Path Integrals on Causal Sets

start position

1

finish position

15

number of steps

1

2

3

4

5

6

7

8

9

10

generate new causal set

This shows a randomly generated causal set. The "start position" and "finish position" denote spacetime locations within the causal set. Specifying the "number of steps" then draws all trajectories within the causal set from the start to the specified final step. To perform a quantum mechanical path integral each trajectory of length

n

is assigned an amplitude (a complex number)

n

a

n-1

b

. Summing these amplitudes for all trajectories from the start to the finish gives the total amplitude for a particle to travel from the start to the finish.