Predictions from the Prequark Model:
Note: The measured Beta value is Beta = 137.0359895
Beta = (1+ first order mixing + sum of the higher order mixing)
First order mixing = [1/Cos(A)]; the mixing angle A = 28.743 degree
Sum of the higher order mixing = 2 (1/48)[(1/64) + (1/2)(1/64)^2 + ... + (1/n)(1/64)^n +...]
Beta = 64 (1 + 1/Cos(A) + .0006561) = 137.0359
In 1980, Klaus von Klitzing discovered quantum Hall effect. The Hall resistance varies stepwise with changes in magnetic field B. Step height is given by a physical constant divided by an integer i. The figure below shows steps for i = 2, 3, 4, 5, 6, 8 and 10. This is termed the integer quantum Hall effect. Klitzing was awarded Nobel Prize in Physics in 1985.
In 1982, Horst Stormer and Daniel Tsui discovered the fractional quantum Hall effect. In the figure below, the dashed diagonal line represents the classical Hall resistance and the full drawn diagonal stepped curve the experimental results. The magnetic fields causing the steps are marked with arrows. Note particularly the step first discovered by Stormer and Tsui (1/3) at the highest value of the magnetic field and the steps earlier discovered by von Klitzing (integers) with a weaker magnetic field. Stormer and Tsui subsequently found more and more new steps, both above and between the integers. All the new step heights can be expressed with the same constant as earlier but now divided by different fractions.
A year after the discovery of the fractional quantum Hall effect, Laughlin offered a theoretical explanation. According to his theory the low temperature and the powerful magnetic field compel each electron to capture three magnetic flux quanta and force the electron gas to condense to form a new type of quantum fluid. This new quantum fluid has many unusual properties. One of the most remarkable is that if one electron is added the fluid will be affected (excited) and a number of fractionally charged "quasiparticles" created. These quasiparticles (consist of composite particles) are not particles in the normal sense but a result of the common dance of electrons in the quantum fluid. Laughlin's quantum fluid has proved capable of explaining all the steps found experimentally. They three (Stormer, Tsui and Laughlin) were awarded Nobel Prize in Physics in 1998.
In Prequark Model, electron is a composite of three Angultrons which form a looped superstring. At fractional quantum Hall effect condition, those looped superstrings can split and rejoin with other electrons to form a composite particle just the same as the quasiparticle in the Laughlin's quantum fluid.
In Prequark Model, electron superstring can be splitted in a two-dimensional plane in following ways.
The picture below was on the cover of Science magazine (June 22, 1990 issue). It is a computer graphics visualizing the Laughlin wave function for the nu = 1/3 FQHE state. The green balls represent electrons that are pinned momentarily in the two-dimensional plane by three magnetic flux quanta which appear as black arrows. The blue mountain represents the charge distribution of one free composited electron quasiparticle moving in the presence of the magnetic field and the potential of the other (green) electrons.