, did recordings, and prepared glasses for pathologists.^{[40]}^{[41]}
Death
Mallon spent the rest of her life in quarantine at Riverside Hospital on North Brother Island. Mallon was quite active until suffering a stroke in 1932; afterwards, she was confined to the hospital.^{[42]} She never completely recovered, and half of her body remained paralyzed.^{[43]} On November 11, 1938, she died of pneumonia at age 69.^{[2]} Mallon's body was cremated, and her ashes were buried at Saint Raymond's Cemetery in the Bronx.^{[44]} Nine people attended the funeral.^{[45]}^{[46]}
Some sources claim that a post-mortem found evidence of live typhoid bacteria in Mallon's gallbladder.^{[16]}^{[13]}^{[47]} Soper wrote, however, that there was no autopsy, a claim cited by other researchers to assert a conspiracy to calm public opinion after her death.^{[48]}^{[16]}
Legacy
A historical poster warning against acting like Typhoid Mary
Aftermath
Research by a reliable source led to an estimate that Mallon had contaminated "at least one hundred and twenty two people, including five dead".^{[49]} Other sources attribute at least three deaths to contact with Mallon, but because of health officials' inability to persuade her to cooperate, the exact number is not known. Some have estimated that contact with her may have caused 50 fatalities.^{[13]}
In a 2013 article in the Annals of Gastroenterology, the authors concluded:
The history of Mary Mallon, declared “unclean” like a leper, may give us some moral lessons on how to protect the ill and how we can be protected from illness...By the time she died New York health officials had identified more than 400 other healthy carriers of Salmonella typhi, but no one else was forcibly confined or victimized as an “unwanted ill”.^{[50]}
Other healthy typhoid carriers identified in the first quarter of the 20th century include Tony Labella, an Italian immigrant, presumed to have caused over 100 cases (with five deaths); an Adirondack guide dubbed "Typhoid John", presumed to have infected 36 people (with two deaths); and Alphonse Cotils, a restaurateur and bakery owner.^{[51]}
The health technology of the era did not have a completely effective solution: there were no antibiotics to fight the infection, and gallbladder removal was a dangerous, sometimes fatal operation. Some modern specialists claim that the typhoid bacteria can become integrated in macrophages and then reside in intestinal lymph nodes or the spleen.^{[52]}^{[53]}
Ethical and legal issues
Mary Mallon's case became the first in which an asymptomatic carrier was discovered and forcibly isolated. The ethical and legal issues raised by her case are still discussed.^{[6]}^{[54]}^{[55]}
Two scholarly sources combined to provide this conclusion:^{[56]}
"This case highlighted the problematic nature of the subject and the need for an enhanced medical and legal-social treatment model aimed at improving the status of disease carriers and limiting their impact on society".
In culture
Today, the phrase "Typhoid Mary" is a colloquial term for anyone who, knowingly or not, spreads disease or some other undesirable thing.^{[57]}
Mallon's urban legend status in New York inspired the name of the rap group Hail Mary Mallon.^{[58]}
Walzer Leavitt, Judith; Numbers, Ronald L., eds. (1997). "Typhoid Mary Strikes Back". Sickness and Health in America: Readings in the History of Medicine and Public Health. 3. Wisconsin: The University of Wisconsin Press. ISBN 0299153207.
Walzer Leavitt, Judith (1995). "Women and Early Public Health". In Linda K. Kerber; Alice Kessler-Harris; Kathryn Kish Sklar (eds.). U.S. History as Women's History: New Feminist Essays. London: Chapel Hill. p. 156. ISBN 0-8078-4495-0.
Cliff, Andrew; Smallman-Raynor, Matthew (2013). Oxford Textbook of Infectious Disease Control: A Geographical Analysis from Medieval Quarantine to Global Eradication. Oxford University Press. p. 86. ISBN 978-0-199-59661-4.
Slow motion computer simulation of the black hole binary system GW150914 as seen by a nearby observer, during 0.33 s of its final inspiral, merge, and ringdown. The star field behind the black holes is being heavily distorted and appears to rotate and move, due to extreme gravitational lensing, as spacetime itself is distorted and dragged around by the rotating black holes.^{[1]}
Einstein's theory has important astrophysical implications. For example, it implies the existence of black holes—regions of space in which space and time are distorted in such a way that nothing, not even light, can escape—as an end-state for massive stars. There is ample evidence that the intense radiation emitted by certain kinds of astronomical objects is due to black holes. For example, microquasars and active galactic nuclei result from the presence of stellar black holes and supermassive black holes, respectively. The bending of light by gravity can lead to the phenomenon of gravitational lensing, in which multiple images of the same distant astronomical object are visible in the sky. General relativity also predicts the existence of gravitational waves, which have since been observed directly by the physics collaboration LIGO. In addition, general relativity is the basis of current cosmological models of a consistently expanding universe.
Widely acknowledged as a theory of extraordinary beauty, general relativity has often been described as the most beautiful of all existing physical theories.^{[2]}
Soon after publishing the special theory of relativity in 1905, Einstein started thinking about how to incorporate gravity into his new relativistic framework. In 1907, beginning with a simple thought experiment involving an observer in free fall, he embarked on what would be an eight-year search for a relativistic theory of gravity. After numerous detours and false starts, his work culminated in the presentation to the Prussian Academy of Science in November 1915 of what are now known as the Einstein field equations, which form the core of Einstein's general theory of relativity.^{[3]} These equations specify how the geometry of space and time is influenced by whatever matter and radiation are present.^{[4]} The 19th century mathematician Bernhard Riemann's non-Euclidean geometry, called Riemannian Geometry, enabled Einstein to develop general relativity by providing the key mathematical framework on which he fit his physical ideas of gravity.^{[5]} This idea was pointed out by mathematician Marcel Grossmann and published by Grossmann and Einstein in 1913.^{[6]}
The Einstein field equations are nonlinear and very difficult to solve. Einstein used approximation methods in working out initial predictions of the theory. But in 1916, the astrophysicist Karl Schwarzschild found the first non-trivial exact solution to the Einstein field equations, the Schwarzschild metric. This solution laid the groundwork for the description of the final stages of gravitational collapse, and the objects known today as black holes. In the same year, the first steps towards generalizing Schwarzschild's solution to electrically charged objects were taken, eventually resulting in the Reissner–Nordström solution, which is now associated with electrically charged black holes.^{[7]} In 1917, Einstein applied his theory to the universe as a whole, initiating the field of relativistic cosmology. In line with contemporary thinking, he assumed a static universe, adding a new parameter to his original field equations—the cosmological constant—to match that observational presumption.^{[8]} By 1929, however, the work of Hubble and others had shown that our universe is expanding. This is readily described by the expanding cosmological solutions found by Friedmann in 1922, which do not require a cosmological constant. Lemaître used these solutions to formulate the earliest version of the Big Bang models, in which our universe has evolved from an extremely hot and dense earlier state.^{[9]} Einstein later declared the cosmological constant the biggest blunder of his life.^{[10]}
During that period, general relativity remained something of a curiosity among physical theories. It was clearly superior to Newtonian gravity, being consistent with special relativity and accounting for several effects unexplained by the Newtonian theory. Einstein showed in 1915 how his theory explained the anomalous perihelion advance of the planet Mercury without any arbitrary parameters ("fudge factors"),^{[11]} and in 1919 an expedition led by Eddington confirmed general relativity's prediction for the deflection of starlight by the Sun during the total solar eclipse of May 29, 1919,^{[12]} instantly making Einstein famous.^{[13]} Yet the theory remained outside the mainstream of theoretical physics and astrophysics until developments between approximately 1960 and 1975, now known as the golden age of general relativity.^{[14]} Physicists began to understand the concept of a black hole, and to identify quasars as one of these objects' astrophysical manifestations.^{[15]} Ever more precise solar system tests confirmed the theory's predictive power,^{[16]} and relativistic cosmology also became amenable to direct observational tests.^{[17]}
Over the years, general relativity has acquired a reputation as a theory of extraordinary beauty.^{[2]}^{[18]}^{[19]}Subrahmanyan Chandrasekhar has noted that at multiple levels, general relativity exhibits what Francis Bacon has termed a "strangeness in the proportion" (i.e. elements that excite wonderment and surprise). It juxtaposes fundamental concepts (space and time versus matter and motion) which had previously been considered as entirely independent. Chandrasekhar also noted that Einstein's only guides in his search for an exact theory were the principle of equivalence and his sense that a proper description of gravity should be geometrical at its basis, so that there was an "element of revelation" in the manner in which Einstein arrived at his theory.^{[20]} Other elements of beauty associated with the general theory of relativity are its simplicity and symmetry, the manner in which it incorporates invariance and unification, and its perfect logical consistency.^{[21]}
From classical mechanics to general relativity
General relativity can be understood by examining its similarities with and departures from classical physics. The first step is the realization that classical mechanics and Newton's law of gravity admit a geometric description. The combination of this description with the laws of special relativity results in a heuristic derivation of general relativity.^{[22]} This is very well explained by Professor Jim Al-Khalili in his BBC program 'Gravity and Me: The Force that Shapes Our Lives'^{[23]}
Geometry of Newtonian gravity
According to general relativity, objects in a gravitational field behave similarly to objects within an accelerating enclosure. For example, an observer will see a ball fall the same way in a rocket (left) as it does on Earth (right), provided that the acceleration of the rocket is equal to 9.8 m/s^{2} (the acceleration due to gravity at the surface of the Earth).
