This summary of modern physics in 9 lines is written to make you wonder, think and enjoy the beauty of nature.
Every observation and every measurement ever made agrees with these 9 lines.
Find a single exception, and you will become famous.
 

Nr.	Line	Meaning	Read more
(I)	δW = 0	Nature dislikes squander: the physical measure of change, the action W=∫L dt, is minimized in local motion. The lines below fix the way to calculate the two fundamental Lagrangians L that define action for particles and for curved space.	Vol. I: Fall, Flow and Heat.
(II)	v ≤ c	Nature dislikes haste: local energy speed v is limited by the speed of light c. This invariant implies special relativity and restricts the possible Lagrangians.	Click for an overview of all limits. Vol. II: Chapters on special relativity.
(III)	F ≤ c4/4G	Nature dislikes excessive force: local force F is limited by c and the gravitational constant G. This invariant implies curved space, general relativity and, together with lines 1 and 2, fixes its Lagrangian.	Click for a simple summary and for published proofs. Vol. II: Chapters on general relativity and cosmology.
(IV)	W ≥ħ	Nature dislikes sloth: action W is never smaller than the quantum of action. This invariant implies the existence of particles, quantum theory, and restricts the possible Lagrangians.	Click for a simple summary and for references. Vol. IV: The Quantum of Change.
(V)	S ≥ k ln2	Nature dislikes perfect order: system entropy S is never smaller than ln 2 times the Boltzmann constant k. This invariant implies thermodynamics.	Click for a simple summary and for published proofs. Vol. I: Fall, Flow and Heat.
(VI)	U(1)	Nature conserves electric charges that attract or repel: U(1) is the gauge symmetry of electromagnetism and yields its Lagrangian when combined with lines 1, 2 and 4.	Proof and details inVol. III: Light, Charges and Brains.
(VII)	SU(3) & broken SU(2)	Nature gives nuclei two further types of charges and forces, and their gauge symmetries describe the two nuclear interactions, yielding their Lagrangians when combined with lines 1, 2 and 4.	Proof and details inVol. V: Pleasure, Technology and Stars.
(VIII)	18 elementary particles	Nature determines the elementary particles: quarks, leptons, gauge bosons, the Higgs and the undetected graviton, with all their quantum numbers, make up everything and, with the interactions, fix the standard model Lagrangian with massive neutrinos.	Click for proof. Vol. V: Pleasure, Technology and Stars.
(IX)	27 numbers	Nature determines the fundamental constants: dimensions, cosmological constant, coupling constants, elementary particle mass ratios, and mixing angles complete the two basic Lagrangians that determine all observations and all colours.	Click for proof. Vol. V: Pleasure, Technology and Stars.

 

Wonders

The 9 lines state that general relativity, the standard model of particle physics with massive mixing Dirac neutrinos,
and thermodynamics describe all of nature. Yes, all of it. Yes, exactly. This is observed.

The simplicity of the 9 lines and their vast domain of validity are fascinating.

The 9 lines will markedly shorten your study of physics.

 

Details

The 9 lines contain all present knowledge about nature and motion, including all physics and all observations ever made.

No known observation and no known measurement contradicts these 9 lines, not even in the last significant digit.

Make a single observation contradicting the 9 lines and you will become famous.

The 9 lines determine all equations of physics:

Lines 1, 2 and 3, together, uniquely determine special and general relativity, cosmology, the Hilbert Lagrangian and Einstein's field equations. (This is shown in a Phys Rev D article and other publications presented here.) If you prefer, you can use the black hole mass per length limit c²/4G instead of the maximum force in line 3.

Line 5, with lines 1 and 4, uniquely implies thermodynamics. (This is shown in this publication: Entropy 25 (2023) 1511.)

Lines 1, 2, 4, and 6 to 9, together, uniquely determine quantum field theory and the Lagrangian of the standard model of particle physics with massive Dirac neutrinos and PMNS mixing. (The equivalence is shown in publications presented here.)
Written out, the Lagrangian of the full standard model is somewhat involved, as Jim Shifflett shows.

The 9 lines show how little math is required to describe nature with high precision.

The 9 lines describe everything that moves - and thus everything that happens in nature.

All mathematics used in physics follows from these 9 lines: Lagrangians, equations of motion, wave functions, Hilbert spaces, Lie groups, Riemannian space, etc.

To achieve a precise description of motion, physics needs the last line, containing the fundamental constants.

The 9 lines prove that Dirac was wrong when he wrote: "One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe. Our feeble attempts at mathematics enable us to understand a bit of the universe, and as we proceed to develop higher and higher mathematics we can hope to understand the universe better." Instead, advanced math, unintentionally, hides the simplicity of nature.

The 9 lines imply the absence of trans-Planckian effects, as detailed here.

No such effect has been observed and no such effect will ever be observed.
In particular, combining the 9 lines implies that twice the Planck length (4G ħ/c³)^1/2 is the smallest length in nature.
Its wide-ranging implications, for unification in particular, are explored on a separate page.

The 9 lines resulted from the work of countless scientists and engineers during 410 years.

Galileo started around the year 1592; line 1 resulted about 150 years later. Line 5 arose from 1824 to 1929, line 6 arose
around 1860, lines 2 and 4 around 1900, line 3 from 1915 to 2002, and lines 7, 8 and 9 from 1936 to 1973.

