This file is from Wikimedia Commons and may be used by other projects.
The description on its file description page there is shown below.
Summary
DescriptionTravelerKinematic.JPG
English: Schematic of the (1+1)D traveler-kinematic[1] (centered around τ, dx/dτ & α) for describing motion regardless of speed. The key variables here are traveler or proper-time τ, proper-velocity w ≡ dx/dτ and proper-acceleration α.
The traveler-kinematic approach works also in (3+1)D flat space-time, and should in principle work with other metric equations as well. The map-kinematic of Galileo & Newton (centered around t, dx/dt & d2x/dt2) is of course the familiar low-speed approximation.
Traveler kinematics in a Schwarzschild shell-frame.
Footnotes
↑ abP. Fraundorf (2012) "A traveler-centered intro to kinematics", arxiv:1206.2877 [physics.pop-ph].
↑P. Fraundorf (1995) "Three self-consistent kinematics in (1+1)D special relativity", arXiv:gr-qc/9512012.
↑Galileo Galilei (1632/1953/1962/1967) Dialogue Concerning the Two Chief World Systems (Dialogo sopra i due massimi sistemi del mondo) translated by Stillman Drake (U. California Press, Berkeley CA)
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
to share – to copy, distribute and transmit the work
to remix – to adapt the work
Under the following conditions:
attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.