At the base of classical mechanics is the notion that a body's motion can be described as a combination of free (or inertial) motion, and deviations from this free motion. Such deviations are caused by external forces acting on a body in accordance with Newton's second law of motion, which states that the net force acting on a body is equal to that body's (inertial) mass multiplied by its acceleration.^{[24]} The preferred inertial motions are related to the geometry of space and time: in the standard reference frames of classical mechanics, objects in free motion move along straight lines at constant speed. In modern parlance, their paths are geodesics, straight world lines in curved spacetime.^{[25]}
Conversely, one might expect that inertial motions, once identified by observing the actual motions of bodies and making allowances for the external forces (such as electromagnetism or friction), can be used to define the geometry of space, as well as a time coordinate. However, there is an ambiguity once gravity comes into play. According to Newton's law of gravity, and independently verified by experiments such as that of Eötvös and its successors (see Eötvös experiment), there is a universality of free fall (also known as the weak equivalence principle, or the universal equality of inertial and passive-gravitational mass): the trajectory of a test body in free fall depends only on its position and initial speed, but not on any of its material properties.^{[26]} A simplified version of this is embodied in Einstein's elevator experiment, illustrated in the figure on the right: for an observer in a small enclosed room, it is impossible for him to decide, by mapping the trajectory of bodies such as a dropped ball, whether the room is stationary in a gravitational field and the ball accelerating, or in free space aboard a rocket that is accelerating at a rate equal to that of the gravitational field versus the ball which upon release has nil acceleration.^{[27]}
Given the universality of free fall, there is no observable distinction between inertial motion and motion under the influence of the gravitational force. This suggests the definition of a new class of inertial motion, namely that of objects in free fall under the influence of gravity. This new class of preferred motions, too, defines a geometry of space and time—in mathematical terms, it is the geodesic motion associated with a specific connection which depends on the gradient of the gravitational potential. Space, in this construction, still has the ordinary Euclidean geometry. However, spacetime as a whole is more complicated. As can be shown using simple thought experiments following the free-fall trajectories of different test particles, the result of transporting spacetime vectors that can denote a particle's velocity (time-like vectors) will vary with the particle's trajectory; mathematically speaking, the Newtonian connection is not integrable. From this, one can deduce that spacetime is curved. The resulting Newton–Cartan theory is a geometric formulation of Newtonian gravity using only covariant concepts, i.e. a description which is valid in any desired coordinate system.^{[28]} In this geometric description, tidal effects—the relative acceleration of bodies in free fall—are related to the derivative of the connection, showing how the modified geometry is caused by the presence of mass.^{[29]}
As intriguing as geometric Newtonian gravity may be, its basis, classical mechanics, is merely a limiting case of (special) relativistic mechanics.^{[30]} In the language of symmetry: where gravity can be neglected, physics is Lorentz invariant as in special relativity rather than Galilei invariant as in classical mechanics. (The defining symmetry of special relativity is the Poincaré group, which includes translations, rotations and boosts.) The differences between the two become significant when dealing with speeds approaching the speed of light, and with high-energy phenomena.^{[31]}
With Lorentz symmetry, additional structures come into play. They are defined by the set of light cones (see image). The light-cones define a causal structure: for each eventA, there is a set of events that can, in principle, either influence or be influenced by A via signals or interactions that do not need to travel faster than light (such as event B in the image), and a set of events for which such an influence is impossible (such as event C in the image). These sets are observer-independent.^{[32]} In conjunction with the world-lines of freely falling particles, the light-cones can be used to reconstruct the spacetime's semi-Riemannian metric, at least up to a positive scalar factor. In mathematical terms, this defines a conformal structure^{[33]} or conformal geometry.
Special relativity is defined in the absence of gravity. For practical applications, it is a suitable model whenever gravity can be neglected. Bringing gravity into play, and assuming the universality of free fall motion, an analogous reasoning as in the previous section applies: there are no global inertial frames. Instead there are approximate inertial frames moving alongside freely falling particles. Translated into the language of spacetime: the straight time-like lines that define a gravity-free inertial frame are deformed to lines that are curved relative to each other, suggesting that the inclusion of gravity necessitates a change in spacetime geometry.^{[34]}
A priori, it is not clear whether the new local frames in free fall coincide with the reference frames in which the laws of special relativity hold—that theory is based on the propagation of light, and thus on electromagnetism, which could have a different set of preferred frames. But using different assumptions about the special-relativistic frames (such as their being earth-fixed, or in free fall), one can derive different predictions for the gravitational redshift, that is, the way in which the frequency of light shifts as the light propagates through a gravitational field (cf. below). The actual measurements show that free-falling frames are the ones in which light propagates as it does in special relativity.^{[35]} The generalization of this statement, namely that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames, is known as the Einstein equivalence principle, a crucial guiding principle for generalizing special-relativistic physics to include gravity.^{[36]}
The same experimental data shows that time as measured by clocks in a gravitational field—proper time, to give the technical term—does not follow the rules of special relativity. In the language of spacetime geometry, it is not measured by the Minkowski metric. As in the Newtonian case, this is suggestive of a more general geometry. At small scales, all reference frames that are in free fall are equivalent, and approximately Minkowskian. Consequently, we are now dealing with a curved generalization of Minkowski space. The metric tensor that defines the geometry—in particular, how lengths and angles are measured—is not the Minkowski metric of special relativity, it is a generalization known as a semi- or pseudo-Riemannian metric. Furthermore, each Riemannian metric is naturally associated with one particular kind of connection, the Levi-Civita connection, and this is, in fact, the connection that satisfies the equivalence principle and makes space locally Minkowskian (that is, in suitable locally inertial coordinates, the metric is Minkowskian, and its first partial derivatives and the connection coefficients vanish).^{[37]}
Having formulated the relativistic, geometric version of the effects of gravity, the question of gravity's source remains. In Newtonian gravity, the source is mass. In special relativity, mass turns out to be part of a more general quantity called the energy–momentum tensor, which includes both energy and momentum densities as well as stress: pressure and shear.^{[38]} Using the equivalence principle, this tensor is readily generalized to curved spacetime. Drawing further upon the analogy with geometric Newtonian gravity, it is natural to assume that the field equation for gravity relates this tensor and the Ricci tensor, which describes a particular class of tidal effects: the change in volume for a small cloud of test particles that are initially at rest, and then fall freely. In special relativity, conservation of energy–momentum corresponds to the statement that the energy–momentum tensor is divergence-free. This formula, too, is readily generalized to curved spacetime by replacing partial derivatives with their curved-manifold counterparts, covariant derivatives studied in differential geometry. With this additional condition—the covariant divergence of the energy-momentum tensor, and hence of whatever is on the other side of the equation, is zero—the simplest set of equations are what are called Einstein's (field) equations:
Einstein's field equations
On the left-hand side is the Einstein tensor, , which is symmetric and a specific divergence-free combination of the Ricci tensor and the metric. In particular,
is the curvature scalar. The Ricci tensor itself is related to the more general Riemann curvature tensor as
On the right-hand side, is the energy–momentum tensor. All tensors are written in abstract index notation.^{[39]} Matching the theory's prediction to observational results for planetaryorbits or, equivalently, assuring that the weak-gravity, low-speed limit is Newtonian mechanics, the proportionality constant is found to be , where is the gravitational constant and the speed of light in vacuum.^{[40]} When there is no matter present, so that the energy–momentum tensor vanishes, the results are the vacuum Einstein equations,
In general relativity, the world line of a particle free from all external, non-gravitational force is a particular type of geodesic in curved spacetime. In other words, a freely moving or falling particle always moves along a geodesic.
where is a scalar parameter of motion (e.g. the proper time), and are Christoffel symbols (sometimes called the affine connection coefficients or Levi-Civita connection coefficients) which is symmetric in the two lower indices. Greek indices may take the values: 0, 1, 2, 3 and the summation convention is used for repeated indices and . The quantity on the left-hand-side of this equation is the acceleration of a particle, and so this equation is analogous to Newton's laws of motion which likewise provide formulae for the acceleration of a particle. This equation of motion employs the Einstein notation, meaning that repeated indices are summed (i.e. from zero to three). The Christoffel symbols are functions of the four spacetime coordinates, and so are independent of the velocity or acceleration or other characteristics of a test particle whose motion is described by the geodesic equation.
The derivation outlined in the previous section contains all the information needed to define general relativity, describe its key properties, and address a question of crucial importance in physics, namely how the theory can be used for model-building.
Definition and basic properties
General relativity is a metric theory of gravitation. At its core are Einstein's equations, which describe the relation between the geometry of a four-dimensional pseudo-Riemannian manifold representing spacetime, and the energy–momentum contained in that spacetime.^{[44]} Phenomena that in classical mechanics are ascribed to the action of the force of gravity (such as free-fall, orbital motion, and spacecrafttrajectories), correspond to inertial motion within a curved geometry of spacetime in general relativity; there is no gravitational force deflecting objects from their natural, straight paths. Instead, gravity corresponds to changes in the properties of space and time, which in turn changes the straightest-possible paths that objects will naturally follow.^{[45]} The curvature is, in turn, caused by the energy–momentum of matter. Paraphrasing the relativist John Archibald Wheeler, spacetime tells matter how to move; matter tells spacetime how to curve.^{[46]}
While general relativity replaces the scalar gravitational potential of classical physics by a symmetric rank-two tensor, the latter reduces to the former in certain limiting cases. For weak gravitational fields and slow speed relative to the speed of light, the theory's predictions converge on those of Newton's law of universal gravitation.^{[47]}
As it is constructed using tensors, general relativity exhibits general covariance: its laws—and further laws formulated within the general relativistic framework—take on the same form in all coordinate systems.^{[48]} Furthermore, the theory does not contain any invariant geometric background structures, i.e. it is background independent. It thus satisfies a more stringent general principle of relativity, namely that the laws of physics are the same for all observers.^{[49]}Locally, as expressed in the equivalence principle, spacetime is Minkowskian, and the laws of physics exhibit local Lorentz invariance.^{[50]}
Model-building
The core concept of general-relativistic model-building is that of a solution of Einstein's equations. Given both Einstein's equations and suitable equations for the properties of matter, such a solution consists of a specific semi-Riemannian manifold (usually defined by giving the metric in specific coordinates), and specific matter fields defined on that manifold. Matter and geometry must satisfy Einstein's equations, so in particular, the matter's energy–momentum tensor must be divergence-free. The matter must, of course, also satisfy whatever additional equations were imposed on its properties. In short, such a solution is a model universe that satisfies the laws of general relativity, and possibly additional laws governing whatever matter might be present.^{[51]}
Einstein's equations are nonlinear partial differential equations and, as such, difficult to solve exactly.^{[52]} Nevertheless, a number of exact solutions are known, although only a few have direct physical applications.^{[53]} The best-known exact solutions, and also those most interesting from a physics point of view, are the Schwarzschild solution, the Reissner–Nordström solution and the Kerr metric, each corresponding to a certain type of black hole in an otherwise empty universe,^{[54]} and the Friedmann–Lemaître–Robertson–Walker and de Sitter universes, each describing an expanding cosmos.^{[55]} Exact solutions of great theoretical interest include the Gödel universe (which opens up the intriguing possibility of time travel in curved spacetimes), the Taub-NUT solution (a model universe that is homogeneous, but anisotropic), and anti-de Sitter space (which has recently come to prominence in the context of what is called the Maldacena conjecture).^{[56]}
Given the difficulty of finding exact solutions, Einstein's field equations are also solved frequently by numerical integration on a computer, or by considering small perturbations of exact solutions. In the field of numerical relativity, powerful computers are employed to simulate the geometry of spacetime and to solve Einstein's equations for interesting situations such as two colliding black holes.^{[57]} In principle, such methods may be applied to any system, given sufficient computer resources, and may address fundamental questions such as naked singularities. Approximate solutions may also be found by perturbation theories such as linearized gravity^{[58]} and its generalization, the post-Newtonian expansion, both of which were developed by Einstein. The latter provides a systematic approach to solving for the geometry of a spacetime that contains a distribution of matter that moves slowly compared with the speed of light. The expansion involves a series of terms; the first terms represent Newtonian gravity, whereas the later terms represent ever smaller corrections to Newton's theory due to general relativity.^{[59]} An extension of this expansion is the parametrized post-Newtonian (PPN) formalism, which allows quantitative comparisons between the predictions of general relativity and alternative theories.^{[60]}
Consequences of Einstein's theory
General relativity has a number of physical consequences. Some follow directly from the theory's axioms, whereas others have become clear only in the course of many years of research that followed Einstein's initial publication.
