Could the Shape of Randomness Help Explain Why Matter Won?
A proposal for a research conversation about Boltzmann statistics, radiation, matter, antimatter, and the early universe
I want to propose an idea carefully.
I am not saying this is proven.
I am not saying current physics is wrong.
I am not saying I have solved the matter–antimatter problem.
I am saying there may be a connection worth discussing:
Maybe the imbalance between matter and antimatter is not only about a tiny starting difference. Maybe it is also about how randomness distributes itself.
The basic mystery is famous. In the early universe, matter and antimatter should have been created together. When matter and antimatter meet, they annihilate. If the balance had been perfect, almost everything would have disappeared into radiation. But that is not what we observe. We observe galaxies, stars, planets, and ourselves. CERN describes the puzzle as a tiny excess of matter — roughly one extra matter particle per billion antiparticles — surviving after annihilation and becoming everything we see today.
That is already an astonishing idea:
Almost everything cancelled out, and the tiny leftover became the universe we live in.
My question begins there.
When particles collide randomly, the result is not pure disorder. Randomness can create structure. In gases, random motion leads to the Maxwell–Boltzmann distribution: a predictable distribution of speeds with a clear peak and a long tail. OpenStax describes this as the predictable speed distribution of many randomly moving molecules.
That shape interests me.
My first intuition was simple:
max peak = matter?
Maybe the most likely region of the distribution — the peak, the maximum, the place where most events happen — somehow becomes the matter side.
But I know that this cannot be taken literally. Matter and antimatter are not just “slow particles” and “fast particles.” They are particle and antiparticle partners. A proton and antiproton are not different just because of speed. In fact, CERN’s BASE experiment found the proton and antiproton charge-to-mass ratios equal within 16 parts per trillion, which strongly supports the idea that matter and antimatter have matching basic properties under known physics.
So I want to refine the idea.
Maybe the peak is not matter itself.
Maybe the peak is the amplifier.
That means the Boltzmann distribution does not directly choose matter. But if there is even a tiny matter-favoring rule somewhere — a tiny asymmetry in decay, scattering, interaction, or freeze-out — then the shape of the distribution could matter enormously.
Why?
Because most particles and events happen near the peak, not in the far tail. So a tiny asymmetry near the peak could have a much bigger effect than the same asymmetry in a rare part of the distribution.
So the better version of the idea is:
The peak is not matter. The peak is where a tiny matter advantage could become statistically powerful.
This connects to existing physics. Scientists already study the matter–antimatter problem through baryogenesis and leptogenesis. A classic starting point is Sakharov’s 1967 idea that a universe with more matter than antimatter requires certain ingredients: matter-number violation, C/CP violation, and departure from thermal equilibrium. CERN Courier describes current searches around these Sakharov conditions, including CP violation, baryon/lepton-number violation, and out-of-equilibrium physics.
That already sounds close to the direction I am thinking in:
not just particles, but processes; not just symmetry, but symmetry breaking; not just equilibrium, but the moment when equilibrium fails.
CERN’s LHCb experiment recently observed CP violation in a baryon decay. That means a matter particle and its antimatter partner did not behave as perfect mirror images in that decay. The measured asymmetry was about 2.45%, with a significance of 5.2 standard deviations. CERN also notes that the CP violation currently known in the Standard Model is still far too small to explain the cosmic matter excess.
So there is a real direction here:
tiny matter–antimatter differences exist, but we still do not know how the universe amplified them enough.
That is where I want to bring in Boltzmann thinking.
Maybe the question should not only be:
Where did the tiny bias come from?
Maybe we should also ask:
How did the statistical shape of the early universe amplify, preserve, or erase that tiny bias?
The Boltzmann equation is already used in this research. Kolb and Wolfram’s classic paper on baryon-number generation in the early universe used the Boltzmann equation to calculate how an excess of baryons over antibaryons could develop over time. Modern papers also study full Boltzmann equations for leptogenesis, sometimes without assuming kinetic equilibrium, and show that the detailed distribution can change the final asymmetry.
That is important for my idea.
