http://www.cellularuniverse.org/D5InfiniteUniversePart1.htm

The Universe is Infinite

—an argument to demonstrate it cannot be otherwise

Conrad Ranzan

2010

The Premise: a 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 space 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]

The Condition and Disclaimer

If you accept the validity of the premise then the argument below is unavoidable. Acceptance of the cosmological principle leads to an inescapable conclusion.

If, however, you do not accept the validity of the principle then the argument below will, for you, be pointless. Your world view is pre-Copernican. Your patron Saint is Plato the disparager of experience as a source of knowledge.[6] Let no one dissuade you from the belief that the acquisition of truth by revelation is superior to knowledge by scientific exploration. Actually, you are part of a majority whose guiding principle is “The truth lies in what you feel, not in what you know.” [7] ... Skip this essay. You’re at the wrong website.

For the rational minority, there is a foolproof argument (based on the cosmological principle) that requires the Universe to be infinite.

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 cosmic shell of embedded galaxies. The radius of the shell (a representative shell) is ten billion lightyears. See Fig. 1.

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. They were then (at the long-ago time of emission) much closer to us —at least according to the Big Bang model. During the time in which the light traveled from the galaxies to the Hubble telescope lens the galaxies drifted from the emission distance to their reception distance —their present and proper 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. We have our Local Group of galaxies; no doubt, Distant Galaxy #1 has 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).

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 Must be Infinite

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. The locations of those galaxies are not special. The view from those galaxies must also include galaxies 10 Gly out in all directions. There is nothing preventing one from applying the argument repeatedly in some common direction. The inescapable conclusion is that the universe is spatially infinite.

Implications

The reader may wonder, why is the argument rarely presented?

The argument is not only embarrassingly simple but it also reveals an embarrassing weakness in expanding universe cosmology. (Notice I did not say expanding space cosmology. Big difference.) The infinite universe is a simple argument, but Academic Cosmology does not like simple arguments (complex erudition involving multi-parameter formulations is preferred). The infinity argument draws attention to an overlooked fundamental problem, but Academic Cosmology, being wedded to a model that has failed, is forever in model-patching mode and unwilling to break free, unable to revise its basic commitments (expounding the certainty of faith placed in its foundation pillars is preferred). It simply cannot divorce itself from expanding universe cosmology. ... All the while the old weaknesses persist and new ones are uncovered.

Let’s be serious. The solution is to apply Occam’s Razor. If the universe is infinite, then excise the redundancy of the notion, the hypothesis, making it more infinite. (Can’t excise the part that claims “the universe is infinite.” That would imply major surgery —the loss of the cosmological principle. A bloody mess.)

Mainstream Cosmology does have a defense for its position. I’ll get to it in a moment. Let me just make one more point.

We agree that the Universe is infinite. We know that Mainstream Cosmology says the universe is expanding —they are more certain of this than any other of their articles of faith. The simple, but potentially devastating, question is What is the infinite Universe expanding into?! ... It is little wonder that the Big Bang (BB) universe is considered to be unnatural and preposterous! —even, yes even, by its proponents!

In mainstream cosmology, expert opinions vary as to whether the standard universe is infinite or finite. They evade the simple choice and prefer to say the universe is bounded —the universe is infinite but its infinitude is somehow limited.

How, then, do they justify having a universe that is infinite (or at least nominally infinite) and still able to expand?

Their key defense is that the BB universe is a 4-dimensional mathematical sphere. Their universe is a Platonic/Pythagorean cosmos in which numbers and their relationships are more real than the physical entities.

Their mathematical universe expands into itself —provided the parameters are properly chosen— according to the general relativity equations that code the Big Bang universe.

The Dynamic Steady State Universe is Infinite

The cosmological principle has a more demanding version —a strong version. It imposes the additional requirement that the universe must be uniform in time —no cosmic process, no cosmic event, 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 (infinite past, present, and infinite future). Sometimes it is stated as, “All the events in the Universe are equivalent.” [8] If all the events IN the Universe are equivalent then so 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.

The first modern universe-model to incorporate the ideals of the perfect cosmological principle was Einstein’s 1917 universe. It was a cosmos everlasting in time and totally homogenous in the spatial directions. Einstein was so strongly confident of the validity of this principle that he actually modified his field equations of general relativity by introducing a cosmological constant [Lambda].[9] (No solution could be found for the original equations that fulfilling such a cosmological 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 the strong version. But he did so, only after he misinterpreted, along with his contemporaries, the observational redshift evidence of distant galaxies.

Incidentally, the BB does not comply with the perfect cosmological principle. The predicted density variation with time disqualifies it. And it is easy to see that those BB versions with a genesis event are blatantly non compliant.

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 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. The cellular cosmos, because it does not evolve (only its subsystems[10] evolve), is temporally infinite.