Schematic representation of the gravitational redshift of a light wave escaping from the surface of a massive body
Assuming that the equivalence principle holds,^{[61]} gravity influences the passage of time. Light sent down into a gravity well is blueshifted, whereas light sent in the opposite direction (i.e., climbing out of the gravity well) is redshifted; collectively, these two effects are known as the gravitational frequency shift. More generally, processes close to a massive body run more slowly when compared with processes taking place farther away; this effect is known as gravitational time dilation.^{[62]}
Gravitational redshift has been measured in the laboratory^{[63]} and using astronomical observations.^{[64]} Gravitational time dilation in the Earth's gravitational field has been measured numerous times using atomic clocks,^{[65]} while ongoing validation is provided as a side effect of the operation of the Global Positioning System (GPS).^{[66]} Tests in stronger gravitational fields are provided by the observation of binary pulsars.^{[67]} All results are in agreement with general relativity.^{[68]} However, at the current level of accuracy, these observations cannot distinguish between general relativity and other theories in which the equivalence principle is valid.^{[69]}
Deflection of light (sent out from the location shown in blue) near a compact body (shown in gray)
General relativity predicts that the path of light will follow the curvature of spacetime as it passes near a star. This effect was initially confirmed by observing the light of stars or distant quasars being deflected as it passes the Sun.^{[70]}
This and related predictions follow from the fact that light follows what is called a light-like or null geodesic—a generalization of the straight lines along which light travels in classical physics. Such geodesics are the generalization of the invariance of lightspeed in special relativity.^{[71]} As one examines suitable model spacetimes (either the exterior Schwarzschild solution or, for more than a single mass, the post-Newtonian expansion),^{[72]} several effects of gravity on light propagation emerge. Although the bending of light can also be derived by extending the universality of free fall to light,^{[73]} the angle of deflection resulting from such calculations is only half the value given by general relativity.^{[74]}
Closely related to light deflection is the gravitational time delay (or Shapiro delay), the phenomenon that light signals take longer to move through a gravitational field than they would in the absence of that field. There have been numerous successful tests of this prediction.^{[75]} In the parameterized post-Newtonian formalism (PPN), measurements of both the deflection of light and the gravitational time delay determine a parameter called γ, which encodes the influence of gravity on the geometry of space.^{[76]}
Ring of test particles deformed by a passing (linearized, amplified for better visibility) gravitational wave
Predicted in 1916^{[77]}^{[78]} by Albert Einstein, there are gravitational waves: ripples in the metric of spacetime that propagate at the speed of light. These are one of several analogies between weak-field gravity and electromagnetism in that, they are analogous to electromagnetic waves. On February 11, 2016, the Advanced LIGO team announced that they had directly detected gravitational waves from a pair of black holes merging.^{[79]}^{[80]}^{[81]}
The simplest type of such a wave can be visualized by its action on a ring of freely floating particles. A sine wave propagating through such a ring towards the reader distorts the ring in a characteristic, rhythmic fashion (animated image to the right).^{[82]} Since Einstein's equations are non-linear, arbitrarily strong gravitational waves do not obey linear superposition, making their description difficult. However, linear approximations of gravitational waves are sufficiently accurate to describe the exceedingly weak waves that are expected to arrive here on Earth from far-off cosmic events, which typically result in relative distances increasing and decreasing by or less. Data analysis methods routinely make use of the fact that these linearized waves can be Fourier decomposed.^{[83]}
Some exact solutions describe gravitational waves without any approximation, e.g., a wave train traveling through empty space^{[84]} or Gowdy universes, varieties of an expanding cosmos filled with gravitational waves.^{[85]} But for gravitational waves produced in astrophysically relevant situations, such as the merger of two black holes, numerical methods are presently the only way to construct appropriate models.^{[86]}
General relativity differs from classical mechanics in a number of predictions concerning orbiting bodies. It predicts an overall rotation (precession) of planetary orbits, as well as orbital decay caused by the emission of gravitational waves and effects related to the relativity of direction.
Precession of apsides
Newtonian (red) vs. Einsteinian orbit (blue) of a lone planet orbiting a star. The influence of other planets is ignored.
In general relativity, the apsides of any orbit (the point of the orbiting body's closest approach to the system's center of mass) will precess; the orbit is not an ellipse, but akin to an ellipse that rotates on its focus, resulting in a rose curve-like shape (see image). Einstein first derived this result by using an approximate metric representing the Newtonian limit and treating the orbiting body as a test particle. For him, the fact that his theory gave a straightforward explanation of Mercury's anomalous perihelion shift, discovered earlier by Urbain Le Verrier in 1859, was important evidence that he had at last identified the correct form of the gravitational field equations.^{[87]}
The effect can also be derived by using either the exact Schwarzschild metric (describing spacetime around a spherical mass)^{[88]} or the much more general post-Newtonian formalism.^{[89]} It is due to the influence of gravity on the geometry of space and to the contribution of self-energy to a body's gravity (encoded in the nonlinearity of Einstein's equations).^{[90]} Relativistic precession has been observed for all planets that allow for accurate precession measurements (Mercury, Venus, and Earth),^{[91]} as well as in binary pulsar systems, where it is larger by five orders of magnitude.^{[92]}
In general relativity the perihelion shift , expressed in radians per revolution, is approximately given by^{[93]}
Orbital decay for PSR1913+16: time shift (in s), tracked over 30 years.^{[94]}
According to general relativity, a binary system will emit gravitational waves, thereby losing energy. Due to this loss, the distance between the two orbiting bodies decreases, and so does their orbital period. Within the Solar System or for ordinary double stars, the effect is too small to be observable. This is not the case for a close binary pulsar, a system of two orbiting neutron stars, one of which is a pulsar: from the pulsar, observers on Earth receive a regular series of radio pulses that can serve as a highly accurate clock, which allows precise measurements of the orbital period. Because neutron stars are immensely compact, significant amounts of energy are emitted in the form of gravitational radiation.^{[95]}
The first observation of a decrease in orbital period due to the emission of gravitational waves was made by Hulse and Taylor, using the binary pulsar PSR1913+16 they had discovered in 1974. This was the first detection of gravitational waves, albeit indirect, for which they were awarded the 1993 Nobel Prize in physics.^{[96]} Since then, several other binary pulsars have been found, in particular the double pulsar PSR J0737-3039, in which both stars are pulsars.^{[97]}
Several relativistic effects are directly related to the relativity of direction.^{[98]} One is geodetic precession: the axis direction of a gyroscope in free fall in curved spacetime will change when compared, for instance, with the direction of light received from distant stars—even though such a gyroscope represents the way of keeping a direction as stable as possible ("parallel transport").^{[99]} For the Moon–Earth system, this effect has been measured with the help of lunar laser ranging.^{[100]} More recently, it has been measured for test masses aboard the satellite Gravity Probe B to a precision of better than 0.3%.^{[101]}^{[102]}
Near a rotating mass, there are gravitomagnetic or frame-dragging effects. A distant observer will determine that objects close to the mass get "dragged around". This is most extreme for rotating black holes where, for any object entering a zone known as the ergosphere, rotation is inevitable.^{[103]} Such effects can again be tested through their influence on the orientation of gyroscopes in free fall.^{[104]} Somewhat controversial tests have been performed using the LAGEOS satellites, confirming the relativistic prediction.^{[105]} Also the Mars Global Surveyor probe around Mars has been used.^{[106]}
Interpretations
Neo-Lorentzian Interpretation
Examples of prominent physicists who support neo-Lorentzian explanations of general relativity are Franco Selleri and Antony Valentini.^{[107]}
Einstein cross: four images of the same astronomical object, produced by a gravitational lens
The deflection of light by gravity is responsible for a new class of astronomical phenomena. If a massive object is situated between the astronomer and a distant target object with appropriate mass and relative distances, the astronomer will see multiple distorted images of the target. Such effects are known as gravitational lensing.^{[108]} Depending on the configuration, scale, and mass distribution, there can be two or more images, a bright ring known as an Einstein ring, or partial rings called arcs.^{[109]}
The earliest example was discovered in 1979;^{[110]} since then, more than a hundred gravitational lenses have been observed.^{[111]} Even if the multiple images are too close to each other to be resolved, the effect can still be measured, e.g., as an overall brightening of the target object; a number of such "microlensing events" have been observed.^{[112]}
Gravitational lensing has developed into a tool of observational astronomy. It is used to detect the presence and distribution of dark matter, provide a "natural telescope" for observing distant galaxies, and to obtain an independent estimate of the Hubble constant. Statistical evaluations of lensing data provide valuable insight into the structural evolution of galaxies.^{[113]}
Artist's impression of the space-borne gravitational wave detector LISA
Observations of binary pulsars provide strong indirect evidence for the existence of gravitational waves (see Orbital decay, above). Detection of these waves is a major goal of current relativity-related research.^{[114]} Several land-based gravitational wave detectors are currently in operation, most notably the interferometric detectorsGEO 600, LIGO (two detectors), TAMA 300 and VIRGO.^{[115]} Various pulsar timing arrays are using millisecond pulsars to detect gravitational waves in the 10^{−9} to 10^{−6}Hertz frequency range, which originate from binary supermassive blackholes.^{[116]} A European space-based detector, eLISA / NGO, is currently under development,^{[117]} with a precursor mission (LISA Pathfinder) having launched in December 2015.^{[118]}
Observations of gravitational waves promise to complement observations in the electromagnetic spectrum.^{[119]} They are expected to yield information about black holes and other dense objects such as neutron stars and white dwarfs, about certain kinds of supernova implosions, and about processes in the very early universe, including the signature of certain types of hypothetical cosmic string.^{[120]} In February 2016, the Advanced LIGO team announced that they had detected gravitational waves from a black hole merger.^{[79]}^{[80]}^{[81]}
Simulation based on the equations of general relativity: a star collapsing to form a black hole while emitting gravitational waves
Whenever the ratio of an object's mass to its radius becomes sufficiently large, general relativity predicts the formation of a black hole, a region of space from which nothing, not even light, can escape. In the currently accepted models of stellar evolution, neutron stars of around 1.4 solar masses, and stellar black holes with a few to a few dozen solar masses, are thought to be the final state for the evolution of massive stars.^{[121]} Usually a galaxy has one supermassive black hole with a few million to a few billion solar masses in its center,^{[122]} and its presence is thought to have played an important role in the formation of the galaxy and larger cosmic structures.^{[123]}
Astronomically, the most important property of compact objects is that they provide a supremely efficient mechanism for converting gravitational energy into electromagnetic radiation.^{[124]}Accretion, the falling of dust or gaseous matter onto stellar or supermassive black holes, is thought to be responsible for some spectacularly luminous astronomical objects, notably diverse kinds of active galactic nuclei on galactic scales and stellar-size objects such as microquasars.^{[125]} In particular, accretion can lead to relativistic jets, focused beams of highly energetic particles that are being flung into space at almost light speed.^{[126]}
General relativity plays a central role in modelling all these phenomena,^{[127]} and observations provide strong evidence for the existence of black holes with the properties predicted by the theory.^{[128]}
Black holes are also sought-after targets in the search for gravitational waves (cf. Gravitational waves, above). Merging black hole binaries should lead to some of the strongest gravitational wave signals reaching detectors here on Earth, and the phase directly before the merger ("chirp") could be used as a "standard candle" to deduce the distance to the merger events–and hence serve as a probe of cosmic expansion at large distances.^{[129]} The gravitational waves produced as a stellar black hole plunges into a supermassive one should provide direct information about the supermassive black hole's geometry.^{[130]}
This blue horseshoe is a distant galaxy that has been magnified and warped into a nearly complete ring by the strong gravitational pull of the massive foreground luminous red galaxy.
