Can the strength of gravity be calculated?
A layman directing commercially available AI wrote down a formula that predicts the strength of gravity — a number physicists have measured for 340 years and never predicted. This page explains it without equations: what the formula says, how well it fits, and how it could be proven wrong.
Gravity is astonishingly weak
Gravity keeps our feet on the ground and the planets around the Sun, so it feels like a mighty force. Between single particles, though, it is tiny.
Take two electrons, the small charged particles found in every atom. Gravity pulls them together; electricity pushes them apart. The electric push wins by a factor of about 1043 — a one followed by 43 zeros.
Physics describes this gap with three numbers, each measured on its own: the strength of gravity (written G), the strength of electricity (written α) and the mass of the electron. Standard physics treats them as independent: knowing two of them tells you nothing about the third. This research asks whether two of them could, after all, fix the third.
Who is asking?
I am Oldřich Dvořák, an entrepreneur and AI-native builder, born in the Czech Republic. I have no physics degree. This research is AI-generated, and I directed it.
I say this so that you can weigh it, not as a reason to believe anything. The claims stand or fall on their calculations and on future measurements.
Author disclosure and publication history.
What is α?
α (the Greek letter alpha) is a single number that says how strongly light and electrons interact — in effect, how strongly electric charges feel each other. It is about 1/137.
It is a pure number, with no units. Measure in metres or in feet, in seconds or in years: you always get the same 1/137.
People have tried to build other numbers of nature out of α before, and their striking matches did not hold up. This research takes that history as a warning: a close match has to be weighed against how many formulas were tried. The exact value used is on the Facts page.
The formula in words
The proposal is short. Take 21 copies of α and multiply them together (α to the power 21). Multiply the result by the fraction 4/3. Finally, apply a small correction, e−5α/2, which is about 0.98 and so lowers the result only slightly.
The outcome is a number for how strong gravity is between two electrons. Using the measured values of α and of the electron’s mass — together with two constants fixed by definition, Planck’s constant and the speed of light — it gives G = 6.674312278 × 10−11 m³ kg⁻¹ s⁻².
The formula has no dial that was turned to hit the target. How its pieces were chosen is another story, told further down.
How well does it fit?
Closely, on today’s numbers. The predicted G agrees with the official 2022 value — published by CODATA, the international committee that recommends values for the constants of nature — to about 2 parts in a million.
The newest measurement, made at the US standards institute NIST and published in 2026, came out a little lower: a bit more than its own margin of error below the prediction. That is not a contradiction, and not a confirmation either.
G is notoriously hard to measure. Results from different laboratories still disagree with each other by more than their stated uncertainties. So the comparison stays open, and the picture shows both values, including the less flattering one. The exact numbers are on the Facts page.
Why a prediction of G would matter
If the formula is a law of nature, it pins down G far more sharply than anyone can measure it: the uncertainty coming from α and the electron’s mass is about six thousand times smaller than the uncertainty of today’s G measurements.
That is what makes it useful. A sharp, fixed number is easy to test — and easy to kill. It does not make the formula right: a very precise calculation can be precisely wrong.
The honest part: how the formula was found
The formula was not written down first and checked later. A computer search found it, at a time when G was already known. The power 21 follows simply from how small the target number is. The finer pieces — the 4/3 and the 0.98 correction — were picked with the answer in view.
A big search tries an enormous number of formulas, and with enough tries some will land close to almost any number by chance. So we counted it fairly. We took the same pool of more than two million formulas, set it on 100,000 randomly chosen target numbers, and checked how often it landed as close as G can be measured today. It did so for about 1.6% of the targets.
Allowing for the fact that this was one of several similar searches, the match alone is weak evidence. On its own it would not convince a careful scientist, and it should not convince you.
Why it is still worth testing
Why bother, then? For three reasons.
First, the formula is fixed. It gives one number with nothing left to adjust, so better measurements can prove it wrong.
Second, it has a tidy mathematical shape. The number 21 is the number of independent ways to rotate an object in seven dimensions. (In our three dimensions there are three, like an aircraft that can pitch, roll and yaw.) One classical object of mathematics, built on those seven-dimensional rotations, produces both the 21 and the small correction at once. That is a clue, not an explanation: nobody has shown why nature would use it, and the 4/3 and one more setting still have to be put in by hand.
