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Cosmological redshifts vs. gravitational redshifts

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Abstract

Under current theory, Einstein's 1916 general theory of relativity applies the Doppler equations of special relativity to motion shifts and gravitational shifts, while cosmological shifts are thought to obey a different shift law. However, geometrical considerations require these arguments and equations to be interchangeable. If this geometrical argument is correct, either the cosmological shift law and/or the core relationships of general relativity will need to be modified.
June 2018



Eric Baird
       

        ! "  
       ! #  
     $   
 %&!
 
          
  !" #$
   %&'(  )   *' + 
),,(,-.,#
$ '   )    - ., )
 ,)# i/0
),-.,) ,
 )#ii
$)1,, #20)3, )
,')4 )
)  #5,)    ,     )
,)'), (.,)
 ),)))  (#
 
5)))  
, #6&) 
))(  ,(
() ) ,()7,
8) ,,))#iii
b
a

9),03 )(
 (#
i: If matter and EM energy undergo the same proportional change in energy when falling across a given gradient, the
gravitational shift on light must agree with the final Doppler shift on a falling body due to its acquired velocity.
ii: … and, conversely, whichever equations apply within cosmology must work for inertia and gravitation.
iii: Some might argue that only the properties along the line a-b are important: we shall also include the immediately adjacent
region to err on the side of caution.
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Cosmological vs. gravitational redshifts, Eric Baird, June 2018
$ ,:)+
0),: iv
t
b
a
t
b
a
← position → ← position →
(#1) Gravitational redshift (#2) Cosmological redshift
In scenario #1,
83)) 
 #)3
)3(
 # /  , )       gravitational 
,      ,        )    (    
!"!"#
In scenario #2,
83 3)#).,(,
 (,   ,0   ,#;)
 cosmological ,
)!"!"#
/,  ) (
,(),( )(,)outside
,(), #$)3
,)7,<1  )(
() ),(
()#
=)3),3
,7,(similar((,identical#5) ,(
( ( ),
,    , )   ( 7,   
 )(00# v
iv: In a fully gravitomagnetic theory we would also have a third option, a gravitomagnetic field due to relative motion
between masses.
v: We might also consider the case of a diagram referenced to an observer moving at high speed with respect to the assumed
references used for our two figures. For this observer, concepts of space and time may be “tilted” or “rotated” with
respect to those expressed in the provided diagrams, so that a “gravitational” shift also appears to have a time component,
or a “cosmological” shift also appears to have a spatial component (“there-and-then” vs. “here-and-now”). Since this
change in arbitrary external reference systems should not physically affect the frequency of the light received by a
detector at , this again suggests a degree of interchangeability for the two components.
page 2 of 4
Cosmological vs. gravitational redshifts, Eric Baird, June 2018
! "
>,)-,:
For GR1916 to support special relativity) ,(-
#
To support an expansion horizon with standard properties ) ,
( 3-#
>, )('.,) )
() ))
,#
$,( :/) () )
 
 (      8  , )   ) 
  )   -
 , (   ( !"      (,
),(,), ,) #vi
# $%
? , (   ,       <  ) 
 ) < (    .,# @,((  ,  (   
 )),3 3
vii,)) #/,)0
 ) ,),(,,
 ,,,)( ) ))
 ),,<,( #viii
& "
) &')0),#
 A *3( ) !3" B  ,)
,!0),"  @,((+ 
3'A,)!())(,
"ix( ),,(#
5,1*'(0,),)
vi: This is especially true if the moving star is associated with gravitomagnetic effects, as both types of recession would then
be associated with curvature along the signal path.
vii: Full unification of motion shifts with gravitational and cosmological shifts would also require more emphasis on
gravitomagnetic principles than is the case with the current system.
viii: Reducing the number of distinct equations in a general theory makes a theory more compact and more powerful as a
“principle-based” theory by predicting a larger number of effects from a smaller number of independent components
(see: Occam’s razor). With Karl Popper’s approach to assessing theories, increasing the number of comparison-points that
must agree for the theory to work also makes a theory “more scientific” by making its internal structure more easily
falsifiable.
