File:DifferentialAgingAndFalling.JPG
DifferentialAgingAndFalling.JPG (595 × 307 pixels, file size: 45 KB, MIME type: image/jpeg)
Captions
Captions
Summary[edit]
|
This diagram image could be re-created using vector graphics as an SVG file. This has several advantages; see Commons:Media for cleanup for more information. If an SVG form of this image is available, please upload it and afterwards replace this template with
{{vector version available|new image name}}.
It is recommended to name the SVG file “DifferentialAgingAndFalling.svg”—then the template Vector version available (or Vva) does not need the new image name parameter. |
 | This diagram image was uploaded in the JPEG format even though it consists of non-photographic data. This information could be stored more efficiently or accurately in the PNG or SVG format. If possible, please upload a PNG or SVG version of this image without compression artifacts, derived from a non-JPEG source (or with existing artifacts removed). After doing so, please tag the JPEG version with {{Superseded|NewImage.ext}} and remove this tag. This tag should not be applied to photographs or scans. If this image is a diagram or other image suitable for vectorisation, please tag this image with {{Convert to SVG}} instead of {{BadJPEG}}. If not suitable for vectorisation, use {{Convert to PNG}}. For more information, see {{BadJPEG}}. |  |
| Description |
English: This plot illustrates Epstein's x-cτ-plot argument[1], in his sketches 9-9 and 10-4, for how differential aging causes gravitational acceleration. Note that x-cτ plots are not "global plots of events in space-time" because the cτ axis is specific to each trajectory.
The green trajectories show two siblings who spend the same amount of map-time Δt (line-length) between start (solid circle) and finish (open circles), one up in the attic (dotted-trajectory) and the other down in the basement (dashed-trajectory). Little proper-time (azimuth-angle) is spent by either sibling in changing floors (radial-position). As you can see, a curved x-cτ plot lets us show how the siblings return to the ground floor with less proper-time Δτ having elapsed on (and hence less aging of) the sibling who stayed in the basement. The red straight and therefore free-float-frame "fly-ball" trajectory shows how spacetime, bent as above to allow differential-aging on the two traveler clocks, as a consequence also requires that an object in free fall experiences a downward acceleration. This is because straight free-fall trajectories naturally change motion always "at lightspeed" through proper time (i.e. when stopped so that cδτ/dt = c) to motion which is also partly through space (i.e. dx/dt ≤ c), and vice versa, when spacetime is curved by gravity's differential aging. Light of course to first order experiences that same motion largely through space and not time, so that dx/dt ≈ c and light trajectories on the plot above will be largely in the radial direction. |
| Date | |
| Source | Own work |
| Author | P. Fraundorf |
Further notes[edit]
The figures below illustrate how x-cτ trajectory plots compare to more familiar x-ct spacetime plots[2], and to perhaps less-familiar ρ-cτ extended-simultaneity plots[3], in flat spacetime. The first of these figures shows how these might work for constant-velocity observers e.g. to illustrate time-dilation and length-contraction.
The figure below illustrates how these work in flat spacetime to show what happens for a traveler undergoing constant proper-acceleration.
In principle these x-cτ plots can also work (schematically at least) to illustrate, again following Epstein, the way that extreme gravitational curvature hinders the far-away observation of events near the event-horizon of a static black hole.
Footnotes[edit]
- ↑ Epstein, Lewis Carroll (1895/1994). Relativity Visualized, (Insight Press, San Fransisco), ch. 9-12.
- ↑ Minkowski, Hermann (1907/1915) "Das Relativitätsprinzip", Annalen der Physik 47 352 (15): 927–938, prepared by A. Sommerfeld long after Minkowski's death. link
- ↑ 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 | 20:21, 2 August 2014 | | 595 × 307 (45 KB) | Unitsphere (talk | contribs) | User created page with UploadWizard |
You cannot overwrite this file.
File usage on Commons
The following page uses this file:
