An appetizerEnjoying
physicsOpen issues in fundamental
physics in the year 2000Requirements
for a final theoryPredictions of the
strand modelStatus of the model and its predictionsSupport
VOLUME VI: THE STRAND MODEL – A SPECULATION ON
UNIFICATION If you enjoy exploring ideas and checking them against the real
world, you might like this volume. It explains why the past proposals for
a final, unified theory of physics – the so-called 'theory of
everything' – have failed. Then, the text presents a better
proposal: a 'theory of motion' called the strand model. This model
agrees with all experimental data known so far and makes clear, falsifiable
predictions. At present, they are being tested in experiments around the
world. The strand model
–
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,
– predicts the standard
model of particle physics – and allows no alternative or extension,
– and solves all open issues of the standard model, gravitation
and cosmology, including the explanation of their two dozen numerical
parameters.
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.
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 below, is free. If you want a paper version in black and white delivered to your address, click here.
| Table of Contents: 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 | 206 |
| 10 | General relativity deduced from strands | 252 |
| 11 | The particle spectrum deduced from strands – and the lack of new physics | 280 |
| 12 | Particle properties deduced from strands – and all predictions of the strand model | 320 |
| 13 | The top of the mountain – the beauty and some new sights | 354 |
An appetizer
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 and 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). Quantum theory and general relativity are thus found to be low-energy 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, some 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. The calculations are under way; the volume is regularly updated.
The strand model also fulfils a famous wish about the final theory of motion: it fits on a T-shirt. This wish is less frivolous than it looks: it asks for a clear and simple fundamental principle.
Enjoying physics
The final theory of physics on a T-shirt? Indeed. The search for unification is fascinating – and a beautiful adventure. Numerous wonders of nature are encountered, including unexpected and fascinating views on determinism, on induction, on Hilbert's sixth problem about the axiomatization of physics, on the mass gap in gauge theories, and on what dreams tell us about nature. 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. The search is a pure pastime: it is just for enjoyment.
The strand model attempts to solve the riddle of unification. Nevertheless, it should not be called 'spaghetti model', as some people do.
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 Lagrangian, wave function, electric charge, particle, gauge symmetry, nature's speed limit 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 the
simplification are used to deduce the general requirements that any final
theory must fulfil; they are listed in the requirements
table below. The requirements explain why the previous approaches
failed. 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.
Discussion and blogs
Discussions about the strand model are possible
on the discussion
wiki. Some background for the strand model is found on my blog
on clear
teaching and my blog
on fundamental research.
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 so-called millennium list of open issues. A description of nature must solve each of these questions. It then qualifies as 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 |
| αw (or θw) | the low energy value of the weak coupling constant (or of the weak mixing angle) |
| αs, θCP | the value of the strong coupling constant at one specific energy value and the strong CP violation parameter |
| mq | the values of the 6 quark masses |
| ml | the values of 6 lepton masses |
| mW | the value of the mass of the W vector boson |
| mH | the value of the mass of the scalar Higgs boson |
| θ12, θ13, θ23 | 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', α1, α2 | 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 = ∫ LSM 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 ⋅ 1026 m | the distance of the horizon, i.e., the ‘size’ of the universe |
| ρde = Λc4/(8πG) ≈ 0.5 nJ/m3 | the value and nature of the observed vacuum energy density, also called 'dark energy' or 'cosmological constant' |
| (5 ± 4) x 1079 | the number of baryons in the universe, i.e., the average visible matter density in the universe |
| f0(1, ..., c. 1090) | the initial conditions for c. 1090 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 |
| ρdm | the density and nature of dark matter |
| c, G | the origin of the invariant Planck units of general relativity |
| δ ∫ LGR dt | the origin of curvature, of the least action principle and of the Lagrangian of general relativity |
| R × S3 | 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.
Each of these requirements appears when quantum physics and general relativity are combined. None of the requirements follows from one theory alone. In other words, the search for the final theory is a hard puzzle, because each requirement contradicts quantum physics and also contradicts general relativity. In a sense, each requirement for the final theory contradicts each part of 20th century physics!
The second half of the text shows, step by step, that the strand model fulfils all the listed requirements. In fact, the strand model is the only present candidate for a final theory that fulfils them.
Predictions of the strand model – from 2008/2009
All predictions 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:
Non-local and non-perturbative effects in longitudinal W and
Z boson scattering will be observed. (For a summer
2012 update, see below.)
almost none from the standard model
appear for any measurable energy scale. In particular, the strand model
implies that SU(2) is broken and P, C and CP are violated in the weak
interaction, and that SU(3), confinement and asymptotic freedom are
properties of the strong interaction. Longitudinal W and Z
scattering is slightly changed at LHC energies. (For a summer 2012 update, see below.)
The theoretical concepts and many predictions of the strand model are unique and differ from those of any other model.
Status of the model and its predictions
Summary and outlook (2013)
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 T-shirt 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 standard model parameters. This project is under way. The
effort for these computer calculations is estimated to be a couple of
person-years
(about one PhD). Sponsors are welcome.
Detailed status of July
2012 and March 2013 – with the lessons from a mistaken prediction
The two experiments at the LHC in Geneva have observed a neutral boson
with a mass around 126 GeV. It has spin 0, positive parity, and no
composite particle seems to fit, so that it seems to be elementary. This
observation contradicts the prediction made in the text in 2009 that the
Higgs boson does not exist. Both the original, mistaken prediction and its
correction are now included in the text.
Assuming that the observed boson is indeed the Higgs boson, 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 asked for a check of those arguments. The check showed that a few arguments were wrong and several other questionable. Correcting the arguments, a more detailed and improved prediction is possible:
– Assuming that the Higgs tangle on the left-hand side of Figure
85 on page 291 is correct, then the tangle predicts a Higgs with vanishing
charge, positive parity and being elementary.
– The Higgs tangle suggests an approximate Higgs mass estimate near
the range from 114 to 117 GeV, as is observed.
– 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 standard-model
Higgs boson exists and the tangle of Figure 85 is correct, the strand
model agrees with all data.
– If only one
standard-model Higgs boson exists and no strand
configuration is 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.
– If no Higgs
boson exists after all, 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 2012, no experiment found any hint for physics beyond the standard model, as predicted by the present model. 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. In tabloid terms, the strand model predicts the so-called 'nightmare scenario': up to almost the Planck scale, particle physics is completely described by the standard model and by nothing else. Precise experimental data that can be compared to this prediction will be published by CERN and by various dark matter experiments in the near future.
Experiment and theory – May 2012
– 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 were predicted by or 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.
In December 2011, the two experiments have published their data on
the Higgs search, followed by an improved data set by ATLAS in March 2012;
the Higgs has not been found yet – and the 2011 hints for its existence are
getting weaker. And neither experiment, nor any other, found
supersymmetry, dark matter, hidden dimensions or 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 space-time (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, recent cosmological models with time-dependent cosmological
constant) confirmed the ideas of the strand model.
In particle physics, the strand model turned out to confirm unpopular older
ideas unknown to the author (Weinberg's proposal that the standard model
plus general relativity is all there is, various Higgsless models
with desert, the 1991 paper by Veltman and Veltman questioning the Higgs
boson,
and the 1980 paper by Battey-Pratt and Racey on the Dirac equation).
Support
You can support the project by solving one or several challenges from list C on the prize challenge page – and earn a prize doing so.
You can also support the project with a donation to our charitable non-profit association. Your donation will be used to complete this research project:
The research project needs another couple of man-years of effort. Thank you in advance for your support!
This research has been partially funded by the Klaus Tschira Foundation.
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