ix: The accuracy of the “biggest blunder” quote has since been questioned: however, the phrase would seem to be in
character for Einstein. By inventing an arbitrary repulsive cosmological constant to explain how the universe could be
static, Einstein missed out on the opportunity to predict the cosmological redshift effect, a decade before Hubble reported
his findings. This would have been one of the theory’s biggest predictive successes.
page 3 of 4
Cosmological vs. gravitational redshifts, Eric Baird, June 2018
,((()1 3
4#/   ,0, () ( ) )  
,  0) 3 ,  -., .,   
 ),(,.,)
#
' 
$,,!"), ) )
 )(  (    # )  (  )  
   ))  ),    ,
,  ought  (  ) )   
#$)(., )<
 in addition   0)  )  <  ,    ())
( #)3- ,(  
see:  i )       ) ) ,
-#
?,C*)
, ,         )x       -
       ) ,  (   #
@ )0  )not((
(.,#
$ (#  )(
))  .,  ) ( 3
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1. Albert Einstein, “Zur Elektrodynamik bewegter Körper” Annalen der Physik vol.17 (1905),
https://doi.org/10.1002/andp.19053221004
… translated and reprinted as “On the electrodynamics of moving bodies
in The Principle of Relativity (Meuthen, 1923) pages 35-65. Dover edition ISBN 0486600815
2. Albert Einstein, “Die Grundlage der allgemeinen Relativitätstheorie” Annalen der Physik vol.49 (1916).
https://doi.org/10.1002/andp.19163540702
… translated and reprinted as “The foundation of the general theory of relativity
in The Principle of Relativity (Meuthen, 1923) pages 109-164. Dover edition ISBN 0486600815
3. Harry Nussbaumer, “Einstein’s conversion from his static to an expanding universe
Eur. Phys. J. H vol. 39 pages 37-62 (2014). https://doi.org/10.1140/epjh/e2013-40037-6
4. Albert Einstein, “Kosmologische Betrachtungen zur allgemeinen Relativitaetstheorie”, Sitzungsberichte der
Preußischen Akademie der Wissenschaften (1917). https://doi.org/10.1002/3527608958.ch10
… translated and reprinted as “Cosmological considerations on the general theory of relativity
in The Principle of Relativity (Meuthen, 1923) pages 175-188. Dover edition ISBN 0486600815
5. Cormac O’Raifeartaigh, Michael O’Keeffe, Werner Nahm and Simon Mitton,
Einstein’s 1917 static model of the universe: a centennial review” Eur. Phys. J. H vol. 42, pages 431–474
(2017) https://doi.org/10.1140/epjh/e2017-80002-5
6. Edwin Hubble, “A relation between distance and radial velocity among extra-galactic nebulae
PNAS March 15, 1929. 15 (3) pages 168-173. https://doi.org/10.1073/pnas.15.3.168
7. Albert Einstein, The Meaning of Relativity, Appendix I: “On the Cosmologic Problem” (added 1946, third
edition onwards) ISBN 0412205602
x: This issue will be addressed in a future paper.
page 4 of 4
... However, in a very real sense, Hubble redshifts REALLY ARE gravitational redshifts, of an unconventional type. [55] When a signal spends millions or billions of years in flight, the ongoing expansion of the universe causes the region in which it is finally detected to be a more rarefied gravitational environment than the region in the earlier, denser universe in which the signal was generated. There is therefore a gravitational field-density differential between the source and destination regions of spacetime -the signal is effectively climbing an "uphill gradient" between a denser (earlier) and a less-dense (later) region, and therefore needs to arrive with a gravitational redshift. ...
... • A Hubble redshift is caused by a density-differential between two periods of time that a signal moves between (the differential and gradient are "temporally-aligned"). [55] We can then say that the difference between a gravitational shift and a cosmological shift is the spacetime alignment of its density-differential. If the density-differential is aligned only with the space coordinates, and is constant over time, then we have a conventional static gravitational field whose strength varies from place to place. ...
... The difficulty faced by Einstein's system, which requires both sets of effects to be different, and to follow different equations, is that the path of a signal in real life makes a diagonal across both space and time, so that, by only looking at the density-differentials along the signal path, we cannot immediately tell whether the supposed cause of the differential is cosmological or gravitational. [55] The principle of local physics says that a system or region's internal data should be enough to predict the behaviour of that system or region without reference to anything external. i ii iii iv i … until "unknowns" have propagated inwards from outside the system sufficiently deeply to affect the items under study. ...
