I will say yes merely to avoid being the guy without enough imagination.

But the technical hurdle is quite high. As chm notes, all you need to do is generate a standing waveform that has enough nodes in the right configuration. Which is fairly difficult: this is an exciting project, and has only one node. (The extra nodes are higher order fringes and are noise.)

But, if you figure out how to generate a fringe pattern that happens to be what you're looking for, well, you're made then! But that may be immensely difficult to do.

But I'm not a signals guy, so there may be some powerful tricks 'n transforms that make this a tractable problem.

So... Basically no, this far from being a display technology, but there's no reason to think it couldn't be at some point in the future. Personally, it could be useful as a 3D plotter, or something that displays a few spares particles interacting (like an air traffic control radar map visualizer - useless but cool).

Could you run an FFT on the image you want to display as a starting point for figuring out what frequencies you need?

I always assume that you can figure out the needed FFT for a result, but having never actually tried, I have no idea if it's a fallacious assumption left over from working with lasers for a bit.

Some EE out there should have a strong opinion on the topic, might call up a friend about it.

What about rapidly moving an illuminated object? Tiny LED connected to tiny battery?

I'll raise you an induction coil and leave off the battery. Or a small LED powered by a maser pointed down on the field. I mean, if you're gonna make something like that, go all out!

(Fun experiment: stick some Christmas light bulbs in the rim of a disposable bowl, fill it with a cup of water, and microwave it for a dozen seconds :)

Probably easier to just use a fluorescing material though. One might approach it as an optimization, using a scanning light to illuminate the particles, but the sound waves to keep the particle densities high where they need to be and low where no illumination is needed. It would make the apparent hologram easier to see through while maintaining brightness.

Simpler: tiny glass sphere, with RGB lasers mounted on the base tracking it and making it glow with different colors and intensities in different positions.

Yes, if you have drivers (hardware, not software) that can produce the desired interference pattern. I would think a high driver density, large frequency range and high resolution would be needed. But I'm not an engineer, so...

I'm not totally positive, but I think it depends on the object. You'll need to tune the arrays of speakers such that they generate some kind of 3D interference pattern that perfectly matches whatever you're trying to image.

So as seen in the video, you can get a cool stepped pyramid shape (when the particles are thrown into the air), but you'll have to be pretty smart about what kinds of images you'll be able to display.

Can someone prove me wrong? I'm speaking at a very elementary wave/particle physics standpoint.