A form of programmed cell death induced by external or internal signals that trigger the activity of proteolytic caspases, whose actions dismantle a cardiac muscle cell and result in its death. Cardiac muscle cells are striated muscle cells that are responsible for heart contraction. [ http://purl.obolibrary.org/obo/CL_0000746 GOC:mtg_apoptosis GOC:tb GOC:dph ]