In the last few years of his life, Albert Einstein tried to find a connection between quantum mechanics and classical mechanics. The mathematics behind this effort are complex, to say the least. But thinking conceptually, with maybe a little bit of science, we can use our imagination to explore this connection.
All objects are thought to have a wave nature, in addition to their physical form. A French scientist by the name of de Broglie theorized that the wave nature is inversely proportional to an object’s mass. For electrons and atoms, the wave function is transparent. For macroscopic objects such as planets, the wavefunction would be astonishingly small. Note that for people fluent in the language of physics, De Broglie’s relation between the phase and group velocities of a matter wave may be derived from first principles by using the wave equation and the Minkowski metric.
Stepping outside of time, we can see the orbit of the Earth as a set of positions it could occupy over the course of a year. A wave function is thought to have a spatial extent, but if we allow it to have a temporal extent as well, an orbit could simply be a coherent state. The actual planet itself could be a collapsed wavefunction, or decoherent state. The ideal that the planet is definitely located in a certain place in spacetime is simply a result of the fact that we ourselves do not exist in a coherent state with the planet, and therefore we perceive the orbit as a time-ordered sequence instead of a multiplicity (i.e. quantum state).
Reverting to classical physics, we can say the following.
The total energy of a mechanical system can be expressed as its Hamiltonian, which its combined kinetic and potential energy. One way to express the conservation of energy is to say that a system will evolve (i.e. generate dynamics) only along a level set of its Hamiltonian. This means that if the system has a certain initial energy (combined potential and kinetic) the system’s orbit is given by a plane passing through the Hamiltonian (total energy) function. This is also a simple statement for an isolated classical system: Energy is able to change form between kinetic and potential however the sum of the two is always conserved.
The curve generated by the Hamilton function in this specific plane is like an orbit. It is possible, therefore to interpret this orbit as a superposition of possible states, if we are allowed to “step outside” of the idea of time.
So what would our planet look like if the superposition was coherent?