Physics

Why the Periodic Table Stops Where It Does: Chemical Stability From One Physical Constant

Chemistry works. Atoms bond, molecules fold into stable shapes, proteins hold their structure, water forms hydrogen bonds that make life as we know it possible. Standard physics treats this as simply how things are. The values of the fundamental constants happen to permit stable chemistry, and if you ask why those specific values rather than some others, the honest answer is that nobody knows. It’s either a brute fact or, in some interpretations, an artefact of anthropic selection across a multiverse of universes with different constants. The Big Flare-Up Theory (BFUT) takes a more direct route in Paper 25: it derives, from a single substrate density, exactly how far the parameters governing atomic structure could shift before chemistry itself would stop working, and shows the actual universe sits comfortably inside the stable zone.

What Actually Holds a Molecule Together

Chemical bonding, at the level relevant here, comes down to a competition between bond energy and thermal energy. Two atoms stay bonded when the energy holding them together, E_bond, exceeds the ambient thermal energy trying to shake them apart, kT: about 0.026 eV at room temperature. Bond energy itself depends on how tightly electron orbitals overlap, which depends in turn on the orbital scale, a_0, the same Bohr-radius-like quantity that sets the size of an atom. Make the orbital scale larger, and overlap at a given bond distance drops sharply: bond energy falls off as roughly 1/f², where f is the factor by which the orbital scale has grown.

That single relationship, bond energy scaling as the inverse square of orbital scale, is what BFUT uses to work out exactly how much room chemistry has to spare.

Three Thresholds, Each With a Specific Number

Working from the derived orbital scale and the corresponding bond-energy relation, Paper 25 identifies three distinct points where increasingly fundamental categories of chemical bonding fail:

At f = 1.4, a 40% increase in orbital scale, van der Waals forces fail. These are the weakest, most diffuse intermolecular attractions, responsible for things like why gases condense into liquids at low temperature. Losing them first, at the smallest threshold, makes physical sense: they’re the weakest bonds in the hierarchy, so they’re the first casualty as bond strength degrades.

At f = 2.8, a 180% increase, hydrogen bonds fail. This is the more consequential threshold. Hydrogen bonding is what gives water its distinctive structure, its high boiling point relative to similarly sized molecules, and its ability to organise around dissolved substances. It’s also what holds the double helix of DNA together and stabilises the folded shapes of proteins. Losing hydrogen bonding doesn’t just change chemistry at the margins: it removes the specific mechanism most directly implicated in the chemistry of life as it actually exists.

At f = 13.2, roughly a twelvefold increase, covalent bonds fail entirely. Covalent bonding is the strongest and most fundamental category, the electron-sharing mechanism that builds molecules in the first place, from the simplest diatomic gas to the largest organic macromolecule. Past this threshold, there are no stable molecules of any kind. Chemistry, in any recognisable sense, stops.

Where the Actual Universe Sits

These aren’t arbitrary round numbers picked to make a point: they come out of the same orbital-scale derivation the paper uses elsewhere, and they line up closely with the specific numerical thresholds the paper’s broader condensation framework produces independently: approximately 90%, 14-fold, and 136-fold shifts, corresponding to f = 1.9 (the transition region spanning van der Waals and hydrogen bonding), f = 14 (matching the derived covalent threshold of 13.2 to within 6%), and f = 136 (complete disruption of electromagnetic molecular structure of any kind). The actual physical value of the relevant substrate-derived constant, K_phys, places the real universe well inside the stable regime for all four bond classes simultaneously: not marginally inside, not balanced on a knife-edge, but comfortably within the range where every category of chemical bonding, from the weakest van der Waals attraction to the strongest covalent bond, functions normally.

Why This Matters More Than a Curiosity

The significance isn’t just that chemistry happens to work: it’s where this result comes from. Every quantity involved in the threshold calculation, the orbital scale, the bond-energy scaling relation, the underlying atomic structure, traces back to the same single substrate density, ρ_s = 5.9 × 10⁻²⁷ kg/m³, that Paper 25 and its companion papers use to derive particle masses, galaxy rotation curves, and weak gravitational lensing. Nothing about the chemistry-specific calculation involved choosing a new free parameter to make the answer come out comfortably inside the stable zone. The same number that fixes the proton mass and the strong coupling constant also happens to fix how much margin chemistry has before it fails, and the actual margin turns out to be generous rather than narrow.

This is the same logic BFUT uses throughout the programme: instead of treating a favourable physical outcome as either luck or a brute fact requiring no explanation, trace it back to see whether it’s a forced consequence of quantities that are independently pinned down by unrelated evidence. Particle masses, atomic stability, and now chemical bond stability all derive from the identical density. None of them were adjusted individually to produce a comfortable answer.

The 3+e Topology Behind It All

The deeper reason any of this is derivable at all traces back further, to Paper 25’s account of why matter organises into stable protons and electrons in the first place: the “3+e” topology, where three condensed substrate units bind together as a compact core (the proton) while mechanically expelling a fourth, smaller counter-rotating unit (the electron). This isn’t an assumed starting point; the paper shows it’s the energetically preferred outcome among the competing geometric possibilities (a 4+0 configuration, a symmetric 2+2 split, and the 3+1 arrangement that maps to ordinary matter), with the 3+1 partition winning decisively: energy 1.40 in model units against 4.00 for the next-best alternative: and remaining the preferred configuration across more than 90% of a full multi-dimensional scan of the underlying coefficient space. Ordinary hydrogen, and by extension all of chemistry, follows from that geometric preference, not from a separately assumed atomic structure bolted onto the theory.

What Would Make This Wrong

The chemical stability thresholds are a genuine, falsifiable consequence of the framework, not an unfalsifiable just-so story. If the independently measured value of ρ_s, fixed by particle masses, galaxy rotation curves, and weak lensing, none of which have anything to do with chemistry, had instead required an orbital scale that pushed past even the weakest of the three thresholds, ordinary chemical bonding would be predicted not to exist, in flat contradiction with the observed universe. The fact that the same number derived from entirely unrelated astrophysical and particle-physics evidence lands comfortably inside the chemically stable zone is exactly the kind of over-determination BFUT treats as the strongest form of evidence: a quantity constrained from several independent directions, agreeing without being separately tuned to do so.

Derived in BFUT Paper 25, “Dark Matter: Connecting Galaxy Clusters, Galaxy Rotations, the Cosmological Constant, W and Z Boson Masses, and Atomic Structure Through One Physical Constant,” Section 2.2.9.

Download BFUT papers, simulation code, and companion materials: vijayshankarsharma.com/downloads/