On the Significance of Gravity Wave Propagation in a Finite Time Universe

The ONLY falsifiable theory regarding observed cosmic redshift.

The recent evidence of energetic gravitational waves as observed by the LIGO interferometer experiment requires reevaluation of related theories over the past century. Here we examine the context of that formative research and reframe their conclusions using 21st century data. Through sincere application of mainstream mathematics, we demonstrate a linear and sustained redshift trend that conforms with strict adherence to relativity, observational data, compatibility with spacetime as well as quantum models, and eschewing all unverified hypotheses of dark forces or arbitrary metric expansion. Research employing this simple and evidenced gravitational wave dilational flooding model will benefit from first principle based falsifiable predictions unavailable to current models. This is also a testament to the enduring relevance of the efforts made by the scientific pioneers of yesteryear.

For upwards of 100 years...

...our knowledge of the cosmos has been vastly expanded in no small part due to the contributions of Albert Einstein and Edwin Hubble. Their work on relativity and deep space observations have taken us from a universe whose extent was believed to be only as far as the edge of our Milky Way to the realization that we are within a seemingly infinite expanse containing more galaxies than we can count.

As our knowledge has expanded, our scientific beliefs have naturally shifted in response. But as new theories have been scaffolded atop the foundations laid by these greats, we collectively neglect to revisit those theories with our modern knowledge while considering the context in which the authors first wrote them. To correct incongruencies between established beliefs and new observations, we seem to favor fantastic rationalizations that promise to patch the outmoded assumptions of a century ago.

Instead of this patchwork process, would comparing the differences between the scientific beliefs during the Progressive era and the seemingly contrary evidence we have today reveal any biases that have not been directly addressed? Even if the mathematical theory remains the same, might the description of the mechanism behind it be different given what we know now?

It is a little-referenced truth that both Einstein and Hubble shared the majority opinion of their time that the universe had no beginning. Their preferred presumption had always been that the cosmos and the contents therein are persistent. This seems counterintuitive from our frame of reference today considering Hubble flow and relativity are often cited as direct theoretical contributors to the Big Bang finite time model. But despite being named dropped in seemingly every paper on the subject (guilty!), they were always reluctant to outwardly agree to the premise even when demanded by their own theories.(1,2)

Edwin Hubble is acknowledged as the first scientist to recognize that some of what we had assumed were stars within our lone galaxy were in fact distant galaxies in their own right.(3) Collaterally, he correlated through light spectrography that the difference between observed and expected light frequencies was proportional to that galaxy’s distance from us. Considering the Doppler effect to be the only sensible cause for that shift in wavelength, he concluded that the evidence suggested an apparent acceleration of distant galaxies away from our own. Such drastic cosmic motion seemed to be in conflict with his personal belief and it required a new and unique physical property of space to accommodate it, but Hubble flow has since become the dominant cosmic model.

Einstein apparently suffered from a similar existential crisis recognizing that his relativity theory implied gravitational collapse without the aid of an outward force.(4) In a permanent universe, especially one consisting of a single galaxy, there is nothing to compel the steady state he desired. Having struggled for years with an arbitrary cosmological constant, his continued discussions with Alexander Friedmann and Georges Lemaître ultimately led to his acquiescence to the metric expansion description of his contemporaries.(5) Seemingly content that the question was settled, he elected to pursue other topics which included debating the apparent disparities between emerging quantum mechanics and his own brainchild of relativity.(6)

Their conclusions fueled considerable scientific progress in the following years. But as the middle of the century approached, new observations resulted in exceptions to metric expansion and relativity akin to the mercurian problem Einstein showed a solution for decades prior. Instead of addressing the shortcomings of their models, these notable deviations have been leveraged to substantiate the hypotheses of increasingly more exotic solutions. For example, the continuing search for definitive evidence of a dark matter or dark energy contributor to serendipitously account for deviations from Hubble’s predictions have yet to mature from divergent mathematical models to confirmed observation. Furthermore a growing divide between a strict adherence to relativity and quantum mechanics betrays the paradox of a Minkowski model and fixed minimum quanta behavior.(7)

We are quick to take ownership of these challenges and claim they are temporally removed from the originators of these models, but this reduces their contribution to a contextless group of symbols on a whiteboard. To sincerely incorporate what was their life’s work, we need to consider the limits to the information they had available.

