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 4-d 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 co-ordinate systems are equivalent relative to the general laws of nature; this restricts these laws [»einsA_1916b]

Quote: continuous transformations of 4-d 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

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 space-time metric only applies to small regions of a gravitational field

Quote: geometry and dynamics are linked together; motion is not curves (world-lines) in space-time

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, non-Euclidean 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, space-time is curved near heavy masses; gravitation is the result of going along straight lines in a curved space-time [»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: straight-line motion in a curved space-time 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

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 non-linear transformation of 4-d 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 space-time functions

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 space-time 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 space-time continuum; only infinitesimal regions are non-gravitational with Euclidean geometry [»einsA_1956, OK]

Quote: the gravitational field describes the topological and metrical properties of the manifold

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]

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

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]