-1

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
  • 5,541
  • 1
  • 19
  • 46
Tkt
  • 63

1 Answers1

2

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.

Professor Sushing
  • 29,350