In an harmonic oscillator (an ideal perfect spring with an ideal punctual mass) the energies are (2n+1)ħ/2*ω. They are all multiples of the minimal value for this oscillator. Note that it is a different set of values for each oscillator.
Each of these energies is associated with a wavefunction with a well defined energy. Combining all these wavefunctions you can represent any wavefunction. (The technical term is "orthonormal base", or simply "base".) This is easy to prove. More details in https://en.wikipedia.org/wiki/Quantum_harmonic_oscillator
So if you try to put the oscillator in a state that is not a wavefunction with a well defined energy, the state can be represented as a linear combination of the wavefunction with a well defined energy, and it will evolve following the laws of QM. It will not get transformed to dark energy or dark matter or get lost by damping.
If you later make measure the energy of the harmonic oscillator, the arbitrary wavefunction will colapse to a wavefunction with a well defined energy, and the probabilities are easy to calculate knowing how the initial state was decomposed in wavefunction with a well defined energy. If you measure the position or speed, the calculation is similar but there are a few more technical details.
In a more realistic system like an Hydrogen atoms, the energies are not multiples of a minimal value, the energies are like -E0/n^2. The corresponding wavefunctions are a base anyway, so any initial state can be decomposed in wavefunction with a well defined energy (that sometimes are calles "orbitals", but sometimes more general states are called "orbitals"). So there is no a fundamental frequency, there is no a minimal energy that is the divisor of all the energies, there is no dark energy.
In atoms with more electrons the calculations are more complicated, there is no nice formula for the energies, but is anyway possible to decompose any initial state without using dark energy.
1. If you squint, the inflation model is something in this spirit. The "inflaton" field corresponds to the harmonic oscillator like variable that ismovingunder a potential, and causing space to expand.
2. The quantization of frequencies for a harmonic oscillator (or a particle in a box) comes from spatial bounds on it's profile -- through some potential function. The quanta are separated by inverse of the region size (like aliasing effects a la Fourier). If we're imagining a field spread all throughout space then the "harmonics" are very closely spaced enough to be considered a continuous spectrum, sort of.
3. All that was just quantum mechanics. A more appropriate framework to have this conversation is quantum field theory (and not just in flat spacetime, but curved spacetime). In that context, quanta refer to number of inflaton particles at a specific frequency, and that goes in a direction different from what we're interested in. So that was just a paranthetical aside.
4. As far as we can tell from observations space hasn't been globally oscillating. So it's more like an overdamped oscillator (with a lot of "friction") than an underdamped one -- see "slow roll inflation". (For examples of where space was locally affected by underdamped oscillations, see baryonic acoustic oscillations).
Beyond just a few technical nuggets, what I hope to have conveyed is that the way to research these things is to take every word/facet seriously and try to operationalize it in an appropriate framework (which is very hard) and verify whether it matches our experience of reality.
Of course your explanation is much more scientific than mine, which is just a hunch.
Such 'resolution' increase of the universe would explain nicely its expansion.
I wonder if the creation of wormwholes that would allow travelling to distant systems in human lifetimes would simply be the opposite effect of damping of this frequence of our universe. By reversing the damping, the "resolution" of the universe may decrease and then moving from one place to the other would require a lot less time.
Also, could gravity be a change of this frequency by mass?
So, if we interpret all matter to be different expressions of a fundamental frequency, it means us, the observers are also made up of the same, and to observe you would be basically sampling reality. Even if you consider measurement instruments to be an observer, they also sample other things that are made up of the same.
Then maybe there's a fundamental limit to what we can sample, hence observe. And that could explain why we only observe harmonics of the s orbital.
Here are some statements of my own, typed quickly on a phone before I head to work:
-Electrons do not in general have quantized energy; only bound electrons have a discrete energy spectrum
-Electrons do not necessarily have a single energy; although energy eigenstates form a basis that can describe all states, very often the electron won't be in a pure eigenstate
-Single electron models are simplifications; in general, atoms will have multielectron states that are very difficult to write down or reason about; it's deep and non-obvious why single electron models do so well at describing behavior of multielectron wavefunctions
Is there anything at all in the whole of physics that isn't, at some point, shoehorned in the "mass on a spring" framework </sarcasm>
No matter how ugly an expression you have for force as a function of distance, if you do the Taylor expansion you inevitably get a constant force term (often zero) and a "mass on a spring" term.
If this were the case, we could think of black holes as nodes on this wave.