Topic: light
Topic: Newtonian physics
Group: philosophy of science
Topic: physics
Topic: science as measurement
Topic: special relativity
Topic: the effect of scale
Topic: time
 
Summary
General relativity is Einstein's explanation of gravity as curved spacetime; i.e., the geometrical properties of space are determined by the objects in that space. Gravity is exactly the same as an accelerating frame of reference. Einstein gained worldwide fame when an eclipse confirmed that light bends around the sun. (cbb 4/06)
Subtopic: general relativity
Quote: relativity is a general principle that applies with great accuracy to mechanics; it should apply to all physical domains [»einsA_1916b]
 Quote: general relativity  equations of the laws of nature must be covariant w.r.t. continuous coordinate transformations
 Quote: laws of nature should be valid in any 4d system of coordinates that preserves neighboring events; like Gauss's theory of surfaces [»einsA_1956, OK]
 Quote: the general principle of relativity states that all Gaussian coordinate systems are equivalent relative to the general laws of nature; this restricts these laws [»einsA_1916b]
 Quote: continuous transformations of 4d coordinates express the topological order of points; i.e., neighboring points have nearly the same coordinates
 Quote: the mathematical abstractions of general relativity enlarge the scope of objective description and eliminate subjective elements [»bohrN_1958]
 Quote: if two tracts are measured as equal once and anywhere, they are equal always and everywhere; a foundation for the general theory of relativity
 Subtopic: relativity as curved spacetime
Quote: by the general theory of relativity, the geometrical properties of space are determined by matter [»einsA_1916b]
 Quote: in the general theory of relativity the spacetime metric only applies to small regions of a gravitational field
 Quote: geometry and dynamics are linked together; motion is not curves (worldlines) in spacetime
 Quote: consider a bug that lives on a hot plate and uses rulers effected by temperature; if the length of a ruler varies by the square of the distance from the origin, the geometry is that of a sphere [»feynRP_1964]
 Quote: construct a consistent, nonEuclidean world as a sphere whose temperature decreases to zero at its surface, and whose lengths are proportional to temperature [»poinH_1902, OK]
 Quote: by Einstein's general relativity, the earth has 1.5 millimeters more radius than it should have for its surface area [»feynRP_1964]
 Quote: from Einstein, spacetime is curved near heavy masses; gravitation is the result of going along straight lines in a curved spacetime [»feynRP_1964]
 Quote: space is curved, matter is the source of the curvature, and it is that curvature that we see as gravitational force
 Quote: in a gravitational field with given starting and finishing conditions, an object moves so as to maximize the time of a clock traveling with the object [»feynRP_1964]
 Quote: straightline motion in a curved spacetime is that motion which maximizes the elapsed time of an object over some fixed local time [»feynRP_1964]
 Quote: a distance must be measured so there is no abstract distance; a property of straight lines includes the measurement [»poinH_1902, OK]
 Quote: no experiment can contradict Euclid's postulate, nor can experiment contradict Lobatschewsky's postulate
 Subtopic: gravity
Quote: a body's force is proportional to the product of its size and the square of its speed; the law of gravity [»leibGW4_1695]
 Quote: equivalence of inert and gravitational mass by nonlinear transformation of 4d space [»einsA4_1950]
 Quote: gravity does not use lines of force; it acts in straight lines independent of third bodies and time; can't be isolated [»faraM_1855, OK]
 Quote: does gravity require time and hence a physical agency?; can't prove since gravity and matter are unchangeable [»faraM_1855, OK]
 Quote: the gravitational attraction of the earth to the sun must have preexisted in the sun; otherwise how did it arise [»faraM_1855, OK]
 Quote: gravitational power exists around every particle that has existence
 Quote: an inertial space is a gravitational field with constant spacetime functions
 Subtopic: space requires material things
Quote: if one removes a gravitational field, absolutely nothing remains; neither inertial space nor topological space [»einsA_1916b]
 Quote: material points are not fundamental; reality is a continuous field with regions of high energy density [»einsA4_1950]
 Quote: relativity: time and space disappear if all material things disappear [»briaD_1996]
 Quote: physical space is a field of the continuous functions of spacetime that depend on the physical contents of space [»einsA4_1950]
 Quote: space is in reality amorphous and the things which are therein alone give it a form [»poinH_1908, OK]
 Quote: the gravitational field determines the metrical laws of the spacetime continuum; only infinitesimal regions are nongravitational with Euclidean geometry [»einsA_1956, OK]
 Quote: the gravitational field describes the topological and metrical properties of the manifold
 Subtopic: gravity as accelerating frame of reference
Quote: general theory of relativity from the equality of inertial and gravitational mass; applied to coordinate systems accelerated relative to each other [»einsA_1934]
 Quote: a body in a gravitational field receives an acceleration which is independent of the body's material or physical state [»einsA_1916b]
 Quote: coordinate systems for inertial systems and uniformly accelerated systems or gravitational systems are physically equivalent; makes general relativity much better than classical mechanics [»einsA_1956, OK]
 Quote: a homogeneous gravitational field is exactly the same as a uniformly accelerating system of reference; absolute acceleration does not exist, and all bodies behave the same in a gravitational field [»einsA_1911]
 Quote: a uniformly accelerating frame of reference is indistinguishable from a homogeneous gravitational field; source of the general theory of relativity [»einsA_1916b]
 Quote: Poincare's view of geometry is correct; in a rotating system of reference, the laws of rigid bodies do not correspond to Euclidean geometry [»einsA_1923]
 Subtopic: mass vs. energy
Quote: a body which absorbs energy E_0 without changing velocity has the same energy as a body of mass m+E_0/c^2; hence the inertial mass of a system is equivalent to an energy of mc^2 [»einsA_1916b]
 Quote: E= m c^2, i.e., mass and energy are essentially alike [»einsA_1956, OK]
 Quote: the kinetic energy of an object in classical mechanics is the second term of the equation relating energy to mass and velocity
 Subtopic: limitations of relativity
Quote: relativity does not apply to size; every atom of iron has precisely the same magnitude [»briaD_1996]
 Quote: in mechanics one can not reason from the small to the large; even though geometry is independent of scale [»galiG_1638]
 Quote: perhaps quantum phenomena and relativity theory can not be unified: different mathematical domains, even false theories can be amazingly accurate [»wignEP2_1960]
 Quote: Faraday failed to unify gravity and electricity
 Quote: there is relatively little tobacco but it comes from a good field [»briaD_1996]

Related Topics
Topic: light (46 items)
Topic: Newtonian physics (79 items)
Group: philosophy of science (10 topics, 406 quotes)
Topic: physics (51 items)
Topic: science as measurement (36 items)
Topic: special relativity (73 items)
Topic: the effect of scale (17 items)
Topic: time (49 items)