Third, the same pattern, with extra assumptions, makes predictions about other things — above all about neutrinos, extremely light particles that barely interact with anything. Experiments that are already running or being built can check them.
What would prove it wrong: measuring G better
The most direct test is to measure G better. The rule was fixed in advance: if at least two independent methods, each accurate to 10 parts in a million or better, agree on a value clearly different from the prediction, the formula is dead.
“Clearly” here means the strict standard physicists demand before they announce a discovery. No date for such measurements has been announced.
Neutrinos: tests with dates on the calendar
Neutrinos come in three kinds with slightly different masses. Two questions about them are still open. The wider pattern of this research answers both — but only under extra assumptions that it does not derive.
The first question is the order of the masses: is the odd one out heavier or lighter than the other two? The research predicts the so-called normal order (the odd one out is the heaviest), provided that one sign in its equations is positive. That sign is assumed, not derived. The JUNO detector in China has been taking data since August 2025; its planned six years point to about 2031, though no clear answer is promised.
The second question is whether neutrinos and their antiparticles behave the same way. Physicists measure this as an angle, the so-called CP phase. If the numbers through which neutrinos get their mass are plain real numbers, the angle must be exactly 0° or 180° (these are assumptions the work cannot yet justify), and in this respect neutrinos and antineutrinos would show no difference. The Japanese Hyper-Kamiokande experiment aims to start in 2028; the American DUNE plans its first beam for 2031. Switching on is not a verdict: the answer comes only once there is enough data.
Cosmology is already pushing back
The pattern also predicts the total mass of the three neutrinos. In its heavier version it comes out at 87.76–89.02 meV (millielectronvolts, a unit for extremely small masses).
The universe itself can weigh neutrinos: their total mass leaves a faint mark on maps of galaxies and on the afterglow of the Big Bang. Under the standard model of cosmology — the usual description of how the universe expanded and built its structures — this heavier version already lies outside the range that the latest data (the DESI galaxy survey combined with the afterglow) allow at the usual 95% level. The research had set itself a warning line in advance, and this result crosses it.
In another, also widely studied description of the universe, in which dark energy changes over time, the prediction still fits. So the verdict depends on which description of the universe is right, and surviving in one of them is not a confirmation. There is also a lighter version of the neutrino assignment, but it needs an extra mechanism that nobody has derived (see the Theory page).
How this was made
This research is AI-generated. AI language models did the algebra, wrote and ran the calculations, searched the scientific literature and wrote the paper. I directed the work and I am responsible for its claims — as said above, a layman without a physics degree.
Nearly all of the work was checking. Calculations were repeated with separately written programs, and AI reviewers read the drafts with the job of finding mistakes. That catches errors in the calculations. It cannot show that nature follows the formula, and agreement between AI models is not evidence about nature.
This is the first result of the larger system I’m building — the first one out, not the last.
Source: October acknowledgments; Appendix A; author disclosure
Not yet reviewed by other scientists
Neither paper has gone through peer review, the assessment by independent experts that scientific journals organise. The preprint server arXiv declined the May paper in May 2026, and Journal of Physics Communications rejected it in July 2026 without sending it to reviewers.
Both papers are publicly archived on Zenodo, a research repository run by CERN. That keeps a permanent record; it is not a stamp of approval.
Author disclosure and publication history.
What is still open
The biggest open question is why. Nobody has derived the formula from a deeper theory; neither the 4/3 nor the small correction is explained. One proposed deeper theory, set in five dimensions, has been calculated in detail, but whether it really exists is still undecided. And one simple route from five dimensions down to our four (three of space, one of time) has been ruled out under the stated assumptions. The neutrino predictions rest on assumptions that are not yet justified.
What the work does offer is a sharply put question and tests with dates attached. It is a target for measurements and for theorists — not a new law of gravity.
Based on: October 2026 paper, §§1–8, 10, 12; Appendix A. 10.5281/zenodo.23157146.