The current models of cosmology are based on Einstein's field equations, which include the cosmological constant since it has important influence on the large-scale dynamics of the cosmos,
where is the spacetime metric.^{[131]}Isotropic and homogeneous solutions of these enhanced equations, the Friedmann–Lemaître–Robertson–Walker solutions,^{[132]} allow physicists to model a universe that has evolved over the past 14 billion years from a hot, early Big Bang phase.^{[133]} Once a small number of parameters (for example the universe's mean matter density) have been fixed by astronomical observation,^{[134]} further observational data can be used to put the models to the test.^{[135]} Predictions, all successful, include the initial abundance of chemical elements formed in a period of primordial nucleosynthesis,^{[136]} the large-scale structure of the universe,^{[137]} and the existence and properties of a "thermal echo" from the early cosmos, the cosmic background radiation.^{[138]}
Astronomical observations of the cosmological expansion rate allow the total amount of matter in the universe to be estimated, although the nature of that matter remains mysterious in part. About 90% of all matter appears to be dark matter, which has mass (or, equivalently, gravitational influence), but does not interact electromagnetically and, hence, cannot be observed directly.^{[139]} There is no generally accepted description of this new kind of matter, within the framework of known particle physics^{[140]} or otherwise.^{[141]} Observational evidence from redshift surveys of distant supernovae and measurements of the cosmic background radiation also show that the evolution of our universe is significantly influenced by a cosmological constant resulting in an acceleration of cosmic expansion or, equivalently, by a form of energy with an unusual equation of state, known as dark energy, the nature of which remains unclear.^{[142]}
An inflationary phase,^{[143]} an additional phase of strongly accelerated expansion at cosmic times of around 10^{−33} seconds, was hypothesized in 1980 to account for several puzzling observations that were unexplained by classical cosmological models, such as the nearly perfect homogeneity of the cosmic background radiation.^{[144]} Recent measurements of the cosmic background radiation have resulted in the first evidence for this scenario.^{[145]} However, there is a bewildering variety of possible inflationary scenarios, which cannot be restricted by current observations.^{[146]} An even larger question is the physics of the earliest universe, prior to the inflationary phase and close to where the classical models predict the big bang singularity. An authoritative answer would require a complete theory of quantum gravity, which has not yet been developed^{[147]} (cf. the section on quantum gravity, below).
Time travel
Kurt Gödel showed^{[148]} that solutions to Einstein's equations exist that contain closed timelike curves (CTCs), which allow for loops in time. The solutions require extreme physical conditions unlikely ever to occur in practice, and it remains an open question whether further laws of physics will eliminate them completely. Since then, other—similarly impractical—GR solutions containing CTCs have been found, such as the Tipler cylinder and traversable wormholes.
The spacetime symmetry group for Special Relativity is the Poincaré group, which is a ten-dimensional group of three Lorentz boosts, three rotations, and four spacetime translations. It is logical to ask what symmetries if any might apply in General Relativity. A tractable case might be to consider the symmetries of spacetime as seen by observers located far away from all sources of the gravitational field. The naive expectation for asymptotically flat spacetime symmetries might be simply to extend and reproduce the symmetries of flat spacetime of special relativity, viz., the Poincaré group.
In 1962 Hermann Bondi, M. G. van der Burg, A. W. Metzner^{[149]} and Rainer K. Sachs^{[150]} addressed this asymptotic symmetry problem in order to investigate the flow of energy at infinity due to propagating gravitational waves. Their first step was to decide on some physically sensible boundary conditions to place on the gravitational field at light-like infinity to characterize what it means to say a metric is asymptotically flat, making no a priori assumptions about the nature of the asymptotic symmetry group — not even the assumption that such a group exists. Then after designing what they considered to be the most sensible boundary conditions, they investigated the nature of the resulting asymptotic symmetry transformations that leave invariant the form of the boundary conditions appropriate for asymptotically flat gravitational fields. What they found was that the asymptotic symmetry transformations actually do form a group and the structure of this group does not depend on the particular gravitational field that happens to be present. This means that, as expected, one can separate the kinematics of spacetime from the dynamics of the gravitational field at least at spatial infinity. The puzzling surprise in 1962 was their discovery of a rich infinite-dimensional group (the so-called BMS group) as the asymptotic symmetry group, instead of the finite-dimensional Poincaré group, which is a subgroup of the BMS group. Not only are the Lorentz transformations asymptotic symmetry transformations, there are also additional transformations that are not Lorentz transformations but are asymptotic symmetry transformations. In fact, they found an additional infinity of transformation generators known as supertranslations. This implies the conclusion that General Relativity (GR) does not reduce to special relativity in the case of weak fields at long distances. It turns out that the BMS symmetry, suitably modified, could be seen as a restatement of the universal soft graviton theorem in quantum field theory (QFT), which relates universal infrared (soft) QFT with GR asymptotic spacetime symmetries.^{[151]}
In general relativity, no material body can catch up with or overtake a light pulse. No influence from an event A can reach any other location X before light sent out at A to X. In consequence, an exploration of all light worldlines (null geodesics) yields key information about the spacetime's causal structure. This structure can be displayed using Penrose–Carter diagrams in which infinitely large regions of space and infinite time intervals are shrunk ("compactified") so as to fit onto a finite map, while light still travels along diagonals as in standard spacetime diagrams.^{[152]}
Aware of the importance of causal structure, Roger Penrose and others developed what is known as global geometry. In global geometry, the object of study is not one particular solution (or family of solutions) to Einstein's equations. Rather, relations that hold true for all geodesics, such as the Raychaudhuri equation, and additional non-specific assumptions about the nature of matter (usually in the form of energy conditions) are used to derive general results.^{[153]}
Using global geometry, some spacetimes can be shown to contain boundaries called horizons, which demarcate one region from the rest of spacetime. The best-known examples are black holes: if mass is compressed into a sufficiently compact region of space (as specified in the hoop conjecture, the relevant length scale is the Schwarzschild radius^{[154]}), no light from inside can escape to the outside. Since no object can overtake a light pulse, all interior matter is imprisoned as well. Passage from the exterior to the interior is still possible, showing that the boundary, the black hole's horizon, is not a physical barrier.^{[155]}
The ergosphere of a rotating black hole, which plays a key role when it comes to extracting energy from such a black hole
Early studies of black holes relied on explicit solutions of Einstein's equations, notably the spherically symmetric Schwarzschild solution (used to describe a static black hole) and the axisymmetric Kerr solution (used to describe a rotating, stationary black hole, and introducing interesting features such as the ergosphere). Using global geometry, later studies have revealed more general properties of black holes. With time they become rather simple objects characterized by eleven parameters specifying: electric charge, mass-energy, linear momentum, angular momentum, and location at a specified time. This is stated by the black hole uniqueness theorem: "black holes have no hair", that is, no distinguishing marks like the hairstyles of humans. Irrespective of the complexity of a gravitating object collapsing to form a black hole, the object that results (having emitted gravitational waves) is very simple.^{[156]}
Even more remarkably, there is a general set of laws known as black hole mechanics, which is analogous to the laws of thermodynamics. For instance, by the second law of black hole mechanics, the area of the event horizon of a general black hole will never decrease with time, analogous to the entropy of a thermodynamic system. This limits the energy that can be extracted by classical means from a rotating black hole (e.g. by the Penrose process).^{[157]} There is strong evidence that the laws of black hole mechanics are, in fact, a subset of the laws of thermodynamics, and that the black hole area is proportional to its entropy.^{[158]} This leads to a modification of the original laws of black hole mechanics: for instance, as the second law of black hole mechanics becomes part of the second law of thermodynamics, it is possible for black hole area to decrease—as long as other processes ensure that, overall, entropy increases. As thermodynamical objects with non-zero temperature, black holes should emit thermal radiation. Semi-classical calculations indicate that indeed they do, with the surface gravity playing the role of temperature in Planck's law. This radiation is known as Hawking radiation (cf. the quantum theory section, below).^{[159]}
There are other types of horizons. In an expanding universe, an observer may find that some regions of the past cannot be observed ("particle horizon"), and some regions of the future cannot be influenced (event horizon).^{[160]} Even in flat Minkowski space, when described by an accelerated observer (Rindler space), there will be horizons associated with a semi-classical radiation known as Unruh radiation.^{[161]}
Another general feature of general relativity is the appearance of spacetime boundaries known as singularities. Spacetime can be explored by following up on timelike and lightlike geodesics—all possible ways that light and particles in free fall can travel. But some solutions of Einstein's equations have "ragged edges"—regions known as spacetime singularities, where the paths of light and falling particles come to an abrupt end, and geometry becomes ill-defined. In the more interesting cases, these are "curvature singularities", where geometrical quantities characterizing spacetime curvature, such as the Ricci scalar, take on infinite values.^{[162]} Well-known examples of spacetimes with future singularities—where worldlines end—are the Schwarzschild solution, which describes a singularity inside an eternal static black hole,^{[163]} or the Kerr solution with its ring-shaped singularity inside an eternal rotating black hole.^{[164]} The Friedmann–Lemaître–Robertson–Walker solutions and other spacetimes describing universes have past singularities on which worldlines begin, namely Big Bang singularities, and some have future singularities (Big Crunch) as well.^{[165]}
Given that these examples are all highly symmetric—and thus simplified—it is tempting to conclude that the occurrence of singularities is an artifact of idealization.^{[166]} The famous singularity theorems, proved using the methods of global geometry, say otherwise: singularities are a generic feature of general relativity, and unavoidable once the collapse of an object with realistic matter properties has proceeded beyond a certain stage^{[167]} and also at the beginning of a wide class of expanding universes.^{[168]} However, the theorems say little about the properties of singularities, and much of current research is devoted to characterizing these entities' generic structure (hypothesized e.g. by the BKL conjecture).^{[169]} The cosmic censorship hypothesis states that all realistic future singularities (no perfect symmetries, matter with realistic properties) are safely hidden away behind a horizon, and thus invisible to all distant observers. While no formal proof yet exists, numerical simulations offer supporting evidence of its validity.^{[170]}
Each solution of Einstein's equation encompasses the whole history of a universe — it is not just some snapshot of how things are, but a whole, possibly matter-filled, spacetime. It describes the state of matter and geometry everywhere and at every moment in that particular universe. Due to its general covariance, Einstein's theory is not sufficient by itself to determine the time evolution of the metric tensor. It must be combined with a coordinate condition, which is analogous to gauge fixing in other field theories.^{[171]}
To understand Einstein's equations as partial differential equations, it is helpful to formulate them in a way that describes the evolution of the universe over time. This is done in "3+1" formulations, where spacetime is split into three space dimensions and one time dimension. The best-known example is the ADM formalism.^{[172]} These decompositions show that the spacetime evolution equations of general relativity are well-behaved: solutions always exist, and are uniquely defined, once suitable initial conditions have been specified.^{[173]} Such formulations of Einstein's field equations are the basis of numerical relativity.^{[174]}
The notion of evolution equations is intimately tied in with another aspect of general relativistic physics. In Einstein's theory, it turns out to be impossible to find a general definition for a seemingly simple property such as a system's total mass (or energy). The main reason is that the gravitational field—like any physical field—must be ascribed a certain energy, but that it proves to be fundamentally impossible to localize that energy.^{[175]}
Nevertheless, there are possibilities to define a system's total mass, either using a hypothetical "infinitely distant observer" (ADM mass)^{[176]} or suitable symmetries (Komar mass).^{[177]} If one excludes from the system's total mass the energy being carried away to infinity by gravitational waves, the result is the Bondi mass at null infinity.^{[178]} Just as in classical physics, it can be shown that these masses are positive.^{[179]} Corresponding global definitions exist for momentum and angular momentum.^{[180]} There have also been a number of attempts to define quasi-local quantities, such as the mass of an isolated system formulated using only quantities defined within a finite region of space containing that system. The hope is to obtain a quantity useful for general statements about isolated systems, such as a more precise formulation of the hoop conjecture.^{[181]}
Relationship with quantum theory
If general relativity were considered to be one of the two pillars of modern physics, then quantum theory, the basis of understanding matter from elementary particles to solid state physics, would be the other.^{[182]} However, how to reconcile quantum theory with general relativity is still an open question.
