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Book by David Michalets

Distant Spectral Shifts

13 Hubble's Law

This is section 13 of 18.

The web page series for Distant Spectral Shifts is based on my book Cosmology Crisis Cleared.

Hubble's Law describes a mathematical relationship between a galaxy's redshift velocity and its distance.

13.1 Description

Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology that galaxies are moving away from the Earth at speeds proportional to their distance. In other words, the farther they are the faster they are moving away from Earth. The velocity of the galaxies has been determined by their redshift, a shift of the light they emit toward the red end of the spectrum.

Hubble's law is considered the first observational basis for the expansion of the universe, and today it serves as one of the pieces of evidence most often cited in support of the Big Bang model. The motion of astronomical objects due solely to this expansion is known as the Hubble flow.  It is often expressed by the equation v = H0D, with H0 the constant of proportionality—Hubble constant—between the "proper distance" D to a galaxy, which can change over time, unlike the comoving distance, and its speed of separation v, i.e. the derivative of proper distance with respect to cosmological time coordinate. (See uses of the proper distance for some discussion of the subtleties of this definition of 'velocity'.)
Hubble constant is most frequently quoted in (km/s)/Mpc, thus giving the speed in km/s of a galaxy 1 megaparsec (3.09×1019 km) away, and its value is about 70 (km/s)/Mpc. However, the SI unit of H0 is simply s?1, and the SI unit for the reciprocal of H0 is simply the second. The reciprocal of H0 is known as the Hubble time. The Hubble constant can also be interpreted as the relative rate of expansion.

The parameters that appear in Hubble's law, velocities and distances, are not directly measured. [R246]


The last sentence in the excerpt clearly identifies the fundamental problem with Hubble's Law.
One must be explicitly clear what exactly IS directly measured. There is only 1 measurement of a galaxy, that of an atom's redshift.
A distance cannot be directly measured.

Only a change in a particular wavelength in a galaxy spectrum from its expected value can be directly measured.

The critical decision is whether the change is only in the atom or also in the galaxy behind it in the line of sight.

The mistake of assigning the atom's velocity to the galaxy has been made consistently for over 100 years.
Any distance cannot be directly measured.
A distance can be calculated based on a few assumptions, such as dimming by distance. This is a simple calculation, but it must have a margin of error based on the reliability of the directly measuring the brightness of both the target object and the benchmark object.

13.2 Background

In 1912, Vesto Slipher measured the first Doppler shift of a "spiral nebula" (spiral nebula is the obsolete term for spiral galaxies), and soon discovered that almost all such nebulae were receding from Earth.
He did not grasp the cosmological implications of this fact, and indeed at the time it was highly controversial whether or not these nebulae were "island universes" outside our Milky Way. [R247]
Edwin Hubble is often incorrectly credited with discovering the redshift of galaxies.
These measurements and their significance were understood before 1917 by James Edward Keeler, Vesto Melvin Slipher, and William Wallace Campbell at other observatories.
Combining his own measurements of galaxy distances with Vesto Slipher's measurements of the redshifts associated with the galaxies, Hubble and Milton Humason discovered a rough proportionality of the objects' distances with their redshifts. [R247]

Slipher measured redshifts of atoms, not velocities of galaxies.

13.2 Initial measurements

I can find no record of Slipher's specific redshift galaxies to discover the atoms being used, but several references agree his blue shift galaxy was Andromeda. Since Slipher measured the same velocity as accepted from the calcium atom, so that one atom is known. Unfortunately, this was a blue shift, so it did not conform to Hubble's Law and could not be part of the initial set.

   The redshift velocity depends on the particular atom being used by the individual astronomer making the measurement in a spectrum.

The distance should have required a standard candle, like a Cepheid or RR Lyrae. The RR Lyrae cannot be used for distances beyond the Local Group so Hubble could use only galaxies having Cepheids. Lemaître claimed to have a value in 1926 while Hubble had one in 1929.

