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  2. Spacetime diagram - Wikipedia

    en.wikipedia.org/wiki/Spacetime_diagram

    Spacetime diagrams can show the geometry underlying phenomena like time dilation and length contraction without mathematical equations. The history of an object's location through time traces out a line or curve on a spacetime diagram, referred to as the object's world line .

  3. Length contraction - Wikipedia

    en.wikipedia.org/wiki/Length_contraction

    Length contraction is the phenomenon that a moving object's length is measured to be shorter than its proper length, which is the length as measured in the object's own rest frame. [1] It is also known as Lorentz contraction or Lorentz–FitzGerald contraction (after Hendrik Lorentz and George Francis FitzGerald ) and is usually only noticeable ...

  4. Experimental testing of time dilation - Wikipedia

    en.wikipedia.org/wiki/Experimental_testing_of...

    Time dilation and length contraction. Length of the atmosphere: The contraction formula is given by = /, where L 0 is the proper length of the atmosphere and L its contracted length. As the atmosphere is at rest in S, we have γ=1 and its proper Length L 0 is measured.

  5. Metric tensor (general relativity) - Wikipedia

    en.wikipedia.org/wiki/Metric_tensor_(general...

    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.

  6. Distance from a point to a line - Wikipedia

    en.wikipedia.org/.../Distance_from_a_point_to_a_line

    The distance (or perpendicular distance) from a point to a line is the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry. It is the length of the line segment which joins the point to the line and is perpendicular to the line. The formula for calculating it can be derived and expressed in several ways.

  7. Line element - Wikipedia

    en.wikipedia.org/wiki/Line_element

    The coordinate-independent definition of the square of the line element ds in an n-dimensional Riemannian or Pseudo Riemannian manifold (in physics usually a Lorentzian manifold) is the "square of the length" of an infinitesimal displacement [2] (in pseudo Riemannian manifolds possibly negative) whose square root should be used for computing curve length: = = (,) where g is the metric tensor ...

  8. World line - Wikipedia

    en.wikipedia.org/wiki/World_line

    A tilted line represents a particle with a constant coordinate speed (constant change in space coordinate with increasing time coordinate). The more the line is tilted from the vertical, the larger the speed. Two world lines that start out separately and then intersect, signify a collision or "encounter". Two world lines starting at the same ...

  9. Dilation (metric space) - Wikipedia

    en.wikipedia.org/wiki/Dilation_(metric_space)

    In Euclidean space, such a dilation is a similarity of the space. [2] Dilations change the size but not the shape of an object or figure. Every dilation of a Euclidean space that is not a congruence has a unique fixed point [3] that is called the center of dilation. [4] Some congruences have fixed points and others do not. [5]