The Universe is Infinite (Part 1)

Overcoming a "central" problem of cosmology theories

Conrad Ranzan
2010-5, rev2015-7

Key Principle of Cosmology

When philosophers and physicists try to understand the Universe —that is, when they construct a conceptual model of the Universe— they almost always include a fundamentally important dictum called the cosmological principle.

The cosmological principle simply holds that the physical universe is homogeneous on a large scale. It means that the Universe is pretty much the same everywhere. It means that wherever you are in the Universe you will see galaxy clusters and super clusters; you will see them in all directions; and you will see them distributed with similar spacing density.

The isotropy portion of the principle is a fact of astronomy; the homogeneity portion of the principle is an assumption of cosmology. Observationally, there is no good reason to doubt its validity.[1]

“The cosmological principle is an important philosophical concept that underpins our understanding of the universe. Spectroscopy is one type of observation that could, in theory, invalidate this concept, although in practice it never has.”
—Cosmological principle (Encyclopedia of Cosmology) [2]

On a historical note, the cosmological principle was so named by astrophysicist Edward Milne in 1933, and was expressed by him in the words: "Not only the laws of nature, but also the events occurring in nature, the world [universe] itself, must appear the same to all observers, wherever they may be." [3]

The cosmological principle

A Long History of Non-Compliance

Greek Cosmology: Aristotle gave the universe a special location when he placed the Earth at the center of the cosmos. ... The Ptolemaic system kept it there for many long centuries.
Copernican Cosmology: Copernicus did the same when he placed the Sun at the center of the universe. Kepler made his concurring contribution.
Early 20^th Century Cosmology: Harlow Shapley (1918) placed the Milky Way at the center of the universe. [5]

General Relativity Cosmology: Einstein, Friedmann, and others constructed a mathematical boundary which ensured that the center-of-the-universe could be anywhere and everywhere (see textbox below).

Einstein asserted, in 1931, that “all places in the universe are alike.” [4] Evidently, discussions in modern cosmology place considerable weight on this principle of universe uniformity.

In practical terms, it means that the universe can have no special location —no central point and no detectable boundary. Unfortunately there has been a long history of non-compliance (see textbox). ... Common sense tells us, a universe that is limited in its 3-dimensional size must have some sort of a diameter. The diameter has a midpoint, joins opposite boundaries and, therefore, locates the center of its finite universe. The simple conclusion is that a finite universe represents a violation of the cosmological principle.

However, a common-sense-defying finite universe was constructed, one that arguably conformed to the principle. Devised by Einstein and elaborated by Friedmann and others it was finite in the sense that it was "bounded" —it had a most clever mathematical boundary. Einstein and his followers relativized a universe of 3 spatial dimensions (plus a time dimension); they hypothesized a general relativity universe filled with a finite volume of spacetime lawfully enclosed by a mathematical boundary.

Extirpating the Center

It may be argued that a universe based on general relativity (GR), such as the Big Bang, does not eliminate the objectionable "center." We are often told that the center of the Big Bang universe is anywhere and everywhere. In a GR universe every observer can legitimately claim to be at the center of it all. Every observer, wherever he may be in the "bounded" GR universe, can argue correctly that a light pulse sent out from his location will, given enough time, circumnavigate the universe and return to the observer's location (provided it is the spherical version, the "closed" version, the version for which the Big Bang will eventually re-collapse).[6]

What about the "infinite" version of the GR universe? Does it extirpate the "boundary and center"? But before addressing this, there is the prior question of whether or not it is really infinite. Let's take a closer look. Here we are dealing with the hyperbolic version, the "open" version, the version for which the Big Bang does not collapse-in-on-itself but instead expands forever, ever faster and faster. In this accelerating universe, when a light pulse is sent out, the light can't bounce back in its circumnavigation of the universe because the mathematical boundary is receding too fast. The important point is that one cannot argue that such a BB universe somehow attains infinite size.

Concept of a Universe Center

The concept of a center applied to a true infinite universe is completely meaningless.

In contrast, the concept of a center applied to a Big Bang universe does have meaning, since the center can be anywhere you choose. This is most obvious for the "closed" version; there, a radial light beam returns to the "center" after crossing or circumnavigating the bound universe.[7] And it does not matter in which direction you aim the lightbeam. Since they are all predicted to return to the point of origin (your location), it becomes difficult to deny your location is special. All those lightbeams obviously "consider" their point-of-origin special; despite following different paths, they all, with mathematical certainty, manage to return to it.

Whatever is finite can never become something infinite. Whatever entity or collection of entities is finite can never grow or expand to attain infinite size. To claim otherwise is to misapprehend the uncompromising meaning of infinity. If the Big Bang started out as a finite ("bounded") system as is claimed, and then at some evolutionary stage transitioned to become an accelerating ("unbounded") system, it may then expand and grow without limit; but it can never be infinite. It simply gets bigger and bigger in its finite size. In the course of its expansion, it can never be claimed: "Now, finally, the model has attained infinite size."

