An appetizerEnjoying physicsOpen issues in fundamental physics in the year 2000Requirements for a final theoryPredictions of the strand modelStatus of the predictions Support
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. The text explains why the past
proposals for a final, unified theory of physics, the so-called 'theory of
everything' in physics, failed. Then, the text presents a better proposal:
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
best called a 'theory of motion'.
In particular, 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.
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.
The colour pdf file with embedded animations is free. If you want a paper version in black and white delivered to your address, click here.
| THE STRAND MODEL – A SPECULATION ON UNIFICATION - Table of Contents | ||
| 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 | 203 |
| 10 | General relativity deduced from strands | 248 |
| 11 | The particle spectrum deduced from strands - and the lack of new physics | 276 |
| 12 | Particle properties deduced from strands - and all predictions of the strand model | 313 |
| 13 | The top of the mountain - the beauty and some new sights | 343 |
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 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 and the lack of any unknown elementary particles. The strand model thus predicts that the standard model, with slight corrections for longitudinal W and Z boson scattering, 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, 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 volume is regularly updated.
The strand model also fulfils a famous wish about the final theory: it fits on a T-shirt. This wish is less frivolous than it looks: it asks for a clear and simple fundamental principle.
The flow of the story
The text starts by listing all open issues in fundamental physics in
the year 2000 (given in the table of the millennium issues
below). It then lists many incorrect approaches to solve these issues.
To find the correct approach, the subsequent chapters first simplify modern
physics as much as possible; these results are then used to deduce the
general requirements that any final theory must fulfil (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.
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 that should be thoroughly enjoyed.
Like the previous volumes, the text reduces math to the minimum; it entertains and surprises on every page. The text only presupposes knowledge about what a Lagrangian, a wave function, the speed limit, electric charge, a particle, a gauge symmetry and space curvature are. 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 fun as possible.
Enjoy the reading!
Christoph Schiller
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 unified and final description of nature must solve all these questions. Many such lists are found in the research literature; they are all contained in this one.
| 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, 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 sixth volume of the Motion Mountain 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 list of requirements is rarely found or discussed. As shown in the text, all the following requirements appear when quantum theory and general relativity are combined. The first half of the text shows how each requirement follows from the expressions for the Compton wavelength and for the Schwarzschild radius.
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 predictions and the strand model
Summary
The strand model is a minimal unified theory of motion. To
falsify the strand model, only a single observation is needed, because all
predictions follow from a single principle. So far, no such observation is
known. So far, the T-shirt with the fundamental principle describes
correctly all known observations. In addition, the model also explains
many observations that are not explained by any other, competing
model, such as the gauge groups, the number of fermion generations, mass
sequences and more. To verify the strand model definitively, calculations
are under way. This is expected to take a couple of man-years.
Detailed status of July & December
2012 – 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 seems to have spin 0, 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' tangle shown in Figure 85 on page 291 might apply to it. The candidate tangle shown in that figure is part of the text since it was published in 2009; it was always mentioned as possible Higgs boson tangle. It suggests an approximate Higgs mass estimate in the range from 114 to 117 GeV. 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 lead to a check of the arguments and prediction. The check showed that several arguments are questionable and a few incorrect. Correcting those arguments, more detailed and improved predictions are possible:
– Assuming that the Higgs tangle on the left-hand side of Figure 85 on page 291 is correct, we have an intuitive proposal for an important part of the mechanisms that determine mass values, complementing tangle knottedness. – 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 only one standard-model Higgs boson exists and the tangle of Figure 85 is correct, the strand model agrees with all data.– 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 beyond the standard model are observed, the strand model is in trouble.
The correspondence between the strand model and the standard model can be tested in future experiments and with additional theoretical research. (In principle, other, so far overlooked strand configurations may also be of importance.) A longer evaluation is found in the text. After correction of the mistaken prediction, there is no contradiction between experiment and the strand model. For example, in 2012, no hint for physics beyond the standard model was found in any experiment, as predicted by the strand model. 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. More experimental data will be published by CERN and by dark matter experiments during 2013. It is wonderful to experience this situation of ongoing suspense.
Detailed status of 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
This research has been partially funded by donations, above all by the Klaus Tschira Foundation. Your support is welcome:
Your donation will be used to complete this research programme. Thank you!
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