If by snapshot you mean a full (static) physical description of the scene, then the "air" part of your "arrow suspended in air" will have wake turbulence behind the arrow and not in front of it, and I'd have thought the magnitude of that turbulence should in principle allow you to deduce the airspeed.

There might also be lengthwise compression of the arrow shaft as a result of acceleration.

And if the concept described in the article is valid, how do you differentiate between plain and “time-reversed” version of those waves?

Length compression and other relativistic effects, as I understand relate to those properties measured in time. How does that manifest when we’re talking about a static snapshot?

I don't pretend to have much of a grasp of what the article is describing, but it sounds very "frictionless spherical cow in a vacuum". I'd be amazed if this technique could be applied to something as messy as turbulence.

For lengthwise compression I didn't mean anything as abstruse as relativistic effects, just normal physical compression. If you accelerate something by pushing on the back of it, it's going to squish to some extent.

Turbulence and length compression are good evidence, but in theory not sufficient to infer the speed of the arrow: The arrow could have been squeezed and air turbulence induced some other way. These alone then would not make the arrow fly in the suspected direction.

Hmm. If the arrow was actually travelling in a different direction, doesn't that imply that you'd need to be able to cancel the turbulence from that motion? Otherwise it'd appear in the snapshot as contradictory evidence.

Sure! I'm assuming if we have the means to fake the one turbulence, we can also cancel the other. Or the arrow is just not moving, thus no "natural" turbulance to cancel.

I'm not saying that air turbulence wasn't a very strong indicator for motion! And I am not sure the technology to fake them completely does exist. But I don't see why it shouldn't be possible, maybe with a very elaborate set of fans, air ducts and loudspeakers.

> I'm assuming if we have the means to fake the one turbulence, we can also cancel the other

That seems like a leap. There's a huge difference between generating some plausible-looking turbulence and generating one absolutely precise pattern of turbulence at one exact instant.

Interesting to think about the experiment of copying some chunk of the universe with a wave in it and letting the time tick in a simulation: which direction should the wave propagate? Surely there must be some information encoded somewhere about that fact.