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Part of a series. This paper addresses the incompatibilities between modern cosmology and Einstein’s assumed symmetries of Doppler shifts, gravitational shifts and timeflow.
... If a cosmological horizon is to obey relativistic principles, and to be observer-dependent, and fluctuate and radiate, it has to follow these same (c-v)/c equations. Since the Hubble expansion shift can also be expressed as a gravitational shift, iii [16] spacetime geometry then requires gravitational shifts to use the same equations, (c-v)/c . Since gravitational shifts can be calculated from the motion shift of a body freefalling across a gravitational differential, velocity shifts are then forced to obey (c-v)/c , as well. ...
... The Hubble expansion shift therefore also needs to be calculable as a gravitational shift. [16] iv Anybody trying to construct a general theory of relativity from scratch in the 1930s, after the general acceptance of the Hubble result, would have been required to use non-SR equations in order to support the behaviour of cosmological horizons. Einstein's SR-centric 1916 system can be characterised as a "pre-Hubble" class of theory, and should probably have been considered obsolete by around 1935. ...
... [7] ii The equations must also be the (c-v)/c set if we require spacetime geometry to work consistently in an expanding universe. [16] iii The equations must also be the (c-v)/c set if we require geometrical physics to work under arbitrary topological transformations, which can map between a fluctuating cosmological horizon, and the horizons caused by conventional gravitational curvature. ...
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Part II of a series. This part derives the necessary universality of gravitomagnetic effects, their required strength, and the gravitomagnetic equations needed to replace those of special relativity.
... i We therefore conclude that in order for a relativistic theory to allow classical Hawking radiation (and agree with our gravitomagnetic description), the Doppler equations that apply in the horizon region must be redder than those of SR by an additional gamma factor, representing the additional effect of geometry-change due to gravitomagnetism. ii This, coincidentally, turns out to be the same modification already required to bring Einstein's GR (which was originally designed around a static universe [45] ) into line with modern expanding-universe cosmology, [46] and to function consistently with gravitomagnetism. ...
... We also know that a gravitomagnetically-compatible theory cannot agree with fixed Minkowski spacetime or the SR relationships, and that an exact (non-SR) Doppler relationship is calculable by assuming relativity and Hawking radiation. [46] Researchers discussing attempts to derive the equations of motion from classical theory by treating masses as point-masses (perhaps censored by a horizon), typically mention how difficult the calculations are, and give incomplete solutions. One tends to wonder whether this use of more complex and approximate methods may be due to the "simpler" approaches giving exact answers that do not agree with our SR-based expectations. ...
... While the Mach-Einstein concept of a general theory was visionary, Einstein's attempted implementation of a general theory, as proposed in 1916, [8] does not work either as a physics or as a geometry. This is due to the 1916 theory's inappropriate adoption of relationships and conventions derived from the 1905 theory's assumption of flat spacetime, which fail in a curvedspacetime context, and make the theory internally inconsistent and incompatible with modern cosmology, [46] gravitomagnetism, and quantum mechanics. ...
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A receding horizon-bounded body generates an "effective", gravitomagnetic horizon between the observer and the usual r=2M horizon surface. This purely observer-dependent horizon does not obey SR concepts of causality or the SR shift relationships, and its classical behaviours instead correspond to those of acoustic metrics and of quantum mechanics (including the emission of classical Hawking radiation). Since the horizon position alters with the relative state of motion of the observer, who can be arbitrarily distant, non-SR "acoustic metric" physics then effectively operates across the entire external visible universe. Adjusting the body's gravitational shift equations to match those of its surroundings then also converts the r=2M surface into an observer-dependent "acoustic" horizon, solving a number of long-standing problems in standard theory, including the black hole information paradox. We conclude that the definitions and relationships of special relativity, originally derived for flat spacetime, do not function properly in a gravitational universe, and should not be thought of as valid components of a general theory of relativity.