Ordinary quantum field theories, which form the basis of modern elementary particle physics, are defined in flat Minkowski space, which is an excellent approximation when it comes to describing the behavior of microscopic particles in weak gravitational fields like those found on Earth.^{[183]} In order to describe situations in which gravity is strong enough to influence (quantum) matter, yet not strong enough to require quantization itself, physicists have formulated quantum field theories in curved spacetime. These theories rely on general relativity to describe a curved background spacetime, and define a generalized quantum field theory to describe the behavior of quantum matter within that spacetime.^{[184]} Using this formalism, it can be shown that black holes emit a blackbody spectrum of particles known as Hawking radiation leading to the possibility that they evaporate over time.^{[185]} As briefly mentioned above, this radiation plays an important role for the thermodynamics of black holes.^{[186]}
The demand for consistency between a quantum description of matter and a geometric description of spacetime,^{[187]} as well as the appearance of singularities (where curvature length scales become microscopic), indicate the need for a full theory of quantum gravity: for an adequate description of the interior of black holes, and of the very early universe, a theory is required in which gravity and the associated geometry of spacetime are described in the language of quantum physics.^{[188]} Despite major efforts, no complete and consistent theory of quantum gravity is currently known, even though a number of promising candidates exist.^{[189]}^{[190]}
Attempts to generalize ordinary quantum field theories, used in elementary particle physics to describe fundamental interactions, so as to include gravity have led to serious problems.^{[191]} Some have argued that at low energies, this approach proves successful, in that it results in an acceptable effective (quantum) field theory of gravity.^{[192]} At very high energies, however, the perturbative results are badly divergent and lead to models devoid of predictive power ("perturbative non-renormalizability").^{[193]}
Simple spin network of the type used in loop quantum gravity
One attempt to overcome these limitations is string theory, a quantum theory not of point particles, but of minute one-dimensional extended objects.^{[194]} The theory promises to be a unified description of all particles and interactions, including gravity;^{[195]} the price to pay is unusual features such as six extra dimensions of space in addition to the usual three.^{[196]} In what is called the second superstring revolution, it was conjectured that both string theory and a unification of general relativity and supersymmetry known as supergravity^{[197]} form part of a hypothesized eleven-dimensional model known as M-theory, which would constitute a uniquely defined and consistent theory of quantum gravity.^{[198]}
Another approach starts with the canonical quantization procedures of quantum theory. Using the initial-value-formulation of general relativity (cf. evolution equations above), the result is the Wheeler–deWitt equation (an analogue of the Schrödinger equation) which, regrettably, turns out to be ill-defined without a proper ultraviolet (lattice) cutoff.^{[199]} However, with the introduction of what are now known as Ashtekar variables,^{[200]} this leads to a promising model known as loop quantum gravity. Space is represented by a web-like structure called a spin network, evolving over time in discrete steps.^{[201]}
Depending on which features of general relativity and quantum theory are accepted unchanged, and on what level changes are introduced,^{[202]} there are numerous other attempts to arrive at a viable theory of quantum gravity, some examples being the lattice theory of gravity based on the Feynman Path Integral approach and Regge Calculus,^{[189]}dynamical triangulations,^{[203]}causal sets,^{[204]} twistor models^{[205]} or the path integral based models of quantum cosmology.^{[206]}
All candidate theories still have major formal and conceptual problems to overcome. They also face the common problem that, as yet, there is no way to put quantum gravity predictions to experimental tests (and thus to decide between the candidates where their predictions vary), although there is hope for this to change as future data from cosmological observations and particle physics experiments becomes available.^{[207]}
Current status
Observation of gravitational waves from binary black hole merger GW150914
General relativity has emerged as a highly successful model of gravitation and cosmology, which has so far passed many unambiguous observational and experimental tests. However, there are strong indications the theory is incomplete.^{[208]} The problem of quantum gravity and the question of the reality of spacetime singularities remain open.^{[209]} Observational data that is taken as evidence for dark energy and dark matter could indicate the need for new physics.^{[210]} Even taken as is, general relativity is rich with possibilities for further exploration. Mathematical relativists seek to understand the nature of singularities and the fundamental properties of Einstein's equations,^{[211]} while numerical relativists run increasingly powerful computer simulations (such as those describing merging black holes).^{[212]} In February 2016, it was announced that the existence of gravitational waves was directly detected by the Advanced LIGO team on September 14, 2015.^{[81]}^{[213]}^{[214]} A century after its introduction, general relativity remains a highly active area of research.^{[215]}
^ ^{a}^{b}Landau & Lifshitz 1975, p. 228 "...the general theory of relativity...was established by Einstein, and represents probably the most beautiful of all existing physical theories."
^Pais 1982, ch. 9 to 15, Janssen 2005; an up-to-date collection of current research, including reprints of many of the original articles, is Renn 2007; an accessible overview can be found in Renn 2005, pp. 110ff. Einstein's original papers are found in Digital Einstein, volumes 4 and 6. An early key article is Einstein 1907, cf. Pais 1982, ch. 9. The publication featuring the field equations is Einstein 1915, cf. Pais 1982, ch. 11–15
^Moshe Carmeli (2008).Relativity: Modern Large-Scale Structures of the Cosmos. pp.92, 93.World Scientific Publishing
^Grossmann for the mathematical part and Einstein for the physical part (1913). Entwurf einer verallgemeinerten Relativitätstheorie und einer Theorie der Gravitation (Outline of a Generalized Theory of Relativity and of a Theory of Gravitation), Zeitschrift für Mathematik und Physik, 62, 225–261. English translate
^Rovelli 2015, pp. 1–6 "General relativity is not just an extraordinarily beautiful physical theory providing the best description of the gravitational interaction we have so far. It is more."
^Rindler 2001, sec. 1.13; for an elementary account, see Wheeler 1990, ch. 2; there are, however, some differences between the modern version and Einstein's original concept used in the historical derivation of general relativity, cf. Norton 1985
^Ehlers 1973, pp. 19–22; for similar derivations, see sections 1 and 2 of ch. 7 in Weinberg 1972. The Einstein tensor is the only divergence-free tensor that is a function of the metric coefficients, their first and second derivatives at most, and allows the spacetime of special relativity as a solution in the absence of sources of gravity, cf. Lovelock 1972. The tensors on both side are of second rank, that is, they can each be thought of as 4×4 matrices, each of which contains ten independent terms; hence, the above represents ten coupled equations. The fact that, as a consequence of geometric relations known as Bianchi identities, the Einstein tensor satisfies a further four identities reduces these to six independent equations, e.g. Schutz 1985, sec. 8.3
^Weinberg, Steven (1972). Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. John Wiley. ISBN 978-0-471-92567-5.
^Cheng, Ta-Pei (2005). Relativity, Gravitation and Cosmology: a Basic Introduction. Oxford and New York: Oxford University Press. ISBN 978-0-19-852957-6.
^For the (conceptual and historical) difficulties in defining a general principle of relativity and separating it from the notion of general covariance, see Giulini 2007
^GPS is continually tested by comparing atomic clocks on the ground and aboard orbiting satellites; for an account of relativistic effects, see Ashby 2002 and Ashby 2003
^Cf. Kennefick 2005 for the classic early measurements by Arthur Eddington's expeditions. For an overview of more recent measurements, see Ohanian & Ruffini 1994, ch. 4.3. For the most precise direct modern observations using quasars, cf. Shapiro et al. 2004
^This is not an independent axiom; it can be derived from Einstein's equations and the Maxwell Lagrangian using a WKB approximation, cf. Ehlers 1973, sec. 5
^From the standpoint of Einstein's theory, these derivations take into account the effect of gravity on time, but not its consequences for the warping of space, cf. Rindler 2001, sec. 11.11
^For the Sun's gravitational field using radar signals reflected from planets such as Venus and Mercury, cf. Shapiro 1964, Weinberg 1972, ch. 8, sec. 7; for signals actively sent back by space probes (transponder measurements), cf. Bertotti, Iess & Tortora 2003; for an overview, see Ohanian & Ruffini 1994, table 4.4 on p. 200; for more recent measurements using signals received from a pulsar that is part of a binary system, the gravitational field causing the time delay being that of the other pulsar, cf. Stairs 2003, sec. 4.4
^Einstein, A (31 January 1918). "Über Gravitationswellen". Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften Berlin (part 1): 154–167. Bibcode:1918SPAW.......154E. Archived from the original on 21 March 2019. Retrieved 12 February 2016.
