An appetizerEnjoying physicsOpen issues in fundamental physics in the year 2000Requirements for a final theoryPredictions of the strand modelStatus of the predictions
SIXTH VOLUME: A SPECULATION ON UNIFICATION
If you enjoy playing with ideas and then checking them against the real
world, you might like this volume. It first tells why the past
proposals for a final, unified theory of physics failed. Then it proposes
a better one: the strand model. This model
agrees with all experimental data known so far
and makes clear, falsifiable predictions that are being tested around the world.
In particular, the strand model
- is based on one simple fundamental principle – and thus is 'beautiful',
- predicts quantum theory – and allows no alternative or extension,
- predicts the standard model of particle physics –
and allows no alternative or extension,
- predicts general relativity – 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 home, click here.
| A SPECULATION ON UNIFICATION - Table of Contents | ||
| 1 | From millennium physics to unification - the open issues of fundamental physics | 17 |
| 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 | 85 |
| 6 | The shape of points - extension in nature - an essential requirement for any final theory | 109 |
| 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 | 159 |
| 9 | The three gauge interactions deduced from strands | 201 |
| 10 | General relativity deduced from strands | 246 |
| 11 | The known elementary particles and their properties deduced from strands - and all predictions of the strand model | 272 |
| 12 | The top of the mountain - the beauty and some new sights | 334 |
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 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.
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 following 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, induction, Hilbert's sixth problem about the axiomatization of physics, and on what dreams tell us about nature.
Like the previous volumes, the text reduces math to the minimum and entertains and surprises on every page. The text only presupposes a general idea about what a Lagrangian, a wave function, the speed limit, electric charge, a particle, a 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. In other words, each requirement 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
All predictions were made in 2008 and 2009, before any conclusive 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:
Status of the predictions and of the strand model - December 2011
The experimental predictions above are all from 2008 and 2009. Those typeset in bold characters (and a few others) are unique to the strand model. Also the theoretical concepts are unique and differ from those of any competing model. The present status is as follows:
- 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, the Tevatron, or the many other particle experiments. In particular, in July 2011 the ATLAS and CMS experiments at LHC have confirmed the standard model of particle physics up to an energy of 1 TeV, in agreement with the predictions presented here. In December 2011, the two experiments have published their latest data on the Higgs search. The Higgs has not been found yet - though there might be hints for its existence. Of course, upcoming experiments and data collection still have many possibilities to falsify the strand model.
- Recent 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) and in particle physics (Weinberg's proposal that the standard model plus general relativity is all there is, various Higgsless models with desert, but also the 1991 paper by Veltman and Veltman) are confirming more and more aspects of the strand model.
Only a single observation is needed to falsify the strand model. But so far, the T-shirt with the fundamental principle describes correctly all known observations.