No two objects are the same. Even a dime, one of billions produced since the Coinage Act of 1792, is not completely identical to any other dime. Of course, comparing one dime to another with our eyes may yield apparent inconsistencies, but we are not just comparing their general shape and composition, we are comparing them down to the atom, quark and string.
The reason why we will be examining dimes, rather than the more traditional snowflake, is because coins are produced under highly controlled conditions and are intended to be identical. Of course, this is true of all coins, but dimes are particularly shiny and cute. Modern American dimes are 91.67% copper and 8.33% nickel, so at least we know that their composition is always consistent, or do we? They may all be 91.67% copper, but what about the decimal place after the 7, or the one after that? We could go on and on until we reach the final decimal place which measures only a single atom of copper. Let’s begin.
We’ll start by calculating how many grams of copper are in a dime.
2.268 * 0.9186 = 2.079 g Cu
Now we divide our copper content by one mole.
2.079 / 63.546 = 0.03272 mol Cu
Then multiply the result by Avogadro’s number.
0.03272 * 6.02 ^ 23 = 27,895,400,042,860,190 atoms of copper in each dime.
Since the U.S. Mint began production, there have been 86,426,821,377 dimes pressed, which is nothing in comparison to the copper atom count in every dime. Given these numbers, it seems unlikely that two of these coins have identical composition, especially since we are ignoring the fluctuation in both the copper to nickel ratio and total number of atoms in the dime.
Every object also experiences different events and conditions from the moment of its creation. Everything is subjected to varying degrees of light, heat and pressure, which makes it more unique. As soon as you touch something you deposit oil, bacteria and flakes of skin onto it, leaving a part of yourself behind.
If we take into account the shape of the coin there is even more room for dissimilarity. Unlike mass, location has no smallest unit of measure because we live in an analogue world. When we measure properties such as length or location, we are using numbers, which are digital, to describe something that cannot be perfectly measured. An atom can be one yoctometer further along on an axis than another atom, or less, because location is not limited by being comprised of physical units. But what if we compare something more basic, like an atom, instead of a dime? At least we can say that each atom of copper in a dime must be the same as the others, can’t we?
For simplicity’s sake, let’s ignore the fact that there’s 29 different copper isotopes and pretend there’s only one type of copper. We have to look at what an atom is made from, then measure those units’ exact count and location. Scientists now say that beyond the quark and gluon, there are strings which are the ultimate building block of matter. The theory is that the frequency with which they vibrate determines all physical properties in our universe. Of course, once we start examining the exact frequency of the vibration, we encounter another analogue property and arrive right back at square one.
It seems unbelievable that of the trillions and quadrillions of physical objects on our planet, no two are equivalent, but, as we learned before, even events that have a statistical possibility may be impossible.
There is always another decimal place.