The 9 lines are complete, correct and simple
The 9 lines contain all present knowledge about nature, including all textbook physics and all observations ever made.
The simplicity of the 9 lines and their vast domain of validity are intensely fascinating.
No known observation and no known measurement contradicts these 9 lines, not even in the last significant digit.
Discover a single contradicting observation and you will become famous.
The 9 lines determine all equations of physics, as the references in the pdf show:
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 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 online 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, extended with massive Dirac neutrinos and PMNS mixing. Written out, the Lagrangian is somewhat involved, as Jim Shifflett showed.
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.
The 9 lines resulted from the work of countless scientists and engineers over 400 years.
Galileo started around the year 1600; line 1 resulted after over 150 years.
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 imply the lack of trans-Planckian effects, as detailed here.
No such effect has been observed and no such effect will ever be observed.
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.
Three questions are open in fundamental physics
IAre all observations in nature described by the 9 lines – or are there phenomena beyond present textbook physics?
In particular, to which line does dark matter belong - or does it not exist at all?
II Are there any undiscovered lines with new physics – or will F ≤ c4/4G remain the last "law" of physics?
Explored mainly in the years
from 1973 to 2002, the force limit is the "law"
of physics discovered last.
The limit value c4/4G ≈ 3.0 · 1043 N for the local force has passed all checks.
It allows deducing Einstein's field equations and is the shortest known summary of general relativity.
Because line 3 on maximum force c4/4G was added to the list only recently, a separate web page is dedicated to it.
Is there any undiscovered "law" of nature?
IIIWhat is the common explanation for the 9 lines?
What determines the
principles in lines 1 to 5? They imply that there is a smallest
length and time interval. How can this be?
What determines the choices in lines 6 to 9, i.e., the force spectrum, the particle spectrum and the fundamental constants?
The last four lines contain the only known physics effects beyond the standard model. How do they arise?
In simple words: Where do COLOURS come from?
Many enjoy searching for answers.
for I and II: it is predicted that there are no phenomena or "laws" beyond the 9
Spoiler III: the origin of the 9 lines and of colours may be this one.
From the 9 lines to Lagrangians
For general relativity, the Hilbert Lagrangian with a cosmological constant is found in every textbook. It follows from lines 1, 2 and 3. Publications prove it.
The Lagrangian of the standard model, extended with massive
Dirac neutrinos and PMNS mixing, follows from lines 1, 2, 4, and 6 to 9.
The best version on the internet is Jim Shifflett's http://einstein-schrodinger.com/Standard_Model.pdf;
a local copy is here.
This other, often cited Lagrangian of the standard model by T.D. Gutierrez includes ghost terms; however, it has half a dozen mistakes and disregards neutrino masses and mixings. See the corrections at https://twitter.com/mmanuF/status/895390592854880260.
A different video summary of the standard model and of general relativity, by David Tong, is found at https://www.youtube.com/watch?v=Unl1jXFnzgo&t=1s. One can argue that the mathematical expression in the video is a combination of all 9 lines, as it contains general relativity and the standard model. However, the lines 6, 7, 8 and 9 and all the physical quantities appearing in the expression are not explained. Worse, Tong's expression contains trans-Planckian quantities, such as arbitrary small length values, which are in contrast to observations.
Sabine Hossenfelder's video on unification concentrates on line 1.
The 9 lines are not a "theory of everything" - but help to find the unified theory of motion
The 9 lines fulfil all requirements for a "theory of everything" found
in tabloids and in popular books.
They do so since the 1970s.
However, the 9 lines are not unified: for example, the origin of lines 6 to 9 has to be clarified first.
In fact, the 9 lines allow measuring progress towards unification, as told in the blog.
Combining the 9 lines implies that twice the Planck
length (4G ℏ/c3)1/2 is the smallest length
Its wide-ranging implications, also for unification, are explored on a separate page.
The 9 lines structure the free Motion Mountain Physics
|Summary||Line||Details||Volume about the topic|
|1. Nature dislikes squander:||dW = 0||Action W=∫L dt is minimized in microscopic motion.
L = Ekin-Epot; the lines below fix the two fundamental Lagrangians L.
Fall, Flow and Heat.
|2. Nature dislikes hurrying:||v ≤ c||Energy speed v is limited by the speed of light c. This invariant implies special relativity and restricts the possible Lagrangians.||Vol. II: Chapters
|3. Nature dislikes excessive force:||F ≤ c4/4G||Force F is limited by c and the gravitational constant G. This invariant implies general relativity and, together with lines 1 and 2, fixes its Lagrangian. (Click for details.)||Vol. II: Chapters
General Relativity and Cosmology.
|4. Nature dislikes sloth:||W ≥ ℏ||Action W is never smaller than the quantum of action. This invariant implies quantum theory and restricts possible Lagrangians. (Details here.)||Vol. IV:
The Quantum of Change.
|5. Nature dislikes perfect order:||S ≥ k ln2||Entropy S is never smaller than O(1) times the Boltzmann constant k. This invariant implies thermodynamics. (To be improved.)||Vol. I (and Vol. VI)|
|6. Electric charges are conserved and attract or repel:||U(1)||is the gauge symmetry of electromagnetism. It yields its Lagrangian when combined with lines 1, 2 and 4.||Vol. III:
Light, Charges and Brains.
|7. Nuclei show two other types of charges and forces:||SU(3) & broken SU(2)||are the gauge symmetries of the two nuclear interactions, yielding their Lagrangians when combined with lines 1, 2 and 4.||Vol. V:
Pleasure, Technology and Stars.
|8. Nature determines the elementary particles:||18 particles||– gauge bosons, the Higgs boson, quarks, leptons and the undetected graviton – with all their quantum numbers, make up everything and, with the interactions, fix the extended standard model Lagrangian.||Vol. V:
Pleasure, Technology and Stars.
|9. Nature determines the fundamental constants:||Finally, 27 numbers||– dimensions, cosmological constant, coupling constants, elementary particle mass ratios, mixing angles – complete the two basic Lagrangians. They determine all observations and all colours.||Vol. V:
Pleasure, Technology and Stars.