How do you make a submarine out of a 2 liter bottle that floats sinks then comes back to the surface when it is put into water without touching it?

The trick is to use Alka-Selter tablets and something to weight it down enough to ensure that the bottle will sink. It's an old trick used by submarine models I had when I was a kid, long before I served onboard real submarines.

Try this:

Use a length of copper tubing and duct-tape it to one side of the bottle as a ballast weight. Punch holes (nail size should be good enough) in the side where the ballast weight is. You'll need to leave the cap off or the water won't flow through the holes in the bottom.

To get it to rise again, you'll need several Alka-Selter tablets along with a surgical or cleaning glove, or alternatively, a long balloon. You'll have to break the tablets (don't crush them) to make them small enough to get through the neck of the bottle.

A balloon is a better choice. Put the tablets into the empty balloon, and then use a plastic tube (or something else) to ensure that the mouth of the balloon stays wide open. Put the balloon with the tablets into the bottle so that the mouth goes in first.

If you do it right, when you put the bottle in the water, the ballast weight should allow the water to come through the holes in bottom and the bottle neck. Eventually as it sinks, the water will enter the mouth of the balloon, and hit the Alka-Seltzer tablets. The gas from the tablets will fill the balloon and it should force it against the bottle neck and keep water from coming in. The gas should also force the water out of the holes in the bottom and float it to the surface again.

You can also try keeping the cap on and putting a hole in the opposite side of the bottle from the weight to let the air out as it sinks, but remember that when the balloon inflates it needs to close the whichever hole you use.

You might have to experiment with the right amount of weight and tablets, but you get the idea.