The 9 lines improve the humorous 9 lines found here.

The 9 lines are the same across the universe, even for extraterrestrials, as already noted 100 years ago.

The 9 lines are the same for men, women, children and Hungarians. (This list includes all the known life forms in the universe capable of doing physics.)

The 9 lines contain all natural sciences.

They contain physics, chemistry, material science, biology, medicine, geology, astronomy and all engineering disciplines.

Again: any single observation contradicting the 9 lines will create a sensation - and will falsify the list.

In the past 50 years, about half a million publications have explored two research questions.

 

Question I: Are all observations and all "laws" of motion described by the 9 lines?

For motion at high speed, the answer for the last 130 years has been: yes, special relativity passes all tests and describes all observations about fast systems starting from the principle of maximum speed c.
For particle motion, the answer for the last 50 years has been: yes, quantum field theory and the standard model with massive neutrinos pass all tests and describe all observations about particles starting from the smallest action, the quantum of action ħ.
For collective motion, the answer for the last 100 years has been: yes, thermodynamics passes all tests and describes all observations in the domain starting from the principle of the smallest system entropy k ln 2.
For motion due to gravity, the answer for the last 100 years has been: yes, general relativity passes all tests and describes all observations about gravity starting from the principle of maximum force c⁴/4G ≈ 3.0 · 10⁴³ N.

One issue remains, in cosmology: the rotation curves of galaxies, galaxy groups and wide binaries, at accelerations around 0.1 nm/s² and smaller, are puzzling. Three research directions are being pursued. (1) Often, this puzzle is assumed to be solved by the postulated idea of cold dark matter particles. However, no dark matter particle has been found, despite intense searches and the promise of eternal fame. (2) The rotation curves might be due to effects that modify gravitation, as Milgrom, Pikhitsa, Verlinde or McGaugh suggest. Stacy McGaugh has dedicated his work to the topic and has a wonderful blog about it. However, despite their charm, such modifications are difficult to confirm. (3) Finally, the rotation curves might be due to pure general relativity, as David Wiltshire, Marco Galoppo, Federico Re and their colleagues suggest. In fact, their research about general relativity suggests the absence of both dark matter and dark energy. (More and more experiments are questioning the idea of dark energy.) If these results are confirmed, the 9 lines describe all nature. If, instead, some unknown dark matter is discovered or some modification of gravity is confirmed, the 9 lines above are falsified.
 

Question II: What is the origin of the 9 lines?

In particular, what determines the apparent choices of the force spectrum, the particle spectrum, and the fundamental constants in lines 6 to 9?c⁴
The unexplained lines 6 to 9 are the only non-trivial effects of relativistic quantum gravity that are known. Lines 1 to 5 are trivial effects.c⁴
Lines 6 to 9, together with line 1, contain the only observations unexplained by general relativity and by particle physics.c⁴
Among these lines, the main unexplained observation about nature is: Where do the colours come from?c⁴
In technical terms: what determines the electron mass value and the fine-structure constant 1/137.0359991(1)? c⁴

The mentioned half a million publications contain only two approaches that claim to deduce the 9 lines, including lines 6 to 9, from a general principle.c⁴
This is not a typo, even though mass media claim otherwise. c⁴
The two approaches are the octonion model by Tejinder Singh and the strand tangle model.c⁴
So far, only the strand tangle model, or tiny theory, deduces all 9 lines from a single statement without predicting new, unobserved effects.c⁴
In the strand model, the single statement describing nature, the fundamental principle, relates topology to observations:c⁴
 
        Crossing switches of fluctuating strands of Planck radius define the quantum of action, the Planck time, and Boltzmann's constant.c⁴
 
Strands explain the principle of least action, general relativity, thermodynamics, spinor wave functions, and the Dirac equation.c⁴
Strands explain the origin of the interactions, their symmetries, the elementary particles, and their quantum numbers.c⁴
Strands explain why the mass of all elementary particles is much smaller than the Planck mass.c⁴
Since 2026, crossing switches of fluctuating strands of Planck radius reproduce the fine structure constant in all (ten) measured digits.c⁴

Since 400 years, all experimental tests confirm the fundamental principle. Nature is simple to build — but hard to calculate.
As long as the fundamental principle is not falsified, it appears to be the only "law" of nature, describing everything. Enjoy challenging it.

About the fundamental principle, see the pedagogical article
L. Kauffman and C. Schiller, How come the quantum? Testing the topological origin of Planck's quantum of action (2026, preprint).
A technical article about the fundamental principle and how it follows from the 9 lines is
C. Schiller, Testing a single fundamental principle yielding general relativity, particle physics, and gauge anomaly cancellation (2026, preprint).
Another technical article is
C. Schiller, Testing a model for emergent spinor wave functions explaining elementary particles, gauge interactions and fundamental constants (2025, preprint).

 

A publication and talks about the 9 lines

C. Schiller, From maximum force to physics in 9 lines and towards relativistic quantum gravity,
published in Zeitschrift für Naturforschung A 78 (2023), 145-159. It also contains the ultimate data availability statement.

Talk slides are here.  German slides are here.  A Clubhouse podcast on the 9 lines is found here. (You will need the app to listen to it.)

 
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