In a large slow cooker, combine the ham bone, split peas, celery, onion and thyme sprigs. Add the water, cover and cook on high for 7 hours, stirring occasionally.
Transfer the ham bone to a bowl and cover. Discard the thyme sprigs and onion. Add the carrots to the soup. Cover and cook on high, stirring occasionally, until the carrots are tender and the soup is thickened, about 5 hours longer.
Remove the meat from the ham bone and cut it into bite-size pieces. Stir the meat into the soup and serve.
The soup can be refrigerated for up to 3 days. Reheat gently.