Actually atoms (or nuclei, etc) don't strictly "go on forever" - there is just a very low probability that a particle in an isolated (or for practical purposes, isolated) atom or molecule will escape the energy well, in the absence of perturbations such as applied electromagnetic fields.
To give a concrete example, the half life before an alpha particle is expected to escape the nucleus of a uranium atom is about 4.5 billion years, yet the solution of the wave equation for the nucleus shows that the natural frequency of the particle in the nucleus is on the order of 1e22 hertz. But to penetrate the potential barrier and escape involves a decaying exponential that's so minuscule that an escape event rarely happens in spite of the seemingly stupefying number of "cycles" the particle will make in all that time.
It is remarkable that the laws of physics are structurally stable enough for so many "cycles" to repeat without the physical constants "drifting"... don't ask me why that is!
Incidentally, electrons don't really have a well defined trajectory due to Heisenberg's inequalities. You can't ever know the position and momentum simultaneously accurately enough to define one, and what is worse, you can't even distinguish identical particles since to do so requires a well defined trajectory. All that remains is the joint wave function, or state vector, for the electrons and other particles making up an atomic system such as an "isolated" atom or molecule.
Actually, despite the fact that particles are indistinguishable, the spin does determine how they interact. Spin 1 particles like photons obey Bose-Einstein statistics, and any exchange of a a pair of such particles leaves the state unchanged, whereas electrons with spin 1/2 obey Fermi statistics; swapping any two negates the wave function, which implies that no two are ever in the same state. It would require a long digression about Clifford algebras and the Dirac equation to even really begin to justify that, but it's an observed reality. |