Because I am not only interested in the total number of particles. I am interested in the shape of the distribution — where most events happen, where rare events happen, and how a tiny rule could be amplified depending on where it acts.
There is also research on CP-violating scatterings. Nardi, Racker, and Roulet studied Boltzmann equations including decay and scattering processes and computed CP-violating scattering asymmetries. Baldes and collaborators studied CP-violating scatterings in baryogenesis and found that scatterings can play a dominant role in part of the parameter space.
This is very close to the intuition I am trying to express:
collisions are not just noise. Under the right conditions, collisions may help shape the final imbalance.
Now I want to add another part of the idea: radiation.
When people say matter and antimatter annihilate and leave “only radiation,” the word “only” can be misleading. Radiation is not nothing. Radiation carries energy, momentum, and sometimes subtle correlations. Fermilab describes matter–antimatter annihilation as producing photons or gamma rays, and electron–positron annihilation commonly produces two gamma-ray photons.
So maybe we should not think of annihilation as simple destruction.
Maybe we should think of it as transformation:
matter + antimatter become radiation.
And radiation can also become matter again, if the energy is high enough. Brookhaven reported evidence for the Breit–Wheeler process, where collisions of light can produce matter–antimatter pairs. The DOE describes this as generating matter and antimatter from collisions of real photons.
This does not mean radiation creates matter alone. Normally, radiation creates matter and antimatter together.
But it does suggest a possible recycling picture:
matter + antimatter → radiation → matter + antimatter again
In the early universe, when everything was extremely hot and dense, this kind of transformation loop may have been part of the active system. Particles annihilate into radiation. Radiation produces pairs. Collisions redistribute energy. Expansion cools the system. Eventually some processes stop happening. That stopping is what physicists call freeze-out.
So my extended proposal becomes:
Maybe the early universe was not just a one-time matter-versus-antimatter event. Maybe it was a recycling system: particles, antiparticles, radiation, collisions, pair creation, annihilation, and freeze-out.
In that system, radiation is not the final trash. It is part of the engine.
This also makes me think about black holes. Black-hole radiation is not the same mechanism as matter–antimatter annihilation. Hawking radiation is a quantum effect where black holes emit particles as if they have a temperature. Hawking’s classic 1975 paper showed that quantum mechanical effects cause black holes to emit particles like hot bodies.
But black holes are interesting here for a different reason: information.
The black-hole information problem asks whether information is destroyed or preserved when black holes radiate. Modern work on Hawking radiation, the Page curve, and “islands” suggests that information may be encoded in subtle correlations in the radiation, at least in certain theoretical models.
So maybe radiation should not be treated as “just leftover heat.”
Maybe radiation is a carrier layer.
Maybe in the early universe, radiation carried energy, structure, and possibly correlations through repeated cycles of annihilation and pair creation.
Again, this alone does not explain why matter wins. Radiation normally creates matter and antimatter together. So we still need a tiny asymmetry somewhere. But radiation could be the middle step, and the Boltzmann distribution could be the statistical amplifier.
So the full idea becomes:
random collisions → Boltzmann-shaped distribution → annihilation → radiation → pair creation → tiny asymmetry → freeze-out → leftover matter
This is not a finished theory.
It is a research direction.
The strongest version is:
The universe’s matter excess may not come only from a tiny microscopic asymmetry. It may also depend on where that asymmetry acts inside the statistical distribution of the early universe.
If the tiny asymmetry acts near the peak, where most particles and interactions are, it could become much more important. If it acts only in the tail, it may have much less effect.
That is why the “max peak” still feels important to me.
Not because the peak literally means matter.
But because the peak may be where matter’s tiny advantage becomes visible.
A mechanical analogy
I think this idea could be explored with a simple mechanical model.
Imagine a tabletop device with many small balls. The balls are randomly agitated, collide, and exit at different speeds. Their speed sorts them into different bins, similar to a mechanical Maxwell–Boltzmann demonstrator.
Now use two colors:
White balls = matter
Black balls = antimatter
First, run a control test. The machine is completely color-blind. Same ball size, same weight, same material, same rules. If everything is truly symmetric, the machine should not produce a stable excess of white or black. It may produce random fluctuations, but not a reproducible winner.
