The somewhat unsatisfying answer to “why does particle decay happen? is”because it can”. On a quantum level, everything that isn’t literally impossible has some probability of happening. If you wait long enough, it will happen.
There’s a huge range of how long “long enough” is, depending on the energies of the system and what types of decay or interaction are physically possible. Some are very stable and decay with low probability. Some are barely keeping it together and decay rapidly. But if it’s possible, it will happen.
Back in the day, someone solved the equation for a particle in a box and found that there’s a little bit of the wave function outside the box. That means if you wait long enough, the particle will somehow be outside the box even though it doesn’t have enough energy to go over the side. Turns out this is quantum tunneling and it happens. Basically any time you have a barrier that isn’t infinite, something that can’t get over the barrier will eventually go *through* it. So you can’t keep things together forever if there’s any way they could decay.
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