It was after the passing of Hubble and Einstein that many of the observations which directly supported a finite time universe model were made. Most notably, the cosmic microwave background (CMB) is recognized as evidence that all we know to exist had a beginning. This ancient signal represents the limits of observation while implying that there is more to the universe beyond it. Attributed to the recombination epoch after the Big Bang(8), it is a foundational piece of cosmic origin theories, and necessitates an even distribution and simultaneity to the conversion of primordial cosmic energies.

Theoretically, before the first second had passed, the universe’s contents had been spread over a volume of at least several dozen parsecs in diameter which would dilute any propagating forces in that brief time to be insignificant. It seems reasonable to infer that particles would be causally naive to one another after cosmic inflation. Although there is continued speculation regarding the impact of relativity in these formative moments, the influence of gravity is necessarily suspended or diluted to permit the inflationary epoch.

Astronomically, intergalactic rates of propagation have only been considered when observing electromagnetic (EM) energy or neutrino detections which are known to be causally compliant with the speed of light. This is why we experience a limited observable range despite the theory that the universe is effectively much larger in volume. However, it is a more recent revelation that gravity should now be given that same consideration.

As expected of all particles and forces by relativity, it had been speculated that the spread of the effect of any perturbation to spacetime, including propagation of a gravitational field, must likewise be limited to the speed of light. Although Einstein is credited with this theory, he seemed reluctant to assign gravitational waves any material significance(9). Since he presumed that the contents of the universe were persistent, the gravitational influence of all masses would have already reached cosmic extents making the point moot. Absent compelling experiments or observations, there was little consensus between those who believed in instantaneous persistent gravitational influence and those who adhered to the strict causality limitations in relativity.

Richard Feynman, defying Einstein’s own assertions on the matter, proposed that propagating gravitation must be energetic and suggested how to prove it observationally. This led to the development of the LIGO project which in the last decade has provided the strongest evidence for energetic gravitational waves as well as confirming a speed of light propagation rate. There is now emergent research to characterize a gravitational wave background similarly to the CMB but to help us observe beyond the recombination epoch.(10)

I attempted to substitute these modern realizations into the context of scientific thought from a century ago, from the gravitational questions inspired by Mercury’s curious orbital progression to the latest research regarding quantum foam. While I gained appreciation for the forward progress across all the physical sciences, it was the discoveries I made looking backwards that interested me the most. This thought experiment led to the realization that we have built the models describing our observably finite time and effectively infinite volume universe on the paradigms of men who often promoted the opposite to be true.

This compelled me to ask: If we consider gravitational waves as a propagating energy in a finite time universe in the same way we do with electromagnetic waves, might that change interpretations of observations made over the last hundred years?

To visualize how one might consider this question, imagine a pool in which a stone is dropped. The stone represents an infant particle at the beginning of the universe, and the outbound ripple is its gravitational influence from the first second after inflation. As suggested by the CMB and the way we treat causality with EM energy, these events occur simultaneously for all the other particles that now exist. So if we drop an immeasurable quantity of pebbles evenly spaced into an infinite pond and the expanding ripples represent the initial interaction between them, we see how an individual ripple front impacts a growing area and the reciprocal effect to that individual. Despite the wavefront diminishing in intensity, the range of causally associated pebbles continues to grow at that velocity.

The very concept of a cosmic horizon and an observable universe implies that the propagation velocity of particles since the beginning of time has limited the distance we can observe, and ostensibly the distance into the universe from which you could observe our point. This is an effect we directly observe electromagnetically and have recently verified to be true gravitationally. Note that for the following illustration all sources are presumed in-phase. Although this is not necessarily the case for EM energy, gravity is strictly additive as there is no evidence for out-of-phase time dilation or other “anti-gravity” properties.

To calculate the influence of a progressive flood of new gravitational wave force from the expanding edge of the observable universe, we consider Sir Isaac Newton’s inverse square law (F=1/R^2) which describes the reduction of radiating power over distance. Originally conceived to describe gravitational force, it is the same trend for any radiated wave whether it be force through a medium or energy emitted in free space. And since the range of gravitational effect is unlimited, one can expect its impact to propagate indefinitely.

Although the outbound trend of gravitational energy from a given mass is clearly established, it is the plurality of inbound force in which we are truly interested. As the time-of-flight distance to the cosmic horizon increases linearly, the surface area of our causality frontier grows exponentially (A=4R^2). It is the combination of these two geometries (expansion of surface area and inverse square power) that result in a linear trend.

