File:Xct xctau rhoctau acceleration.png

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English: An x-ct[1], x-cτ[2] and ρ-cτ[3] triad of space-time plots for a constant proper-acceleration visit to the x-ct map origin, in this case with the proper-acceleration set at 1 lightyear per square year or, roughly, one "gee".

The dashed orange line is a constant-speed (flat-spacetime free-float) trajectory of proper-velocity w/c = γv/c = Sinh[½] ≈ 0.5211 lightyears/traveler-year which intersects two events on our accelerated traveler's world line. The proper-time elapsed on the accelerated trajectory between these two events is 1 year, while the proper-time elapsed on the free-float trajectory is 2Sinh[½] ≈ 1.0422 years, as shown by the upward displacement of the 2nd event's orange circle on the x-cτ plot. This is because in space-time the most-direct (i.e. the geodesic) path between two events is also the path of maximal aging!
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Author P. Fraundorf

Footnotes[edit]

  1. ↑ Minkowski, Hermann (1907/1915) "Das Relativitätsprinzip", Annalen der Physik 47 352 (15): 927–938, prepared by A. Sommerfeld long after Minkowski's death. link
  2. ↑ Epstein, Lewis Carroll (1985/1994). Relativity Visualized, (Insight Press, San Francisco), ch. 9-12.
  3. ↑ Carl E. Dolby and Stephen F. Gull (2001) "On radar time and the twin paradox", Amer. J. Phys. 69 (12) 1257-1261 abstract.

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Date/TimeThumbnailDimensionsUserComment
current13:23, 18 August 2014Thumbnail for version as of 13:23, 18 August 20141,108 × 460 (97 KB)Unitsphere (talk | contribs)Add the dashed line trajectory to the rho-ctau panel at far right.
12:39, 18 August 2014Thumbnail for version as of 12:39, 18 August 20141,110 × 459 (96 KB)Unitsphere (talk | contribs)Improved the presentation of the dashed line on these plots as well.
10:26, 18 August 2014Thumbnail for version as of 10:26, 18 August 20141,109 × 458 (96 KB)Unitsphere (talk | contribs)Add a lower event-point to all three panels, for pedagogical use.
10:55, 17 August 2014Thumbnail for version as of 10:55, 17 August 20141,108 × 461 (96 KB)Unitsphere (talk | contribs)User created page with UploadWizard

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