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Chapter X: The Question of Galactic Redshift Periodicity

Gravitational redshift is a well known phenomenon, first predicted by Einsteinís relativity theories and then verified experimentally. According to general relativity, the redshift of a photon within the gravitational field of a non-rotating uncharged spherically symmetric mass is viewed by a distant observer as

Equation 10-1-1


where the redshift , and its equivalent velocity are defined as

Equation 10-1-2


and


where provides the difference between the radiation wavelength measured at the inertial rest frame of the observer, denoted , and the wavelength of the same radiation line emitted by a ďfreeĒ atom measured at the inertial rest frame of the emitting atom, denoted .

Therefore, it is not surprising that the gravitational field of a galaxy may influence the amount of redshift of its radiation. However, it was not expected that the amount of redshift may show periodicity. The first researcher to observe such periodicity was William G. Tifft in the 1970s (Tifft, 1973). Tifft reported that galaxies in the Coma Cluster show periodic redshift, with periodicity of about , followed by the later discovery of periodicity of about . A similar phenomenon was observed to occur in the redshift of quasars as well (Burbidge, 1968). Additional studies by Arp (Arp 1987), Tifft (Tifft 1980,1995, 2003), Napier (Napier, 1997) and their collaborators, conducted on larger sets of galaxies more widely distributed, seem to validate these findings. Specifically, in a limited trial on galaxies in the Virgo cluster, Bruce Guthrie and William Napier reported that away from the dense central core of the galaxy the redshifts were offset from each other in multiples of about , and further reported a periodicity of about in the Coma Cluster (Guthrie & Napier, 1990). While spiral galaxies were observed to display strong redshift periodicity, no significant periodicity was found for two separate groups of irregular galaxies. The increased accuracy achieved with the introduction of the redshift measurements, and by correcting for the distortion effect caused by the velocity of the Solar System relative to the cosmic microwave background, led to the finding of additional redshift velocities.

General relativity can provide redshift periodicity to the extent reported only via a very particular distribution of matter. Such a distribution is very unlikely to form spontaneously or to persist for a long period of time. Consequently, it is quite difficult to explain the observations of periodic redshift reported in a considerable number of galaxies. Therefore, the existence of redshift periodicity may require a paradigm shift, which can explain the great deal of skepticism among the astronomical community as to the merit of these findings. It has been suggested that the observed periodicity, or ďquantization,Ē of galactic redshift may be due to measurement or analysis error, due to coincidence, or due to geometrical effects resulting from the correlated positions of galaxies (Sepulveda, 1987).

The UG theory suggests the occurrence of redshift periodicity, or quantization, resulting as a consequence of the tendency of ordinary matter to accumulate within a distinct set of potential energy minima created by the interaction between the galactic superheavy particles and the ordinary matter of the orbiting gas or objects. Substituting the distinct set of minima provided by equation 2-1-42, (for), in equation 10-1-1 yields


As long as the vast majority of the mass of the galactic ordinary matter is within the distance , and , thereby demonstrating a periodic redshift with a periodicity of .1 However, as the UG theory violates the equivalence principle at distances where rings or spiral arms occur, a UG analysis of redshift periodicity should not rely on an equation of general relativity. Therefore, an alternative approach is used, where the gravitational redshift is derived from the equivalence of mass and energy under special relativity.

In accordance with special relativity, the mass of the emitting electron and the masses of protons in the nucleus of the same atom deviate from their rest masses, due to their interactions with the galactic superheavy particles and ordinary matter. The rest masses of the electron and proton are denoted as and , and the masses of the interacting electron and proton are given by and respectively. Radiation occurs when an electron transitions from a higher energy quantum state to a lower energy quantum state, while the energy of the emitted radiation is equal to the energy difference between the two states. As the energy level of either atomic state depends on the mass of the electron as well as on the masses of protons, the emitted radiation energy measured by the distant observer will deviate from the energy measured in the inertial rest frame of an identical free atom.2 Therefore, the effective masses of the electron and the protons deviate from their rest masses by a distinct set of values, resulting in a clear periodic set of wavelengths, rather than continuous radiation energies or wavelengths.