^In consequence, in the parameterized post-Newtonian formalism (PPN), measurements of this effect determine a linear combination of the terms β and γ, cf. Will 2006, sec. 3.5 and Will 1993, sec. 7.3
^Hobbs, George; Archibald, A.; Arzoumanian, Z.; Backer, D.; Bailes, M.; Bhat, N. D. R.; Burgay, M.; Burke-Spolaor, S.; et al. (2010), "The international pulsar timing array project: using pulsars as a gravitational wave detector", Classical and Quantum Gravity, 27 (8): 084013, arXiv:0911.5206, Bibcode:2010CQGra..27h4013H, doi:10.1088/0264-9381/27/8/084013, S2CID56073764
^For the basic mechanism, see Carroll & Ostlie 1996, sec. 17.2; for more about the different types of astronomical objects associated with this, cf. Robson 1996
^For a review, see Begelman, Blandford & Rees 1984. To a distant observer, some of these jets even appear to move faster than light; this, however, can be explained as an optical illusion that does not violate the tenets of relativity, see Rees 1966
^For stellar end states, cf. Oppenheimer & Snyder 1939 or, for more recent numerical work, Font 2003, sec. 4.1; for supernovae, there are still major problems to be solved, cf. Buras et al. 2003; for simulating accretion and the formation of jets, cf. Font 2003, sec. 4.2. Also, relativistic lensing effects are thought to play a role for the signals received from X-ray pulsars, cf. Kraus 1998
^The evidence includes limits on compactness from the observation of accretion-driven phenomena ("Eddington luminosity"), see Celotti, Miller & Sciama 1999, observations of stellar dynamics in the center of our own Milky Way galaxy, cf. Schödel et al. 2003, and indications that at least some of the compact objects in question appear to have no solid surface, which can be deduced from the examination of X-ray bursts for which the central compact object is either a neutron star or a black hole; cf. Remillard et al. 2006 for an overview, Narayan 2006, sec. 5. Observations of the "shadow" of the Milky Way galaxy's central black hole horizon are eagerly sought for, cf. Falcke, Melia & Agol 2000
^Bergström & Goobar 2003, ch. 9–11; use of these models is justified by the fact that, at large scales of around hundred million light-years and more, our own universe indeed appears to be isotropic and homogeneous, cf. Peebles et al. 1991
^Evidence for this comes from the determination of cosmological parameters and additional observations involving the dynamics of galaxies and galaxy clusters cf. Peebles 1993, ch. 18, evidence from gravitational lensing, cf. Peacock 1999, sec. 4.6, and simulations of large-scale structure formation, see Springel et al. 2005
^Namely, some physicists have questioned whether or not the evidence for dark matter is, in fact, evidence for deviations from the Einsteinian (and the Newtonian) description of gravity cf. the overview in Mannheim 2006, sec. 9
^Carroll 2001; an accessible overview is given in Caldwell 2004. Here, too, scientists have argued that the evidence indicates not a new form of energy, but the need for modifications in our cosmological models, cf. Mannheim 2006, sec. 10; aforementioned modifications need not be modifications of general relativity, they could, for example, be modifications in the way we treat the inhomogeneities in the universe, cf. Buchert 2008
^More concretely, the potential function that is crucial to determining the dynamics of the inflaton is simply postulated, but not derived from an underlying physical theory
^Bondi, H.; Van der Burg, M.G.J.; Metzner, A. (1962). "Gravitational waves in general relativity: VII. Waves from axisymmetric isolated systems". Proceedings of the Royal Society of London A. A269 (1336): 21–52. Bibcode:1962RSPSA.269...21B. doi:10.1098/rspa.1962.0161. S2CID120125096.
^Strominger, Andrew (2017). "Lectures on the Infrared Structure of Gravity and Gauge Theory". arXiv:1703.05448 [hep-th]. ...redacted transcript of a course given by the author at Harvard in spring semester 2016. It contains a pedagogical overview of recent developments connecting the subjects of soft theorems, the memory effect and asymptotic symmetries in four-dimensional QED, nonabelian gauge theory and gravity with applications to black holes. To be published Princeton University Press, 158 pages.
^Israel 1987. A more exact mathematical description distinguishes several kinds of horizon, notably event horizons and apparent horizons cf. Hawking & Ellis 1973, pp. 312–320 or Wald 1984, sec. 12.2; there are also more intuitive definitions for isolated systems that do not require knowledge of spacetime properties at infinity, cf. Ashtekar & Krishnan 2004
^The laws of black hole mechanics were first described in Bardeen, Carter & Hawking 1973; a more pedagogical presentation can be found in Carter 1979; for a more recent review, see Wald 2001, ch. 2. A thorough, book-length introduction including an introduction to the necessary mathematics Poisson 2004. For the Penrose process, see Penrose 1969
^The fact that black holes radiate, quantum mechanically, was first derived in Hawking 1975; a more thorough derivation can be found in Wald 1975. A review is given in Wald 2001, ch. 3
^Here one should remind to the well-known fact that the important "quasi-optical" singularities of the so-called eikonal approximations of many wave-equations, namely the "caustics", are resolved into finite peaks beyond that approximation.
^The restriction to future singularities naturally excludes initial singularities such as the big bang singularity, which in principle be visible to observers at later cosmic time. The cosmic censorship conjecture was first presented in Penrose 1969; a textbook-level account is given in Wald 1984, pp. 302–305. For numerical results, see the review Berger 2002, sec. 2.1
^Gourgoulhon 2007; for a review of the basics of numerical relativity, including the problems arising from the peculiarities of Einstein's equations, see Lehner 2001
^Komar 1959; for a pedagogical introduction, see Wald 1984, sec. 11.2; although defined in a totally different way, it can be shown to be equivalent to the ADM mass for stationary spacetimes, cf. Ashtekar & Magnon-Ashtekar 1979
^For a pedagogical introduction, see Wald 1984, sec. 11.2
^Wald 1984, p. 295 and refs therein; this is important for questions of stability—if there were negative mass states, then flat, empty Minkowski space, which has mass zero, could evolve into these states
^Put simply, matter is the source of spacetime curvature, and once matter has quantum properties, we can expect spacetime to have them as well. Cf. Carlip 2001, sec. 2
^In particular, a perturbative technique known as renormalization, an integral part of deriving predictions which take into account higher-energy contributions, cf. Weinberg 1996, ch. 17, 18, fails in this case; cf. Veltman 1975, Goroff & Sagnotti 1985; for a recent comprehensive review of the failure of perturbative renormalizability for quantum gravity see Hamber 2009
^At the energies reached in current experiments, these strings are indistinguishable from point-like particles, but, crucially, different modes of oscillation of one and the same type of fundamental string appear as particles with different (electric and other) charges, e.g. Ibanez 2000. The theory is successful in that one mode will always correspond to a graviton, the messenger particle of gravity, e.g. Green, Schwarz & Witten 1987, sec. 2.3, 5.3
^A review of the various problems and the techniques being developed to overcome them, see Lehner 2002
^See Bartusiak 2000 for an account up to that year; up-to-date news can be found on the websites of major detector collaborations such as GEO600 and LIGO
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Will, Clifford; Poisson, Eric (2014). Gravity: Newtonian, Post-Newtonian, Relativistic. Cambridge University Press. ISBN 978-1107032866.
1915 international socialist conference in Switzerland
The Hotel Beau Séjour, site of the Zimmerwald conference, in 1864
The Zimmerwald Conference was held in Zimmerwald, Switzerland, from September 5 to 8, 1915. It was the first of three international socialist conferences convened by anti-militarist socialist parties from countries that were originally neutral during World War I. The individuals and organizations participating in this and subsequent conferences held at Kienthal and Stockholm are known jointly as the Zimmerwald movement.
