Predictive Cosmology: The Standard Model Revisited

The theoretical value of the muon-electron mass ratio is announced!

Computed value: 206.768 283 185(77)(7)(5)(5)
vs.
2006 CODATA value: 206.768 2823(52)

Two familiar principles of physics display features that fill gaps in the standard model (SM) of particle physics. The new pieces shed light on the process of particle creation in the newborn universe. Thereby, they solve the mystery of the three particle generations and reveal the purpose of the electromagnetic, strong, and weak forces. Several quantities, which were previously thought to be determined by chance, prove to be theoretically calculable.

Remarkably, no innovative ideas are involved. All pieces of the puzzle have been available for a long time — the main pieces being:
• Conservation of momentum
• Conservation of energy
• Conservation of mass
• Dirac’s large-number hypothesis (LNH) — proposed in the 1930s but later dismissed
• Dirac’s new equation from 1971 — forgotten, since no application for it was found
• Scalar QED (similar to spinor QED, but not applicable to any observed particle)
• Established SM: spinor QED, electroweak theory, and QCD

PIECE 1: The Pressureless Momentum Equation

The crucial piece is furnished by the momentum equation (also known as the fundamental hydrodynamic equation), which expresses conservation of momentum (or Newton’s second law of motion) for a fluid. The momentum equation has a stationary solution,

ρ = ρ0 (1 − v 2/ f v 2) f / 2,

which connects density (ρ) to velocity (v) via a parameter ( f ) that specifies degrees of freedom.
What makes this strikingly simple equation so highly remarkable is its lack of reference to pressure (p) and, thereby, to molecules and temperature.
If, back in the 1880s, Albert Michelson had known about this molecule-free space equation, he would have realized why his attempts to measure the speed of the ether wind was doomed to failure. Instead of concluding that the ether doesn’t exist, he would have noted that it is by necessity unobservable.
Similarly, Albert Einstein, noticing that a perfectly smooth space implies distance undefinability, would have had no problems understanding quantum phenomena. There would have been no need for him to coin the expression “spooky action at a distance.”
Paul Dirac, in turn, would have seen first his LNH hypothesis and later his new equation neatly fit into the SM puzzle.

The only practicable way of interpreting the “space equation” (the pressureless momentum equation stated above) is to assume that f = 3 is connected with charge, f = 2 with spin, and f = 1 with expansion of space. Thus, conservation of momentum governs the growth of the universe by connecting expansion of space to spin and charge and, thereby, to energy. A straightforward calculation shows that expansion causes gravity with Newton’s gravitational potential U = −Gm/r replaced by

U = −Gm/r(1 − r2/R2),

where R is the radius of the universe and G is the gravitational constant.
The potential U describes a long-range attractive force that, for ultra-long distances when r approaches R, becomes repulsive, which enables gravity to “balance itself” on a global scale. The balance between gravity’s push and pull must by necessity be exact because gravity is the only existing long-range force and, being but a side effect of the unperturbable expansion, it cannot affect the overall expansion. Consequently, general relativity is confined to its natural role as a theory for the gravitational force.

In summary, with the first piece put in place, the nature of space (which used to be a problem of metaphysics) has become a question for ordinary theoretical physics.
It should be stressed that the initially mentioned “space equation” does not apply to the space of today’s universe. It only applied to space momentarily — in two phase transitions that took place very early in the history of the universe.
Of interest today is the fact that the space equation yields a numerical constant,

B = 0.666 001 731 498,

which connects the fine-structure constant α to the zeroth-order muon-electron mass ratio via the relation

mμ/me = 1/ = 205.759 223 442(77).

Using standard methods in QED and electroweak theory, corrections to the zeroth-order value may be calculated and a precise prediction for the measured mass ratio obtained.

PIECE 2: Global Conservation of Energy

The other major piece in the cosmology puzzle is provided by the law of conservation of energy. When it is assumed that total energy is conserved in a volume coexpanding with the universe, it becomes evident that energy conservation governed the physical processes in which elementary particles were initially formed.
Thus, the energy principle comprises global conservation of energy in addition to the well-known local conservation of energy.

