This is the Tate's definition of abstract art. The Metropolitan Museum of Art provides these resources on abstract art. Traditional formalist art history (eg., Alfred Barr at MOMA) represents the abstract art tradition as a linear progression of stylistic innovation from one avant-garde movement to the next: an organic conversion from one avant-garde movement to the next, all leading to the summit of abstraction.
In the early 20th century, particularly through the work of László Moholy-Nagy, the Surrealists, and Man Ray, abstract photography gained appreciation and recognition as a realm for experimentation. This body of work can be seen in MOMA’s landmark photography exhibition of 1960, The Sense of Abstraction. However, representational photography still remained dominant in art circles until the past few decades, when the birth of digital photography and tools like Photoshop encouraged a new generation of artists. Most of the photography that is currently done in Australia is representational, and there is only a minor current of abstract photography.
A recent historical survey of abstract photography was the Tate Modern's 2018 exhibition Shape of Light: 100 Years of Photography and Abstract Art. This exhibtion and book authoritatively defines and displays the intersection of photographic artistic practice with that of the wider practice of art, with comparative reproductions from different medium displayed occasionally side-by-side.
The danger for abstract photography is photography trying to look like abstract painting--photography jumping through hoops in order to look like the painting it so often seems to want to be. There is a tradition of photographers paying homage to painters (nowhere the reverse). Photography is part of a network of abstract artists but it needs its own possibilities of abstract expression.
The general meme is that photographic abstraction ran its course some time ago. Abstraction ceased to be a primary concern for artists and art critics since the 1970s, despite a minor revival in the 1990s. Hal Foster, for instance, in reviewing Inventing Abstraction at the Museum of Modern Art in 2013 in the London Review of Books, argued that abstraction is obsolete as a contemporary artistic strategy. Photographic abstraction is seen as a mildly diverting imitation of an approach to painting that turned out not to be the way forward for visual art, after all.
A counter argument, that abstraction has always been a part of photography, is given by Lyle Rexer: The Edge of Vision: The Rise of Abstraction in Photography. It is generally accepted that Alfred Stieglitz series Music – A Sequence of Ten Cloud Photographs, is the first intentional set of abstract photographs. Created in 1922, this started twelve years of Stieglitz taking hundreds of cloud photographs, which he ended up titling Equivalents.
The traditional art history idea is that abstraction represents fundamental break with the old model of the perspectival picture, with its metaphor of a window onto a world. However, this ignores how the early abstractionists like Kandinsky, Malevich and Mondrian who cancelled any resemblance to reality, also affirmed an ontology of the real; even as they rejected painting as a picture of the epiphenomenal world, they insisted on painting as an analogue of a noumenal world: appearance was sacrificed at the altar of transcendence.