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When a magnetic elementary particles enters a uniform magnetic field in a direction parallel to the field lines, its magnetic moment aligns instantaneously to the field direction, becoming either parallel or antiparallel to this direction. Inside the field this alignment appears from the first moment, because these two mentioned orientations are the only possible, all intermediate orientations are forbidden, not only by the laws of classical electromagnetism, but also by the rules of quantum mechanics. And just because of this alignment of its magnetic moment to the force lines, the initial energy $E$ of the particle becomes $(E-MB)$ if inside the field its magnetic moment $M$ is parallel to $B$, or $(E+MB)$ if $M$ is antiparallel to $B$, although both velocity and motion direction of the particle do not change after entering the field. In both cases the energy variation of the particle after entering the field is evidently $ΔE = MB$.

For all that, in magnetic resonance equation the energy variation taken into account is $ΔE = 2MB$, which corresponds to an inversion of magnetic moment orientation within the field B. Or, such a flip-flop of the magnetic moment is impossible, as long as (1) inside the field the particle moves strictly in a straight line parallel to the field direction since the Lorentz force is null, and (2) its magnetic moment is permanently aligned to the force lines, therefore no precession motion of its magnetic moment and spin around the field direction can occur.

On what grounds these elementary truths have been ignored yet?

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Experimental data themselves imposed as obligatory the energy variation $ΔE = 2MB$ right from the first experiments of magnetic resonance, because only so their ratio $ΔE/ν$ was equal to the Planck’s constant used until then in theoretical physics, even if, conforming to precession theory developed long before, the necessary precession of elementary magnetic moments around the field direction cannot occur under the given conditions. Still this obviousness was much less important than the total deadlock that would have resulted from an alternative ½ reduction of the action constant acknowledged until then.

At the same time, the energy variation $ΔE = MB$ of any magnetic elementary particle with magnetic moment $M$ right from the moment of its entering a uniform magnetic field $B$ simply disappeared, although this energy variation $ΔE = MB$ was already well known since 1895 due to Zeeman’s experiments.

Such a distortion of an energy equation by a forced introduction of a 2-factor was repeated some decades later, when the Josephson transitions raised similar issues (see in this regard my PSE posts entitled One photon and two electrons and Emission and absorption of photons by electrons).

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