A FUN SPECULATION: THE STRAND MODEL

The strand modelOpen issues in physics in 2000Requirements for a final theoryPredictionsEnjoying physicsBetting  
 

If you enjoy playing with ideas and then checking them against the real world, you might like the following proposal for the final theory of physics. The colour pdf file with embedded animations is free. If you prefer a paper version in black an white delivered to your home, click on paper volume VI.
 

SIXTH VOLUME:   A SPECULATION ON UNIFICATION   (9MB)   Includes predictions on masses, mixing angles and coupling constants. Requires Adobe Reader 8.
1	From millennium physics to unification	17
2	Physics in limit statements	22
3	General relativity versus quantum theory	48
4	Does matter differ from vacuum?	54
5	What is the difference between the universe and nothing?	77
6	The physics of love - an intermediate report	100
7	The shape of points - extension in nature	110
8	The basis of the strand model	142
9	Quantum theory of matter deduced from strands	158
10	Gauge interactions deduced from strands	197
11	General relativity deduced from strands	236
12	Particles and their properties deduced from strands	261
13	The top of the mountain	308

 
The pdf file presents an approach to the unified and final 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 postulate: events and Planck units are crossing switches of strands. Surprisingly, this postulate allows to deduce Dirac's equation (from the belt trick), the principles of thermodynamics, and Einstein's field equations (from the thermodynamics of strands). They all follow as low-energy approximations of processes at the Planck scale. In particular, strands explain the entropy of black holes.

As a further surprise, in the same approximation, the postulate 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. The strand model does not permit any further interaction, gauge group or symmetry group.

As a final surprise, the postulate 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.

A natural method for the calculation of coupling constants, particle masses and mixing angles appears. Mass sequences, some mass ratios and the weak mixing angle are predicted correctly.

The first seven chapters of the text deduce the requirements that any unified and final theory must fulfill. The strand model seems to satisfy each of the requirements. 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, seems to be unique, seems to be unmodifiable, and works in three spatial dimensions. However, dimensionality is not a parameter, but a result of the model: other numbers of dimensions are impossible. The strand model also fulfils a famous wish: it fits on a T-shirt.

Additional points are found on the page on clear teaching and the page on fundamental research. Discussions about the strand model are possible on the fun discussion wiki.

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Open issues in fundamental physics in the year 2000: the millennium list

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, basic postulate 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.

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, 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 couping 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 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 sixth volume shows how each requirement follows from the expression 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. Thus, the search for unification is difficult 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 that the strand model fulfils all these requirements. In fact, the strand model is the only present candidate for a final theory that fulfils them.

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Some predictions of the strand model, all made before conclusive experiments (at the LHC, on neutrinos, on electric dipole moments, about QCD, on dark matter searches, and 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. 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. Dark matter is a mixture of known elementary particles and black holes. Dark matter detectors will not detect anything new. 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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Enjoying physics

The final theory on a T-shirt? Yes. The search for unification is fun - and a beautiful adventure. One encounters many unexpected wonders of nature. Enjoy the reading!

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Betting against the strand model

Do you want even more fun? Following European legislation, even many private bets must be agreed upon outside the internet. Following these laws, many bets are chance games. On the other hand, the validity of the strand model does not depend on chance. If you are convinced that the Higgs exists, that supersymmetric particles exist, that yet unknown elementary particles exist, that dark matter contradicts the standard model, that large electric dipole moments exist or that some other aspect of the strand model is wrong, email me at christoph@motionmountain.net.

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