Toss together the popcorn and apples in a large mixing bowl.
Combine the granulated sugar, brown sugar, corn syrup and 1/3 cup water in a medium saucepan. Bring the mixture to a boil; when it reaches 240 degrees F, remove the pot from the heat and swirl in the butter. Return the mixture to the heat and when it reaches 300 degrees F, remove from the heat completely. Carefully add the baking soda and salt. The caramel will bubble and spurt, so stir with caution.
Pour the caramel over the popcorn mixture and use a rubber spatula to gently fold it together. The caramel will still be hot, so be careful. Once the popcorn mixture is completely coated and cool enough to work with, lightly coat your hands with butter. Use your greased hands to form popcorn balls about the size of a tennis ball. Transfer to the prepared baking sheet and insert a lollipop stick in the center of each ball. Place the baking sheet in the refrigerator until the caramel is completely set, about 1 hour.