The following discussion will provide a more rigorous analytical treatment of this phenomenon, specifically for the case of the hydrogen radiation lines. The hydrogen atom will be assumed to remain isolated and unaffected by nearby objects, and to travel in a circular orbit of radius around a non-rotating galaxy center. The atomís orbital radius is assumed to lie beyond the zonal oscillation range of ordinary matter of mass and all but the dominant SHP type. The dominant superheavy particles of mass are assumed to be located and at rest at the center of the galaxy. Note that the above assumptions are made for simplification, and do not significantly restrict the generality of the discussion.

Whereas the radiation energy is given by , where according to the law of conservation of energy, is the energy between the initial and final energy states of the emitting electron, where denotes the frequency of the radiation, and is Planckís constant.

The following analysis is applied for the case of non-relativistic atom velocity, where the energy of a free particle (an electron or proton) of rest mass and velocity can be described accurately by the equation . Initial studies of galactic redshift measured the redshift spectra of the transitions between the various hydrogen () orbital levels. The electron orbital energy levels are given by3

Equation 10-1-3a


where provides the rest mass of the electron, is the reduced mass of the electron-nucleus system in the inertial rest frame of the emitting atom, and denotes the number of protons in the atom. The fine-structure constant is defined as , where is the elementary charge, is Planckís constant, is the speed of light and provides the vacuum permittivity. The quantum numbers of the hydrogen quantum states are denoted as and , where is a positive integer, , , and where is defined as

Equation 10-1-3b


Note that is independent of the masses of the protons and the electron. In the case of the hydrogen atom , and .

The wavelength of the radiation due to the electronís transition from level to level is subsequently given by

Equation 10-1-4


The observer is assumed to be positioned at sufficient distance from the galaxy to remain unaffected by its gravitational field. However, as the galactic superheavy particles and ordinary matter are expected to influence the masses of the electron and proton of the emitting hydrogen atom, and therefore its reduced mass , the actual observed radiation is equal to

Equation 10-1-5


where the redshift of the electronís orbital energy level is given by

Equation 10-1-6


Defining and as the respective mass ratios of the proton and the electron, and substituting μ, , and for the case of hydrogen () in equation 10-1-6 yields

Equation 10-1-7



where , and with the exception of extreme gravitational fields,

. Therefore, .

Later studies of redshift periodicity started using the more sensitive line for quantifying redshift. The line is assumed to be created by the magnetic field induced by the nucleus magnetic moment, resulting in the splitting of the triplet and the singlet spin state energy levels (this energy split is also called the hyperfine structure). The energy difference between the triplet and the singlet spin states at the ground level of the electron is given by

Equation 10-1-8


where provides the reduced gyromagnetic ratio of the proton. Following the same process, the redshift of the line is given by


Equation 10-1-9


Assuming that provides

Equation 10-1-10a


If, in addition, ,

Equation 10-1-10b



yielding the same results as obtained for the case of the regular spectra of the hydrogen atom.

As observed, and demonstrated by the theory developed in Chapter III, the rotational velocities within and external to the galactic disk relative to the galaxy center are of the order of hundreds of , too slow to cause any appreciable relativistic effects. This is also true in the case of an observer located outside of the given galaxy moving at a non-relativistic velocity relative to the galactic center. Therefore, no velocity-related relativistic corrections are required. However, according to Einsteinís mass equation for a bonded electron-proton pair within a hydrogen atom , viewed by a distant observer, the energy of the proton is given by

Equation 10-1-11



where provides the overall bonding energy of the proton to the electron, which must be negative,4 is the rotational velocity of the atom around the galaxy center, and is the mass of the ordinary matter within a sphere of radius from the galaxy center. Additionally, the distribution of the galactic ordinary matter around the center of the galaxy is assumed to be spherically symmetric. Therefore,

