• An appetizer• Enjoying physics• Discussions and blogs• Open issues in fundamental physics in the year
2000• Requirements for a final
theory• Predictions of the strand
model• Status of the predictions and of the
model• Support
What determines colours? What is motion?
All colours in nature derive from the fine
structure constant 1/137.035 999 1(1). This is the most famous unexplained number
in nature. What determines its value?
All motion in nature
is described either by quantum theory or by Einstein's general relativity,
two theories that contradict each other. How can they be unified in a
final theory?
If you enjoy exploring ideas and checking them against the real
world, you might like this volume. It first explains why the past
proposals for a final, unified theory of physics – the socalled
'theory of everything' – have failed. Then, the text presents a
better proposal: a final theory called the strand model. This model
agrees with all experimental data known so far and makes clear, falsifiable
predictions. They are being tested in experiments around the world. The
strand model
– predicts the standard model of particle physics – and allows
no alternative or extension,
– is based on one simple
fundamental principle – and thus is 'beautiful',
–
predicts general relativity – and allows no alternative or extension,
– predicts quantum theory – and allows no alternative or
extension,
– and solves the open issues of the standard model,
gravitation and cosmology, including the explanation of all fundamental
constants.
All these results follow naturally from one simple principle.
Prepare yourself for a roller coaster ride trough modern physics, and for
the excitement of solving one of the oldest physics puzzles known. This is
an adventure that leads beyond space and time – right to the limits
of human thought. For example, the adventure shows that the term
'theory of everything' is wrong, whereas 'final theory' is correct.
Fast reading: for a quick overview of the book, just read the 'summary' section in each chapter.
The colour pdf file with embedded animations, shown just below, is free. If you want a paper version delivered to your address, click one of the 'Buy' links at the top left of the page.
An appetizer: a simple unified theory
The text presents an approach to the final, unified theory of physics with a simple basis but intriguing implications. The model is based on featureless strands that form space, particles and horizons; the model sums up textbook physics in a single fundamental principle: events and Planck units are crossing switches of strands.
Surprisingly, this fundamental principle, which works in three dimensions only, allows to deduce Dirac's equation (from the belt trick), the principles of thermodynamics and Einstein's field equations (from the thermodynamics of strand crossing switches). As a result, quantum theory and general relativity are found to be lowenergy approximations of processes at the Planck scale. In particular, strands explain the entropy of black holes (including the numerical factor).
As a further surprise, in the same approximation, the fundamental principle yields the three gauge groups and the Lagrangians of quantum electrodynamics, of the strong and of the weak interaction, including maximal parity violation and SU(2) breaking. The three Lagrangians appear as a natural consequence of the three Reidemeister moves of knot theory. The strand model does not permit any further interaction, gauge group or symmetry group. The strand model might even be the first unified model predicting the three gauge interactions – and the lack of other ones.
In QED, the strand model proposes a simple understanding of Feynman diagrams and of Schwinger's formula for the anomalous magnetic moment of the electron and the muon.
As a final surprise, the fundamental principle predicts three fermion generations, the Higgs boson, and the lack of any unknown elementary particles. The strand model thus predicts that the standard model is the final description of particle physics. The quark model and the construction of all mesons and baryons are shown to follow from strands. In other words, tangles of strands and their crossing switches explain all known elementary particles, all their quantum numbers, and the lack of any other elementary particles. The strand model might be the first unified model predicting the elementary particle spectrum.
A natural method for the calculation of coupling constants, particle masses and mixing angles appears. So far, mass sequences, several mass ratios, the weak mixing angle, the sequence and the order of magnitude of coupling constants are predicted correctly. Again, the strand model might be the first unified model allowing such calculations. More calculations are under way; the volume is regularly updated.
The strand model thus fulfils a famous wish about the final theory of motion: it fits on a Tshirt. This wish is less frivolous than it looks, because it asks for a clear and simple fundamental principle.
Enjoying physics
The final theory of physics on a Tshirt? Indeed. (To support the project, you can buy the Tshirt here.) The search for a unified description of all motion in nature is fascinating – and a beautiful adventure. Numerous wonders of nature are encountered, including unexpected and captivating views on determinism, on induction, on the axiomatization of physics and on the mass gap in gauge theories. The search is fascinating, but not more than that: unification has no application in technology or in business and confers no power whatsoever. Anybody who assigns to unification more importance than to a riddle is already on the wrong track. Searching for unification is like looking for a beautiful flower in a large field during a walk through the countryside. The search is a pure pastime: it is just for enjoyment.
