general theory of relativity

general theory of relativity. The general theory of relativity is a geometric theory of gravitation published by Albert Einstein in 1915. It revolutionized the understanding of gravity by describing it not as a force, but as a curvature of spacetime caused by the presence of mass and energy. The theory has profound implications for cosmology and our understanding of the universe, from the orbit of Mercury to the evolution of the cosmos itself.

Overview and historical context

The development of the theory was primarily the work of Albert Einstein between 1907 and 1915, building upon his earlier special relativity. Key influences included the equivalence principle and the mathematics of non-Euclidean geometry, notably the work of Bernhard Riemann and Gregorio Ricci-Curbastro. The famous field equations were presented to the Prussian Academy of Sciences in November 1915. Early confirmation came from Arthur Eddington's 1919 expedition, which observed the bending of starlight by the Sun during a solar eclipse, catapulting Einstein to global fame. The theory's framework challenged the Newtonian conception of gravity that had dominated since the Philosophiæ Naturalis Principia Mathematica.

Fundamental principles

The theory rests on two core postulates. The first is the equivalence principle, which states that the effects of gravity are locally indistinguishable from acceleration, a concept Einstein called his "happiest thought." The second is the principle of general covariance, meaning the laws of physics must be expressed in a form that is valid in all coordinate systems. This leads to the central idea that matter and energy, described by the stress–energy tensor, tell spacetime how to curve, and that curved spacetime, in turn, tells matter how to move. This geometrization of gravity departs fundamentally from the action-at-a-distance described by Isaac Newton.

Mathematical formulation

The theory is encapsulated in the Einstein field equations, a set of ten interrelated, non-linear differential equations. These equations equate the geometry of spacetime, represented by the Einstein tensor (derived from the Ricci curvature and metric tensor), to the distribution of matter and energy, represented by the stress–energy tensor. The solutions to these equations are Lorentzian metrics that define the spacetime geometry. The mathematics relies heavily on the tensor calculus developed by Gregorio Ricci-Curbastro and Tullio Levi-Civita, and the differential geometry of Bernhard Riemann and Carl Friedrich Gauss.

Solutions and predictions

Exact solutions to the field equations describe specific physical scenarios. The Schwarzschild metric, found by Karl Schwarzschild, predicts black holes and the gravitational redshift. The Kerr metric, by Roy Kerr, describes rotating black holes. The Friedmann–Lemaître–Robertson–Walker metric forms the basis of the Big Bang model in modern cosmology. Key predictions include the bending of light by massive objects (gravitational lensing), the slow rotation of orbits (perihelion precession of Mercury), and the existence of gravitational waves, ripples in spacetime propagating at the speed of light.

Experimental tests and evidence

The theory has passed every stringent experimental test. The perihelion precession of Mercury provided an early anomaly that Newtonian gravity could not explain. The 1919 Eddington expedition confirmed the predicted deflection of starlight. The Shapiro time delay effect was confirmed by radar echoes from Venus and Mars. The Hafele–Keating experiment demonstrated gravitational time dilation using atomic clocks on airplanes. The direct detection of gravitational waves by the LIGO and Virgo collaborations from merging black holes and neutron stars provided spectacular confirmation. Observations of the binary pulsar PSR B1913+16 by Russell Alan Hulse and Joseph Hooton Taylor Jr. provided indirect evidence for gravitational waves, earning them the Nobel Prize in Physics.

Relationship to quantum mechanics

A major unsolved problem in modern physics is the reconciliation of this theory with quantum mechanics. The theory is a classical field theory, while quantum mechanics governs the microscopic world. Attempts to quantize gravity, such as string theory and loop quantum gravity, have yet to produce a complete, experimentally verified theory of quantum gravity. Phenomena like the physics of the Big Bang singularity or the interior of a black hole require such a union. Research at institutions like the Perimeter Institute for Theoretical Physics and CERN continues to probe this fundamental frontier. Category:Theories of gravitation Category:Albert Einstein Category:1915 in science