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June 2018
Eric Baird
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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.
page 1 of 4
Cosmological vs. gravitational redshifts, Eric Baird, June 2018
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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
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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
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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