An article titled "How Hubble Found Distances"
Offers an explanation.

From observations of the apparent magnitudes of the brightest stars in 14 more nebulae, Hubble estimated their distances. Now he could calculate an average absolute magnitude for the brightest stars in all 20 nebulae. Comparing this value with the apparent magnitudes of the stars in four nebulae in the still more distant Virgo Cluster of galaxies, he determined their distance too. [R248]

Hubble used a few galaxies with Cepheids to compare their magnitudes with others. He created estimated distances, not measured.

Harvard has a relevant page: THE HUBBLE CONSTANT

It was made possible by in part by Vesto Slipher's measurements of the apparent radial velocities of nebulae, but primarily by Edwin Hubble's estimates of distances to nearby galaxies. Hubble deserves the credit for the discovery of the expansion, even though papers by Georges Lemaitre and H. P. Robertson using Hubble's data on the velocity-distance relation preceded his 1929 landmark, because it was his systematic program of measuring galaxy distances and his 1924 discovery of Cepheid variable stars in M31 and his actual plot of the relation that finally convinced the community at large. Low level controversy ensued almost immediately. [R249]


This controversy involved the age of the universe implied by the initial value of Hubble's constant which was only 2Gy, while the Earth was assumed to have an age of 3Gy.

The article has more interesting details, but it also reveals something more important.

This observation with my emphasis is critical when trying to understand the origin of the crisis with the constant.

Slipher measured the velocities while Hubble estimated the distances. Others, like Lemaitre and Robertson, were using Hubble's data for their papers.

Hubble estimated distances, without a precise measurement.

The essential problem for astronomers is finding an acceptable velocity for an acceptable distance to calculate an acceptable value of Hubble's Constant.

13.3 Recent measurements

There is a 2014 study titled:

"The Most Luminous z= 9-10 Galaxy candidates yet found: The Luminosity Function, Cosmic Star-Formation Rate, And The First Mass Density Estimate At 500 Myr"

 Excerpt from this paper about galaxies with z from 9 to 10:
The identification of LBGs in the epoch of reionization makes use of the almost complete absorption of UV photons shortward of the redshifted Ly-alpha line due to a high neutral hydrogen fraction in the inter-galactic medium. [R250]


The Lyman-alpha emission line is emitted when a proton captures an electron becoming a hydrogen atom. The velocity and direction of the proton at the instant of captures causes a shift in this characteristic wavelength.

These galaxies are not moving at z from 9 to 10, because the extreme red shift is from the high velocity proton, not a velocity of the galaxy.

As noted in this book's introduction:

In my opinion, one's first response to any value of z>1 should be: 

"This superluminal velocity is impossible for a massive galaxy, so its measurement must be a mistake."

13.4 Consistency

The study of high redshift galaxies confirmed the red shifted Ly-alpha line is being used for the measured redshift value.

This line is emitted when a proton in the line of sight captures an electron. The velocity of the proton at that instant shifts the wavelength. Therefore, the high red shift galaxies have a high red shift mechanism unlike other galaxies using the neutral hydrogen emission line for the wrong velocity.

Inconsistent methods of measurement result in inconsistent comparison of values. Comparing values from different lines can be misleading. This study found the protons moving toward these galaxies had similar velocities, for the group   to be measured in the range of z = 9 to 10.

However, any absorption or emission lines cannot be
applied to a galaxy's velocity.

The galaxies in the survey were not identified. NED did not have an entry for the long galaxy names being assigned to these special galaxies. In other words, they do not have NGC numbers, at the time that I compiled the data.

Hubble's Law was based on the shift of the absorption or emission lines noted by the astronomer for that particular galaxy. Currently, astronomers can use whatever lines are found in a star's spectrum, so astronomers measure galaxies just like stars.

13.5 Lateral motion

Astronomers had never attempted to measure a galaxy's lateral motion, not just a Doppler driven velocity in the line of sight, until recently.

