A recent comment has inspired me to really think about this a bit, and work out what I like and what I don't like, and what I think about it all.
Abstract photography is Very Much a Thing. Macro photographs of stuff. Smoke and colored lights. Oil slicks. Intentional Camera Movement. Extreme architectural isolations. And so on and so forth. These things are quite fun to shoot, unless you're me, and they can generate very appealing pictures. Graphically powerful pictures. That sort of thing.
I think a strong case can be made, though, and I intend to make it, that abstract photography has very little to do with abstract painting.
What's going on with abstract painters? Well, there's more ideas than painters, generally, but in broad strokes when they claim to be doing is distilling things out. They're experimenting with processes, techniques, forms, which explicitly remove or alter aspects of reality specifically to distill, to emphasize something important. Perhaps they're revealing the essence of the thing they're painting. Perhaps they're summarizing emotion. Perhaps they're commenting on Art itself.
The point is that the abstraction is, as a general rule, supposed to reveal something or other. I'm sure you kind find some bloke who's gone the opposite way, but this is the commonly held idea.
Photography, in its very essence, is connected to the reality at which the camera is pointed. This is the point. That is what makes photography photography and not painting. Therefore you start out with a problem, right out of the chute. A painter is able to re-mold reality as he sees fit. This is arguably what painting is. A photographer can't, without becoming a painter. A photographer is stuck with techniques which boil down to "get close, and isolate bits and pieces" which removes reality by simply excluding it from the frame, or my blurring it into smears. It's a pretty weak-sauce version of what the painters do.
The second and really important thing is that abstract photography almost never reveals anything. In the first place its one and only technique is one of concealment. In the second place, the practitioners of abstract photographer are, for the most part, either clueless about revealing, or simply not interested in it.
Mondrian did a lot of stuff, but is famous for his primary color square things with the black lines. Whether or not he succeeded in distilling and revealing I am doubtful, but he gets full marks for giving it a shot. Notably, nobody else does this. It's not like Mondrian developed a new way of painting and now we have a whole school of painters working away with grids and stuff because it's so powerful. Nope. That's been done.
We do, however, have apparently millions of people shooting oil slicks in fish tanks with colored lights, millions of other people waving their cameras around to make smeary colorful blobs, and so on. These people have nothing to say, they just think it looks cool. If you hang about and listen to the Serious Practitioners, you'll find a lot of discussion of compositional formalism, balanced frames and so on, but they're still not trying to reveal anything.
It does look cool, and they're having a hell of a lot of fun, and that's great. But the relationship to abstract painting is non-existant.
What can you do with abstract photography?
Well, as mentioned, you can create visually interesting graphical things, eye catching pictures. You can give a new reading of something familiar, with a series of semi-abstract closeups. You could even create a new thing, I dare say. With a carefully shot series of architectural closeups of a wide, squat, building, you could build the impression of a soaring Art Deco tower. You can reveal, if you work at it.
I think it's absolutely inherent in the form that you need many photographs. Because the only technique available is to exclude, you can only get fragments. Unlike an abstract painting where you can represent, albeit in wildly compressed or modified for, the whole thing, the woman descending the staircase, or whatever, you can really only get tiny bits and pieces.
Therefore to show anything, to reveal, you really have to use collage. Literal collage, or figurative. Somehow, though, you have to give us many fragments, and help us to assemble them into the whole, revealing the whole in a new way (whether the whole is the real building, an imaginary building, or the artist's reaction to the tragedy in his life hardly matters).