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 contain everything we know about fundamental physics - and highlight everything we do not.
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.
Slides for a talk on the 9 lines are here. Here is a version in German.
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.
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.
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?
Many enjoy searching for answers.
For general relativity, the Hilbert Lagrangian with a cosmological constant is found in every textbook.
The best Lagrangain of the standard model, extended with massive
Dirac neutrinos and PMNS mixing, that is found on the internet is
due to Jim Shifflett; see 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 ghost terms, has half a dozen mistakes, and disregards neutrino masses and mixings. See some 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
The mathematical expression in the video can be seen as
a symbolic combination of the 9 lines.
In contrast, the 9 lines are complete and precise. Line 1, the principle of least action, is part of David Tong's mentioned video. Line 1 is also the topic of Sabine Hossenfelder's video on least action at https://www.youtube.com/watch?v=A0da8TEeaeE.
Are the 9 lines a "theory of everything"? They
do fulfil all requirements 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. (An attempt is found here.)
The 9 lines allow measuring progress towards unification, as told in the blog. The blog also has further comments about the 9 lines.
Combining the 9 lines implies that twice the Planck length (4G ℏ/c3)1/2 is the smallest length in nature. This needs to be told more often. Conversely, the assumption of continuous space implies a vanishing Planck length. This implies a vanishing quantum of action, a vanishing gravitational constant, or both. The assumption also implies the lack of most physical measurement units. In other words, exact continuity contradicts all of modern physics. It may be comforting to note that this and all issues due to the combination of gravity and quantum theory disappear if space is seen as effectively continuous, and only so for all lengths longer than twice the Planck length.
The 9 lines and the minimum length imply that the future unified theory has no evolution equation and no Lagrangian. This lack of mathematics in the unified theory is shown in C. Schiller, "Relativistic quantum gravity has no evolution equations – only an inequality" at https://www.researchgate.net/publication/364261495.
The 9 lines also provide requirements for the common constituents of space and particles in the future unified theory. In particular, the 9 lines imply that the common constituents are filiform, of Planck radius, and fluctuating. Details about the requirements and their consequences are found in "From maximum force to physics in 9 lines and towards relativistic quantum gravity" at https://www.researchgate.net/publication/365750175. (And a proposal to realize the requirements is found here.)
The 9 lines imply that the complete theory of relativistic quantum gravity – the “theory of everything” or “final theory” – has only two experimental effects: (1) general relativity and (2) the standard model of elementary particle physics, extended with massive Dirac neutrinos and PMNS mixing.
Therefore, the decisive test of any proposed complete theory of relativistic quantum gravity is the calculation of the values for the elementary particle masses, of the mixing matrices and of the coupling constants. The prediction of the neutrino masses might well be the only prediction that is still possible in fundamental physics. All other constants have already been measured.
The 9 lines also structure the 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.||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.