That is important. It would show that the distribution shape alone does not magically choose matter.
Then add a tiny controlled bias — a mechanical version of a CP-like asymmetry. For example, a tiny difference in how balls near the peak-speed region are routed or retained.
Then add an annihilation stage, where white and black balls can remove each other in pairs.
The question becomes:
Does a tiny bias near the peak leave a much larger visible excess after many rounds than the same tiny bias in the tail?
If yes, the device would not prove the universe works exactly this way. But it would demonstrate the principle:
random collisions + peaked distribution + tiny asymmetry + annihilation = visible leftover imbalance
That is the core intuition.
Why this idea is interesting
The idea is interesting because it connects several real pieces of physics:
Random collisions create distributions.
Matter and antimatter nearly cancel.
Tiny CP-violating differences exist.
Boltzmann equations are already used in baryogenesis.
Full distributions can matter, not only total particle counts.
Radiation can be produced by annihilation and can later create particle–antiparticle pairs.
Freeze-out can preserve a leftover imbalance.
It also gives a visual way to think about the matter–antimatter problem.
Instead of imagining the early universe as a simple coin toss between matter and antimatter, we can imagine it as a dynamic system:
a sea of collisions, radiation, pair creation, annihilation, and statistical filtering.
In that sea, a tiny asymmetry might not matter equally everywhere. It may matter most where the distribution is densest.
What could be wrong
There are serious challenges.
First, the Maxwell–Boltzmann curve by itself cannot choose matter. A speed distribution is not a matter–antimatter label. Matter and antimatter partners should have the same speed distribution if they have the same mass and are in the same thermal environment.
Second, radiation normally creates matter and antimatter together. So radiation alone cannot explain a net matter excess.
Third, a color-blind mechanical device should not create a stable color excess. If it does, there is probably a hidden bias in the device.
Fourth, large nearby matter–antimatter domains are strongly constrained. Cohen, De Rujula, and Glashow argued that a matter–antimatter patchwork universe would produce annihilation signals at boundaries, including gamma-ray and cosmic microwave background effects, and concluded that a matter–antimatter symmetric universe is empirically excluded unless our matter domain is basically the whole visible universe. CERN Courier also reported in 2026 that diffuse gamma-ray background and cosmic microwave background observations show no evidence for antimatter on large scales and rule out a matter–antimatter symmetric universe in the observable region.
So the proposal should not be:
“The Boltzmann peak is matter.”
The stronger proposal is:
“Boltzmann-shaped collision statistics may amplify a tiny matter-favoring asymmetry, especially if that asymmetry acts near the most populated region of the distribution.”
That is much more careful and much more interesting.
The proposal in one sentence
Maybe matter won not only because there was a tiny microscopic bias, but because the statistical shape of the early universe amplified that bias in the right place, before annihilation and freeze-out locked in the leftover matter.
What I would like to explore next
This idea could be explored in three ways.
First, with a simple simulation: particles are created, annihilate, scatter, and freeze out. The simulation can test whether a tiny bias near the distribution peak produces a larger surviving excess than the same bias in the tail.
Second, with a mechanical tabletop model: random agitation creates a speed distribution; two colors represent matter and antimatter; a tiny controlled bias is added; an annihilation stage removes pairs; the leftover imbalance is measured.
Third, with a literature bridge: compare this intuition to existing work on Boltzmann equations, CP-violating scatterings, leptogenesis, baryogenesis, freeze-out, non-equilibrium physics, and radiation/information.
I am not presenting this as a conclusion.
I am presenting it as a question:
Could the shape of randomness be part of why matter won?
Could the shape of randomness help explain why matter won over antimatter?
This is not a finished theory. It is a proposal for a research conversation.
The idea is that random collisions in the early universe may have created Boltzmann-like distributions with a peak and a tail. The peak does not literally “equal matter.” But the peak may act as an amplifier: if a tiny matter-favoring asymmetry acts where most particles and interactions are, it could become much more important before annihilation and freeze-out.
