Question
what would happen if i grew, say, a carrot in a 4 inch deep container?

Answer
Hi Michael,
Thank you for your question.  What do YOU think would happen?  Using common sense and looking at the average length of carrots sold at the grocery store, one should be able to reason that the root would bend and become misshapen if it were to hit an obstacle at 4 inches.  There are varieties such as Tonda di Parigi and Dutch varieties of ball-shaped carrots which are no longer than a couple inches and more like a golf ball,that can be grown in containers and probably would not be adversely affected by a barrier at 4 inches.  I hope this helps.

Tom