Tag Archives: redshift

Gravitational Redshift & Expanding Spherical Wavefronts

An earlier post on Expanding Spherical Wavefronts made a qualitative argument that an ESW should sustain an energy loss as it expands through the Cosmos. In a more recent post it was argued that gravitational effects are a consequence of matter/electromagnetic-radiation interactions. As a follow-up, this post offers a quantitative demonstration that standard gravitational-redshift-based-math can be applied to an ESW to generate a cosmological redshift correlated with distance:

Terms & Definitions:
z = ((1-(rs/Resw))^(-1/2))-1
rs = Schwarzschild radius = 2GM/c2
Res = successive radii for an Expanding Spherical Wavefront in lightyears
Resw = successive radii for an ESW in meters
M = Calculated mass for a sphere at selected radii, assuming an average cosmological density of 1E-26 kg/m3. The average density is a free parameter in the model but the results are highly sensitive to this particular value. A variation of +/- 10% produces outcomes that seem unrealistic.

All in all, this is nothing more than a proof of concept – but it is an intriguing one. Two pieces of standard physics can be put together to produce a cosmological redshift-distance relation that is similar to the one presented by the standard model. The three graphs of redshift-distance are taken from the table and illustrate scale differences over the range of the table. A short discussion follows the 3rd graph.

Res (Ly) Resw (meters) rs M (kg) z
17.50E+077.08E+232.22E+191.48E+461.57E-05
21.00E+089.44E+235.25E+193.52E+462.78E-05
32.50E+082.36E+248.20E+205.50E+471.74E-04
45.00E+084.72E+246.56E+214.40E+486.96E-04
51.00E+099.44E+245.25E+223.52E+492.79E-03
61.50E+091.42E+251.77E+231.19E+506.32E-03
72.00E+091.89E+254.20E+232.82E+501.13E-02
82.50E+092.36E+258.20E+235.50E+501.79E-02
93.00E+092.83E+251.42E+249.50E+502.60E-02
103.50E+093.30E+252.25E+241.51E+513.59E-02
114.00E+093.77E+253.36E+242.25E+514.77E-02
124.50E+094.25E+254.78E+243.21E+516.16E-02
135.00E+094.72E+256.56E+244.40E+517.78E-02
145.50E+095.19E+258.74E+245.85E+519.65E-02
156.00E+095.66E+251.13E+257.60E+511.18E-01
166.50E+096.13E+251.44E+259.66E+511.43E-01
177.00E+096.61E+251.80E+251.21E+521.73E-01
188.00E+097.55E+252.69E+251.80E+522.46E-01
199.00E+098.49E+253.83E+252.57E+523.49E-01
201.00E+109.44E+255.25E+253.52E+525.02E-01
211.10E+101.04E+266.99E+254.68E+527.50E-01
221.20E+101.13E+269.07E+256.08E+521.24E+00
231.30E+101.23E+261.15E+267.73E+523.10E+00
241.31E+101.24E+261.18E+267.91E+523.71E+00
251.32E+101.25E+261.21E+268.09E+524.74E+00
261.33E+101.25E+261.24E+268.28E+527.00E+00
2713,350,000,0001.26E+261.25E+268.37E+521.00E+01
2813,400,000,0001.26E+261.26E+268.47E+523.49E+01
2913,405,000,0001.26E+261.26E+268.48E+521.75E+02
3013,405,100,0001.26E+261.26E+268.48E+522.39E+02
3113,405,200,0001.26E+261.26E+268.48E+526.48E+02
Graph1 Rows 1-6 of table
Graph2 Rows 1-26
Graph3 Rows 1-27

Discussion

There are several interesting aspects to these results. The initial radius of 75M lightyears is arbitrary and lies just inside the 100Mly radius that can be considered to encompass the “local” Cosmos. The final radius is in the asymptotic range imposed by the math.

What is happening in the math is the Schwarzschild radius (rs) is catching up with the Expanding Spherical Wavefront being modeled. This is because the rs is increasing in proportion to the enclosed mass which is increasing as Resw3 while the ESW itself is only increasing as Resw2. This is the inverse of what happens (according to the Schwarzschild solution to GR) in the case of a mass undergoing gravitational collapse. In that situation the collapsing body converges inward toward the rs as the mass remains constant.

It should be noted that the rs is an artefact of the model; it is a coordinate singularity and not physically significant. This indicates that the model has broken down at that point by virtue of having produced a division by zero result. It can be argued that this is a consequence of the model not taking into account the variation in the speed of light in a gravitational gradient.

