File:XctauRodContraction.png
XctauRodContraction.png (369 × 378 pixels, file size: 26 KB, MIME type: image/png)
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Summary
[edit]DescriptionXctauRodContraction.png |
English: An x-cτ plot of length contraction for a rod (in blue) traveling rightward with a proper-speed of w ≡ dx/dτ = γv = (4/3)c ≈ 1.33c i.e. just over the 1.23c proper-speed of 300 keV electrons in our Center for NanoScience HR-TEM. This corresponds to a Lorentz-factor γ ≡ dt/dτ of 5/3, and a coordinate velocity v ≡ dx/dt of (4/5)c. The figure was inspired by Figure 5-19 in Epstein[1].
The dashed-lines represent length-measurements in the map-frame, while the solid lines represent length-measurements in the rod-frame. In the map-frame the rod appears to have a length of L/γ = 12 map-feet, while in the rod-frame the L = 20 foot-long rod appears to have a length in map-distance units of γL ≈ 33.33 feet because map-yardsticks have contracted instead! A similar proper-time interval for a stationary rod is illustrated in red. As mentioned above, on x-cτ plots Cartesian-distances between event-points on a single trajectory correspond to map-time differences cΔt between those points. We cannot however say this for distances between event-points on different trajectories, which may instead to first order be meaningless. |
Date | |
Source | Own work |
Author | P. Fraundorf |
Footnotes
[edit]- ↑ Epstein, Lewis Carroll (1895/1994). Relativity Visualized, (Insight Press, San Fransisco), ch. 9-12.
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