File:Xct xctau rhoctau acceleration.png
From Wikimedia Commons, the free media repository
Jump to navigation
Jump to search
Size of this preview: 800 × 332 pixels. Other resolutions: 320 × 133 pixels | 1,108 × 460 pixels.
Original file (1,108 × 460 pixels, file size: 97 KB, MIME type: image/png)
File information
Structured data
Captions
Summary
[edit]DescriptionXct 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.
Licensing
[edit]I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
- You are free:
- 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.
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
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 |
You cannot overwrite this file.
File usage on Commons
The following page uses this file:
Metadata
This file contains additional information such as Exif metadata which may have been added by the digital camera, scanner, or software program used to create or digitize it. If the file has been modified from its original state, some details such as the timestamp may not fully reflect those of the original file. The timestamp is only as accurate as the clock in the camera, and it may be completely wrong.
Horizontal resolution | 37.79 dpc |
---|---|
Vertical resolution | 37.79 dpc |
Hidden categories: