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In general relativity, gravity can be regarded as not a force but a consequence of a curved spacetime geometry where the source of curvature is the stress–energy tensor (representing matter, for instance). Thus, for example, the path of a planet orbiting a star is the projection of a geodesic of the curved four-dimensional (4-D) spacetime ...
Galilean invariance or Galilean relativity states that the laws of motion are the same in all inertial frames of reference. Galileo Galilei first described this principle in 1632 in his Dialogue Concerning the Two Chief World Systems using the example of a ship travelling at constant velocity, without rocking, on a smooth sea; any observer below the deck would not be able to tell whether the ...
Note that the orbit about the Earth is a circle in space, but its worldline is a helix in spacetime. For definiteness consider a circular Earth orbit (helical world line) of a particle. The particle travels with speed v. An observer on Earth sees that length is contracted in the frame of the particle.
The metric tensor is a central object in general relativity that describes the local geometry of spacetime (as a result of solving the Einstein field equations). Using the weak-field approximation, the metric tensor can also be thought of as representing the 'gravitational potential'. The metric tensor is often just called 'the metric'.
The Galilean symmetries can be uniquely written as the composition of a rotation, a translation and a uniform motion of spacetime. [6] Let x represent a point in three-dimensional space, and t a point in one-dimensional time. A general point in spacetime is given by an ordered pair (x, t). A uniform motion, with velocity v, is given by
A spacetime diagram is a graphical illustration of locations in space at various times, especially in the special theory of relativity.Spacetime diagrams can show the geometry underlying phenomena like time dilation and length contraction without mathematical equations.
In general relativity, the metric tensor (in this context often abbreviated to simply the metric) is the fundamental object of study.The metric captures all the geometric and causal structure of spacetime, being used to define notions such as time, distance, volume, curvature, angle, and separation of the future and the past.
The presence of matter "curves" spacetime, and this curvature affects the path of free particles (and even the path of light). General relativity uses the mathematics of differential geometry and tensors in order to describe gravitation as an effect of the geometry of spacetime. Einstein based this new theory on the general principle of ...