This summary of modern physics in one table is written
to make you wonder, check, and enjoy the beauty of nature.
The summary has been thoroughly tested by a huge number of scientists and engineers. (See here on how this is done.)
The summary might save you a year of study.
This 9-line summary of textbook physics agrees with 400 years of experiments. Exactly.
The 9 lines state that general relativity,
the standard model of particle physics – extended with mixing massive Dirac
as well as thermodynamics describe all of nature. Yes, all of it. The 9 lines also highlight what we do not know.
Details are given in C. Schiller, From maximum force to physics in 9 lines and
towards relativistic quantum gravity,
published in Zeitschrift für Naturforschung A (2022). It also contains the ultimate data availability statement.
A clubhouse podcast on the 9 lines is found here.
Talk slides are here. Here is a version in German.
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.
Find a single contradicting observation or experiment and 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, as told here.
Line 5, with line 1 and 4, uniquely implies thermodynamics. (The line will be improved soon.)
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 given above improve the humorous 9 lines found here.
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 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 additional "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.
Spoiler for I and II: probably there are no phenomena or "laws" beyond the 9 lines.
Spoiler III: the origin 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.
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 contains also 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.
An independent 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. The mathematical expression in the video is a combination of many, but not all of the 9 lines. In comparison, Sabine Hossenfelder's video on unification only speaks about line 1.
The 9 lines are not a "theory of everything"
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: 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.
From the 9 lines to the minimum length - and to the unified theory
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.