There are a few frequently asked questions on the proposed theory answered below. This is a less strict approach to explain what is it about.

We propose a quantum mechanical theory that explains why an ultra diluted gas of any kind may become completely translucent. Moreover particles of such gas hardly interact with each other and with other matter objects. We call it smeared gas. Such a gas retains its mass and energy but becomes invisible. Particularly when immersed in space vacuum, far from stars and light. The clue of this theory is to model gas particles as independent wave packets instead of finite size „balls”.

It was shown in the paper how to derive Beer-Lambert law from proposed transmittance equation. Beer-Lambert law is the first order approximation of the proposed model. It’s applicability conditions are outlined in the paper. The first order approximation is the same technique that was used to show that Newtonian gravity law is an approximation of Einstein’s field equations.

Gas cloud transmittance (transparency) depends on many factors: number of gas particles per unit volume, particle mass, particle mean free time, light path length, wavelength dependent cross section and detector size. For small particles, long enough free time and small detector transmittance limit is 100%.

Yes, there are a few dozens equations in the paper. I’d say the 21th is crucial:TR ( \overline{t},\lambda )=\prod_{n=1}^N\left ( 1-P_n^{obs} ( \overline{t},\lambda ) \right ) This is the smeared gas transmittance equation derived with probabilistic model. The first part of the paper leads to this equation while the second studies some of it’s properties.

Schrödinger equation is good enough because we develop a non-relativistic model. We assume low enough energies of gas particles. Extension to higher energies may be a very interesting adventure.

The motivation for this work was to face the macroscopic Dark Matter issue, galactic scales.
1. The presented model is a semi-classical one in a sense that we don’t take into consideration full QM or QFT techniques where we find it not necessary. A model of a light cone (the detectability tunnel) is one of them. We decided to treat light paths classic way because this tunnel is of a macroscopic scale comparing to light wavelengths (length of many Mpc, diameter of meters). We assume amplitudes of paths out of the tunnel cancel each other.
2. The presented model is a generalization of the classic Beer-Lambert law. The B-L law derivation do not take into account light paths out of the volume where an absorbing agent is present. And let us mention that B-L term is a part of radiation transfer equation widely used in astrophysics.
3. Common sense shows that objects out of a classic light path do not overlap (approaching macrosopicaly) light sources. This is a way our model was build: we analyzed how particles’ spread (of particles inside and possibly outside the detectability tunnel) may affect passing light. We may understand this (classic detectability tunnel confinement) simplification in a similar way the geometric optic simplifies wave optics.
This is why we decided to approximate light path with a classical trajectory.
We must agree however than possible further refinements of the proposed model (e.g., when designing a micro scale experiments) may require taking into account light paths out of the detectability tunnel. In such cases higher order terms may become significant. It’s not a case here as we focus on a cosmic scale effects. We didn’t decide to elaborate more on this topic in the paper due to paper length constraints.

Again, this is because of the macroscopic scales considered in the paper. We tried to keep the model as simple as possible.
Gas molecules are modeled as independent wave functions but the classic light path approximation let us use squared wave functions for transmittance calculations. There is no need to calculate probability amplitudes directly from pure wave functions. Although there are relatively simple equations derived in the paper this idea is deeply quantum mechanic. It requires gas molecules wave functions to be non local.

This is a very bold statement raised by one of peer reviewers.
Well, the proposed model takes directly from the simplest Schrödinger equation solution. The free particle solution which yields to spreading wave packets. This is one of the most fundamental physics equations. There are countless experiments confirming predictions of this equation. It was shown [i.e. 10.1103/PhysRevLett.66.2689] that entire atoms may behave quantum way. That’s my favourite helium double slit experiment.
Indeed ideal gas is a corpuscle model. But we propose another gas model and study its properties. Physics is an experimental science. A new theory can’t be rejected on prejudice. It can’t be rejected because current, perfect model is different. It can be falsified with an experiment only. In the paper there are many falsification experiments proposed. And a few observed but unexplained phenomena may be covered by this model.

This is the key question on non-locality of quantum mechanics. Are wave functions real? Are they spread all over Universe? Schrödinger equation says nothing on the maximum spread of a free particle wave packet. There are many different QM interpretations dealing with non locality, hidden variables and so on. They are discussed for many years. No conclusion yet. This theory requires a non-local interpretation.
There is an interesting coincidence of an average galaxy diameter and a „diameter” of hydrogen wavefunction spreading for a free time in the order of magnitude of Universe age. If you plug the hydrogen mass and the age of Universe to the solution of this equation it turns out that standard deviation (a kind of „diameter”) of hydrogen atom probability distribution is more or less 10.000 light years. A typical galaxy size is a few dozens thousands light years. https://hubblesite.org/science/galaxies https://en.wikipedia.org/wiki/Galaxy
Why hydrogen? As far as we know hydrogen is the most abundant component of interstellar gas (ISM).

It doesn’t explain Dark Matter origin. It just shows that smeared gas is a perferct candidate to be Dark Matter or one of Dark Matter components. Smeared gas’ full transparency and retained mass makes it fitting dark matter definition literally.

This is bold question. As a matter of fact we don’t know. What we know is that mass and energy is conserved by a smeared gas cloud. But particles are non local. This is the same type of problem as determining gravitational pull of an electron or atom passing two slit experiment. Maybe it’s a step towards quantum gravity?

We followed ideal gas and Beer-Lambert approach. Gas particles are assumed to be independent entities. A photon scattering event may occur on any of them. Markov chain is a tool to compute probability of photon bypassing all particles along its way towards detector. Bypassing all particles is a necessary condition to reach detector.

Although the proposed theory is valid in all scales the model presented in the paper is simplified and it relates to large scales only. It can’t be applied directly to small scales experiments. It relies on a classic light path approximations. Small scales requires taking into account more fundamental Feynman’s path integral approach. A bit more complicated equations should be derived.

There are many experiments proposed in the paper. We decided to undertake the one with two small detectors of different area measuring transmittance of the same gas cloud in a relatively big vacuum chamber. We expect to measure higher transmittance with the smaller detector.

We hope we’re not. We developed self-checking methodology. There are control runs designed. We use laboratory grade equipment. Experiment is about to finish soon. We’re preparing a full report on that. All data, source code, diagrams and methods will be published along with error estimations. We expect independent researchers to repeat this experiment or undertake one of anothers proposed. This experiment is surpisingly easy and cheap.