It is fun to find out how playing with strands at Planck scale reproduces quantum theory, general relativity and the standard model, including its gauge groups and its particle spectrum. Despite this playfulness, the strand model should not be called 'spaghetti model'. (And the model is not related to loop quantum gravity nor to string theory.)
Like the previous volumes, the text reduces math to a minimum; it entertains and surprises on every page. The text only presupposes knowledge about the concepts of electric charge, particle, Lagrangian, wave function, gauge symmetry, and space curvature. If you need to learn about these topics, read the previous five volumes of the Motion Mountain series; they provide an introduction to these concepts – and to established physics in general – with as little math and as much pleasure as possible.
Enjoy the reading!
The flow of the story
The text starts by listing
all open issues in fundamental physics in the year 2000. They are given in
the table of the millennium issues below. The text
then discusses many incorrect approaches to solve these issues. To find a
better approach, modern physics is first simplified as much as possible.
The results of this simplification are used to deduce the general
requirements that any final theory must fulfil; the main ones are listed in the requirements table below. The requirements
also explain why the previous approaches failed. It is shown that the main
requirement is the extension of nature's constituents. Then the
strand model is introduced and discussed; it is shown, step by step, that
it satisfies each requirement, that it solves all open issues, and that it
agrees with all experimental data. In particular, the strand model is
based on Planck units, uses neither continuity nor discreteness as
fundamental concepts, and does not assume that points or sets exist at
Planck scale. The model has no free parameters, is unique and
unmodifiable, and works in three spatial dimensions only. However,
dimensionality is not a parameter, but a result of the model: other numbers
of dimensions are impossible. As required from any final theory, the
strand model makes definite experimental predictions, also
given below. The predictions are quite unpopular and contradict those
of other unification proposals, but so far, none is
falsified by experiment.
Download volume VI (16MB)  THE STRAND MODEL – A SPECULATION ON UNIFICATION  
1  From millennium physics to unification – the open issues of fundamental physics  16 
2  Physics in limit statements – simplifying physics as much as possible  24 
3  General relativity versus quantum theory – their contradictions and our quest  52 
4  Does matter differ from vacuum? Not always – first requirements for any final theory  59 
5  What is the difference between the universe and nothing? – More requirements for any final theory  84 
6  The shape of points – extension in nature – an essential requirement for any final theory  108 
7  The basis of the strand model – and the full list of requirements for any final theory  138 
8  Quantum theory of matter deduced from strands  160 
9  The three gauge interactions deduced from strands  207 
10  General relativity deduced from strands  260 
11  The particle spectrum deduced from strands – and the lack of new physics  289 
12  Particle properties deduced from strands – and all predictions of the strand model  329 
13  The top of the mountain – the beauty and some new sights  366 
Discussion and blogs
Discussions about the strand model are found here. Some background is found on my blog on fundamental research and also on my blog on teaching.
Open issues in fundamental physics in the year 2000
This is the full list of questions that were unsolved in fundamental physics in the year 2000, the socalled millennium list of open issues. A correct description of nature must solve each of these questions. Such a description then qualifies as a unified and final theory.