Apparent Time Paradox Explained

When demanding global energy conservation, a computer simulation (see Simulation.for) of the evolution of the early universe resolves an “age paradox” (a paradox that in the 1970s led physicists to mistakenly dismiss Dirac’s large-number hypothesis). The result implies that:
• In our local picture of the universe (when we study a galaxy or perform laboratory experiments), the velocity of light (c) is constant, and we define the (constant) unit of time in terms of atomic-clock ticks or particle lifetimes (τ).
• In the global picture of the universe (when a cosmic volume coexpanding with the universe is being considered), global conservation of energy makes (via a varying c) particle rest energy (mc²) grow to compensate for the loss of radiation energy caused by the redshift. In this picture, the lifetime τ (that is, our local picture’s constant unit of time) increases with c.
• Thanks to quantum indeterminacy (or position and distance undefinability, which follows from the space equation and manifests itself as a “spooky action at a distance”), there is no conflict between the two pictures (one with distances constant, the other with increasing over time).
In the global picture, when counting “cosmic seconds,” the universe is less than 6 billion years old. In our standard, local picture, where we count atomic-clock ticks or “atomic seconds,” it is many times older. The high age of the universe implies that it is decelerating so slowly that it should appear to be expanding at a constant rate. However, the deceleration is accompanied by a slow decrease in G, which has the effect that the universe appears to be accelerating.

NEW AVENUES OF RESEARCH

Research in Particle Physics

With the long overlooked pieces of SM now put in place, our picture of the elementary particles becomes clearer. Thus, the amended SM explains:
• The reason why there are three particle generations (global conservation of energy)
• The lepton mass ratios (determined by energy conservation)
• The value of the fine-structure constant α (determined via me/mμ)
• The purpose of the electromagnetic force (recreate matter from radiation)
• The purpose of the strong force (create stable matter — the proton)
• The purpose of the electroweak force (transfer energy from leptons to quarks)
• The purpose of parity (P) violation (stabilize matter)
• The cause of charge-parity (CP) violation (global energy conservation)
• The complexity of the electroweak force (repeated energy transfer)
No freely adjustable parameters appear in the theory. Consequently, its predictions are unambiguous and precise. Among the quantitative predictions of the amended SM are:
• 206.768 283 185(78) for mμ/me, a value 67 times more precise than the measured value, 206.768 2823(52)
• Low Higgs and neutrino masses, such as 0.065 MeV/c2 for the tauon neutrino
In addition, there are a number of tasks that remain to be accomplished. Some of them might even appear trivial to persons skilled in the respective area. Here are some examples in particle physics:
• Amend the FORTRAN program listed in Section G.2 and compute 1/α to see how well the result matches the experimentally obtained value of 137.035 999 084(51).
• Develop the QED theory for the (primordial) D particle proposed by Dirac in 1971.
• Improve the scalar perturbation calculation in Section 8.
• Perform the QED calculations suggested in footnote 5 in Appendix F.
• Reinvestigate the JBW hypothesis in the light of the Higgs calculation (Appendix C).
• Find the electroweak model that fits in with the scenario described in Appendix E.8.
• Predict the outcome of CERN’s LHC experiment.
• Clarify if the “Pioneer anomaly” may be a “spooky” effect due to distance indeterminacy.
Theories of Everything

The two pieces now put in place say nothing direct about dynamic interactions between particles. Still, they may guide physicists in their search for a theory of everything (TOE). For instance, they suggest that one should:
• Study consequences for string theory of the external conditions discussed at the end of Section 11.
• Investigate consequences of the internal cosmological radius of elementary particles (see footnote 2 in Section 3).
• Consider the implications for quantum-gravity theories of the close connection between charge, spin, expansion, and gravity.
• Research the effect on general relativity (GR) of the modified gravitational potential.
• Investigate the effect on GR of global energy conservation.
Astrophysics

