Final Theory of Physics

A fascinating speculation: The strand model

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What determines colours?  What is motion? • An appetizer• Enjoying physics• Discussions and blogs• Open issues in fundamental physics since the year 2000• Requirements for a final theory• Predictions of the strand model• Status of the predictions and of the model• Support  

Free pdf of vol.  6 of
The fascinating quest for a final theory, with testable predictions and an estimate of the fine structure constant and of the Higgs/Z mass ratio. 454 pages, 34 MB, February 2016.

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 so-called '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 deducing 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 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, 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 T-shirt. This wish is less frivolous than it looks, because it asks for a clear and simple fundamental principle.


Enjoying physics

|  Grey T-shirt  ||  White T-shirt  |

The final theory of physics on a T-shirt? Indeed. (To support the project, you can buy the T-shirt 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 since 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.

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 since the year 2000

This is the full list of questions that are unsolved in fundamental physics since the year 2000, the so-called millennium list of open issues. (In fact, they are unsolved for an even longer period of time.) A correct description of nature must solve each of these questions. Such a description then qualifies as a unified and final theory.

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 constant
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. The full list of requirements that appear is given in the text. That list can be summarized in the following way:

  • At the Planck scale and all other energy scales, the final theory must describe nature, and in particular particles, space and horizons, as made of extended constituents fluctuating in a background.
  • In the final theory, the fluctuations of the constituents must explain all observed examples of everyday, quantum and relativistic motion: the fluctuations must describe all observations and experiments with maximum precision, imply all concepts of physics and explain all fundamental constants.

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:

  • Nature has three spatial dimensions, three gauge symmetry groups – namely U(1), SU(2) and SU(3) – and three generations of quarks and leptons. These statements are related and follow from topological arguments only.
  • No additional elementary particle will be discovered. (For an update, see below.) The unitarity of scattering for longitudinal W and Z bosons is maintained at all energies.
  • No additional elementary gauge bosons, preons, superpartners, magnetic monopoles, axions, sterile neutrinos, WIMPs, microscopic black holes, additional fermion families or leptoquarks exist. No new energy scale appears.
  • Dark matter is a mixture of known elementary particles and black holes. Dark matter detectors will not detect anything new.
  • Gauge couplings, particle masses, mixing angles and their running can be calculated with help of knot, polymer or cosmic string simulation programs.
  • All neutrinos have mass and differ from their antiparticles. Neutrinoless double-beta decay will not be observed.
  • Hadron form factors can be calculated ab initio.
  • The light scalar mesons are mostly tetraquarks; knotted two-quark states and knotted glueballs are ruled out.
  • The probable non-existence of glueballs needs a better argument.
  • The electric dipole moment of elementary fermions is at most of the order of the Planck length times the elementary charge.
  • The quark mixing and the neutrino mixing matrices are unitary.
  • The coupling constants, particle masses and mixing angles are constant in time.
  • There are only three fermion generations. The proton and the positron charge are equal.
  • The highest chromoelectric (and chromomagnetic) field in nature is given by the highest force divided by the colour charge; similar limits exist for the weak interaction. The limits can be checked in neutron/quark stars or other astrophysical objects.
  • No gauge groups other than those of the standard model exist in particle physics. No form of GUT, technicolour or supersymmetry is valid. No other interaction exists. Protons do not decay.
  • No additional spatial dimensions, fermionic coordinates, non-commutative spacetime or different vacua exist in nature. No dilaton exists.
  • No quantum gravity effect will ever be observed – not counting the cosmological constant and the masses of the elementary particles.
  • No deviations from QCD and 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 boson scattering is slightly changed at LHC energies through non-local and non-perturbative effects. (For an update, see below.)
  • No deviations from quantum theory or quantum electrodynamics appear for any measurable energy scale. The QED energy dependence of the fine structure constant is reproduced.
  • No deviations from thermodynamics appear for any measurable energy scale.
  • The universe's integrated luminosity is c^5/4G.
  • If the cosmological constant is non-vanishing, it decreases with time.
  • If the cosmological constant is non-vanishing, minimal electric and magnetic fields, a minimum force and a minimum acceleration exist.
  • The universe has trivial topology at all measurable energies.
  • No singularities, wormholes, time-like loops, negative energy regions, cosmic strings, cosmic domain walls, information loss, torsion or MOND exist; inflation did not occur.
  • No deviations from special or general relativity appear for any measurable energy scale. No doubly or deformed special relativity arises in nature.
  • There are maximal electric and magnetic fields in nature.
  • No deviations from electrodynamics appear for any measurable energy scale.
  • The Planck values are the smallest measurable length and time intervals, the Planck momentum and energy are the highest measurable values for elementary particles. A maximum curvature exists and the generalized indeterminacy principle holds. (As predicted by many.)
  • The highest force and power values measurable locally in nature are c^4/4G and c^5/4G. (As shown by Gary Gibbons and several others.) By the way, even the black hole merger published in 2016 remained below the power limit by a factor of about 3000 - or maybe 300 at peak power; the power limit c^5/4G corresponds to transforming into massless radiation about 50 000 solar masses per second.
  • The smallest entropy in nature is of the order k. (As shown by many.)
  • The quantum of action, hbar, is the smallest action value measurable in nature. (As shown by Niels Bohr.)
  • The speed of light, c, is the highest energy speed measurable locally in nature. (As shown by Hendrik Lorentz, Albert Einstein and others.)



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 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 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 man-years.

In the summer of 2014, a reader suggested that the tangles proposed so far for the W and Z might be wrong, out of aesthetic 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 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.
– 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 standard-model Higgs boson exists and if the tangle of Figure 85 is correct, the strand model agrees with all data.
– If only one standard-model 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 so-called 'high-energy 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 space-time 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 time-dependent 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 wound-up strings, and the 1980 paper by Battey-Pratt 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.



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