... The SR component also makes horizons absolute rather than relative, which puts the theory into disagreement with quantum mechanics, [30] and when Einstein's system (which was designed for a constant-size universe) is retrofitted with expansion behaviour, the non-SR expansion redshift and the SR-compatible gravitational redshift obey different Doppler laws, despite the fact that Hubble redshift can be treated as a gravitational shift. [31] Einstein's general theory is a failure in the sense that although it sets out founding principles that are supposed to define the theory [1] (chiefly the general principle, and perhaps also the principle of equivalence of inertia and gravitation), the manner of its implementation results in those principles being violated. ...
... And since the Newtonian equations are already those required for cosmological redshifts, [31] we have no trouble making gravitational and cosmological redshifts "dual", too. ...
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Comparing Einstein's route to general relativity via SR equations and flat spacetime, to an alternative route via Newtonian equations and gravitomagnetism.
... Main paper: [47] "Cosmological vs. gravitational redshifts" ...
... If expansion redshifts can be calculated as gravitational redshifts, then this situation must represent an intersection of both geometries -the same equations, as a function of recession velocity, must apply to both. [47] Under Einstein's general theory, they don't -Hubble shifts necessarily follow a non-SR shift law, while gravitational shifts are forced to inherit and obey the SR shift law in order to allow compatibility with SR. This breaks spacetime geometry. ...
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The unavoidability of velocity-dependent gravitomagnetic effects, with more than twenty(!) supporting arguments explaining why these effects must exist, ranging from conservation of energy, conservation of momentum, observerspace principles and classical and quantum theory requirements, to the necessity of v-gm for accelerative and rotational gravitomagnetism, required by any general theory of relativity. Profound incompatibility of the effect with the SR shift equations.
... GM-centric inertial physics flows smoothly into a GM-centric general relativity, which then (somewhat coincidentally) already has the exact non-SR equations required for compatibility with quantum mechanics [17] and with expanding-universe cosmologies. [18] Einstein vs. Gravity ...
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Relativistic Gravitation (“RG”) is the application of the principle of relativity to bodies with gravitational fields. The finite speed of gravitational signalling required by relativity means that the motion of gravitational sources must always be associated with gravitomagnetic side-effects. Since gravitomagnetism does not exist in the SR equations or “flat” Minkowski spacetime, an attempt to extend the Newton/Galileo relativity principle to include gravity necessarily generates non-SR relationships.
... Einstein's GR is the currently accepted theory of gravitation which describes many astrophysical phenomena and objects such as gravitational waves, black holes, precession of stars, planet orbits, and lensing effects. In cosmological terms, a solution of EFE in which the space is not expanding, but rather is an apparent phenomenon as a result of a time dilation effect, is formally conceived in the scientific literature by other important studies (Potter and Preston, 2007;Li, 2014;Baird, 2018) and in other inquiries due to the influence that the encounter of photons has with astronomical objects in space (Churchman, 2004;Meures and Bruni, 2012). For this reason, this study aims to define a metric in the EFE capable of describing the influence that the distorted fabric of spacetime has on photons from a temporal perspective during their long journey throughout space and from which we can draw important conclusions on the cosmological redshift origin. ...
Article
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In response to all current cosmological controversies, this paper provides a reliable explanation of the Hubble tension and of the apparent acceleration of space expansion detected by SN Ia. In the first place, it calculates the redshift from Einstein field equations (EFE) assuming a Friedman-Lemaitre-Robertson-Walker-Trinchera (FLRWT) metric framework due to the deformation of the spacetime fabric, causing a redshift due to a time dilation. In the second place, this study computes the dominant cosmological redshift contribution given by the transit redshift due to multiple interactions between photons and electrons in the intergalactic medium and not sustained in Einstein field equations. It is fully consistent with Wigner's solid-state physics and Ashmore's physics which predict the crystallization of free electrons at very low temperatures and the interaction with photons of light without scattering and blurring effects. The outcome of this inquiry fully matches the observational data given by the redshift-independent extragalactic distances (NED-D) and by the Chandra/XMM-Newton database of quasars for a specific density of matter in the Universe.
... This subject is addressed in another paper ). [5] ii Where we can consider a gravitational field to be the spatial extension of a body's mass, the gravitomagnetic field can be thought of as the spatial extension of its momentum or momenergy. [6] iii Another reason why we have no definitive theory of gravitomagnetism is that any such theory would inevitably conflict with the description given of inertial physics by special relativity. ...
