If two pennies are not identical, then what about two atoms of hydrogen?
This is actually a really cool and subtle question.
As you point out, two pennies are almost certainly not quite the same - they'll have slightly different weights and shapes. Even if they were made identical, handling would corrode each one differently and the two pennies would ultimately have characteristics that make them different.
Two hydrogen atoms, however, are, we are quite sure, identical. That is to say, if we take a proton and an electron and put them together in the most stable way, we get what's called a hydrogen atom. We can make "heavy hydrogen" (also called deuterium) by tossing in an extra neutron, and we can "excite" hydrogen in various ways by giving the electron some energy, but if by "hydrogen" we mean the lowest energy combination of one electron and one proton, then all hydrogen atoms are identical.
You might find this an amazing claim, but in various situations in physics and chemistry you have to count up all the ways things can happen, and there are huge differences if atoms are exactly the same or just similar.
For example, putting three hydrogen atoms in a row happens just one way if you can't tell the hydrogen atoms apart. If each is a little different - say hydrogen A, hydrogen B, and hydrogen C, then we have six ways to arrange them: three choices for the first hydrogen (A, B, or C), two for the second, and just one possibility for the last one. When you do the math, you always get the wrong answer if you assume that there is any possible way to tell one hydrogen atom from another.
How do we explain this? Ultimately, we don't really know how to. All we can do is describe it in a self-consistent manner. It's really quite amazing that, at its most fundamental level, our universe seems to be made of just a handful of absolutely identical things (all protons and electons are the same), stuck together in all sorts of wonderful ways to make everything that we see around us.
Dr. Knowledge is written by physicists Stephen Reucroft and John Swain, both of Northeastern University. E-mail questions to drknowledge@globe.com.
