Making sense of Avengers Endgame’s time travel

In the film, the Avengers use the quantum realm to travel through time, thus creating universes parallel to the ones they came from if not for their own presence in the past.

With a little imagination, it can be interpreted as something equivalent to the Hilbert space, a vector space whose elements represent the states of quantum systems.

The evolution in time of a physical system is, according to quantum mechanics, a path in Hilbert space, which can be travelled in either direction.

In fact, the rules of quantum mechanics do not distinguish evolution from or towards the past and do not impose any preferred time direction, which instead emerges from statistical aspects in classical physics.

The fact that an object made small by Pym particles becomes subject to quantum mechanics, and that there is no fundamental arrow of time, could be a plausible hypothesis to justify the Avengers’ time travel, along with the well-known many-worlds interpretation.

One can imagine dialogues that appear at least indistinguishable from real science, in where Tony asks Friday to construct a closed topology in Hilbert space and calculate its eigenstates, for instance.

The concept of time travel as a path on a loop was instead intuitively expressed by a path on a Möbius strip.