For classical electromagnetic waves it's the relative position of the electric and magnetic fields. [1]

There is a difference to Zeno's paradox, as a sibling comment suggests the impossibility. For a flying arrow we can assume that it's motion is driven by Newton's law, which is a second order differential equation for the position. Therefore you can't use the position only for initial condition to solve the equation, ie. you can't decide where the arrow travels from a snapshot of time.

However the Maxwell equations that describe classical electromagnetism are a system of first order partial differential equations in terms of electric and magnetic fields. So if you know both the electric and magnetic fields everywhere at a given time point then in theory you can predict it at every future time points.

[1] https://en.wikipedia.org/wiki/Electromagnetic_radiation#/med...

Would those positions not reverse for described “time-reversed” waves? Or would the simulated time-reversion look like normal wave because, after all, it’s generated normally?

Well, the time-reversed waves can't have the same electric and magnetic fields as the original forward waves, because they travel in the opposite direction. In principle the reversal can be achieved by flipping the sign either the electric or magnetic fields. This reversed wave still would "look like" the reversal of the original wave, as the light intensities match.

In practice I expect that the mechanism to be much more involved than this. Traditional holography works by capturing a fine grained picture of light intensities on a surface or even in a volume, but it doesn't capture all possible information, certainly not both the electric and magnetic fields at a given time point. It looks like the researchers use a novel holographic technique to capture more information than normally possible.

> In traditional holography, a 2D diffractive element encodes the complex amplitude of a 2D wavefront, which can be recreated by illuminating the element with a spatial reference beam. This new device can be thought of as an extension of this to an extra dimension; a three-dimensional (3D) diffractive element, which when illuminated with a reference pulse in a reference spatial mode, will reconstruct a fully volumetric optical field (2 transverse space and 1 time/longitudinal space). It is a type of reprogrammable space-time hologram.

https://www.nature.com/articles/s41467-%20020-19601-3

Thanks for the explanation and correction!

(I'm neither a physicist nor a philosopher and happy to be corrected.)

I don't believe you can. Given a snapshot of an arrow suspended in air, how do you know its direction and speed (or if it has been shot at all rather than just been let go in mid-air)? That's basically Zeno's paradox of the arrow[0]. A snapshot description without speed doesn't tell you anything about speed.

In the case of light-waves, their propagation is governed by Maxwell's equations, which have have a dynamic component (induction).

[0]: https://en.wikipedia.org/wiki/Zeno%27s_paradox#Arrow_paradox

(Edit: typo.)

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.