Equation 10-1-12


Over time, the rotating atom is likely to gravitate toward an orbital radius near a potential energy minimum. Since the force applied on the proton at any of the minima is zero, the orbit must shift slightly from the minimum to allow the resultant gravitational force to balance the centrifugal force. However, due to the steep slopes of the potential energy at zonal indices , the orbital radii at which the overall energy minima occur must be very close to the radii where the overall potential energy of the atom has a local minimum. Using equation 2-1-42 and restricting the discussion to distances of , where and confines the potential energy minima of the proton or the atom to

Equation 10-1-13a


where for or . For sufficiently large (and therefore, sufficiently small ), , and

Equation 10-1-13b


As , equation 10-1-12 can be rearranged as follows:

Equation 10-1-14

or


At the range of interest , substituting equation 10-1-13b in equation 10-1-14 provides a minimum contour at

Equation 10-1-15


Similarly, for the electron,

Equation 10-1-16

or

Equation 10-1-17

The electron and the proton are bonded together, and thus travel at the same velocity around the galaxy center. However, as the masses of the electron and the proton differ substantially, the locations of the potential energy minima of their interaction with a superheavy particle of mass vary accordingly. Since the proton mass is over 1,836 times larger than the mass of the electron, the atom is expected to reside near a minimum of the proton-SHP interaction, which may be at substantial distance from any minimum of the SHP-electron interaction. The electron is therefore subject to the UG gravitational force, which aims to draw the electron toward a UG potential energy minimum. However, the electron is usually prevented from migrating toward this minimum by its electromagnetic interaction with the proton. Hence, for the case of a non-ionized hydrogen atom, the location of the electron is given by
, rather than by . Substituting for in equation 10-1-17 provides

Equation 10-1-18



Using equations 10-1-15 and 10-1-18 yields

Equation 10-1-19


The value of can be estimated from the rotational velocity of a typical spiral galaxy, shown in section VI-3 of chapter VI to be equal to . Thus, for a rotational velocity of , , which is far smaller than the overall galactic mass by a factor of the order of at least . Therefore,

and . The magnitude of the term depends on the quantum state of the hydrogen atom. At the lowest ground state, , and therefore . Consequently, . As long as the value of ,

Equation 10-1-20

Substituting equation 10-1-20 in equation 10-1-7 (or equation 10-1-10b) yields the shift for the hydrogen orbital lines (as well as for the line), given by

Equation 10-1-21


Therefore, as long as ,

Equation 10-1-22

where is an integer. Note that demonstrates periodic behavior with a periodicity of

Equation 10-1-23



Note that this intrinsic redshift is in addition to the expected redshift contributed by the velocity of the galaxy relative to the observer.

Using equation 10-1-23, a redshift periodicity of , which is equivalent to the reported redshift velocity of , leads to5

. To achieve a periodicity of , the ratio of the overall galaxy mass and the dominating SHP mass is given by .

Similar calculations provide a value of for the case of . The above analysis, in addition to the fact that galaxies and galactic clusters are observed to produce a distinct set of redshifts with the same periodicity values shared by a significant number of unrelated galaxies, suggests that the ratios between the mass of the galactic center and the mass of the SHP tend to assume specific values.

Section X-2: Unified Gravitation and the Redshifts of Quasars


Quasars, or quasi-stellar objects, are astronomical objects that are observed to emit highly redshifted radiation. According to the standard model of cosmology, large redshifts are interpreted as Doppler shifts, which lead to the following conclusions:

  1. The large radiation redshifts observed in quasars indicates that they must recede from us at very high speeds.

  2. More than 200,000 quasars are known with redshifts ranging between and . Applying Hubbleís law, which indicates that the velocity at which various galaxies are receding from Earth is proportional to their distance from us, leads to the conclusion that the known quasars are located between 790 million and 28 billion light years away from us, with most calculated to be over three billion light years away.