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A simple thought-exercise using only Newtonian gravity reveals how the effective gravitational field differential between two bodies depends on how they are moving.
... But a Hubble-shifted signal must also have a gravitational redshift, as it originates in a younger, smaller universe with a greater gravitational flux-density. [27] Local geometry does not care why a lightpath is curved, so geometrical physics next has to make gravitational and cosmological shifts dual and equivalent. Since gravitational shifts can also be derived directly from motion shifts, ii a properly-functioning general theory then has to unite three different classes of physical effect under a common "curved" description and set of equations. ...
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Although SR-style "frame" arguments work well in flat spacetime, the mass-dependent curvatures inherent in a general theory of relativity prevent a physical observer's local properties from being extrapolated cleanly across the surrounding region. We question the geometrical sense of using frame arguments in a general theory, list some of the resulting difficulties, and conclude that special and general theories of relativistic physics must be regarded as alternative and distinctly-different logical frameworks. The "frame" problem shows that, within a GR environment, the SR solution can only apply exactly to unphysical observers, and not to real masses with relative motion-a valid general theory cannot reduce to SR physics.
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Einstein’s 1905 special theory of relativity is famous for supposedly depending on only two postulates. In reality, the special theory requires at least one additional postulate or definition to separate it from other relativistic models. Each possible form of this third required postulate seems to be at odds with basic principles and accepted physical evidence.
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We present a historical review of Einstein's 1917 paper 'Cosmological Considerations in the General Theory of Relativity' to mark the centenary of a key work that set the foundations of modern cosmology. We find that the paper followed as a natural next step after Einstein's development of the general theory of relativity and that the work offers many insights into his thoughts on relativity, astronomy and cosmology. Our review includes a description of the observational and theoretical background to the paper; a paragraph-by-paragraph guided tour of the work; a discussion of Einstein's views of issues such as the relativity of inertia, the curvature of space and the cosmological constant. Particular attention is paid to little-known aspects of the paper such as Einstein's failure to test his model against observation, his failure to consider the stability of the model and a mathematical oversight in his interpretation of the role of the cosmological constant. We discuss the insights provided by Einstein's reaction to alternate models of the universe proposed by Willem de Sitter, Alexander Friedman and Georges Lema\^itre. Finally, we consider the relevance of Einstein's static model of the universe for today's 'emergent' cosmologies.
Article
Data for 24 galaxies shows a correlation between distance and radial velocity.
On the electrodynamics of moving bodies
  • Albert Einstein
Albert Einstein, "Zur Elektrodynamik bewegter Körper" Annalen der Physik vol.17 (1905), https://doi.org/10.1002/andp.19053221004 … translated and reprinted as "On the electrodynamics of moving bodies" in The Principle of Relativity (Meuthen, 1923) pages 35-65. Dover edition ISBN 0486600815
The foundation of the general theory of relativity
  • Albert Einstein
Albert Einstein, "Die Grundlage der allgemeinen Relativitätstheorie" Annalen der Physik vol.49 (1916). https://doi.org/10.1002/andp.19163540702 … translated and reprinted as "The foundation of the general theory of relativity" in The Principle of Relativity (Meuthen, 1923) pages 109-164. Dover edition ISBN 0486600815
Einstein's conversion from his static to an expanding universe
  • Harry Nussbaumer
Harry Nussbaumer, "Einstein's conversion from his static to an expanding universe" Eur. Phys. J. H vol. 39 pages 37-62 (2014). https://doi.org/10.1140/epjh/e2013-40037-6
Kosmologische Betrachtungen zur allgemeinen Relativitaetstheorie
  • Albert Einstein
Albert Einstein, "Kosmologische Betrachtungen zur allgemeinen Relativitaetstheorie", Sitzungsberichte der Preußischen Akademie der Wissenschaften (1917). https://doi.org/10.1002/3527608958.ch10 … translated and reprinted as "Cosmological considerations on the general theory of relativity" in The Principle of Relativity (Meuthen, 1923) pages 175-188. Dover edition ISBN 0486600815
The Meaning of Relativity, Appendix I
  • Albert Einstein
Albert Einstein, The Meaning of Relativity, Appendix I: "On the Cosmologic Problem" (added 1946, third edition onwards) ISBN 0412205602