Final answer:
The patient's symptoms of sharp, tearing pain radiating from the shoulder blades to the back, along with a significant blood pressure difference between arms, most likely indicate an aortic dissection, which requires immediate medical attention.
Step-by-step explanation:
The condition you would most likely suspect in a 49-year-old patient presenting with intense, sharp, tearing pain between the shoulder blades radiating to the lower back, with onset while eating and with a significant blood pressure differential between arms, is an aortic dissection. This condition occurs when there is a tear in the inner layer of the aorta, causing blood to split the layers of the artery wall. This can lead to aortic rupture or decreased blood flow to organs. The symptoms described, especially the blood pressure discrepancy and the nature of the pain, are classic for this condition, though it should be distinguished from an acute myocardial infarction (heart attack), which generally involves chest pains (angina) and could also radiate to the back. However, the specific pattern of pain and the blood pressure difference between arms is more indicative of an aortic dissection. Immediate medical assessment using imaging and prompt treatment are critical in this scenario.