  3. As the brightness of an object reduces proportionally to the square of its distance from the observer, quasars are presumed to be extremely luminous objects, radiating at rates that can exceed the output of average galaxies.

  4. The great distances calculated between Earth and the known quasars lead to the conclusion that quasars were much more common in the early universe.


The assumption that substantial redshifts are due exclusively to Doppler effectshas led to far-reaching conclusions. This assumption was challenged by Halton Arpís claim that the redshifts of quasars are not always an indication of their distances or their ages, as currently believed (Arp, 1988). Arp contested that many quasars with otherwise high redshifts can be linked to nearby objects of significantly lower redshifts, and are therefore nearby.

According to special relativity, the masses of the electron and the proton , as viewed by an external observer, cannot be negative, and therefore and cannot be negative. In the case of sufficiently small values of and , the term in equation 10-1-18 is negligible, and may assume values greater or less than . Thus, the objectís radiation frequency may either be blueshifted or redshifted due to gravitation. On the other extreme, in the case of , of equation 10-1-18 assumes a negative value, which is forbidden by special relativity. The physical meaning of this discrepancy is that the given emitting atom lies within the horizon of the object, thus its radiation is trapped in a black hole and cannot reach the external observer.

According to equation 10-1-18, at distance ranges where ,, and according to equation 10-1-7 (or 10-1-10b), the radiation redshift due to the gravitational interaction is given by .

The matter trapped by the object is expected to accumulate mainly in vicinity of the potential energy minima. As noted above, at sufficiently high indices, the radiation is trapped within a black hole, and cannot escape or be detected by the distant observer. Denote as the largest even integer index at which , where a minimum occurs.6As the potential energy slope is especially steep near a black hole horizon, and as the minimum is the closest minimum to the horizon, the density of ordinary matter in the vicinity of is likely to be significantly greater than the density anywhere external to the horizon. Hence, the redshift associated with the minimum may dominate the observed spectrum.7

Following equation 10-1-21, in the case where , the redshift of the observed radiation will approach infinity. In cases where, in addition, , most of the radiation emitted by the star is extremely redshifted, as observed in quasars. Thus, the astronomical object is expected to provide an intrinsic redshift that is significantly larger than the Doppler redshift created by the objectís velocity relative to the observer. Therefore, according to the theory of unified gravitation, it is very possible that Arpís claim is in fact true, and that at least some of the observed quasars may be substantially closer, younger, smaller and less luminous than currently believed.






1 Note that the much smaller UG contribution of the electrons was neglected.

2 The effect of the galactic gravitational field on the mass of nucleons and electrons is also true for Newtonian gravitation within special relativity, with the exception that according to the UG theory, the atoms or molecules of a galaxy are likely to be arranged in the vicinity of distinct potential energy minima of the SHP-proton pairs, rather than in the continuous distribution predicted by the Newtonian theory.

3 For further reading, see Quantum Field Theory by Claude Itzykson and Jean-Bernard Zuber, Dover Publication, Inc., Mineola, New York, 2005.

4 The value of must be negative in order for the electron to bond with the proton. In the general case, where the atom is part of a molecule or a larger object, may denote the overall bonding energy of the proton to the object as a whole. However, for simplicity, the current scenario deals with an isolated hydrogen atom.

5 Note that the resultant periodicity of the redshift is indeed larger than the value by a factor of (even at the lowest value) and less than for all , fullfilling, within this range, the conditions required for the assumption that .

6 Therefore, is the largest even integer where and where the minimum is not washed out by the contribution of the objectís ordinary matter.

7 Note that the effect of the SHP rotation as well as the Doppler effect due to the relative speed between the distant galaxy and the observer, or due to the velocity of the emitting atom relative to the center of galaxy, are assumed in the present case to be relatively small.



©2018 Gil Raviv

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