Eight out of every 10 adults with acute low back pain get better in one to two weeks. The rest will get better slowly over a month to six weeks or develop chronic pain that results in disability.
There's no sure fire way to predict who will recover and who won't. Researchers are actively investigating this idea. It's clear that fear and avoidance of movement will reduce or delay recovery.
General back care guidelines support the idea that patients with low back pain should rest for a day or two but then slowly resume all activities. In most cases of acute back pain the old saying "motion is lotion" is quite true.
There may be no way to convince your brother. He may have to live through the experience and find out for himself. As much as possible, encourage him to keep moving.