Radiation may also be part of the loop. Matter and antimatter annihilate into radiation, but high-energy radiation can also create matter–antimatter pairs again. So the early universe may have been a recycling system: particles, antiparticles, radiation, pair creation, annihilation, collisions, and freeze-out.
The question is:
Did matter win only because of a tiny microscopic asymmetry, or also because the statistical shape of the early universe amplified that asymmetry in the right place?
Core background: antimatter and the cosmic puzzle
CERN — Antimatter
https://home.cern/science/physics/antimatter/
CERN — The matter–antimatter asymmetry problem
https://cds.cern.ch/record/1998489?ln=en
CERN Courier — Exploring the origins of matter–antimatter asymmetry
https://cerncourier.com/a/exploring-the-origins-of-matter-antimatter-asymmetry/
CERN Courier — All that antimatters in the universe
https://cerncourier.com/all-that-antimatters-in-the-universe/
Maxwell–Boltzmann distribution and statistical mechanics
OpenStax — Distribution of Molecular Speeds / Maxwell–Boltzmann distribution
https://openstax.org/books/university-physics-volume-2/pages/2-4-distribution-of-molecular-speeds
Khan Academy — What is the Maxwell–Boltzmann distribution?
https://www.khanacademy.org/science/ap-physics-2/x0e2f5a2c%3Athermodynamics/x0e2f5a2c%3Agases/a/what-is-the-maxwell-boltzmann-distribution
David Tong — Cosmology notes, thermal distributions and chemical potentials
https://www.davidtong.org/teaching/cosmology/cosmohtml/S2
Foundational baryogenesis papers and reviews
Sakharov — Violation of CP Invariance, C Asymmetry, and Baryon Asymmetry of the Universe
https://inspirehep.net/literature/51345
Sakharov original paper listing, OSTI
https://www.osti.gov/biblio/4449128
Kolb & Wolfram — Baryon Number Generation in the Early Universe
https://inspirehep.net/literature/8589
Kolb & Wolfram PDF
https://content.wolfram.com/sw-publications/2020/07/baryon-number-generation-early-universe.pdf
Kolb & Wolfram — The Development of Baryon Asymmetry in the Early Universe
https://content.wolfram.com/sw-publications/2020/07/development-baryon-asymmetry-early-universe.pdf
James Cline — Baryogenesis
https://arxiv.org/abs/hep-ph/0609145
Antonio Riotto — Theories of Baryogenesis
https://arxiv.org/abs/hep-ph/9807454
Björn Garbrecht — Why is there more matter than antimatter?
https://arxiv.org/abs/1812.02651
Davidson, Nardi & Nir — Leptogenesis
https://arxiv.org/abs/0802.2962
Boltzmann equations, full distributions, and leptogenesis
Enomoto, Su, Zheng & Zhang — Boltzmann Equation and Its Cosmological Applications
https://arxiv.org/abs/2301.11819
Published version:
https://www.mdpi.com/2073-8994/17/6/921
Hahn-Woernle, Plumacher & Wong — Full Boltzmann equations for leptogenesis including scattering
https://arxiv.org/abs/0907.0205
Garayoa, Pastor, Pinto, Rius & Vives — On the full Boltzmann equations for Leptogenesis
https://arxiv.org/abs/0905.4834
Nardi, Racker & Roulet — CP violation in scatterings, three body processes and the Boltzmann equations for leptogenesis
https://arxiv.org/abs/0707.0378
Baldes, Bell, Millar, Petraki & Volkas — The role of CP violating scatterings in baryogenesis
https://arxiv.org/abs/1410.0108
Kainulainen — CP-violating transport theory for Electroweak Baryogenesis with thermal corrections
https://arxiv.org/abs/2108.08336
Freeze-out, annihilation, and dark-matter-related baryogenesis
Yanou Cui — A Review of WIMP Baryogenesis Mechanisms
https://arxiv.org/abs/1510.04298
Bernal, Colucci, Josse-Michaux, Racker & Ubaldi — On baryogenesis from dark matter annihilation
https://arxiv.org/abs/1307.6878
Cui & Sundrum — A WIMPy Baryogenesis Miracle
https://arxiv.org/abs/1112.2704
