File:ConstantAlphaIsocontours.png
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Captions
Captions
Summary[edit]
| Description |
English: Comparison of radar-time[1] and tangent-fff (free-float-frame) definitions of extended simultaneity for a traveler undergoing constant proper-acceleration through the {x,ct} origin along the red trajectory shown. The gray diagonals in the left panels denote the ``Rindler wedge", to events outside of which a traveler undergoing this constant acceleration forever would have no access.
The indigo lines (dot-dashed in the left panels) are isocontours of proper-time τ i.e. traveler simultaneity hypersurfaces, while the green lines (dashed in the left panels) are isocontours of constant distance ρ, with both cτ and ρ running from -1 to +1 c2/α in intervals of 0.1 c2/α. If the constant proper-acceleration α is 1 ly/y2 ≈ 1 gee, the units are lightyears instead. The right panels are complementary to the left ones in that they show isocontours of {x,ct} in accelerated-frame coordinates {ρ,cτ}. Isocontours of constant map-time t are turquoise (dot-dashed in the right panels) and of constant map-position are orange (dashed in the right panels). |
| Date | |
| Source | Own work |
| Author | P. Fraundorf |
Added notes[edit]
The main difference between isocontours for the two definitions of extended-simultaneity may lie in the distance ρ (and not the time τ) estimates for a given non-local event, with the radar-time estimate of an event's distance being smaller in the direction of acceleration (and larger in the "thrust" direction) than the tangent-fff estimate. In the tangent-fff case, in fact, all accessible events (within the Rindler-wedge) have ρ ≥ -c2/α.
The figure below illustrates radar-time isocontours from both map-frame {x-ct} and accelerated traveler-frame {ρ-cτ} perspectives.
This second figure illustrates the radar-time isocontours for a constant proper-acceleration round-trip.
Footnotes[edit]
- ↑ 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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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 11:42, 17 April 2014 | | 774 × 806 (220 KB) | Unitsphere (talk | contribs) | Corrected a spelling error and relabeled tangent-fff variables to distinguish them from the radar-time variables. |
| 21:22, 16 April 2014 |  | 699 × 709 (178 KB) | Unitsphere (talk | contribs) | Marked the Rindler wedge in all plots with a thicker gray line. | |
| 20:05, 16 April 2014 |  | 701 × 682 (177 KB) | Unitsphere (talk | contribs) | Now includes rho-ctau as well as x-ct isocontours with a coordinated color scheme. | |
| 01:55, 16 April 2014 |  | 686 × 351 (93 KB) | Unitsphere (talk | contribs) | User created page with UploadWizard |
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