How Our Reality May Be a Sum of All Possible Realities - Quanta Magazine

The gift shop there even sells a coffee mug displaying an equation that can be used to calculate the path integral’s key ingredient: the action of the known quantum fields.

Practitioners of this “lattice” quantum field theory approach can use the path integral to calculate properties of protons and other particles that feel the strong force, overcoming rickety mathematics to get solid answers that match experiments.

The British physicist Paul Dirac, left, rejiggered quantum mechanics in 1933 in a way that considers the whole history, or path, of a particle, rather than its moment-to-moment evolution.

Einstein’s equations allow for such exotic shapes, but forbids changes that would lead to them; rips or mergers would violate causality and raise time travel paradoxes.

Stephen Hawking, for instance, championed a path integral that accommodates rips, wormholes, doughnuts and other wild “topological” changes between shapes of space.

Hawking used this timeless, “Euclidean” path integral to argue that time began at the Big Bang and to count the space-time building blocks inside a black hole.