When the Second International, the primary international socialist organization before World War I, was founded in 1889, internationalism was one of its central tenets. "The workers have no Fatherland", Karl Marx and Friedrich Engels had declared in The Communist Manifesto. Paul Lafargue, Marx's son-in-law, in his keynote address at the International's founding congress called upon socialists to be "brothers with a single common enemy [...] private capital, whether it be Prussian, French, or Chinese".^{[1]} Despite this commitment to internationalism and the establishment in 1900 of the International Socialist Bureau (ISB) based in Brussels to manage the movement's affairs, the International remained but a loose confederation of national organizations, which considered political issues in national terms.^{[2]}
The French delegate Edouard Vaillant told the Second International's founding congress that "war, the most tragic product of present economic relations, can only disappear when capitalist production has made way for the emancipation of labor and the international triumph of socialism." Opposition to war became a pillar of its program,^{[3]} but the question of what to do if war broke out would preoccupy socialists throughout the International's history and was the most controversial question discussed among the International's leading figures.^{[4]}Domela Nieuwenhuis from the Netherlands repeatedly suggested calling a general strike and launching an armed uprising if war should break out, but his proposals failed.^{[5]} The Second International did not seriously address the question of how it intended to oppose war until its 1907 congress in Stuttgart, after the 1905–1906 Moroccan Crisis brought the issue to the fore. In Stuttgart, the French Section of the Workers' International (SFIO) suggested employing all possible means to prevent war, including demonstrations, general strikes, and insurrections. The Social Democratic Party of Germany (SPD) was strongly opposed to any mention of general strikes. As a result, the resolution the congress promulgated was contradictory. It called on workers to "exert every effort to prevent the outbreak of war by means they consider most effective," but eschewed resistance to war as impractical, in favor of organizing opposition.^{[6]} When the 1912 Balkan War threatened to escalate into a wider conflict, the socialists organized a special congress in Basel, not in order to debate, but to protest military escalation. Like the 1907 meeting, it failed to yield any agreement on what tactics to employ in order to prevent war.^{[7]}
Vladimir Lenin
The socialist movement was beset by fundamental political disagreements, which led to organizational splits in several countries. The International's wavering on anti-war tactics reflected these political differences. The revisionist right advocated a gradual evolution towards socialism within the framework of the nation-state, defended European colonialism, and supported patriotism.^{[8]} Centrists at times pushed back against these positions, but also supported certain forms of patriotism. The German social democrat August Bebel, for example, was determined "never to abandon a single piece of German soil to the foreigner." The French leader Jean Jaurès criticized Marx and Engels' maxim that the "workers have no Fatherland" as "vain and obscure subtleties" and a "sarcastic negation of history itself." In 1912, Karl Kautsky, one of the chief Marxist theorists, began to push back against the notion that capitalist imperialism necessarily led to militarism and predicted an era of ultra-imperialism in which capitalist cooperation could maintain international peace.^{[9]} The radical left was most decidedly anti-war. It considered war a consequence of imperialism, which became a central concept in the left's analyses. "Imperialism grows in lawlessness and violence, both in aggression against the non-capitalist world and in ever more serious conflicts among the competing capitalist countries. The mere tendency toward imperialism by itself takes forms that make the final phase of capitalism a period of catastrophe", according to Rosa Luxemburg. Vladimir Lenin similarly argued against defending one's nation.^{[10]}
Outbreak of World War I
On June 28, 1914, the Austrian Archduke Francis Ferdinand was assassinated in Sarajevo, leading to the outbreak of war on July 28. Socialists were surprised by how quickly the issue escalated to war and their reactions were improvised. Most believed that the war would be short and that their respective nations were engaged in self-defense.^{[11]} On August 4, the Reichstag, Germany's parliament, voted for war credits. The socialist delegates unanimously voted for the measures. The socialist policy of supporting the government's war efforts became known as the Burgfrieden or civil truce. On the same day, socialists also rallied behind the war in France, where socialist acquiescence became known as the union sacrée. The following day, the Parliamentary Labour Party in the United Kingdom voted to support the government in the war. The socialist parties in most belligerent countries eventually supported their country's war effort. Even some on the left of the international socialist movement such as the German Konrad Haenisch, the French Gustave Hervé and Jules Guesde (the latter becoming a government minister), and the Russian Georgi Plekhanov supported this policy. Socialists in the initially non-belligerent nations generally denounced the war and insisted their governments remain out of it, but several parties collaborated with their governments to give them war-time powers.^{[12]}
Socialists' support for the war partly reflected workers' patriotic sentiments. Before hostilities commenced, there were anti-war demonstrations in all major European cities, including a march of 20,000 in Hamburg on July 28. However, when the war began many welcomed it. According to the French labor leader Alphonse Merrheim, anyone resisting the war might have been shot by French workers, rather than the police.^{[13]} By 1914, the European labor movement was in many ways firmly integrated into the capitalist system it opposed. While advocating revolution, in effect socialism mostly carved out a position for workers within capitalist society. Socialist support for governments at war was the result of this evolution. With this support, socialists hoped to solidify their place within the national community.^{[14]} Even if socialists had tried, they may not have been able to stop the war. Large demonstrations alone likely would not have been enough to force governments to stop the war. They did not have majorities in parliaments, had not prepared for mass strikes, and the way the International was organized did not lend itself to quick coordinated action.^{[15]} Rather than oppose the war and risk being suppressed by their governments, most socialists decided to support their governments in the war.^{[16]}
Socialist support for the war was not universal. Many socialists were shocked by their parties' acquiescence to the war. Luxemburg and Clara Zetkin reportedly considered suicide upon hearing the news. Until August 20, the Romanian socialist press chose to disbelieve reports that the SPD intended to support the German war effort.^{[17]} While most of the right and the center of the socialist movement supported their governments in the war and most of the left was opposed, socialists' responses to the new situation did not neatly follow a left–right split.^{[18]} In Germany, fourteen of the ninety-two socialist Reichstag members were opposed to voting in favor of war credits in the parliamentary fraction's internal caucus, but they bowed to party discipline to make the vote unanimous. Among the fourteen was Hugo Haase, the party co-chairman who announced the socialists' support to the Reichstag.^{[19]} In December 1914, the left-winger Karl Liebknecht flouted party discipline by casting a lone vote against war credits. He became the most prominent socialist opponent of the war in Europe. The left including Liebknecht and Luxemburg formed the International Group which criticized the war and the socialist leadership's support. Fearing that the left would gain support, anti-war centrists including Kautsky and Haase also began to promote peace.^{[20]} In France, the opposition to the war and the union sacrée began to rally in the fall of 1914. The Federation of Metal Workers and its leader Merrheim were at the forefront of the opposition to the war. At the August 1915 national conference of the General Confederation of Labor (CGT) an anti-war resolution introduced by Merrheim and Albert Bourderon was voted down seventy-nine to twenty-six. There was also an opposition in the SFIO. Overall, the French opposition remained cautious.^{[21]} The Italian Socialist Party (PSI) was an exception in Europe in that it was as a whole opposed to the war, although a minoritarian pro-war faction led by Benito Mussolini advocated intervention on behalf of the Allies, but he was expelled from the party.^{[22]} Throughout Europe, the socialist opposition to the war was initially weak and fragmented into moderates and revolutionaries. It was hindered by censorship and restrictions on movement and communication that resulted from the war. The progression of the war, popular war fatigue, and the material hardships caused by the war all contributed to the growth of this opposition.^{[23]}
The split in the socialist movement was not just a result of the war, but of the incompatibility between different versions of Marxism that co-existed within the Second International. As the German socialist Philipp Scheidemann later stated: "The war gave rise to a schism within the party, but I believe it would eventually have come to pass even without the war."^{[24]} The war made continuing the Second International's activities impossible. The SFIO and the Belgian Labor Party (POB) refused to engage with socialists from the Central Powers and the ISB was paralyzed.^{[25]} Socialists who opposed the war drew a variety of conclusions from what they considered the International's failure. Most felt that pre-war socialism could be revived. P.J. Troelstra from the Netherlands held that the Second International had only been too weak to stop the war and was still alive. Others held that the failure was complete. Luxemburg stated that "everything is lost, all that remains is our honour". Leon Trotsky called the Second International a "rigid shell" from which socialism must be liberated. Lenin denounced it as a "stinking corpse" and, at a Bolshevik conference in Berne in early 1915, called for the formation of a Third International.^{[26]}
Preparations
Oddino Morgari
With the Second International inactive, the maintenance of relations between socialists fell to independent initiatives. Representatives of socialist parties from neutral countries met in Lugano, Switzerland in September 1914, in Stockholm in October 1914, and in Copenhagen in January 1915. The conference in Lugano, which involved members of the Swiss SPS and the Italian PSI, denounced the war as "the result of the imperialist policy of the great powers", and called on the ISB to resume its activities. This meeting would become known as the cradle of the Zimmerwald movement.^{[27]} Pro-war socialists also held conferences. Those from Allied countries met in London in February 1915 and those from the Central powers followed suit in Vienna in April 1915.^{[28]} Socialists from opposing sides of the war first came together at socialist women's and youth conferences in Berne in March and April 1915, respectively. Both conferences resolutely denounced the war and socialists' support for it.^{[29]}
In late 1914 and early 1915, the Swiss and Italian parties, hoping to revive the International, looked to continue the dialogue started in Lugano. They intended to convoke a conference for socialists from all neutral countries with the ISB's blessing.^{[30]} In April 1915, the Italian parliamentary deputy Oddino Morgari, after consulting with the Swiss, traveled to France on behalf of the Italian party. Morgari, though part of the PSI's right wing, was a pacifist and in favor of the socialist movement actively working for peace. He met with the Belgian socialist leader Emile Vandervelde, chairman of the Executive Committee of the Bureau, seeking the ISB's support. His proposals were flatly rejected by Vandervelde, whom Morgari accused of holding the ISB hostage, to which Vandervelde replied: "Yes, but a hostage for freedom and justice." In Paris, Morgari also held discussions with the MenshevikJulius Martov who convinced him of the necessity of a conference of anti-war socialists independent of the ISB. This idea was boosted by the fact that at the same time as discussions with Morgari were taking place, a manifesto written by the anti-war opposition in the SPD had made its way to France and inspired the French opposition. He also met with Trotsky, Victor Chernov, and French anti-war socialists grouped around Merrheim and Pierre Monatte. From Paris, Morgari traveled to London where the Independent Labour Party (ILP) and the British Socialist Party (BSP) expressed interest in a general conference of anti-war socialists.^{[31]} At a party meeting on May 15–16, the PSI endorsed a meeting of all socialist parties and groups opposed to the war. Morgari discussed the proposal with Robert Grimm of the SPS. Grimm, a young, eloquent, and ambitious leader on the Swiss party's left wing, was unable to obtain his party's support for the proposal, but it did approve "individual" action for peace. Grimm, with the PSI's blessing, became the project's prime mover and announced a preparatory meeting to take place in Berne in July.^{[32]}
Robert Grimm
The July 11 organizing conference was attended by seven delegates: the Bolshevik Grigory Zinoviev, the Menshevik Pavel Axelrod, Angelica Balabanoff and Oddino Morgari of the Italian Socialist Party, Adolf Warski of the Social Democracy of the Kingdom of Poland and Lithuania, Maksymilian Horwitz of the Polish Socialist Party – Left, and Robert Grimm of the Social Democratic Party of Switzerland.^{[33]} Only the Italians arrived from abroad, as the others, besides Grimm, were exiles residing in Switzerland.^{[34]} The meeting began with discussions of whom to invite to the conference. Grimm proposed that all socialists opposed to the war and in favor of a renewal of class struggle be welcomed. Zinoviev countered that participation be limited to the revolutionary left. In the end, the meeting decided to invite all socialists explicitly opposed to the war, including French and German anti-war centrists such as Haase and Kautsky. Zinoviev also called for the participation of various left groups, but was again voted down as none of the delegates supported his proposal. The meeting decided to limit participation to members of the Second International, but this restriction was ultimately not enforced.^{[35]} The Bolshevik representative advocated discussing the formation of a Third International, but this controversy was tabled. The meeting unanimously endorsed the PSI's moderate May 17 and June 18 declarations which emphasized the struggle for peace.^{[36]} A second preparatory conference was planned for August, but ultimately canceled.^{[37]}
