For about a century, contemporary physics has been facing an enigma that it summarizes in an apparently innocuous but actually fundamental question:
"What is the energy density contained in the empty regions of the universe?"
It condenses into a few words and a question mark the bewilderment born from the contradictory answers provided by two established theoretical approaches: the theory of gravitation and quantum field theory.
For the former, there is practically nothing or very little in empty zones; to be convinced of this:
The density of perceptible matter in intergalactic space (between galaxies) is about 0.2 protons per cubic meter (10-30 g/cm3).
In interstellar space (between stars), it is about one million atoms per cubic meter (10-21 g/cm3).
The best laboratories on Earth know how to create ultra-high vacuums reaching a value of 10-13 g/cm3.
Concomitantly with these measurements, it escapes no one that empty regions constitute—by far—the overwhelming majority of the universe's volume.
This observation fuels the idea, now considered iconoclastic or heretical, that material particles are only the tip of an invisible energy iceberg.
This is what the estimates from the second approach (quantum field theory) seem to suggest, ... despite all the renormalization efforts made to reduce the gap separating it from the relativistic vision.
I will not embark on yet another description of this famous experiment conducted in 1801, and I will simply recall that it is perfectly understood within the framework of wave optics theory thanks to the concept of interference; these being sometimes constructive and sometimes destructive.
Quantum physics assigns particles a probability of presence and the concept of an orbital. This is an indirect consequence of the Heisenberg uncertainty principle regarding the pair (spatial position, spatial velocity).
Is there a common thread linking the physical information contained in the three examples? This is the question.
The two theoretical pillars of contemporary physics seem globally and largely correct, each within its own domain of validity.
Could it be, then, that these two theories are perhaps not measuring exactly the same energies?
Indeed, there are multiple types of energy in physics: kinetic, thermal, potential, etc.
The theory of gravitation estimates, observes, and measures visible energies often linked to material manifestations; quantum field theory estimates oscillation energies that are ultimately and generally invisible.
If two great families of energy coexist, the visible and the invisible, then searching for errors in theoretical models is pointless; it becomes a waste of time.
It is better, then, to start from a physical principle that admits the existence of these two types of energy and to search for mathematical tools that allow for the transmutation of one type into the other.
Complex numbers, quaternions, or even octonions have an analogous formal structure. They all have a real part and an imaginary part. Their respective multiplication tables all share the same remarkable property: the product of one imaginary element by another provides a new element whose non-imaginary part is not necessarily zero.
I see this as an invitation to use these numbers as tools potentially capable of bridging the gap between what is imaginary (invisible) and what is not (visible).