Changing time with speed and diffusion fixed shows how drift and diffusion both use the same clock. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
One second moves the mean two metres
Hold drift speed at 2 metres per second and diffusion at 2 square metres per second. At time 1 second, the mean position is 2 metres and diffusive spread is 4 square metres.
2⋅1=2
Two seconds doubles the mean and spread ledgers
At time 2 seconds, the mean becomes 4 metres and the spread ledger becomes 8 square metres.
2⋅2⋅2=8
Three seconds reaches the original audit time
At time 3 seconds, the checked mean is 6 metres and the checked spread is 12 square metres. The model is a ledger, not a random sample path.