On August 19, Grimm announced that the conference was scheduled for September 5.^{[38]} In the period leading up to that date, Grimm worked hard to secure participation in the conference, particularly from moderates. He invited "all parties, labor organizations, or groups within them" opposed to the war and loyal to the Second International's anti-war resolutions. He also made the final preparations for the conference. He put significant effort into keeping it secret, reserving the rundown Hotel Beau Séjour in Zimmerwald, a village near Berne, for an "ornithological society". Morgari visited London to invite internationalists from the ILP and BSP.^{[39]} Lenin, staying at a mountain resort in Sörenberg, expressed both excitement and skepticism upon hearing of the conference. He thought most participants would criticize militarism without drawing the proper revolutionary conclusions from this critique and thereby "help the bourgeoisie nip the revolutionary movement in the bud." His plan was to attend the conference in order to bring together the left and criticize the moderates. He wrote to his contacts to ensure that the left was well-represented.^{[40]} His efforts were not entirely successful. He was most disappointed that the Dutch left refused to participate in a conference also attended by moderates, even offering to pay for their trip to Switzerland.^{[41]}
In the days leading up to the conference, several private preparatory meetings took place as the delegates arrived in Berne.^{[42]} On September 4, a day before the start of the conference, Lenin invited the left to a meeting at Zinoviev's residence in Berne to prepare its strategy. It became clear that the left would be a minority. The leftists decided on a draft manifesto written by Radek, but with several amendments proposed by Lenin.^{[43]} French and German delegates came together at another pre-conference meeting to prepare efforts for reconciliation between the two countries, but this meeting yielded few results.^{[44]}
The British delegation consisting of Frederick Jowett and Bruce Glasier of the ILP and Edwin C. Fairchild of the BSP did not make it to Switzerland, because the British authorities refused to issue them passports.^{[54]}Willi Münzenberg, the organizer of the April youth conference, was not admitted as a delegate of the newly founded Youth International.^{[55]} Karl Liebknecht could not attend because he had been conscripted. Austrian anti-war socialists decided not to attend because they did not want to exacerbate divisions within their party.^{[56]} Some sources erroneously list , Nadezhda Krupskaya, Inessa Armand, or Kautsky among the conference's participants.^{[57]}
The Zimmerwald Conference brought together delegates from both sides of the war, but disagreements did not follow national lines.^{[58]} The participants split into three factions, although the divisions were at times blurred and there were disagreements within the factions. Eight delegates, Lenin, Zinoviev, Radek, Borchardt, Berzin, Platten, Höglund, and Nerman, formed the left. They favored openly revolutionary struggle and breaking with the Second International. They were opposed by the right who viewed the conference only as a demonstration against the war. The right made up a majority of the delegates consisting of nineteen or twenty delegates: most of the Germans, the French, the Mensheviks, and some of the Italians and Poles. In between was the center, which included among others Grimm, Trotsky, Balabanoff, and Roland-Holst.^{[59]} Compared to the International's pre-war congresses, the conference's number of participants and the range of countries represented was almost negligible. According to the political scientist Yves Collart, its composition was not necessarily representative of the socialist movement as a whole, or even of its left wing. The selection of delegates was haphazard and a result of personal contacts and practical circumstances.^{[60]}
Sessions
Hotel Beau Séjour in 1904
Grimm greeted the delegates at the Volkshaus in Berne on the morning of September 5, before they moved on to Eiglerplatz. From there they left in four coaches for a two-hour ride to Zimmerwald, a small Prealpine village consisting of twenty-one houses some ten kilometers (six miles) to the south.^{[61]} According to Trotsky, on their way to Zimmerwald the delegates joked that "half a century after the formation of the First International it was still possible to fit all the internationalists in Europe into four coaches", but they were in an optimistic mood.^{[62]} In order to keep the meeting secret, the delegates were prohibited from sending letters while in Zimmerwald and they received no news from the outside world. In their spare time, they hiked the surrounding mountains and were entertained by Grimm's yodeling and Chernov's renditions of Russian folk tunes.^{[63]}
September 5 and 6
Grimm opened the conference at 4 p.m. on the afternoon of September 5. He recounted how the meeting came to be and attacked the ISB for its inactivity. Nevertheless, he emphasized that the conference's goal was to rebuild the Second International, not to form a Third International. He called on the conference to "raise up the flag of socialism, which had slipped from the hands of the appointed representatives of socialism, and to erect over the gory battlefields the true symbol of humanity".^{[64]} Karl Liebknecht, the most prominent figure in the socialist resistance against the war, addressed the conference in a letter, which was delivered to Grimm by Liebnecht's wife Sophie, as he was unable to attend himself. It called for "civil war, not civil peace", referring to the Burgfrieden, and for a new International "to rise from the ruins of the old". The letter was read aloud and received considerable applause.^{[65]}
The first two days were spent on disputes over procedural matters and on delegates' opening statements on the situation in their respective countries.^{[66]} The highlights among the opening statements, according to the historian Agnes Blänsdorf, were the reports by the German and French delegations. In Merrheim's view, the conference's main task was Franco-German reconciliation. Both French delegates pointed out that the anti-war minorities in both countries had to work together: "If we supported each other, the movement against the war would grow and it could become possible to put an end to the butchery", according to Bourderon. The Germans Ledebour and Hoffmann agreed with the French.^{[67]} Ledebour's speech emphasized the importance of pragmatic tactics. Disagreements within the German delegation erupted on who had a right to speak for the German opposition, with the Reichstag members on the one side and the International Group on the other.^{[68]} According to the historian R. Craig Nation, the Scandinavian youth leagues gave the strongest opening statement. It called for support for anti-war actions by the masses and deemed revolution a prerequisite for peace.^{[69]} Of the Russian delegates, Axelrod was the main speaker. He pointed out that of the European socialist movements, Russian social democracy was the only movement that was united in its opposition to the war. He explained that this was due to the fact that Russian Czarism was so unambiguously counter-revolutionary.^{[70]} Axelrod and Zinoviev both sought to dispel the notion that exiled Russian socialists were mere doctrinaires with no connection to the workers' movement and stated that both wings of Russian social democracy wished to overcome the schism and re-establish socialist unity.^{[71]} Lapinski gave the opening statement for the three Polish groups, describing the war-time situation in Poland as "thousand times worse than in Belgium". Berzin in his statement on Latvia was optimistic that the movement in the Baltics was growing.^{[72]}
The conference decided to establish an Executive Bureau consisting of Grimm, Lazzari, and Rakovski to handle procedural matters. Squabbling within the German delegation erupted over Borchardt's status. The other Germans objected to his participation as a delegate with a mandate and threatened to leave. Lenin, outraged at the prospect of the only German on the left being excluded, defended Borchardt. During this dispute Ledebour, or possibly one of the other Germans, and Lenin passed notes to one another continuing the argument in private. The Executive Bureau agreed to demote his status to that of an observer without voting rights.^{[73]} The Bolsheviks suggested that each Polish and Russian organization be allocated an independent mandate. The Bureau decided that each national delegation should be granted five votes, to be distributed as each delegation sees fit. This had the effect of diminishing the influence of the left.^{[74]}
September 7
Discussions on the central issue, the agenda item "Peace Action by the Proletariat", did not begin until the third day.^{[75]} The delegates hoped to achieve unanimous decisions, as this would send a signal of strength. This unanimity turned out to be difficult to achieve.^{[76]} Most of the discussion on this agenda item turned on the question of what was to be the goal of the movement. Lenin and the left pushed the debate in this direction. Radek was the first speaker and presented the resolution the left had agreed upon. Peace, he proclaimed, could only be achieved through revolution, but revolution could not stop at putting an end to war, but must lead to a struggle for socialism. Therefore, socialists already had to start preparing for revolution. Lenin added that this preparation entailed abandoning the existing organizations and forming a Third International. Socialists faced a choice between "true revolutionary struggle" and "empty phrases" about peace. Lenin's and Radek's positions were supported by the other left delegates.^{[77]}
Grimm was the first to challenge the left's presentation. He considered Radek's reasoning "unsuitable", asking him: "Do we want a manifesto for party comrades or for the broad masses of the workers?"^{[78]} Except for Serrati, the Italian delegation's position was diametrically opposed to that of the left. The Italians insisted that the conference's purpose was only to resist the war and promote peace. Lazzari dismissed Radek's tone as "pretentious", expressed doubt that insurrections could be successful at this time, and was concerned that radicalism could exacerbate the splits within the International.^{[79]} The French expressed similar views. Merrheim called Lenin's suggestions the fantasies of a sectarian. According to him, the French working class had lost confidence in socialism and this confidence could only be regained by speaking of peace. The Germans Ledebour and Hoffmann agreed. They accused the left of not following their own calls for demonstrations and revolution as they were comfortable in exile. Hoffmann added that the only thing to be done at that moment was to return to the old forms of class struggle and to call for peace. Ledebour held that "to restore the International and to work for peace" were the only purposes of the conference. He introduced a draft resolution of his own, in opposition to the left's.^{[80]}
Leon Trotsky
The positions of Trotsky, Chernov, Thalheimer, and Meyer were similar to the left's, but they disagreed on some tactical issues. Thalheimer and Meyer objected to the left wanting to dictate party tactics to national sections and Thalheimer deemed the left's manifesto "tactically unwise". Serrati proclaimed that "if the war were not a fact, I would vote for Lenin's resolution. Today it comes either too early or too late."^{[81]} The debate continued well into the night of September 7. The left, though in the minority, succeeded in determining the structure of the debate and preventing a consensus among the moderates. Merrheim eventually succeeded in uniting the moderate majority, arguing that the proletariat was disillusioned and not yet ready for revolution. He attacked Lenin: "A revolutionary movement can only grow from a striving for peace. You, comrade Lenin, are not motivated by this striving for peace, but by the desire to set up a new International. This is what divides us." It was decided to create a commission to write the conference resolution. It consisted of Ledebour, Lenin, Trotsky, Grimm, Merrheim, Modigliani, and Rakovski.^{[82]} The same disagreements continued in the commission. Another confrontation arose when Lenin suggested including a call for parties to vote against war credits. Ledebour managed to deflect this initiative by threatening that the Germans would leave Zimmerwald if such a call were to be included. In the end, Trotsky was tasked with writing a draft resolution.^{[83]}
September 8
Trotsky's draft was put before the full conference for discussion the next morning. Grimm directly asked Lenin not to endanger the movement's unity by overemphasizing strategic disagreements. The controversy over support for war credits arose again. Roland-Holst and Trotsky joined the left in demanding that a call for socialists to vote against war credits under any circumstances be included in the manifesto. Ledebour again shut the discussion down by issuing another ultimatum. Grimm successfully deflected further suggested amendments.^{[84]} Chernov objected that the draft did not specifically mention the Russian Czar, the Russian monarchy's culpability for the war, the peasantry's suffering during the war, or the prospect of agrarian socialism. Ledebour threatened to withhold his support if Radek, who had been excluded from the SPD before the war, signed it. Finally, Morgari to the other delegates' surprise threatened to veto the manifesto. He insisted that it state that Germany was more to blame for the war than other countries. Morgari was talked into withdrawing his objection. Eventually, Grimm put an end to the debate. Everyone agreed to support the draft manifesto, although the two Socialist Revolutionaries Chernov and Natanson had to be pressured into this.^{[85]} The delegates cheered and sang "The Internationale".^{[86]}
After passing the manifesto, the conference, at Ledebour's suggestion, decided to create the International Socialist Commission (ISC) to coordinate socialist anti-war activities. The left considered this a first step towards the creation of a new International, while the others insisted that its role was merely to facilitate the "exchange of correspondence", as Ledebour stated. The latter view prevailed. Grimm, Naine, Morgari, and Balabanoff, who was to act as interpreter, were chosen as the ISC's permanent members. No representative of the left was included. The secretariat of the ISC was to be located in Be