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Hubble's Law and its assumption

Quotes are from wikipedia.
In 1929 Hubble examined the relation between these distances and their radial velocities as determined from their redshifts.
combining his distances with measurements of the redshifts of the galaxies by Vesto Slipher, and by his assistant Milton L. Humason, he found a roughly linear relationship between the distances of the galaxies and their radial velocities (corrected for solar motion), a discovery that later became known as Hubble's law.

It is critical to note the red shift was  observed to be proportional to distance.  The velocity was calculated from the red shift.

A paper from Caltech (linked below) published results from analysis of a quasar spectrum.

This quasar has an interesting environment. The light from the quasar passes through neutral hydrogen several times before getting to Earth.

Around the quasar AGN core are a number of different elements' ions as shown by their absorption lines. The paper's table 1 lists the ions being observed by their absorption lines.
These ions are not moving real fast, just "tens to hundreds of km/s." They are red shifted so all are moving toward the AGN core, or away from us.
Beyond that there are somewhat dense intergalactic neutral hydrogen gas clouds. These atoms produce wide Lyman-alpha absorption lines. The density of the hydrogen clouds results in many absorption lines; this observation is called the "Ly-a forest."

Beyond that the light is in intergalactic space.

From that paper from Caltech (linked below)

However, the vast majority of absorption lines in a typical quasar spectrum are ``intervening'', produced by gas unrelated to the quasar that is located along the line of sight between the quasar and the Earth.

A structure along the line of sight to the quasar can be described by its neutral Hydrogen column density, N(HI), the number of atoms per cm2. N(HI) is given by the product of the density of the material and the path length along the line of sight through the gas. Each structure will produce an absorption line in the quasar spectrum at a wavelength of lambda-obs = lambda-rest (1 + zabs), where zabs is the redshift of the absorbing gas and  lambda-rest = 1215.67 Angstroms is the rest wavelength of the Lyalpha transition. Since zabs < zQSO, the redshift of the quasar, these Lyalpha absorption lines form a ``forest'' at wavelengths blueward of the Lyalpha emission. The region redward of the Lyalpha emission will be populated only by absorption through other chemical transitions with longer lambda-rest. Historically, absorption systems with N(HI) < 1017.2 cm-2 have been called Lyalpha forest lines, those with 1017.2 < N(HI) < 1020.3 cm-2 are Lyman limit systems, and those with N(HI) > 1020.3 cm-2 are damped Lyalpha systems. The number of systems per unit redshift increases dramatically with decreasing column density, as illustrated in the schematic diagram in Figure 2. Lyman limit systems are defined by a sharp break in the spectrum due to absorption of photons capable of ionizing HI, i.e. those with energies greater than 13.6 eV.

These scientists concluded as the wave length matching the absorption line of neutral hydrogen passes through neutral hydrogen atoms the wave length progressively increases, or a red shift. This behavior continues into intergalactic space where neutral hydrogen has a very low density.

This behavior of a red shift due to neutral hydrogen in the line of sight to a distant object should apply to all distant objects, not just quasars, the subject of this paper.

They concluded this red shift is related to the hydrogen density and the path length, or the distance the light travels in the hydrogen.

This is the same observation by Hubble that a red shift for a distant object is proportional to its distance.
Cepheid variables provided distance measurements for Hubble.

The obvious conclusion is the observed hydrogen red shifts are related only to distance. There is nothing observed here for the light to relate the red shift to a velocity in any direction.

Hubble's law has an interesting wrong assumption. The observed red shift is assumed to be from velocity not distance.

Distant galaxies show a red shift due to their distance through intergalactic hydrogen. Hubble's Law assumes their distance defines their velocity.

When assuming this absorption behavior is caused by velocity not hydrogen one incorrectly concludes all distant galaxies are moving away.

These scientists have shown this is an invalid assumption.

The conclusion of these scientists about hydrogen absorption lines matches Hubble's observation. I linked to the paper, that includes figures.


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