Astrophysical calculations require simulation of the evolution of phase 4. Even a crude simulation should suffice to yield indicative results (see Simulation.for). The theory already explains:
• The age and flatness of the universe (the expansion obeys dV/dt = constant)
• The repulsive force (gravity’s “other side”)
• The reason why antimatter disappeared (the antiproton’s decay into an electron)
• The origin of the universe’s early heat (antiproton decay)
• The homogeneity of the background radiation
• The large photon-baryon number ratio (nγ/nb)
Among the theory’s quantitative predictions in astrophysics are:
• Ω = 2, or a density of the universe twice as high as it is commonly believed to be
• H0 = 56.8 km/s/Mpc for the present-day Hubble expansion rate
• nγ/nb = 2.786 × 109 photons per baryon (original value)
With the aid of a detailed computer simulation, it should be possible to:
• Estimate the distribution of black holes in the universe.
• Estimate their average size and compare them with the Jupiter-mass black holes, which according to Michael Hawkins’ observations constitute 99 percent of the universe.
• Estimate the rate of decrease of G and H.
• Obtain the corresponding dG/dt and dH/dt from type Ia supernova observations.
• Investigate the effect of a slowly declining G on the luminosity of distant stars.
• Correct the distance scale assuming a slowly decreasing gravity.
• Clarify if G declines fast enough to save the earth when the sun turns into a red giant.

A simple model describing a pure QED universe

Abstract

A particle model derived from Newton's second law pictures an electron in an expanding universe. The model unifies charge, spin, and expansion. Expansion causes gravity. Massive particles pick up energy released via radiation redshift, and a purely radiative, matter-free, universe is forbidden. Therefore, the universe is forced to undergo a series of matter-creating phase transitions — from literally nothing (phase 0), via decaying neutral spinless matter (phase 1), charged spinless matter (phase 2), and charged spinning matter (phase 3), to the strongly and weakly interacting stable matter of today (phase 4). The tauon-muon and muon-electron mass ratios tell how much the rest energies of the massive particles grew in phase 1 and phase 2, respectively. The model contains no adjustable parameters, and makes unambiguous predictions, such as H0 = 56.8 km/s/Mpc for the present-day Hubble expansion rate and 1/ = 205.759 223 (with B = 0.666 001 731) for the muon-electron mass ratio. To the zeroth-order predictions of the particle model must be added radiative contributions calculated using standard QED and electroweak theory. Thus, mμ/me = 1/ + 1/(1 − 2) = 206.769 039 is the muon-electron mass ratio of the pure QED universe (phase 3). This value is larger than the measured phase-4 value 206.768 283(6). A simple electroweak calculation shows that the appearance of the weak force caused a sudden decrease in lepton masses. Thus, a one-Higgs model adds −0.000 2076 to mμ/me. The corresponding decrease in tauon mass explains how the creation of the proton was energetically possible, and why the previously cold universe acquired a high temperature. The numerical value 1 + 2(mpmπ) / 4(mπme) = 3.872 = 4 − 0.128 informs that four Higgs bosons act to decrease the tauon mass, while a weak (presumably flavor-changing) effect slightly corrects the mass upward. It is concluded that the corresponding total weak correction to the muon-electron mass ratio is −0.000 2076(4 − 0.128 log(mτ/mμ)) = −0.000 755, yielding mμ/me = 206.768 284, which agrees with the measured value.

See:
Paper.pdf

See Universe.pdf for final conclusions and Index.doc for links and references to articles on extended SM (xSM).

2012-05-04: See Conclusions.pdf for summary and suggested experiments.

2013-03-22: See article On the origin of mass in the standard model, Int. J. Mod. Phys. E 22 (2013) 1350002, http://dx.doi.org/10.1142/S021830131350002X.
For an author-created version of this article (with Contents, Index, and Errata), see
Article.pdf.

2013-10-27: For solved puzzles in particle physics, see Article2.pdf.
2014-10-15: For 13 possible appearances of a light Higgs boson, see Article3.
2014-11-10: For corrections of errors in Paper.pdf, see Errata.

2016-06-27: See revised Article3.
2016-06-27: See revised Errata.

2016-11-26: See added article How can “137.036” be calculated?
2016-11-26: See added article A maximally simple model (MxSM).

2018-06-13: For a one-page summary of fundamental physics, see Advertisement.

2019-03-31: Version 5 of Book posted.