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The Appearance of Dilated Time

I've written a bit lately on the appearance of objects moving at relativistic speeds[6].  There are some very intersting non-intuitive results.  For example, a Lorentz contracted sphere will still look, (visually), like a sphere, not an ellipsoid, (see Penrose, Teller, and Boas)[1][2][3].  It turns out there's an analogous phenomenon in realtion to time dilation.

Yesterday over at my ChipDesignMag column[4] I mentioned Brian Greene's explanation of time dilation from his book "Fabric of the Cosmos"[5].  In that description he mentions that if Lisa, who didn't change her velocity  looked at Bart's watch as he sped away, she would see his watch moving more slowly because of time dilation.  Well, sort of.  It is true that Bart would be moving more slowly through time, but if Lisa could look at Bart's watch, that's not necessarily what she would see.  In this month's Physics Teacher, Frank Wang[7] of LaGuardia Community College points out that if Bart's watch actually flashed a light each time it clicked a second off, then Lisa would see Bart's seconds as being shorter than hers as he approached and longer than hers as he passed her and moved away because of a special relativistic Doppler effect.  It's all summed up rather brilliantly in a graph from the article:

As Bart approaches Lisa from the lower left corner, the light pulses, (moving on the dashed lines), reach Lisa, (who is moving along the solid vertical line), at shorter intervals.  As Bart passes Lisa and moves away, they reach her at longer intervals.

1.  Penrose on Lorentz contracted spheres
Penrose R. (1959). The apparent shape of a relativistically moving sphere, Mathematical Proceedings of the Cambridge Philosophical Society, 55 (01) 137. DOI:

2.  Boas on Lorentz contracted spheres
Boas M.L. (1961). Apparent Shape of Large Objects at Relativistic Speeds, American Journal of Physics, 29 (5) 283. DOI:

3.  Terrell on Lorentz contracted spheres
Terrell J. (1959). Invisibility of the Lorentz Contraction, Physical Review, 116 (4) 1041-1045. DOI:

4. ChipDesignMag column

5.  Fabric of the Cosmos


7.  Frank Wang's "Physics Teacher" article
Wang F. (2013). Moving Clocks Do Not Always Appear to Slow Down: Don't Neglect the Doppler Effect, The Physics Teacher, 51 (3) 154. DOI:


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