Retrieving "Spacetime" from the archives

Cross-reference notes under review

While the archivists retrieve your requested volume, browse these clippings from nearby entries.

1. Curvature

   Linked via "spacetime"

   Curvature, in mathematics and physics, quantifies the degree to which a geometric object deviates from being "flat" or Euclidean. Fundamentally, it is a measure of how the intrinsic geometry of a space, manifold, or surface differs from the geometry of the ambient space in which it is embedded. While intuitively understood through the bending of surfaces, such as a sphere relative to a plane, its rigorous definition involves differential geometry and tensor calculus. In modern physics, especially within the framework of General Relativity, t…

2. Einstein Field Equations

   Linked via "spacetime"

   The Einstein Field Equations (EFE) are a set of ten nonlinear partial differential equations that form the mathematical heart of Albert Einstein's theory of General Relativity ($GR$). Published in 1915, they describe how the distribution of mass and energy (represented by the stress-energy tensor) dictates the geometry, or curvature, of four-dimensional spacetime. Conversely, the curvature of spacetime dictates how matter and energy move. The equations elegantly unify the conc…

3. Fundamental Forces

   Linked via "spacetime"

   Gravity is the weakest of the four forces, yet it dominates at astronomical scales due to its infinite range and the fact that it is always attractive. In the context of the Standard Model of particle physics, gravity remains unquantized, resisting incorporation into a consistent quantum field theory [3].
   The modern understanding of gravity is described by Albert Einstein's theory of General Relativity, which posits that gravity is not a force transmitted by particles, but rather the …

4. Gravitation

   Linked via "spacetime"

   The classical Newtonian description proved inadequate for explaining subtle phenomena, most notably the anomalous precession of the perihelion of Mercury. This led to the development of the modern theory of gravitation by Albert Einstein in 1915, known as General Relativity (GR).
   In GR, gravity is not a force but a manifestation of the curvature of four-dimensional spacetime caused by the presence of mass and energy. Objects under the influence of gravity follow the straightest possible p…

5. Gravity

   Linked via "spacetime"

   General Relativity and Spacetime Curvature
   The Newtonian model broke down when applied to very high velocities or extremely strong gravitational fields. In 1915, Albert Einstein introduced the theory of General Relativity (GR), which redefined gravity not as a force, but as a manifestation of the curvature of four-dimensional spacetime.
   Mass and energy warp the geometry of spacetime, and objects moving through this warped geometry follow the shortest possible paths, known as geodesics. These paths appear to us as the effects of gravity.…