Smeared gas


This page is dedicated to research on the physical properties of ultra-diluted gas. We propose a new physical model describing such gas and check its consequence. This model considers account the quantum mechanical effects occurring at the level of individual gas particles. It turns out that such gas will have properties different from the ones predicted by the classical theories referring to the so-called ideal gas. One of the most interesting predictions is that such gas can be almost entirely transparent to light and does not react with other physical objects. At the same time, it retains its mass and therefore interacts gravitationally with other objects. Such properties make it an ideal candidate to be a component of Dark matter.

Below you will find a popular science description. If you are an experienced reader, you may refer directly to the papers.

Gas, quantized

What are the differences between this model and the classical ideal gas model? The ideal gas model assumes that individual particles (atoms or molecules) are independent of each other and look like small “balls”. The balls are in a continuous motion and very often bounce off one another, transferring energy and momentum to one another. Energies and momenta manifest statistically as temperature and pressure etc. In the new model, we have proposed that the particles should be modeled as independent wave functions, subject to the Schrödinger equation. So the particles look more like “clouds” than balls. In addition, these clouds are non-local objects, i.e., they simultaneously “occupy” all space and overlap each other. It is a bit unintuitive, but that is what quantum mechanics is like. The solution of the Schrödinger equation for a free particle tells us that such a cloud becomes more and more smeared over time. Namely, it looks as if it occupied an increasingly larger area. Still, at the same time, the likelihood of any reaction with it occurring in particular places within this area decreased. It is not surprising then that we have called this smeared gas model.

I can’t see

The 300 years old Beer-Lambert law classically describes an ideal gas cloud’s transparency (scientific name: transmittance). In short: the more particles there are, the more light each absorbs, and the longer the path of light in the cloud, the less transparent the gas cloud is. You can check this by looking, for example, at a storm cloud or smoke coming out of a chimney. In the article, we demonstrate that the transparency of the smeared gas depends not only on these apparent parameters. It turns out that it also depends on the diameter of the detector we use (e.g., eye, binoculars, telescope, etc.). The smaller detector we use, the more transparent smeared gas becomes! Moreover, the transmittance increases the more rarely the gas particles interact with anything. Namely, the less often a particle absorbs a photon or collides with another particle, the more free time it has for spontaneous spread (of the wave function). And it is increasing particles’ spread that increases the gas transmittance. However, this phenomenon is not the mere result of particles (or probabilities) escaping somewhere outside the cloud. This paper shows that transmittance may increase even in the closed (conserved mass) system.

Where is it?

We can’t find smeared gas here on Earth. The atmosphere is too dense, and there is too much matter. Gravitation is too strong, and the sunlight is too bright. But we have checked that appropriate conditions for spontaneous smearing of particles may exist in deep space, even inside galaxies. We have checked this for atomic hydrogen gas, respecting its density and the electromagnetic radiation of the galactic and extragalactic backgrounds (do not confuse it with CMB). Hydrogen gas is important because it’s considered to be the most abundant component of interstellar matter.

Experiments, experiments, experiments!

A good physical theory should be falsifiable, and this one is. We proposed several experiments that can exclude or follow its predictions. Even more, we conducted one such experiment. Scientific Reports published its results. It involved testing the difference in transmittance measured simultaneously using two detectors with different diameters. In a relatively large vacuum chamber, we used an infrared laser shining through water vapor under very low pressure. As for experimental physics, this experiment is relatively inexpensive and straightforward. It costs as much as a mid-range car and lasts no longer than several weeks. We are looking forward to more laboratories that will undertake such research.

Deep impact

Why is this interesting? Undoubtedly, ultra-diluted gas is the most abundant form of matter in our Universe – at least in terms of volume but maybe also in terms of mass. The correct understanding of its behavior is critical for all cosmological models, many astrophysical theories, and most astronomical measurements. For example:

  • The widely accepted ΛCDM cosmology, among others, relies on the Planck/BAO measurements of cosmological parameters. One of them is the optical depth τ. This particular parameter is constrained using classic transmittance models. It seems that our transmittance model may be more appropriate, which would result in a different value of τAs all (six) major ΛCDM parameters depend on each other, adjusting τ may change others. E.g., as a consequence, it may release the tension on the Hubble constant. It will help us understand better where our Universe and we come from.
  • The above is an important example of a transmittance model being a part of the radiation transfer equation. The radiation transfer equation is an essential ingredient for countless physical models. The proper understanding of energy transfer can’t be overestimated. The following astrophysical phenomena depend on this equation, to name a few: galaxy formation, star formation, planetary systems formation, or Sunyaev-Zeldovich effect. E.g., the last one is a tool for measuring Universe expansion and Dark Energy impact.
  • Predictions of the model surprisingly resemble Dark Matter requirements. There are dozens of DM experiments, millions of dollars spent, and hundreds of physicists involved. Current estimates by astrophysicists predict that there is approximately 5 times more “invisible” matter in space than the “ordinary” one. Perhaps it is the smeared gas that makes up the missing 85% of the mass of the Universe?
  • Quantitative spectroscopy is one of the primary astronomical tools. The model shows how the size of the instrument affects a measurement outcome interpretation on scattering medium density. If the theory is valid, astronomers may need to reinterpret some observations, e.g., regarding gas clouds’ mass, composition, etc. This is bold, but the transmittance equation underlies so many models.
  • There is an entirely new prediction that background radiation intensity may directly affect ultra-diluted gas density. If not only gravity affects density, many theories on cosmic structure formations need to be reevaluated.
  • The model developed requires the full non-locality of wave functions. Potential experimental confirmation of the model will be an important voice in the discussion about the interpretations of quantum mechanics. In particular, we will exclude pilot wave type interpretations because they contradict the predictions of the rising transmittance of the smeared gas. We discuss it in this paper, and there is also a video presentation.

The next steps

What’s next? We don’t stop. We are preparing the new experiment. We work on the smeared gas transmittance equation taking into account detectors of sizes comparable to the wavelength of incident light. We investigate astrophysical consequences of the model.


This is an independent project. We have neither grant nor general funding from any government, research agency, or commercial. Our curiosity and a little help from our friends drive this research. You also may support or join us if you wish.

Stay in touch

On this website, you will find articles describing the theory, information about the conducted experiment, the extra experiment data, answers to frequently asked questions, or our gallery. See the Quantum 2020 conference short video presentation on the consequences of the model for quantum mechanics interpretations. The Mathematica’s notebook with interactive transmittance calculator and the plot tool is available for download

See on-line interactive transmittance demo calculator.

Any questions? Write to us: jakub [at]