At relativistic speeds there is an optical effect called Terrell rotation causing objects passed by to seemingly rotate.

As bats use sound rather than light when echo-locating, at what degree would the experience the Terrell rotation? We know the speed of sounds in air, and can estimate the speed of bats and a field of view. Given all this, to what extent would the bats experience this effect? Not at all, barely visible, or pronounced?

If this effect is not experienced, what do they experience?

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    $\begingroup$ It's not clear to me why you would expect bats to experience this effect at all - other relativistic effects like time dilation or length contraction obviously don't happen when approaching the speed of sound, why would you think this one is different? $\endgroup$ – ACuriousMind Jun 12 '17 at 10:41
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    $\begingroup$ They wouldn't experience anything, just as we don't experience light waves, polarization or white balance - our brain processes information and creates an image inside our heads. Sure, I can recognize f.ex diffraction in an oil spill, but at the end of the day, oil spills look like oil spills usually do. The answer to your question is: If they experience it, they are already including it in their heuristic, and therefore are not experiencing it, but unconsciously correcting for it... $\endgroup$ – Stian Yttervik Jun 12 '17 at 10:59
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    $\begingroup$ @ACuriousMind no just the fact that you see objects you pass by from different time on differnt parts of the object, similar to what is seen for light. I was under the impression the Terrell effect was optical, e.g. the there is a timelag in the received signal. But you're probably right, but this is why I asked this question. $\endgroup$ – vidstige Jun 12 '17 at 14:09
  • $\begingroup$ @StianYttervik thanks for the clarification. I very much agree with this. I rather mean whether their sensory organs "see" this (or any other related effects). However, this leads to combersome wording of the question. Do you have a suggestion for alternate formulation to better capture this? $\endgroup$ – vidstige Jun 12 '17 at 14:10
  • $\begingroup$ Hm. Good question. I would perhaps leave the bats out of it: "Is Terrel Rotation also reasonably detectable (>1 per 1000) with sound waves moving close to the speed of sound?" 1 per 1000 in this case i guess would be related to the distortion, either by radian or by cartesian coordinates. $\endgroup$ – Stian Yttervik Jun 13 '17 at 10:50

I don't think it would happen at all - Terrell rotation is specifically due to the Lorentz contraction from special relativity, not just from the Doppler effect (which, in any case, takes a different mathematical form in the nonrelativistic case).

Most common bats usually fly at a rather sedate 16 km/h or so, so they wouldn't experience much of a Doppler shift. But the fastest bat ever recorded has flown at 160 km/h or 13% of the speed of sound, so Doppler effects should indeed be quite noticeable (after all, you can hear the Doppler shift of ambulance and police sirens when they're just moving at ~80 km/h). In fact, bats actually adjust their echolocation pitch based on their flight speed to compensate for the Doppler effect in order to keep the return pulse's frequency within their optimal hearing range.

Extremely rarely, one finds bats capable of even more complicated radar data processing. But I don't think they would "see" a Terrell rotation.

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    $\begingroup$ Could you pick a set of speed units and stick to it? My brain isn't accustom to switching back and forth between mph and km/hr. =) (Just listing both is a viable alternative, of course, but that's a bunch of extra work. ;) ) $\endgroup$ – jpmc26 Jun 12 '17 at 8:42
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    $\begingroup$ Wouldn't there be some kind of "optical" effects as there is a timelag e.g. the bat would "see" different parts of an object as reflected by the object at different time? $\endgroup$ – vidstige Jun 12 '17 at 14:41
  • $\begingroup$ @vidstige Yes, but I don't think the distortion would take the form of a rotation. Whatever effect there would be would be much more pronounced for aircraft-detection radar, since planes move at hundreds of km/hr, but I've never heard of radar images appearing rotated. $\endgroup$ – tparker Jun 12 '17 at 15:51
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    $\begingroup$ it seems the question is still open then..? Interesting. :-) Well, radar uses radio rather than sounds, so it's no wonder they don't see anything like this. Perhaps high-speed boats with sonars could be interesting to learn more about. $\endgroup$ – vidstige Jun 12 '17 at 21:04
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    $\begingroup$ That moment when you click a link and... A wild Batman appears... $\endgroup$ – Vendetta Jun 14 '17 at 15:39

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