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Dark matter inferred by redshift of 21 cm hydrogen lines is highly questionable
Galaxy rotation curves inferring the presence of dark matter based on radio telescope measurements of thermal emissions from hydrogen atoms are problematic as temperature fluctuations in atoms are forbidden by the Planck law of quantum mechanics
The W-F effect [1, 2] couples the spin temperature of neutral hydrogen to the Ly-α excitation of the 21 cm line of hydrogen at 1420 MHz. W-F stands for Wouthuysen-Field and Ly-α for Lyman-alpha photons, the Ly-α photons having Planck energy of 10.2 eV at 121.6 nm. Most of the hydrogen in the Universe is in the ground state where the electron spins are parallel having a slightly higher energy than antiparallel spins, the relative occupation of the spin levels given by the spin temperature Ts. The W-F effect assumes hydrogen atoms by absorbing and re-emitting Ly-α photons may enter either of the two spin states. Since the energy difference of the spin states is very small, a hydrogen atom can wait on average a few million years before undergoing the 21 cm emission. Even so, the large amount of hydrogen gas in the Universe means that enough hydrogen atoms are emitting 21-cm radiation that can easily be detected with radio telescopes.
Radio telescopes measure the 21 cm recession velocity of the hydrogen atom in a gas cloud based on the thermal power P received per unit bandwidth by, P = kTs, where k is the Boltzmann constant. The W-F effect assumes the spin temperature Ts is produced under Ly-α absorption is the same  as that occurring in a gas in thermal equilibrium at the kinetic temperature Tk of the cloud.
Unlike the galaxy velocities inferred from Hubble redshift of the optical emission from an atom integral with the galaxy surface, redshift of the 21 cm emission from a free hydrogen atom in a gaseous cloud of a galaxy follows the rules of QM and not classical physics. QM stands for quantum mechanics. Because of the high surface to volume ratio of the hydrogen atom, the energy of a single Ly-α photons is confined to the atom surface thereby providing high EM confinement that by the Planck law of QM requires its heat capacity to vanish. QM refutes the assumption of classical physics that allows the free hydrogen atom to have heat capacity irrespective of EM confinement.
Beyond the obvious argument that not all hydrogen atoms in the galaxy cloud are receding at the same velocity, galaxy velocities inferred from the thermal power P measured by the radio telescope that depend on the spin temperature Ts of the atom are highly questionable because of thermal noise. The thumbnail shows the signal to noise ratio of radio telescope power P is very low suggesting noise may be being interpreted as 21 cm radiation. What this means is radio measurements of 21 cm radiation may have nothing to do with galaxy velocities, or for that matter, the existence of dark matter inferred from flat rotation curves of galaxies. Non-thermal 21 cm emission is suggested, but radio telescopes only measure the power P of thermal and not non-thermal radiation.
In this regard, RIXS has shown chemical reactions initiated by molecular vibration changing atomic positions  of atoms in reactant molecules need not be initiated by temperature, but rather non-thermally by X-rays. RIXS stands for resonant inelastic scattering. Similar to chemical reactions, the hyperfine lines of the 21 cm state may be being excited similar to RIXS upon the absorption of a single X-ray photon. See "Atoms conserve heat by producing X-rays" at https://www.prlog.org/
The W-F effect coupling the spin temperature of hydrogen to the Ly-α excitation of the 21 cm line of hydrogen is superseded by non-thermal fluorescence of the 21 cm line of hydrogen by a single X-ray photon. Fluorescence at X-ray energy levels is expected to efficiently excite the 13.6 eV ground state of hydrogen more than Ly-α photons at 10.2 eV. See diverse applications of vanishing heat capacity at the nanoscale by the Planck law at http://www.nanoqed.org/
QM by the Planck law questions the thermal W-F effect in the excitation of the hyperfine states of the hydrogen atom described by the spin temperature Ts. In fact, the 21 cm excitation can only be optical and not thermal. Radio telescope measurements based on thermal power P = kTs emitted by the hydrogen atom have no physical meaning as the atom is forbidden to thermally conserve the Ly-α photon because its heat capacity vanishes by QM.
Radio telescopes measuring the thermal power P emitted by the hydrogen atom are most likely measuring noise. Only optical telescopes can infer the non-thermal 21 cm emission, say by measuring the redshift of Ly-α radiation. But this is also problematic as cosmic dust permeates the Universe. For a Ly-α photon already redshift by the recession velocity of a galaxy, subsequent absorption in a dust particle increases  the redshift. What this means is Ly-α redshift observed on Earth requires correction for the redshift in cosmic dust to avoid overstating galaxy recession velocities.
Experiments should be conducted to determine if single X-ray photons can spontaneously excite and emit the 21 cm line from free hydrogen atoms compared to Ly-α photons.
 S. A. Wouthuysen, "On the excitation mechanism of the 21-cm interstellar hydrogen emission line," Astrophys. J., vol. 57, pp. 31-32; April, 1952.
 G. B. Field, "Excitation of the Hydrogen 21-CM Line," Proc. IRE, 46, 240-250, 1958.
 R. C. Couto, et al., "Selective gating to vibrational modes through resonant X-ray scattering,"
 T. Prevenslik, "Cosmic dust as dark matter," See Paper in 'Dark Matter as Redshift in Cosmic Dust' at http://www.nanoqed.org, 2017.
Page Updated Last on: Jul 23, 2017