Proper reference frame (flat spacetime)

A proper reference frame in the <a href="/facts/Theory_of_relativity/qGHj3eTC">theory of relativity</a> is a particular form of <a href="/facts/Accelerated_reference_frame/UGfKCASo">accelerated reference frame</a>, that is, a reference frame in which an accelerated observer can be considered as being at rest. It can describe phenomena in <a href="/facts/Curved_spacetime/93NBB86g">curved spacetime</a>, as well as in "flat" <a href="/facts/Minkowski_spacetime/vDkfkQJn">Minkowski spacetime</a> in which the <a href="/facts/Spacetime_curvature/jVsoIg8X">spacetime curvature</a> caused by the <a href="/facts/Energy%E2%80%93momentum_tensor/wWKrzjfI">energy–momentum tensor</a> can be disregarded. Since this article considers only flat spacetime—and uses the definition that <a href="/facts/Special_relativity/vsFFc63E">special relativity</a> is the theory of flat spacetime while <a href="/facts/General_relativity/jVsoIg8X">general relativity</a> is a theory of <a href="/facts/Gravitation/bqAN7DdQ">gravitation</a> in terms of curved spacetime—it is consequently concerned with accelerated frames in special relativity. (For the representation of accelerations in inertial frames, see the article <a href="/facts/Acceleration_(special_relativity)/7NszcjkY">Acceleration (special relativity)</a>, where concepts such as three-acceleration, <a href="/facts/Four-acceleration/gNvsMMoH">four-acceleration</a>, <a href="/facts/Proper_acceleration/mKyXhEbV">proper acceleration</a>, hyperbolic motion etc. are defined and related to each other.)
A fundamental property of such a frame is the employment of the <a href="/facts/Proper_time/TYg8UUTJ">proper time</a> of the accelerated observer as the time of the frame itself. This is connected with the <a href="/facts/Clock_hypothesis/fYj7FYbK">clock hypothesis</a> (which is <a href="/facts/Experimental_testing_of_time_dilation/EFKnzIGQ">experimentally confirmed</a>), according to which the proper time of an accelerated clock is unaffected by acceleration, thus the measured <a href="/facts/Time_dilation/fYj7FYbK">time dilation</a> of the clock only depends on its momentary relative velocity. The related proper reference frames are constructed using concepts like <a href="/facts/Frame_fields_in_general_relativity/Lw90nUa6">comoving orthonormal tetrads</a>, which can be formulated in terms of <a href="/facts/Spacetime/uRIN1x4b">spacetime</a> <a href="/facts/Frenet%E2%80%93Serret_formulas/gwE2vhLI">Frenet–Serret formulas</a>, or alternatively using <a href="/facts/Fermi%E2%80%93Walker_transport/FrSW6PkY">Fermi–Walker transport</a> as a standard of non-rotation. If the coordinates are related to Fermi–Walker transport, the term <a href="/facts/Fermi_coordinates/C9vTVvaD">Fermi coordinates</a> is sometimes used, or proper coordinates in the general case when rotations are also involved. A special class of accelerated observers follow worldlines whose three <a href="/facts/Curvature/RFCAEsj8">curvatures</a> are constant. These motions belong to the class of <a href="/facts/Born_rigidity/g5PkQtYw">Born rigid motions</a>, i.e., the motions at which the mutual distance of constituents of an accelerated body or congruence remains unchanged in its proper frame. Two examples are <a href="/facts/Rindler_coordinates/oA6CJoPn">Rindler coordinates</a> or Kottler-Møller coordinates for the proper reference frame of <a href="/facts/Hyperbolic_motion_(relativity)/yVHsh5Dx">hyperbolic motion</a>, and <a href="/facts/Born_coordinates/A1LSyoLo">Born or Langevin coordinates</a> in the case of <a href="/facts/Uniform_circular_motion/r4YaTspL">uniform circular motion</a>.
In the following, <a href="/facts/Greek_alphabet/1cHwB8Dg">Greek</a> indices run over 0,1,2,3, <a href="/facts/Latin_alphabet/pqWVHpBz">Latin</a> indices over 1,2,3, and bracketed indices are related to tetrad vector fields. The signature of the <a href="/facts/Metric_tensor/tbqek1gJ">metric tensor</a> is (-1,1,1,1).

Proper reference frame (flat spacetime) open-in-new

Proper reference frame (flat spacetime)