merely a mathematical device (or trick) to calculate answers about real space-time.
A second feature that we believe must be part of any ultimate theory is EinsteinΓÇÖs idea that the gravitational field is represented by curved space-time: particles try to follow the nearest thing to a straight path in a curved space, but because space-time is not flat their paths appear to be bent, as if by a gravitational field. When we apply FeynmanΓÇÖs sum over histories to EinsteinΓÇÖs view of gravity, the analogue of the history of a particle is now a complete curved space-time that represents the history of the whole universe. To avoid the technical difficulties in actually performing the sum over histories, these curved space-times must be taken to be Euclidean. That is, time is imaginary and is indistinguishable from directions in space.
