Interesting Question on Ants

One minute at most. Imagine that ants "go through" each other. Whether the ants bounce off each other or walk past each other without changing direction has the same end effect: we have two ants approaching each other, then they meet, then they diverge from each other with that same speed of $1\text{m}/\text{min}$. So just assume that they do not bounce, but instead they keep walking the same direction, so it will take at most $1$ minute before they all fall off the edge.

Judging from the comments, it seems people disagree with the above argument, or have difficulty following/understanding it, so I offer a different interpretation. Say each ant carries a piece of paper with a written number on it. (You may call that piece of paper a baton, think of a relay race.) At the beginning all ants are numbered (from $1$ to $n$), and each ant holds a piece of paper with its own number on it. When two ants meet, they exchange their pieces of paper, and then bounce from each other. Note that while ants change direction when they bounce, the pieces of paper do not change direction. Thus these pieces of paper go with constant speed and direction $1 \text{m}/\text{min}$, so all the pieces of paper would fall off the stick in less than a minute. But, if there are no pieces of paper left on the stick, there are no ants either.

Just a comment on the first approach (when you could think ants pass by each other, instead of bouncing). Imagine that all ants look alike so much that you can't really tell them from each other. So two ants meet and bounce. But how could you tell, if you can't tell which ant is which? Perhaps you thought they bounced, but in reality each continued in its path without changing direction, passing by each other, and you do not know which is the case since these ants look so identical that you can't tell what exactly happened. Say ant A was going to the right towards ant B, and ant B was going to the left towards ant A. They meet and at the next moment you see them diverging from each other but you can't tell which ant is ant A and which ant is ant B. Perhaps the ant that now goes to the left is ant A, perhaps it is ant B. If it is ant A then they must have bounced, but if it is ant B then they must have passed next to each other without changing direction. But, it doesn't matter, since the "end result" is the same: immediately after they meet, we have two ants diverging from each other whether they bounced or they passed by each other. So assume now you have a different problem, in which ants do not bounce, but instead pass by each other (so each ant just keeps going, without changing direction). Clearly in this version of the problem all ants clear the stick in at most one minute. But, if you can't tell ants from each other, then you can't tell the two problems from each other either, so the answer to your original problem is at most a minute.

Since you put forward the name of Einstein in one of the comments, I feel entitled to involve physics in my answer. If the ants are particles, then they bounce from each other. But, if the ants are waves, then they "go through" each other, or pass next to each other. So, does light consist of particles, or waves, was Newton right (with his corpuscular theory of light), or was Huygens right (with his wave theory of light), and how is it that both theories are right?