Musculoskeletal strain or degenerative disc disease: Given the patient's age and the nature of the pain (mid back pain radiating to lower back), musculoskeletal issues are common and likely. The absence of systemic symptoms or significant urinary findings supports this diagnosis.

Kidney stones: Although there's no evidence of white blood cells or nitrates, the presence of minor blood in urine (hematuria) could suggest kidney stones, especially if the stones are causing irritation or minor trauma to the urinary tract.
Urinary tract infection (UTI) without typical symptoms: In elderly patients, UTIs can present atypically, without the usual symptoms of dysuria, frequency, or urgency. The minor blood in urine could be a clue, even in the absence of white blood cells or nitrates.
Pyelonephritis: An infection of the kidney, which could cause back pain and hematuria. The absence of white blood cells in the urine does not rule out this diagnosis, especially in an elderly patient whose immune response might be blunted.

Renal cell carcinoma or other urinary tract malignancies: Hematuria, even minor, in an elderly patient warrants consideration of malignancy. These conditions can present with back pain and hematuria.
Aortic aneurysm or dissection: Although less likely, given the lack of other symptoms such as severe abdominal pain or hypotension, an aortic aneurysm or dissection can cause back pain and, if it involves the renal arteries, could lead to hematuria.
Pulmonary embolism: While the presentation is not typical, pulmonary embolism can cause back pain and, in rare cases, hematuria if there is associated renal vein thrombosis.

Spinal metastasis: Cancer that has spread to the spine can cause back pain. While less likely without a known primary cancer, it's a possibility, especially in an elderly patient.
Paget's disease of bone: A condition that can cause bone pain, including back pain, and potentially hematuria if there's associated renal involvement due to hypercalcemia or other mechanisms.
Sickle cell disease crisis: Although rare in an 80-year-old, if the patient has sickle cell disease, a crisis could cause back pain and potentially hematuria due to sickling in the kidneys.