Q: What causes young tomatoes to get a black bottom that turns to rot?
A: Blossom end rot is caused by lack of calcium in the tomato sap nearby when the small fruit is just starting out.
Applying calcium (lime), egg shells or gypsum to the soil doesn’t help much. Calcium sprayed on the leaves doesn’t work either because calcium can’t move into the sap that way.
The real cause of blossom end rot is inconsistent watering, and perhaps over-fertilizing. Too much fertilizer causes lots of vine growth, which robs calcium from the fruit. Mulch your plants and keep the soil moist (but not soggy) to keep blossom end rot at bay.