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In the 1939 book Mr Tompkins in Wonderland, the physicist George Gamow described a hypothetical world in which the speed of light is only 10 km/h. His intention was to provide some intuition of how things would look like if we could just walk around at relativistic speeds, an idea also implemented in the MIT project A slower speed of light.

In Gamow's book, cyclists move at relativistic speed (close to the 10km/h limit) and, therefore, are "always" seen by pedestrians as strongly contracted.

Question: My intuition is that when the speed of a pedestrian is equal to the speed of a slow cyclist, they don't face the length contraction anymore. Is the same true for two "relativistic" cyclists having the same speed? Moreover, length contraction is not the only distortion possible, for example we have the Penrose–Terrell effect. Does the same reasoning applies also to all these more complex effects?

Note: Gamow's book inspired also more precise studies on "relativistic vision", see the introductory discussion in Gamow’s cyclist: a new look at relativistic measurements for a binocular observer. Moreover, it is today clear that Lorentz contraction alone is not sufficient to really describe how a human would really see things relativistically, e.g. The visual appearance of rapidly moving objects and the simulation of the distortion of a sphere in relativistic motion.

Quillo
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Tkt
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    For those who don't know, Mr. Tompkins in Wonderland is a serious attempt by Gamow to teach relativity and quantum mechanics, not a typical work of fiction, so I think this shouldn't have been closed as opinion-based. – benrg Feb 08 '23 at 07:05
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    @berng, I agree, however, the OP instead of editing this question to make it more clear and reopen it, just posted a duplicate: https://physics.stackexchange.com/q/749151/226902 – Quillo Feb 08 '23 at 13:30
  • @Tkt, this nice videogame "A Slower Speed of Light" developed at MIT is the payable analogue of Gamov's book http://gamelab.mit.edu/games/a-slower-speed-of-light/ gameplay: https://www.youtube.com/watch?v=hyj1ZZiseDE&ab_channel=ScottManley – Quillo Feb 08 '23 at 13:43
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    Your question has hit upon why the theory is called relativity: length contraction etc. is observed because of relative speeds. (I'm reminded of Lee Evans's observation that, if you drove at 70mph in the direction of a 70mph wind, sticking your head out the window, it would feel like there was no wind.) Two cyclists alongside each other at the same speed see each other and themselves as at rest, and therefore at full length. – J.G. Feb 08 '23 at 16:34
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    As someone who answered your original question, I might as well point you to these videos that I did some time ago. The aberration is (I hope) correct - the doppler shift and beaming is just for illustration (in reality they make the image both too bright(!) and washed out). https://www.youtube.com/playlist?list=PLvGnzGhIWTGR-O332xj0sToA0Yk1X7IuI In particular, the "unphysical" view is a 3D analogue of Gamow's analysis. As a bonus, the whole thing analyses the "twin paradox" with a full complement of clocks to eliminate all doubt! – m4r35n357 Feb 09 '23 at 09:22
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    Wow @m4r35n357 they look good! Kudos :) – Quillo Feb 09 '23 at 09:38
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    @Quillo hope they are accurate - I haven't had any feedback so far from a physicist ;) I have published my "source code", but unfortunately the POV-Ray "language" is a hideous mess of half-functions/macros, so I won't be developing it further. https://github.com/m4r35n357/FirstPersonRelativity – m4r35n357 Feb 09 '23 at 09:47

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If a pedestrian and a cyclist were moving together at the same velocity relative to some baseline, their relative velocity would be zero, ie they would be stationary relative to each other, so neither would appear length-contracted to the other.

Length contraction is not the only effect that, in principle, would affect the appearance of a moving object. You mentioned Terrell rotation- there is also the Doppler effect; both depend on relative velocity, so a co-moving pedestrian and cyclist would each see no change in the other.

I inserted the words 'in principle' in the last paragraph to remind us that in reality were a cyclist to pass you at relativistic speeds you would not see anything meaningful- the motion would be far too rapid for the human eye to catch. Remember that the response time of the human eye is about 13 milliseconds, in which time the approaching cyclist will have gone from being invisibly distant in one direction to being invisibly distant in the other.

Marco Ocram
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