There has been a weather prediction problem called the Butterfly Effect that has bothered some people. Some claim that a butterfly flapping its wings in China will affect the weather in America next week. It is similar to the Classic Greek paradox of the rabbit never getting to his destination because he must first go halfway, but before that is accomplished he must go halfway, and so on until the halfway movement is so infinitesimally small that he can’t move at all. It is obviously preposterous, but all the same some people’s minds get locked into it and are permanently frozen. I happened to attend the funeral of a philosophy professor at the University of California, Berkeley, a couple of years ago and during the eulogy one professor talked for over a minute about the rabbit problem. Is that evidence that intelligent people still discuss these things? Or was it a joke? I don’t know. These are silly problems which natural reality solves continuously, or we wouldn’t be here, and in case you haven’t noticed, we are here, although these same professors will probably challenge that too.
The more empirically inclined have shown that there is a limit to how small things can get, and it’s called Planck’s limit. What it states and has been demonstrated, in labs as well as words, is that there is a granularity to our physical world and when one observes below the tiniest bit of things there is random chaos. The Planck constant (denoted h, also called Planck’s constant) is 6.62606957(29)×10−34. Observe that number has been accurately measured to nine significant figures. That’s like measuring the distance from a particular sub-atomic speck in Los Angeles to a particular sub-atomic speck in New York to an accuracy of within a foot – between two defined points at either end of the foot. The location of this “speck” once you get to its location is between the two precisely postulated points, but the Planck limit is much smaller and that’s where the -34 comes into play. It was 10 followed by 34 zeros smaller, and in our travels from Los Angeles to New York we only used up nine of those zeros, and we still have 25 left to go. Thus we would have to do this same measurement three more times, going increasingly smaller, using the previous end points to come to the Planck limit. It is very, very, very tiny, but it has been measured.
The point is that beyond this Planck limit things cannot be measured at all, because they are chaotic. Things do well up from this abyss of chaos, but they do so in a random way. Measured physical things beyond this limit can not be known, and so when looking at a single thing, when at any size, it will have some random quality. But, not to despair or even worry, because reality that we know and live with in daily life is made up of things of a scale of +34 zeros up from the Planck limit, and everything smooths out in our daily reality and behaves in exactly the way we expect it to. There are so many Planck operations taking place in the head of a pin that constantly cancel each other out that in billions of years nothing much would change to our level of sensory observation of that pin. Of course tiny things do affect later outcomes, but beyond a certain level they are random and are canceled out by other forces.
Rabbits and butterflies behave with their 10−34. Planck effects canceling out.