FINAL THEORY OF PHYSICS

A FASCINATING SPECULATION: THE STRAND MODEL

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The strand modelAn appetizerEnjoying physicsOpen issues in fundamental physics in the year 2000Requirements for a final theoryPredictions of the strand modelStatus of the predictions  
 

pdf  SIXTH VOLUME:   A SPECULATION ON UNIFICATION  
       with experimental predictions. The fascinating quest for a final theory of physics. Edition 24.32.
       Click for free download: 406 pages, 11 MB. Requires Adobe Reader 8 or higher.

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

 
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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.

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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.

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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.

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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 precision of the final theory must be complete; the final theory must describe all motion and all experiments, and explain all open issues from the millennium list. (If it did not, it would neither be final nor unified.)
  • Any modification of the final theory must be impossible; it must be 'hard to vary'. (If it could be modified, it would not be an explanation.)
  • In the final theory, vacuum and particles must not differ from each other at the Planck scale because of limitations of measurement precision. Thus vacuum and particles must be described by common fundamental constituents. (If common constituents did not exist, the theory would not describe black holes.)
  • The fundamental constituents must be extended and fluctuating, (If they were not, they would not explain black hole entropy, spin, the observer-invariance of space-time homogeneity, and spatial isotropy.)
  • The fundamental constituents must be as simple as possible, to satisfy Occam's razor. (If they were not, the theory would be fiction, not science.)
  • The fundamental constituents must determine all observables. They must also determine all coupling constants and particle masses. (If they did not, the theory would not be final.)
  • The fundamental constituents must be the only unobservable entities. (If they were observable, the theory would not be final; if more entities would be unobservable, the theory would be fiction, not science.)
  • Non-locality must be part of the description; non-locality must be negligible at everyday scales, but important at the Planck scale. (Otherwise, the contradictions between quantum theory and general relativity would not be solved.)
  • Physical points and sets must not exist at Planck scale, due to limitations of measurement precision; points and sets must only exist, approximately, at everyday scales. (Otherwise, the contradictions between quantum theory and general relativity would not be solved.)
  • The final theory cannot be a set of differential or evolution equations. (If it were, it would contradict the limits to measurement precision.)
  • Physical systems must not exist at Planck scale, due to limitations of measurement precision; systems must only exist, approximately, at everyday scales. (Otherwise, quantum theory and general relativity cannot be unified.)
  • Due to limitations of measurement precision, the universe must not be a physical system. (Otherwise, quantum theory and general relativity cannot be unified.)
  • Due to limitations of measurement precision, each Planck unit is a limit value for measurements. Infinitely large or small quantities do not exist. (Otherwise, quantum theory and general relativity cannot be unified.)
  • The Planck scale description of the final theory must imply quantum field theory, the standard model of elementary particle physics and general relativity. (Otherwise, quantum theory and general relativity would not be unified.)
  • Planck's natural units must define all observables. They must also define coupling constants and particle masses. (Otherwise, the theory would be neither final nor unified.)
  • The relation to experiment must be as simple as possible, to satisfy Occam's razor. (Otherwise, the theory would not be falsifiable.)
  • The final theory must depend on the existence of a background, as background-independence is logically impossible in physics. (Otherwise, the theory would not be a description of nature.)
  • Background space-time must be equal to physical space-time at everyday scale, but must differ globally and at Planck scale. (Otherwise, quantum theory and general relativity would not be unified.)
  • The big bang is not an event. (Otherwise, sets and points would exist, and quantum theory and general relativity would not be unified.)
  • Circularity in concept definitions must be part of the final theory, as a consequence of it being 'precise talk about nature'. (Otherwise, the theory would not be final.)
  • An axiomatic description of the final theory must be impossible, as nature is not described by sets at the fundamental level; the final theory must leave Hilbert's sixth problem without a solution. (Otherwise, the theory would not be final.)
  • Due to the limits to measurement precision, space is undefined at Planck distance, and the dimensionality of physical space at Planck distance is undefined. (Otherwise, quantum theory and general relativity cannot be unified.)
  • Due to the limits to measurement precision, symmetries are undefined at Planck distance. (Otherwise, quantum theory and general relativity cannot be unified.)
  • Due to the limits to measurement precision, nature is similar at Planck scale and at cosmic horizon scale. (Otherwise, quantum theory and general relativity cannot be unified.)

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.

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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:

  • No additional elementary particle will be discovered: the Higgs boson does not exist. The unitarity of scattering for longitudinal W and Z bosons is maintained at all energies.
  • Non-local and non-perturbative effects in longitudinal W and Z boson scattering will be observed.
  • 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 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 elementary gauge bosons, preons, superpartners, magnetic monopoles, axions, sterile neutrinos, additional fermion families or leptoquarks exist.
  • 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 scattering is slightly changed at LHC energies.
     
  • 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 nonvanishing, it decreases with time.
  • If the cosmological constant is nonvanishing, 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.)
  • The smallest entropy in nature is of the order k. (As stated by many.)
  • The quantum of action, hbar, is the smallest action value measurable in nature. (As stated by Niels Bohr.)
  • The speed of light, c, is the highest energy speed measurable locally in nature. (As stated by Hendrik Lorentz, Albert Einstein and others.)

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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.

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