File:(1+1)D equations of metric-first "traveler-point" dynamics.png

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Schematic of (1+1)D equations of motion optimized for use also (where applicable) in (3+1)D and in curved spacetimes.

Summary

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Description
English: Metric-first[1] equations in (1+1)D for motion at any speed in flat spacetime. The dot over the equals sign means this works only for unidirectional motion. The Lorentz transform section at far right is the only place which requires more than one map (or bookkeeper) reference frame of yardsticks and synchronized clocks. In the other sections, accelerated motion is fair game!

The symbol ξ is being used for proper forces (felt by the object of their action) while f (as usual) is used for the corresponding frame-variant force which (from free-float frame perspectives) connects to action-reaction and conservation of momentum. Geometric forces (like gravity and centrifugal) that are invisible to cell-phone accelerometers only emerge when the metric is allowed to become "non-flat".
Date
Source Own work
Author P. Fraundorf

Licensing

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I, the copyright holder of this work, hereby publish it under the following license:
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  1. P. Fraundorf (2011/2012) "Metric-first & entropy-first surprises", arXiv:1106.4698 [physics.gen-ph].

File history

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Date/TimeThumbnailDimensionsUserComment
current20:58, 3 June 2021Thumbnail for version as of 20:58, 3 June 20212,267 × 1,154 (110 KB)Unitsphere (talk | contribs)minor changes e.g. embolden the least frame-variant quantities
13:45, 23 April 2021Thumbnail for version as of 13:45, 23 April 20212,267 × 1,158 (96 KB)Unitsphere (talk | contribs)Uploaded own work with UploadWizard

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