Concerning Robert Nozick's Tomato Juice

Robert Nozick, critiquing Locke's argument that one gets ownership of unproduced resources by mixing your labor with them, wrote:

"If I own a can of tomato juice and spill it in the sea so that its molecules … mingle evenly throughout the sea, do I thereby come to own the sea, or have I foolishly dissipated my tomato juice?"

It occurred to me to wonder how certain it was that if I did something with the ocean, swam in it or desalinated some of it for drinking water, I would be disturbing some of Nozick's tomato juice. So I did the arithmetic:

The volume of the ocean is 1.3x10^18 cubic meters. Tomato juice is mostly water, with a molecular weight of 18, so a can of tomato juice contains about ten moles of soup, 6x10^24 molecules, mostly water. If the juice is evenly spread through the ocean it should have about 5,000,000 molecules of Nozick’s tomato juice per cubic meter or five per cubic centimeter, making it almost certain that if I do anything in the ocean I disturb at least a few of them.

The ocean is very large. But molecules are very very small.