Surface of a sphere

Consider a point at the center of a sphere, the surface of which is defined by equidistantly spaced energy sources of equal output. Then a second incrementally larger sphere but with the same surface density of sources equally spaced. Measuring the apparent power at the center of each sphere individually will show the same result.

Force of gravity between masses

If both spheres coexist, the measured value is their sum.

Inverse square law

For each additional sphere added to this exercise, an equivalent amount of energy is added to the measurement.
There is a linear trend to an expanding quantity of spheres of identical surface density regardless of the diameter.

Now consider an infinitely repeated luminous matryoshka of these concentric spheres. Each layer is an equivalent diameter larger than the last, and the surface density of lights is constant. If such a massive array is simultaneously placed into a distributed existence, say in a sudden inflationary period taking less than a second, there is a causality delay for each radius until the energy reaches the center.

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Dilation Flooding Equation.

This equation reflects the combination of the inverse square law and the expansion of mass area integrated over a range of radii. Since the cosmic microwave background suggests that the distribution of mass is effectively even at cosmic scales, the value for M remains constant. With r(max) being essentially the comoving distance to the cosmic horizon, the F(total) continues to grow linearly with it. Therefore, using gravitational force equations considered accurate since the 17th century combined with 20th century relativistic effects and 21st century interferometric astronomy, this model predicts a linear trend of changing gravitational potential.

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Wavelength change due to gravitational potential.

However, these algebraic gymnastics are only interesting if they conform to observations. With the ongoing debate over which direction the rate of metric expansion will skew, analysis of redshift returns a surprisingly linear distance relationship in nearly all cases. If we instead accept this trend as a long term reality, observe gravitational causality, and apply Einstein’s equivalence principle to substitute an accelerated frame with gravitational potential, then cosmic expansion can be directly replaced by cosmic gravitational accretion. As it stands, the calculation of wavelength change due to gravitational potential is a linear relationship suggesting that the gravitational model described here results in observations identical to those currently attributed to accelerated metric expansion.

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Time dilation

If we consider a change in gravitational potential, then we must also include time dilation as a factor. This directly impacts measurement of signals (clock rates) as well as propagation rate, both of which may impact perceived wavelength. The calculated effect in this case is hyperbolic, yet the impact is nearly linear except for considerably dilated conditions.

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If we consider a change in gravitational potential, then we must also include time dilation as a factor. This directly impacts measurement of signals (clock rates) as well as propagation rate, both of which may impact perceived wavelength. The calculated effect in this case is hyperbolic, yet the impact is nearly linear except for considerably dilated conditions.

It took the peculiar orbit of a small planet close to its star for an observable scenario extreme enough to first betray this effect. Now it is the timing precision required for geosynchronous positioning satellites that serves as constant confirmation. But if this force is gradually applied in equal measure throughout the cosmos as suggested, then all relativistic frames are impacted to the same degree masking the impact to clock rates.

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Zayani, CC BY-SA 3.0 , via Wikimedia Commons

However, dilational curvature of space does directly impact relative propagation times. This “dilational metric expansion” would be nearly indistinguishable from a linear measurement change except at such notable distances that a curve becomes apparent. The strongly hyperbolic relationship in time dilation conforms with the observably linear redshift trend for at least the first gigaparsec with accelerating values only measurable after this distance. Simple conversion of redshift values into gravitational time dilation produces values that appear to be within the range predicted by the ΛCDM model making this method a candidate to directly address the cosmological constant problem.(11) This dilation-centric approach unifies the purpose of the constant (Λ) as Einstein first proposed it with the observations we make today.(12)

One might wonder if considerations like I’ve suggested here have been made before. Although several gravity-centric theories have been published over the years,(13,14,15,16,17) they all suffer from the same deficiency as the Hubble flow metric expansion theory they seek to supplant. In every case it is necessary to include assumptions or inferences that, regardless of the reasonableness, cannot be demonstrated on a small scale or deduced by direct observation.

In contrast, all I’ve described here requires only Einstein’s seminal paper on relativity and the expanding cosmic horizon of a finite time universe. Observations of cosmic redshift and causality compliant gravitational waves confirm predictions as opposed to directing the mathematics. Revisiting these empirically sound scientific properties clearly shows a progressive gravitational wave “flooding” as an equivalent and elegant substitution for extra-relativistic metric distortion or other yet unidentified arbitrary forces.