Back to the question of the elimination of the "boundary and center". All the while that the Big Bang universe is into its accelerating phase, we may continue to say that the "center" is anywhere and everywhere. All points, after all, shared a common origin. This feature is inherent in the nature of expanding models and allows such a claim.

It turns out there is really only one way to avoid having a center, any center whatsoever; only when the universe is truly infinite (not merely tending toward it). Only an infinite universe will conform to the full meaning of the cosmological principle —not some watered-down version based solely on appearances.

Our Universe Is Not Expanding

It has been proven, in various other articles, that the universe is not expanding. We do not live in a GR universe; not an Einstein (cosmological constant) universe; not a Friedman (space curvature) universe. General relativity is only applicable as a local (regional) theory. There was no big bang. We live in a universe that is stably cellularly structured. Moreover, the structure on a large scale has a Euclidean geometry.

We apply the cosmological-principle argument to our 3-dimensional Euclidean universe as follows.

What We See

The Hubble space telescope is able to compile images of galaxies that are now, for example, ten billion lightyears away from our Milky Way galaxy. We “see” these galaxies in all celestial directions, as would be expected in a universe that is isotropic. The Milky Way galaxy, then, is surrounded by a hypothetical cosmic shell of embedded galaxies. The radius of the shell (a representative shell) is ten billion lightyears. See Fig. 1.


	Fig. 1. According to the cosmology principle, no matter where you are in the physical universe you will be surrounded by cosmic shells of galaxies. One such shell contains the galaxies that are 10 Giga lightyears from where the observer happens to be. (Not to scale)

Now, these galaxies are at their proper distance, which means they are at the ten-billion-lightyear distance right now —at this very instant in time. The light we actually see through telescopes, was, of course, emitted by those galaxies ten billion Earth-years ago. And since our universe is not expanding, they were then (at the long-ago time of emission) also at the ten-billion-lightyear distance. Of course, during the time in which the light traveled from the galaxies to the Hubble telescope lens the galaxies would have been involved in some localized motion, but practically insignificant when compared to the total distance.

Let us select one of these galaxies and call it Distant Galaxy #1. The line of sight from the Milky Way to Distant Galaxy #1 determines a convenient reference axis. See Fig. 2(a) below.

Next, consider the universe from the viewpoint of Distant Galaxy #1. But first, realize that Distant Galaxy #1 is now actually ten billion years older than the Hubble telescope image of it. It may have undergone radical change. It may have been swallowed by another galaxy. It may no longer exist! With this in mind, the new viewpoint need not necessarily be the observed distant galaxy itself but may simply be its remnant or some other galaxy in its neighborhood. The Milky Way galaxy is part of our Local Group of galaxies; no doubt, Distant Galaxy #1 belongs to something equivalent.

What They See

At, or from, the location of Distant Galaxy #1 the universe will appear the same —not in detail, of course, but in general. Distant Galaxy #1, like the Milky Way, is surrounded by a cosmic shell of ten-billion-lightyear-distant galaxies. Some of those galaxies will be near our reference axis. A viewer, say, some alien intelligent being at Distant Galaxy #1, can select one. We will label that selection Distant Galaxy #2 as in Fig. 2(b). This is a scenario of the present (not in the future, not in the past). Invoking the cosmological principle, the alien viewer applies the same analysis of emission distance and reception distance. And concludes that the "now" distance of Distant Galaxy #2 is ten billion lightyears.

And so, for the viewer located ten billion lightyears from us there is another galaxy ten billion lightyears still farther away —right now.

Similarly, at Distant Galaxy #2 (20,000,000,000 lightyears from us) there is another hypothetical viewer; another viewer who observes another galaxy, Distant Galaxy #3, along the reference axis, as shown in Fig. 2(c).

Fig. 2. Democracy of cosmic location in a Euclidean universe.

(a) By means of the cosmic redshift, observers in the Milky Way determine Distant Galaxy (DG) #1 to be 10 billion lightyears (10 Gly) away.
(b) At the same time, a viewer located at DG#1 observes a distant galaxy, DG#2 and determines its proper distance to be 10 Gly. By the cosmological principle his claim to the correctness of his view is as valid as ours from the Milky Way —which means that DG#2 is 20 Gly from us.
(c) At the same "now" time, a viewer at DG#2 can apply the same reasoning to an analysis of DG#3. Which in turn means that DG#3 is 30 Gly away from us (and we are still in now time).
(d) The same reasoning can be applied to any spatial sequence of galaxies or locations. Since the cosmological principle tolerates no cosmic edge, the argument can be repeated without end. Galaxy number n goes to infinity.

This argument may be repeated without end. At Distant Galaxy #n (Fig. 2(d)) it is always possible to have a viewer who observes another galaxy, Distant Galaxy #(n+1), along the reference axis. And as explained above, there is no time difference involved; all the viewers may capture their similar universe images right now.

The Universe Has no Spatial Limits

If the cosmological principle holds, and all practicing astrophysicists believe that it does, then n has no limit. It follows that the universe is infinite. See Fig. 3.

