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Friday, April 16, 2021

Muon g-Value Anomaly

Muon g-Value and Muonium Anolmalies

Quantum spin magnetism is really one of the most enduring quantum mysteries and yet it is still not very well explained. And yet, spin is at the root of both the anomalous g-value as well as the fine-structure constant of spin magnetism. All quantum particles have spin magnetism as well as charge and classically, that magnetism is due to the classical spin of a sphere of surface charge. However, the quantum definition of spin is much more mysterious and luxurious.

A classical particle as a charged sphere does not have any magnetism unless it is moving...or spinning. However, a classical spinning particle does not also oscillate in spin amplitude nor show any quantization of spin. The magnitude of quantum spin magnetism is also twice that of a spinning classical sphere of equivalent charge… thus the luxurious quantum mystery of spin. Like the fine-structure constant, the g-value, g = 2, has a long quantum history and the g-value is also twice the classical magnetism due to the velocity of the spinning classical sphere surface, which turns out to be the speed of light divided by the fine-structure constant, c/𝛼.

Well, quantum electrodynamics, QED, precisely predicts the g-value = 2 (1 + 𝛼 / (2𝜋) +...) as a perturbation series and so the anomalous g-value prediction was and still is the most significant validation of QED and therefore of the standard model of nuclear physics as well. Schwinger in 1948 and Feynman in 1950 independently showed that the anomalous electron magnetic spin was due to the self energy of the electron magnetism. The electric field of the electron oscillates and that electric field change generates the spin magnetic field and both of those fields affect themselves as well. Gravity has no self-energy correction since gravity is a distortion of space and time and really not a field. Quantum electrodynamics precisely predicts the g-value as a perturbation series of a progression of Feynman diagrams, whose integrals predict the g-value to an arbitrary precision.

2.00233184122(82), muon measured g-value
2.00233183620(86), muon g-value by QED calc

2.00231930436256(35), electron g-value by QED calc
2.0023193043617(15), electron measured g-value

The muon is a second generation lepton that is much heavier than the electron but as a quantum particle, its wavefunction should still have the analogous QED self-energy correction given the mass difference with the electron. So the small difference between the muon measured and calculated g-values represents a great challenge to QED and the standard model.

One of the possible reasons for a difference is that the muon has a quite short lifetime of 2.2 microseconds. However, the lifetime of a particle should not affect the standard model QED calculation of the muon g-value...unless of course, this is the missing link for grand unification between charge and gravity forces.

A similar discrepancy showed up with precision measurement of muon hydrogen, the short-lived atom formed from the muon bonded to a proton. Despite it increased mass, spectrum of muon hydrogen should correspond to the predictions of quantum mechanics and yet there is a significant difference between the prediction of quantum mechanics and the measurement. The interpretations vary from the proton diameter was incorrect or one should use quaternion calculations. Neither of these explanations depends on the muon lifetime.

 The universe is a pulse of matter in the many billions years of cosmic time that I call the Grand Wavefunction. The Grand Wavefunction of quantum gravity is not yet unified with the quantum wavefunction of muon lifetime 2.2 microsecond pulse. The ratio of the muon and universe pulse lifetimes is 2.6e-24 and the dimensions are atomic/cosmic seconds, which is a fundamental axiom of the matter-action universe. The ratio of muon mass 1.88e-28 kg and 2.2e-6 s lifetime is its decay rate as 8.54e-23 kg/s. The universal decay constant, mdot = 1.12e-10 kg/s, is what drives all force and for muon weak force decay to an energetic electron and two neutrinos as

The muon g-factor difference is 2.51e-9 and this implies that the muon decay rate is 7.06e-28 kg/s as 1.12e-10 x (2.51e-9)2, which means that the muon decay mass is 1.55e-33 kg given its 2.2e-6 s lifetime. This means that 99.93% of the muon decay ends up as an energetic electron mass and only 0.17% as neutrino mass.

Unlike a classical spinning sphere, quantum spin is also oscillating with a frequency that is in phase with its spin rotation. The oscillation of quantum spin amplitude has many very important outcomes. For example, the rotation of quantum spin by 360° or 2p radians does not result in the same quantum spin and it actually takes a rotation of 720° or 4p radians to result in the same quantum spin. The 4p rotational symmetry of quantum spin is a direct result of quantum oscillation of the spin wavefunction.

Muonic Hydrogen Spectrum

The fine-structure constant is a measure of the coupling of spin magnetism to the orbital magnetism of electron orbital motion. The coupling of spin and orbital magnetism results in spectral lines that Michelson and Morely first measured as the fine-structure constant in 1885. Nevertheless, it still took some 55 years for Sommerfeld to explain the fine structure quantum nature in 1940, some 16 years after the Schrödinger equation in 1924. 

The spectrum of muonic hydrogen shows an anomalous shift from the spectrum of electron hydrogen. Muonic hydrogen is a muon in orbit around a proton instead of an electron in orbit around a proton, which is normal hydrogen. The muon charge is the same as the electron and so binds to a proton in a very predictable way, but the muon mass is 207 times that of hydrogen and yet the muon decays very quickly with a lifetime of just 2.2 microseconds. Even with such a short lifetime, though, the quantum prediction is exact for muonic hydrogen, the quantum calculation with the same proton radius and other constants should give the same spectrum for both electron as well as muonic hydrogen. Instead, muonic hydrogen spectrum is blue shifted from that of electron hydrogen as the figure shows.

There are many fundamental constants that are the basis for this calculation and one interpretation of muonic hydrogen spectra is that the proton radius is much different for muonic hydrogen as the figure shows. There are other measurements for the proton radius such as the two shown in the figure, but neither of them agrees with the muonic hydrogen calculation. Each of the electron and muonic hydrogen spectroscopy results are valid by mainstream science and are determined within mutually exclusive uncertainties. There is therefore not a single proton radius and neither explanation is more valid than the other.

Thus, there is a dilemma. What is the real proton radius...0.8758 or 0.84087 fm? Both measurements of electron hydrogen and muonic hydrogen appear to have sufficient precision to preclude each other.

One alternative explanation is in the universal decay of aether, which means energy states also depend on their lifetimes. In aethertime, incorporation of the muon lifetime shifts the spectrum of the muonic hydrogen to now agree with that of atomic hydrogen. The shift is

which the figure above shows as 0.075 THz, which now agrees with the observed 0.072 THz and well within the precision of that measurement.

The observed 0.072 THz spectral shift of 49.885 THz is equivalent to a matter decay of 0.15% and so, once again, 99.95% of the muon decay of only 0.15% of its total mass whereas the g-value difference was 0.17% of muon mass decay.

While in mainstream science, the lifetime of a muon state does not affect its spectrum, in aethertime, the lifetime of muon does indeed affect its spectrum very slightly.

The proton diameter is a fundamental constant that describes a very slight shift in the energy of two states of hydrogen. An S state shows non-zero electron density at the proton in hydrogen and therefore shifts in energy while a P state has a near zero electron density at the proton. This energy shift defines the radius of the proton.

If the proton radius is truly fundamental, S and P states of hydrogen should show the same kind of shifts for hydrogen that has the muon instead of the electron. A very interesting experiment measures the diameter of the proton by means of the spectroscopy of the muon form of hydrogen and finds a much different shift in the frequency of muon hydrogen lines due to the finite diameter of the proton. The electron in the hydrogen S ground state has a certain probability of being at the proton surface but not inside the proton diameter and so the S state frequency shifts very slightly as a result. The electron in a P excited state on the other hand has no probability for being at the proton center and a very low probability of being at the proton surface as well.