Statistical-distribution variations and related speculative directions
Dehpour — Thermal leptogenesis in nonextensive cosmology
https://arxiv.org/abs/2401.00229
Dehpour — Thermal leptogenesis in anisotropic cosmology
https://arxiv.org/abs/2312.10677
CERN / experimental matter–antimatter tests
CERN — A new piece in the matter–antimatter puzzle / LHCb CP violation in baryon decay
https://home.cern/new-piece-matter-antimatter-puzzle/
LHCb paper — Observation of charge-parity symmetry breaking in baryon decays
https://arxiv.org/abs/2503.16954
CERN — BASE breaks new ground in matter–antimatter comparisons
https://home.cern/base-breaks-new-ground-matter-antimatter-comparisons/
Nature — 16-parts-per-trillion measurement of antiproton-to-proton charge-to-mass ratio
https://www.nature.com/articles/s41586-021-04203-w
CERN — ALPHA experiment observes influence of gravity on antimatter
https://home.cern/alpha-experiment-at-cern-observes-the-influence-of-gravity-on-antimatter/
Nature — Observation of the effect of gravity on the motion of antimatter
https://www.nature.com/articles/s41586-023-06527-1
Radiation, annihilation, and matter from light
Fermilab — What is annihilation?
https://www.fnal.gov/pub/science/inquiring/questions/annihilation.html
Fermilab — Electron–positron annihilation and gamma rays
https://www.fnal.gov/pub/science/inquiring/questions/annihilation2.html
Symmetry Magazine — What is annihilation?
https://www.symmetrymagazine.org/article/what-is-annihilation?language_content_entity=und
Brookhaven — Collisions of Light Produce Matter/Antimatter from Pure Energy
https://www.bnl.gov/newsroom/news.php?a=119023
DOE — Making Matter from Collisions of Light
https://www.energy.gov/science/np/articles/making-matter-collisions-light
OSTI version — Making Matter from Collisions of Light
https://science.osti.gov/np/Highlights/2022/NP-2022-01-a
Cosmic radiation / CMB
ESA — Cosmic Microwave Background radiation
https://www.esa.int/Science_Exploration/Space_Science/Cosmic_Microwave_Background_CMB_radiation
ESA — Planck and the cosmic microwave background
https://www.esa.int/Science_Exploration/Space_Science/Planck/Planck_and_the_cosmic_microwave_background
NASA WMAP overview
https://science.nasa.gov/mission/wmap/wmap-overview/
Matter–antimatter domains / “two regions” question
Cohen, De Rujula & Glashow — A Matter-Antimatter Universe?
https://arxiv.org/abs/astro-ph/9707087
PDF:
https://arxiv.org/pdf/astro-ph/9707087
von Ballmoos — Antimatter in the Universe: Constraints from Gamma-Ray Astronomy
https://arxiv.org/abs/1401.7258
Black-hole radiation and information
Hawking — Particle Creation by Black Holes
https://link.springer.com/article/10.1007/BF02345020
DOI link:
https://doi.org/10.1007/BF02345020
Caltech record:
https://authors.library.caltech.edu/records/2wsvj-qrt68
Almheiri, Hartman, Maldacena, Shaghoulian & Tajdini — The entropy of Hawking radiation
https://arxiv.org/abs/2006.06872
Replica Wormholes and the Entropy of Hawking Radiation
https://arxiv.org/abs/1911.12333
Replica Wormholes and the Black Hole Interior
https://arxiv.org/abs/1911.11977
Raju — Lessons from the Information Paradox
https://arxiv.org/abs/2012.05770
Speculative black-hole / antimatter-related ideas
Popławski — Spinors with torsion and matter–antimatter asymmetry
https://arxiv.org/abs/2101.04212
Popławski — Matter–antimatter asymmetry and dark matter from torsion
https://arxiv.org/abs/1101.4012
Baryon asymmetry, dark matter, and density perturbation from primordial black holes
https://arxiv.org/abs/1401.1909
Gravitational baryogenesis and dark matter from primordial black holes
https://arxiv.org/abs/2110.14660
Post created via email from emin@nuri.com