OBSERVABLE  PROPERTY UNEXPLAINED IN THE YEAR 2000 
α  1/137.0359991(1), the low energy value of the electromagnetic coupling constant 
α_{w} (or θ_{w})  the low energy value of the weak coupling constant (or of the weak mixing angle) 
α_{s}, θ_{CP}  the value of the strong coupling constant at one specific energy value and the strong CP violation constant 
m_{q}  the values of the 6 quark masses 
m_{l}  the values of 6 lepton masses 
m_{W}  the value of the mass of the W vector boson 
m_{H}  the value of the mass of the scalar Higgs boson 
θ_{12}, θ_{13}, θ_{23}  the value of the three quark mixing angles 
δ  the value of the CP violating phase for quarks 
θ'_{12}, θ'_{13}, θ'_{23}  the value of the three neutrino mixing angles 
δ', α_{1}, α_{2}  the value of the three CP violating phases for neutrinos 
3 x 4  the number of fermion generations and of particles in each generation 
J, P, C, etc.  the origin of all quantum numbers of each fermion and each boson 
c, ħ, k  the origin of the invariant Planck units of quantum field theory 
3+1  the number of dimensions of physical space and time 
SO(3,1)  the origin of Lorentz and Poincaré symmetry (i.e., of spin, position, energy, momentum) 
S(n)  the origin of particle identity, i.e., of permutation symmetry 
U(1)  the origin of the electromagnetic gauge group (i.e., of the quantization of electric charge, as well as the vanishing of magnetic charge) 
SU(2)  the origin of weak interaction gauge group and its breaking 
SU(3)  the origin of strong interaction gauge group 
Ren. group  the origin of renormalization properties 
δW = 0  the origin of wave functions and of the least action principle in quantum theory 
W = ∫ L_{SM} dt  the origin of the Lagrangian of the standard model of particle physics 
0  the observed flatness, i.e., vanishing curvature, of the universe 
1.2 ⋅ 10^{26} m  the distance of the horizon, i.e., the ‘size’ of the universe 
ρ_{de} = Λc^{4}/(8πG) ≈ 0.5 nJ/m^{3}  the value and nature of the observed vacuum energy density, also called 'dark energy' or 'cosmological constant' 
(5 ± 4) x 10^{79}  the number of baryons in the universe, i.e., the average visible matter density in the universe 
f_{0}(1, ..., c. 10^{90})  the initial conditions for c. 10^{90} particle fields in the universe (if or as long as they make sense), including the homogeneity and isotropy of matter distribution, and the density fluctuations at the origin of galaxies 
ρ_{dm}  the density and nature of dark matter 
c, G  the origin of the invariant Planck units of general relativity 
δ ∫ L_{GR} dt  the origin of curvature, of the least action principle and of the Lagrangian of general relativity 
R × S^{3}  the observed topology of the universe 
As shown in the text, the strand model proposes an answer to each of these open issues. Each answer follows unambiguously from the single, fundamental principle that strand crossing switches define the Planck units.
Requirements for a final theory
Any final theory must fulfil certain requirements. The first half of the text shows how each requirement follows from the expressions for the Compton wavelength and for the Schwarzschild radius, i.e., when quantum theory and general relativity are combined. The full list of requirements that appear is given in the text. That list can be summarized in the following way:

The full list of requirements appears only when quantum physics and general relativity are combined. The requirements and their details do not follow from one theory alone. This makes the search for the final theory a special challenge; in a sense, the requirements for the final theory contradict quantum physics and also contradict general relativity. The final theory must thus contradict each part of 20th century physics.
The second half of the text shows, step by step, that the strand model fulfils the full list of requirements. In fact, the strand model is the only present candidate for a final theory that fulfils them. In addition, the strand model makes several predictions that can be tested against observation.
Predictions of the strand model – from 2008/2009
All predictions (except the corrected one) of the strand model were made before any experiment at the LHC in Geneva, or on neutrinos, on forbidden muon decays, on electric dipole moments, on QCD, on dark matter searches, or in astrophysics. The predictions that are typeset in bold characters (and a few others) are unique to the strand model:

Status of the predictions and of the model
Summary and outlook in 2015
The
strand model is a minimal unified theory of motion. To
falsify the strand model there are many possibilities: a single
observation that disagrees is sufficient, because all predictions follow
from a single principle. So far, no such falsifying observation is known,
and the Tshirt with the
fundamental principle describes correctly all known observations. In
addition, the strand model explains many observations that are not
explained by any other, competing model, such as the gauge groups,
parity violation, the number of fermion generations, the particle spectrum,
certain mass ratios, many mass sequences, and more. These results
encourage to proceed. To verify the strand model, however, there is
only one possibility: to calculate the constants of the standard model.
This project is under way; the first crude approximation of 2013 yielded a fine
structure constant value of 1/191, instead of the measured value
1/137.036(1). The result, possibly the first known estimate from first
principles, is not too disappointing. The remaining effort for these
computer calculations is estimated to be 2
manyears.
In the summer of 2014, a reader suggested that the tangles proposed so far for the W and Z might be wrong, out of esthetical and consistency reasons. His suggestion has good chances to be correct. This seems to explain the crude values that were obtained so far for the fine structure constant and the W/Higgs mass ratio. The strand model thus remains a work in progress.
