This summary of modern physics in one table is written
to make you wonder, think, and enjoy the beauty of nature.
The summary has been thoroughly tested with experiments and observations
by practically all scientists and engineers.
The summary will markedly shorten your study of physics.
This 9-line summary of textbook physics agrees with all observations. Exactly.
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. The 9 lines also highlight what we do not know. All of
it.
Details are explained in 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,
which also contains the ultimate data availability statement.
Talk slides are here. These slides are in German.
A clubhouse podcast on the 9 lines is found here.
The 9 lines are simple, complete and correct.
The 9 lines contain all present knowledge about nature, including all textbook 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 simplicity of the 9 lines and their vast domain of validity are fascinating.
The 9 lines determine all equations of physics, as the references in the pdf at the top of the page 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 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.
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 410 years.
Galileo started around the year 1592; 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.
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 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.
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Half a million publications about the 9 lines have explored two
questions.
I. Are really all observations and "laws" of motion described by the 9 lines?
For particle physics,
the answer for the last 50 years has been:
yes, quantum field theory and the standard model with massive
neutrinos describe all observations about particles.
For thermodynamics, the answer for the last 100 years has been:
yes,
thermodynamics passes all tests and describes all
observations starting from the principle of the smallest system entropy k ln 2.
For gravity, the answer for the last 100 years
has been: yes, the principle of maximum force
c4/4G ≈ 3.0 · 1043 N
summarizes general relativity,
passes all tests, and describes all
observations about gravity.
One issue remains in cosmology: the rotation curves of galaxies, galaxy
groups and wide binaries, at accelerations around 0.1 nm/s2 and
smaller, remain a puzzle. Often, this puzzle is assumed to be solved by
(cold) dark matter.
However, the only known types
of dark matter, black holes (cold) and neutrinos (hot), do not explain the
rotation curves at low accelerations.
The puzzle remains a research topic.
as Stacy McGaugh explains.
The rotation curves might be due to quantum effects or even
to classical effects, as David Wiltshire and his colleagues suggest.
II. What is the common origin of all 9 lines?
In particular, what determines the
apparent choices in lines 6 to 9, i.e., the force spectrum, the particle
spectrum, and the fundamental constants?
Lines 6 to 9
contain the only definitively unexplained observations of nature and the only observations
definitively beyond textbook
physics.
The unexplained observations of nature include the electron mass and the fine structure constant.
A typical question that includes all unknown aspects of nature is:
Where do colours come from?
In simple words, the 9 lines are not unified. To
be unified, they must be shown to follow from a single line.
Explaining lines 6 to 9 is an objective way to
measure progress towards unification.
The mentioned half a million publications contain only two unification approaches that claim
to deduce all 9 lines from a single one. This is not a typo.
The two unification approaches are the octonion model by Tejinder
Singh and the strand tangle model.
Mass media tout additional approaches,
but none of these additional approaches reduced lines 6, 7, 8 or 9
to a smaller number. None.
This article and
this
article provide
pedagogical introductions showing how the strand tangle model deduces
all 9 lines from a single fundamental principle:
The topology of fluctuating strands defines the quantum of action,
the Planck length, and the Planck time. This fundamental principle
yields all the 9
lines.
If all experimental tests continue to confirm it,
the fundamental principle is the only "law" of nature: it summarizes
physics in 1 line.
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The 9 lines summarizing physics structure the free Motion Mountain Physics
Textbook
Summary | Line | Details | Volume about the topic |
1. Nature dislikes squander: | dW = 0 | Action W=∫L dt is minimized in microscopic motion.
Often, L = Ekin-Epot; the lines below fix the two fundamental Lagrangians L. | ![]() Fall, Flow and Heat. |
2. Nature dislikes haste: | v ≤ c | Energy speed v is limited by the speed of light c. This invariant implies special relativity and restricts the possible Lagrangians. | ![]() Special Relativity. |
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.) | ![]() 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.) | ![]() The Quantum of Change. |
5. Nature dislikes perfect order: | S ≥ k ln2 | Entropy S is never smaller than ln 2 times the Boltzmann constant k. This invariant implies thermodynamics. | ![]() |
6. Nature conserves electric charges that attract or repel: | U(1) | is the gauge symmetry of electromagnetism. It yields its Lagrangian when combined with lines 1, 2 and 4. | ![]() Light, Charges and Brains. |
7. Nature gives nuclei two further 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. | ![]() 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 standard model Lagrangian with massive neutrinos. | ![]() 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. | ![]() Pleasure, Technology and Stars. |
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