It is also striking that the redshift of the ESW model goes asymptotic at approximately the same cosmological distance (13.4Gly) that the standard model redshift does (13.8Gly). The difference is that in the ESW model the redshift is a consequence of the energy loss to the expanding spherical wavefront attributable to its gradual absorption by intervening galaxies. In the standard model the energy loss is a consequence of a model-inferred but unobservable “universal expansion” – which leaves the lost energy physically unaccounted for.

One other point of note, in the ESW account of redshift the cosmological conditions at the source of the redshifted light are assumed to be approximately the same as they are in our “local Cosmos”. In the standard model, of course, the cosmological conditions at the largest implied redshift distances are thought to be significantly different due to the nature of the evolving “expanding Universe” that the model assumes. The recent JWST observations contradict the standard model’s picture of an evolving “Universe”.

Energy Loss And The Cosmological Redshift

Modern cosmology has an interesting approach to the question of where the energy lost by light goes as that light becomes redshifted over large cosmological distances. There seem to be several, not entirely coherent ways of approaching the question. Probably the most conventional approach is this, where Ethan Siegel seems to say, a “universal” expansion is causing the energy loss, but at the same time, the energy lost is driving the expansion of the “Universe” :

The photons have an energy, given by a wavelength, and as the Universe expands, that photon wavelength gets stretched. Sure, the photons are losing energy, but there is work being done on the Universe itself by everything with an outward, positive pressure inside of it!

It is all well and good, to claim that mathematically either view is correct, however, physically speaking, either claim is nonsense. One view posits a bounded, constrained, “Universe” against which the contents are doing work by pushing the boundary outward. There is no evidence for this peculiar viewpoint other than you can arrive at it by assuming, without question, certain things the standard model assumes – without question. It is a mathematicist argument with no basis in the physics of observed phenomena.

The other possibility from the mathematicist’s perspective, is that an otherwise imperceptible, but somehow substantive, spacetime is expanding and so stretching the wavelength of the photon. Again, this has no basis in observed phenomena; it is just an appeal to a purely theoretical construct, one which only serves to obscure whatever physics is actually taking place.

So, how can you account for the energy loss of a cosmologically redshifted photon without veering off into the metaphysical nerd-land presented by mathematicism? Simply put, you have to model light emitted from distant sources (galaxies on the cosmological scale) as consisting of expanding spherical wavefronts. Those wavefronts can be thought of as hyperspheres which are related to the mathematical-geometrical concept of a light cone.

The expanding spherical wavefront view of cosmological radiation rests only on the realistic assumption that galaxies radiate omnidirectionally. This is, in terms of modern cosmology, a simplifying assumption, one which eliminates the need for an expanding “Universe”. It is this expanding spherical wavefront phenomenon that has been misinterpreted in the standard model, to imply a “universal” expansion. The only things undergoing expansion in the Cosmos are the expanding spherical wavefronts of light emitted by galaxies.

The theoretical, light cone concept, closely parallels the physical structure of an expanding spherical wavefront considered 4-dimensionally. In the theory of light cones the surface of the light cone is the aggregate of all the hyperspheres which are themselves, sections of the light cone. All of the points on the light cone have no spatial or temporal separation. The 4-dimensional surface of the light cone constitutes a simultaneity – in 4-dimensions.

Deploying this mathematical model in the context of the observed expanding wavefronts suggests that when a 3-dimensional observer interacts with the light cone, at a specific 3-spatial + 1-temporal, dimensional location, the observer is observing the simultaneous state of the entire expanding wavefront, which, in the model, is the state of the hypersphere of the light cone that intersects with the observer’s 3+1-dimensional “now”.

A 3D observer cannot observe the entirety of the 4D light cone, only the portion of hypersphere (spherical wavefront) with which it directly interacts. However since all the points on the hypersphere are identical, information about the state of the hypersphere is available at the point of observation.

At large cosmological distances that wavefront will be observed to be redshifted, reflecting a net energy loss to the spherical wavefront. This energy loss is caused by the wavefront’s encounter with and partial absorption by, all the intervening galaxies (and other matter) encountered over the course of its expansion.

This energy loss can be crudely estimated using the standard General Relativity equation for gravitational redshifting. That, in turn, suggests the possibility that all observed gravitational effects are a consequence of the interaction between 3-dimensional matter and 4-dimensional electromagnetic radiation.

This post is based on a recent Quora answer.