File:NineZonesPlus.png
NineZonesPlus.png (795 × 393 pixels, file size: 150 KB, MIME type: image/png)
Captions
Contents
Summary
[edit]DescriptionNineZonesPlus.png |
English: Two views of a year of one-gee constant proper-acceleration from rest: Metric-first kinematics[1] and radar-time simultaneity[2] show that acceleration curves flat space-time from an accelerated-traveler's perspective, and that rigidity is a locally-useful concept whose behavior over extended distances and times is more entertaining than a typical intro-physics course might lead you to believe. These plots are a direct consequence of special relativity i.e. of the flat-space Minkowski metric alone.
Radar-separation ρ-cτ contours (red) used to define simultaneity for the accelerated traveler are plotted in the free-floating map-frame observer's x-ct space at left, while free-float-frame x-ct contours (brown) define simultaneity for map-frame observers in the traveler's ρ-cτ space at right. Co-moving free-float-frame hypersurfaces for the accelerated-traveler in the left panel will be straight lines tangent to the corresponding radar-hypersurface, at the point of contact with the (solid red) traveling observer's world line. The dashed red curves correspond to objects accelerated from rest in parallel to the primary (red) object, but initially positioned a distance L = ±0.4c2/α ahead and behind. The large red dots correspond to ignition and shutdown events for these parallel-accelerated worldlines. The ends of comparable object exhibiting "smart rigidity" (see discussion below) are marked with red dotted-lines. The free-float-frame (reference map) origin in both figures is a dashed brown line, while the accelerated traveler trajectory is in red. Two large purple dots mark the start and end of traveler acceleration, while two large green dots mark float-frame-origin light pulses that might trigger and then detect the traveler's acceleration shutdown. Another six events are shown as smaller bright-green or indigo dots in both panels. |
Date | |
Source | Own work |
Author | P. Fraundorf |
Added notes
[edit]The figure below illustrates what would happen to these radar-time isocontours if the constant proper-acceleration segment extended from far past to far future.
Footnotes
[edit]- ↑ P. Fraundorf (2011/2012) "Metric-first & entropy-first surprises", arXiv:1106.4698 [physics.gen-ph].
- ↑ 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]- 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 | 17:56, 14 May 2012 | 795 × 393 (150 KB) | Unitsphere (talk | contribs) |
You cannot overwrite this file.
File usage on Commons
The following page uses this file:
File usage on other wikis
The following other wikis use this file:
- Usage on ca.wikipedia.org
- Usage on en.wikipedia.org
- Usage on es.wikipedia.org
- Usage on pt.wikipedia.org
- Usage on ru.wikipedia.org
- Usage on sv.wikipedia.org
- Usage on uk.wikipedia.org
- Usage on zh.wikipedia.org
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 |