I just saw a reference to one such argument which was made a few years ago in an article by Avshalom C. Elitzur and Shahar Dolev called “Quantum Phenomena Within a New Theory of Time”. This was published in the 2005 collection Quo Vadis Quantum Mechanics?, Avshalom C. Elitzur, Shahar Dolev, Nancy Kolenda, Eds.
Elitzur and Dolev examine several puzzles over the nature of time in quantum mechanics and are led to the hypothesis that quantum interactions (measurements) themselves are responsible for the creation of spacetime.
A couple of quotes from section 17.10, titled “An Outline of the Spacetime Dynamics Theory”:
Could it be, then, that the two phenomena – time’s passage and wave-function collapse – are not only real, but the latter is the very manifestation of the former? A wave function, after all, is a sum of many equally possible outcomes, while the measurement brings about the realization of one out of them, the others vanishing. Is this not the very difference between future and past? And is collapse not elusive because it creates the elusive ‘now’?
Suppose that there is indeed a ‘now’ front, on the one side of which there are past events, adding up as the ‘now’ progresses, while on its other side there are no events, and hence, according to Mach, not even spacetime. Spacetime thus ‘grows’ into the future as history unfolds.
What role does the wave function play in this creation of new events? The dynamically evolving spacetime allows a radical possibility. Rather than conceiving of some empty spacetime with which the wave function evolves, the reverse may be the case. The wave function evolves beyond the ‘now’, i.e., outside of spacetime, and its ‘collapse’ due to the interaction with other wave functions creates not only the events, but also the spacetime within which they are located in relation to one another. The famous peculiarities of the quantum interaction – nonlocality, the coexistence of mutually exclusive states, backward causation and the inconsistent histories presented in the previous sections, thus become more natural.
Can the reciprocal effects of spacetime and matter – the celebrated lesson of general relativity – thus possible gain a quantum mechanical explanation? Perhaps it is the wave function, we submit, that is more primitive than spacetime, and the spacetime connecting the two events is the product of their interacting wave functions.