Relying solely on first principles, this approach also enjoys wide interpretive compatibility. For example, a radiative gravitational particle could replace Minkowski gravity wells with quantum dilation energy springs in a static universe volume. Or we could invoke the infinite bounded volume that Einstein hypothesized(18) allowing gravitational waves from a fixed mass to continue shifting the gravitational potential range of an infinite time wraparound space. Although that is not a model I subscribe to, this possibility would appeal to the timeless universe sensibility of that era.

The implications of the paradigm I’m suggesting might be considered an affront to faith in these gods of science by nailing up theses as if in protest. To the contrary, I am calling for a Wesleyan revival of first principles to affirm their persisting relevance. It is through this practical reframing of existing theory that a new light might shine on the demons of dark properties, casting out those devoid of empirical substance and canonizing the scientifically fundamental.

We have only just begun this crusade to understand our physical reality, and it is my hope that we remember to revisit the context of our past successes to illuminate our best way forward.

Works Referenced

1 Hubble, Edwin P. The Observational Approach to Cosmology. Oxford University Press, 1937.

2 Einstein, Albert. “Cosmological Considerations in the General Theory of Relativity.” Annalen der Physik, vol. 354, no. 7, 1917, pp. 769–822.

3 Hubble, Edwin P. “NGC 6822, a Remote Stellar System.” The Astrophysical Journal, vol. 62, 1925, pp. 409–433.

4 Kragh, Helge. “Albert Einstein’s Finite Universe.” Masters of the Universe: Conversations with Cosmologists of the Past, Oxford, 2014; online edn, Oxford Academic, 19 Mar. 2015. Accessed 4 Mar. 2024. doi:10.1093/acprof:oso/9780198722892.003.0005.

5 Nussbaumer, Harry. “European Physics Journal — History.” European Physics Journal — History, vol. 39, 2014, pp. 37–62. doi:10.1140/epjh/e2013–40037–6.

6 Heisenberg, Werner. Encounters with Einstein : And Other Essays on People, Places, and Particles. Princeton University Press, 1989.

7 Wheeler, John Archibald, and Kenneth Wilson Ford. Geons, Black Holes, and Quantum Foam: A Life in Physics. W. W. Norton & Company, 2010.

8 Peebles, P. J. E. Principles of Physical Cosmology. Princeton University Press, 1993.

9 Halpern, Paul. “How Richard Feynman Convinced The Naysayers 60 Years Ago That Gravitational Waves Are Real.” Forbes, 7 Mar. 2017, www.forbes.com/sites/startswithabang/2017/03/07/how-richard-feynman-convinced-the-naysayers-that-gravitational-waves-were-real-60-years-ago/?sh=1b15b353ab11. Accessed 4 Mar. 2024.

10 Romano, Joseph D., and Neil J. Cornish. “Detection Methods for Stochastic Gravitational-Wave Backgrounds: A Unified Treatment.” Living Reviews in Relativity, vol. 20, no. 1, 2017, p. 2. doi:10.1007/s41114–017–0004–1.

11Adler, Ronald J., Brendan Casey, and Ovid C. Jacob. “Vacuum catastrophe: An elementary exposition of the cosmological constant problem.” American Journal of Physics, vol. 63, no. 7, 1995, pp. 620–626. doi:10.1119/1.17850.

12 Planck Collaboration. “Planck 2018 Results: VI. Cosmological Parameters.” Astronomy & Astrophysics, vol. 641, 2020, p. A6. Crossref, https://doi.org/10.1051/0004-6361/201833910.

13 Sandved, Patrik Ervin. “A Possible Explanation of the Redshift.” Journal of the Washington Academy of Sciences, vol. 52, no. 2, 1962, pp. 31–35.

14 Marmet, Paul. “A Possibility of Gravitational Redshifts.” Canadian Journal of Physics, vol. 41, no. 1, 1963, pp. 147–152.

15 Assis, André K.T. “A Steady-State Cosmological Model Derived Relativistically.” Progress in Physics, vol. 3, no. 3, July 2007, pp. 88–92.

16 Gentry, Robert V. “A New Redshift Interpretation.” Modern Physics Letters A, vol. 12, no. 37, Dec. 1997, pp. 2919–25. doi:10.1142/s0217732397003034.

17 Bunn, Edward F., and David W. Hogg. “The Kinematic Origin of the Cosmological Redshift.” American Journal of Physics, vol. 77, no. 8, 2009, pp. 688–694.

18 Einstein, Albert. “Cosmological Considerations in the General Theory of Relativity.” Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften (Berlin),Part 1, 1917, pp. 142–152.

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