Ahh, time. Humans have grappled with time for… a long time. This is actually a really hard question—for very philosophical reasons.
When you think about it, for most of human history, the very concept of “age” really described large-scale, molecular processes. Seasons change. Plants grow. Cells replicate. People die. Food spoils.
Our traditional notions of “oldness” just don’t well too well when we start looking at smaller scale.
When you start getting down into some of the smallest building blocks of matter, ideas like “old” start to fall apart. Atoms don’t come stamped with a born-on dates. And atoms are not fundamental particles—they can be created and destroyed.
The 5th grade science-class answer is something like, “the atoms were created when whatever precursor stars died and created the heavier elements which became the Earth.”
The reality is much more complicated. How do you even determine an atom’s age? That’s really hard. I’ll use a few examples to suggest why.
Thorium-232 is present in the Earth, and has a half-life of about 14.5 billion years. It decays into radon. Is the radon atom “new” or did it just change form? We might think no. But radon atoms “can’t tell” the difference.
So, there’s a fundamental philosophical issue here about identity of a collection of subatomic particles.
Nitrogen atoms in the atmosphere can collide with a neutron, creating Carbon-14. Some of this carbon-14 enters the carbon cycle, and eventually decays into stable carbon-12. And that’s the basis for radiocarbon dating. But we still don’t know the age of any specific carbon-14 atom. We just know the statistical rate at which a large mass of carbon-14 atoms will decay. So, based upon certain assumptions, we can determine the age of carbon-containing material if it’s not too old. But… that doesn’t actually tell us the age of the “new” carbon-14 individual atoms.
… and even then, suppose there were some carbon-14 atoms created long ago during a star collapse or any other source—it is impossible to tell which specific carbon-14 atoms were created where. Our ability to obtain this information is constrained. The idea that an atom’s age is “only a number” doesn’t apply—you can’t find that number anywhere.
Then, the simplest atom is simply composed of a proton and an electron. Whenever these two “free” particles combine, you have a new atom. This happens often enough, depending on you want to do some chemical accounting.
In short, when you start looking at things at very small scale, things start to get a little weird. And when you zoom in even further… the very idea of time starts to get wonky too.
How so? A muon is a heavy subatomic particle (about 1/10 the mass of a proton), created when a cosmic ray strikes the atmosphere at around 10 km in altitude. Then, a muon screams away at about 98% the speed of light.
The average life-span of a “slow” muon is about 2.2 microseconds. In 2.2 microseconds, a muon should decay long before it can span the 10 km to the ground. But a lot of them don’t decay! In fact, about 1 muon is hitting every square centimeter of the Earth all the time—and it penetrates deeply into the Earth’s rock.
That should be impossible. Yet, we see it.
Why? Muons are traveling at such high speeds that, according to the theory of relatively, traveling at 98% of the speed of light causes them to “age more slowly”. From the average muon’s own perspective, it only lives about 2.2 microseconds. But from our sloth-y viewpoint, a muon from a cosmic ray collision—again, from our perspective—appears to live a geriatric 7.8 microseconds.
Whew! See how weird things can get? The very concept of time starts to get pretty wonky.