The two Magellanic Clouds are galaxies close to our Milky Way, but their far Southern position inhibits viewing by Northern telescopes.

Announced in 2006, measurements with the Hubble Space Telescope suggest the Large and Small Magellanic Clouds may be moving too fast to be orbiting the Milky Way.
 In 2014, measurements from the Hubble Space Telescope made it possible to determine that the LMC has a rotation period of 250 million years. [R253]

From this news story about this measurement:

" CfA reveals Magellanic Clouds are first-time visitors" 

Earlier this year, CfA astronomers reported measuring the 3-D velocities of the Magellanic Clouds through space with greater accuracy than ever before. The velocities were anomalously high. Two explanations were proposed: 1) the Milky Way is more massive than previously thought, or 2) the Magellanic Clouds are not gravitationally bound to the Milky Way. Further analysis by Besla and her colleagues verified the second explanation. The parabolic orbit they calculated for the clouds, based on the observed velocities, shows that both are on their first pass by the Milky Way. [R253]


It is ironic there are only 2 galaxies in the universe having an attempt to measure a 3-D velocity, and both were fast in passing, when the unjustified assumption using Doppler effect is all galaxies have no lateral motion.

All other galaxies, lacking any attempt to measure any such motion, are just assumed to have motion only in the direction of their line of sight from Earth.
13.6 Definition of Hubble's Constant

Descriptions of this constant indicate its value is misunderstood.

The Hubble constant has been interpreted as the relative rate of expansion.

Hubble's Law is based on a ratio's numerator being a consistent motion of atoms toward the galaxy in the line of sight, but this motion is treated as the galaxy's velocity. This redshift has nothing to do with a fictitious expansion. When the atoms move in proportion to distance, this is the result of these atoms interacting with light and plasma within the space between galaxies, called the intergalactic medium, or IGM. Light having energy of ultraviolet or higher can ionize matter

The ratio's denominator is the galaxy's distance.
Cepheids are a distance benchmark because a decrease in expected brightness can be attributed to dimming by a specific distance, so a Cepheid in the galaxy could provide this value for its host galaxy. A Cepheid is called a standard candle because it has a predictable luminosity curve, enabling the dimming by distance calculation.

A Cepheid distance measurement establishes the denominator for the ratio or relationship of Velocity divided by Distance
This ratio applies to its host galaxy and is assumed applicable to other galaxies with a uniform expansion.
Currently, there is no other reliable alternative to a Cepheid.

Everything dims by distance. Stars require instruments having very high resolution to measure individual stars among the billions in a galaxy. Efforts to use the known luminosity of certain bright, giant stars also encounter this limitation.
Supernovae were also candidates for a standard candle. I did a detailed analysis of the study using supernovae to justify the false expansion, and it was riddled by many errors including mistakes with redshifts. The supernovae had a luminosity curve like a variable star. The spectrum of a supposed supernova matched that of a variable star.  The change in spectrum during the change in luminosity was claimed to be a redshift. This study is worthless. Supernovae are not consistent, as they must be to qualify as a possible benchmark.

13.6 Consequences of Hubble's Law

When astronomers get a redshift. A distance can be calculated.
When astronomers get a distance, like from a Cepheid in a galaxy, a velocity can be calculated. That is an unjustified uniform and consistent universe.
Astronomers formed invalid conclusions using this law.

An earlier reference included:

 "Hubble's law is considered the first observational basis for the expansion of the universe, and today it serves as one of the pieces of evidence most often cited in support of the Big Bang model. "

This claim of evidence is quite unjustified.

Currently, all galaxies and quasars have invalid velocities.

There are no galaxies having a correctly measured velocity.

Therefore, Hubble's Law and its assumed relationship between redshift velocity and distance are invalid.
Therefore, there is no observational evidence supporting a big bang theory based on all distant galaxies in recession while all have invalid velocities, while having no attempt to measure the proper motion, independent of Earth, of any galaxy.

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;ast update: 01/06/2022