Fig. 3. The premise is that the view of the universe from every regional location and from every galaxy is approximately the same (not in detail, but in character). It is a fact that astronomers at the location of the Via Lactea observe galaxies 10 billion lightyears (Gly) away —in all directions. The locations of those galaxies are not special; so, the view from those galaxies also includes galaxies 10 Gly out in all directions. There is nothing preventing one from applying the argument repeatedly in some common direction, say, along the axis shown. The inescapable conclusion is that the universe is spatially infinite.

Implications of an Infinite Universe

We know that Mainstream Cosmology is obsessed with the phenomenon of universe expansion —proponents are more certain of this than they are of any other of their articles of faith. However, with an infinite universe the question of a Hubble-type whole-universe expansion becomes redundant. Think about it, why would an infinite universe expand itself?

Why would an infinite universe strive to become MORE infinite?! ... Does it even make sense to have an infinite something become MORE infinite? (Maybe it does to mathematicians.)

It seems rather pointless. And sounds somewhat odd —something like saying “that which is unique becoming more unique.”

How, then, do they justify having a universe that is infinite (or at least nominally infinite) and still able to expand? Their universe is a Platonic/Pythagorean cosmos in which numbers and their relationships are more real than the processes and entities. In a sense, their mathematical universe expands into itself —provided the parameters are properly chosen— according to the general relativity equations that code the Big Bang universe.

For the most part, the implications for academic cosmology are practically nil. Before the Crisis of 1998, the academics embraced the idea of bounded ("closed") universe; thereafter, after the supposed discovery of acceleration, they adopted the idea of an unbounded ("open") version. The latter is nominally an infinite universe, but its infinitude is somehow limited by purportedly having grown/expanded from an extremely small volume. Recognition of the true infinite Universe is not on the agenda.

The implications for popular cosmology, however, is profound. It means a complete break from the GR universe, bounded or unbounded, finite or infinite. It means a rejection of the expanding-universe paradigm. It means our Universe has no center whatsoever.

A True Infinite Universe: The Dynamic Steady State Universe

A true infinite universe is one that conforms to a much stronger version of the cosmological principle, a stricter version that imposes the additional requirement that the universe must be uniform in time —no cosmic event, no cosmic process, has special status. Called the perfect cosmological principle, it states that the way the universe is structured, on the large scale, is uniform everywhere (all distances, all directions) and at all times (past, present, and future). Sometimes it is stated as, “All the events in the Universe are equivalent.” [8] Furthermore, if all the events IN the Universe are equivalent then so too must all the events OF the Universe. The Universe cannot expand in one epoch and then contract in another. The strong version is quite clear —no special events: No beginning event, no future death event, and certainly no special events in between.

It is of historical interest that Einstein had attempted to incorporate the ideals of the perfect cosmological principle in his 1917 model. The model was designed to be a cosmos everlasting in time and totally homogenous in the spatial directions. Einstein was so strongly confident of the validity of the "perfect" principle that he actually modified his field equations of general relativity by introducing a cosmological constant (Lambda).[9] (He was motivated by the fact that no solution could be found for the original equations that would fulfill the requirements of the perfect principle.) Ironically, the introduction of Lambda did not produce the desired result. Einstein’s 1917 universe was unstable. It teetered on a knife-edge between the opposite tendencies of expanding and collapsing.
Much later, in 1932, Einstein abandoned his 1917 model along with the perfect principle. But he did so, only after he misinterpreted, along with his contemporaries, the observational redshift evidence of distant galaxies.

The Dynamic Steady State Universe (DSSU) conforms to the perfect cosmological principle. It agrees with all relevant observations and violates no physical laws. It solves the stability problem —the problem that had plagued Einstein and now plagues all those trying to model a single cell universe. It fulfills Einstein’s quest. No beginning event, no future death event, and no special events in between. That means no whole-universe evolutionary events. The DSSU is a non-evolving universe. The DSSU, as a whole, had no creation event and can have no end-time event.

The DSSU is necessarily infinite. With its stable (dynamically balanced) cell structure it is spatially Euclidean and spatially infinite. Furthermore, this cellular cosmos, because it does not evolve (only its subsystems [10] evolve), is time-wise infinite. 

2010-5 rev2015-7 Copyright by Conrad Ranzan www.CellularUniverse.org

References and Notes

[1] E. R. Harrison, Masks of the Universe, Changing Ideas on the Nature of the Cosmos (2nd ed. Cambridge University Press, Cambridge, UK, 2003) p196

[2] Encyclopedia of Cosmology, Norriss S. Hetherington, Editor (Garland Publishing, Inc. NY & London, 1993)

[3] As in Harrison, Masks of the Universe, p195

[4] Ibid., p196

[5] David Layzer, Cosmogenesis, the Growth of Order in the Universe (Oxford University Press, New York, 1991) p43

[6] Encyclopedia Britannica 15th Edition, Vol.16, p789-790

[7] Ibid.

[8] On the possible role of massive neutrinos in cosmological structure formation by Massimiliano Lattanzi, Remo Ruffini, and Gregory Vereshchagin. (arXiv:astro-ph/0305035 v1 2 May 2003 )

[9] Ibid.

[10] Life is one of the subsystems.

2015-7

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