Detailed status on the Higgs –
with the lessons from a mistake
The two experiments at
the LHC in Geneva have observed a neutral boson with a mass around 125 GeV.
It has spin 0, positive parity, no composite particle seems to fit, and it
indeed seems to be elementary.
Assuming that the observed boson is indeed the Higgs boson  and there is no reason to question this  the 'dirty trick' candidate tangle shown on the left of Figure 85 on page 291 seems to apply to it. The candidate tangle shown in that figure is part of the text since it was published in 2009 and was always mentioned as possible Higgs boson tangle. In 2009, it was argued that the candidate tangle could not be correct and thus the lack of a Higgs was predicted. The discovery of the Higgs boson in 2012 required a check of those arguments. The check showed that the arguments were wrong. Correcting the arguments, a more detailed and improved prediction is possible:
– Assuming that the Higgs tangle on the lefthand side of Figure
85 on page 291 is correct, then the tangle predicts a Higgs with vanishing
charge, positive parity and being elementary.
– That Higgs
tangle suggests a crude mass approximation for the Higgs boson of 109 GeV.
– Assuming that the Higgs tangle is correct, we have an
intuitive proposal for one of the mechanisms that influences mass values,
complementing tangle knottedness.
– If only one standardmodel
Higgs boson exists and if the tangle of Figure 85 is correct, the strand
model agrees with all data.
– If only one standardmodel Higgs
boson exists and if no strand configuration would be possible, then the
strand model is wrong. However, Figure 85 excludes this
possibility.
– If several Higgs bosons exist or if the tangle of
Figure 85 does not apply, the strand model is in trouble.
–
The strand model continues to predict the lack of
supersymmetry.
– In the case that effects or particles or
interactions beyond the standard model are observed, the strand model is in
trouble.
A longer evaluation is found in the text. After correction of the mistaken prediction, there is no contradiction between experiment and the strand model. The correspondence between the strand model and the standard model can be tested both in future experiments and through additional theoretical research. For example: in principle, other, so far overlooked strand configurations may also be of importance in nature; such configurations will be discussed in the text if they appear. Another example: no experiment has found any hint for physics beyond the standard model. In tabloid terms, the strand model predicts the socalled 'highenergy desert', also called the 'nightmare scenario': up to almost the Planck scale, particle physics is completely described by the standard model and by nothing else.
Experiment and theory on strands – status
of 2015
So far, not a single
experimental result contradicts the predictions of the strand model
deduced from the fundamental principle, not even the most recent results
from the LHC at CERN, the Tevatron, or the many other particle experiments.
In particular, the results for the main aims of the LHC, namely to find the
Higgs, to find supersymmetry, to clarify dark matter and to search for the
new and unexpected, are exactly those that are compatible with the strand
model. The ATLAS and CMS experiments at LHC have confirmed the standard
model of particle physics up to an energy of 1 TeV, and found nothing new.
Neither experiment, nor any other, found supersymmetry, dark matter, hidden
dimensions nor anything else that is unexpected. Of course, upcoming
experiments, at the LHC and elsewhere, still have many possibilities to
falsify the strand model.
After the strand model was proposed, independent theoretical investigations in general relativity and spacetime appear to confirm, independently, a number ideas of the strand model. Examples are Botta Cantcheff's fluctuating strings in space, Carlip's fluctuating lines in space, Verlinde's emergent gravity, Kempf's model with both continuity and discreteness, and recent cosmological models with timedependent cosmological constant. In particle physics, the strand model turned out to confirm unpopular older ideas unknown to the author that are scattered through the research literature. Examples are Weinberg's proposal that the standard model plus general relativity is all there is, Susskind's speculations of black holes as single woundup strings, and the 1980 paper by BatteyPratt and Racey deducing the Dirac equation from a tethered ball.
The proposed tangles for the leptons and those for the W and Z most probably need improvement. Future research will tell.
Support
The remaining effort for the research program is estimated to be 2 manyears.
You can support the project by solving one or several challenges from list C on the prize challenge page – and even earn prizes doing so.
You can also sponsor the project with a donation to our charitable nonprofit association. Your donation will be used (as controlled by the German tax authority) to complete the research project:
Thank you for your support! I also thank the German donor of 2010/2011.
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