The Theory
The full theory is described in the article. The overview presented below is based on the poster prepared for the Cosmic Controversies 2019 conference.
Background
Dark Matter &
nonlocality
 It is generally believed that Dark Matter can’t be baryonic gas (H, He) or dust because it would be opaque. This is in accordance with the classic BeerLambert law (and it derivatives) that relates gas transmittance to optical path length l, concentration c and molar absorptivity \epsilon(\lambda) only, assuming molecules locality: TR(\lambda)=10^{lc\varepsilon(\lambda) }
 Increasing number of experiments show nonlocal matter properties, e.g. quantum entanglement, BoseEinstein condensate, helium Young’s type doubleslit experiment, etc
Hypothesis
New transmittance model is required
 The classic BeerLambert law is not applicable to interstellar medium
 We should take into account a solution of the Schrödinger equation for a free particle for each gas molecule for ultra diluted gas
 Wavefunctions spreading & detector size affects optical transmittance measurement
Methods
Nonlocality applied for transmittance model
 Model a non relativistic gas molecule as a gaussian wave packet
 A molecule is free between consecutive collisions with either *photon or *molecule: mean free* time \overline{t}
 Molecules’ wavefunctions spread according to the Schrödinger equation for a free particle, it is smeared gas
 Assume a wavelenght dependend cross section \sigma(\lambda) remains constant on spreading, i.e. constant Einstein coefficients
 If a detector area A is smaller than molecule spread, a photon scattering out of detectability tunnel T can’t be observed, probability of possibly observed scattering event reads as:P^{obs}\left ( \overline{t},\lambda \right )=C(\sigma(\lambda), \sigma_A, geometry)\int_T\left  \mathit{\Psi} (\boldsymbol{r}, \overline{t} ) \right ^2dr , where C depends on geometry of actual setup, total crosssection and detector dimensions and efficiency
 Taking N independent molecules, where incident photon may be scattered by any of them, a Markov chain is used for the transmittance equation:TR ( \overline{t},\lambda )=\prod_{n=1}^N\left ( 1P_n^{obs} ( \overline{t},\lambda ) \right )
 Analytical form of the transmittance lower limit may be presented
Results
Measured gas transmittance may raise to 100%
 Transmittance of smeared gas depends also on a detector size and mean free* time \overline{t}

Raising mean free* time \overline{t} leads to raising gas transmittance measured with a small detector:
TR ( \overline{t},\lambda )\geqslant \prod_{n=1}^N\left [ 1 \frac{C(...)}{4} \left ( erf \left( \frac{dist_n\sqrt{A}}{\sqrt2 stdev(\bar{t})} \right) \newline  erf \left( \frac{dist_n+\sqrt{A}}{\sqrt2 stdev(\bar{t})} \right) \right )^2 \right ]
where \Deltainitial position measurement accuracy, mmolecule mass, dist_n distance from \left \langle x_n \right \rangle to tunnel T axis and stdev(\bar{t})=\sqrt{\frac12 \left( \Delta^2+\frac{\hbar^2\bar{t}^2}{m^2\Delta^2} \right)}  Transmittance smaller as detector gets bigger
 Interstellar medium transmittance depends on background radiation intensity
 Calculations confirm intragalactic radiation is so weak thay neutral atomic hydrogen (HI) may form smeared gas clouds
 It is shown, the classic BeerLambert law is the firstorder approximation of the proposed model
Conclusions
Model is falsifiable,
the ideal candidate for Dark matter
 Achieved results interesting for QM measurement & decohorence discussions
 A variety of possible laboratory or orbital experiments for detecting smeared gas are proposed in the paper
 Geocorona may be smeared (H) gas as its observed „density” depends on Earth shadow & Sun activity
 Baryonic (H, He) Dark Matter would be ultra diluted gas, intragalactic radiation is weak enough so clouds of smeared gas may be a component of Dark matter