Low back pain of musculoskeletal origin (due to prolonged sitting, carrying or moving heavy objects etc.) is not directly associated with caffeine intake, unless you are having concomitant poor sleep or difficulty sleeping, then reducing your caffeine intake (including not only coffee but also soda, tea and chocolate) would actually help you sleep better and therefore in an indirect way help with reducing your back pain. Caffeine may be implied in low back pain of renal (kidney) origin as caffeine is a known diuretic (drives fluids out of the body in the form of urine) and can cause dehydration which in itself may precipitate an episode of renal colic.