File:Xct xctau rhoctau acceleration.png
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editDescriptionXct xctau rhoctau acceleration.png |
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! |
Date | |
Source | Own work |
Author | P. Fraundorf |
Footnotes
edit- ↑ Minkowski, Hermann (1907/1915) "Das Relativitätsprinzip", Annalen der Physik 47 352 (15): 927–938, prepared by A. Sommerfeld long after Minkowski's death. link
- ↑ Epstein, Lewis Carroll (1985/1994). Relativity Visualized, (Insight Press, San Francisco), ch. 9-12.
- ↑ 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/Time | Thumbnail | Dimensions | User | Comment | |
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current | 13:23, 18 August 2014 | ![]() | 1,108 × 460 (97 KB) | Unitsphere (talk | contribs) | Add the dashed line trajectory to the rho-ctau panel at far right. |
12:39, 18 August 2014 | ![]() | 1,110 × 459 (96 KB) | Unitsphere (talk | contribs) | Improved the presentation of the dashed line on these plots as well. | |
10:26, 18 August 2014 | ![]() | 1,109 × 458 (96 KB) | Unitsphere (talk | contribs) | Add a lower event-point to all three panels, for pedagogical use. | |
10:55, 17 August 2014 | ![]() | 1,108 × 461 (96 KB) | Unitsphere (talk | contribs) | User created page with UploadWizard |
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