Thoughts on the Big Bang Theory

© 1998 by Richard J. Eisner

In 1997 public television aired a program called Stephen Hawking’s Universe, which explicated various current cosmological theories, especially the Big Bang. Here I’ll present a few observations on the theory, my main purpose being to put the notion of the universe that it implies into perspective.

            According to the program, Stephen Hawking predicated his contribution to the Big Bang theory on the work of Roger Penrose regarding stars. Penrose had posited that, when a sufficiently large, massive star dies; at some stage, as the star loses fuel, it begins to collapse, all of its energy and mass contracting. As the star contracts, it grows denser. As it grows denser, the gravitational pull at the center increases, which in turn accelerates this contraction, eventuating in all the star’s matter and energy constituting a single, infinitely dense point.

            Hawking adapted this model to the universe as a whole, thinking that it could contract in the same way; and he postulated, reversely, that it began as an infinitely dense point, which exploded (the Big Bang), producing a universe that, as astronomical observations bear out, is expanding, becoming larger but less dense, the space between bodies of matter, such as galaxies, growing wider and wider.

             Now, consider for a moment that assumed cosmic starting point. Frankly, I don’t know (if it was mentioned, I missed it) whether such point is held to be actually infinitesimally small spatially (implicitly, it would be either infinitesimal or finite) or whether it’s supposed to hold an infinite amount of mass/energy. Of course, for that primeval entity to be infinitely dense, one of those conditions must exist: it must be infinitesimally small spatially, or (if it’s spatially finite) contain an infinite amount of mass/energy.

             The latter condition (infinitely much stuff) could not have been, for, if it had, then, given that the primal universe expands at a finite speed (see the arguments below), this present Big Bang-produced universe would be infinitely dense (infinite divided by finite is infinite). But it’s not infinitely dense.

             Nor, though, could the former condition (infinitely small space) have existed, since, how can an infinitesimal expand? When in the course of its “expansion” would an infinitesimal become finite?

             Therefore, the proto-universe could not have been infinitely dense.

             The Big Bang theory, however, has a bigger problem. The assumption that the universe once was only finitely large means that it will always remain so, as follows. The interval between two points is finite: Picture an unending road, marked by mileposts; any point is by some post, and, while the number of markers is infinite, each is designated with a particular finite number . . . and the difference (distance) between any two (finite) marker numbers is finite. This means also that there’s no such thing as infinite speed, for, whereas finite speed involves traveling a finite distance in a finite time, infinite speed involves traveling an infinite distance in a finite time, which cannot be, as it implies something reaching a point infinitely far from its origin, two points infinitely far apart, which is impossible. Accordingly, the outermost elements of the exploding Big-Bang sphere, however rapidly and for however long they travel out from the nucleus, will continue to be a finite distance from the center, and from each other. And since a sphere’s outmost points determine its diameter, its diameter is permanently finite, and hence, as envisioned by the Big Bang theory, our universe’s volume is permanently finite.

             However large that universe might be, being finite, in the context of infinite theoretical space, it’s a mere speck in a vast, limitless ocean. If it’s all that is, then, in all of immensity, going out and out, without limit or boundary, all that exists is this one speck. Which seems a rather provincial, and unlikely, view of existence. It seems more probable that, just as our sun is not the only star, our little existent speck is not the only one. In fact, if we conjecture that there are just finitely many others, we’re back to the narrow view we started with, the image of one unique speck anywhere. This is true because, as we’ve seen, the extent of two points is finite; thus any finite number of things, however far apart, can be encompassed by a single orb of some (finite) size: in other words, again, a tiny, lone speck in all of endless everywhere. So it’s most likely that there are an infinite number of them (distributed over an infinite space).

             Wherefore, because universe connotes something of ultimate comprehensiveness, denoting all that is, anywhere and everywhere, without limitation or qualification; proponents of the Big Bang theory, short of redefining existing terms or coining new ones, should speak of it as a theory, not of the universe, but rather of our universe; or else acknowledge that the theory entails an extremely small, limited view of things.

On the above reasoning we may further surmise that intelligent life elsewhere is not only probable, but probably infinite. We can generalize that, in an infinite universe, it’s unlikely that a given class of entity (such as matter—or intelligent life) exists in one place but nowhere else. And if other civilizations exist, there should be infinitely many of them, as, if there were only a finite number, it would still mean that we (us together with them) are singular, all contained within a finite area, in an infinite (overall) universe. ( . . . In an infinite universe, the finite—even if numerous—is unique. . . . From a cosmic viewpoint, we’re either alone or merely one among infinitely many similar entities; there’s no in-between. And the former [uniqueness] seems overwhelmingly—astronomically—improbable.)

The Fermi paradox is this: If intelligent extraterrestrial civilizations are highly probable, where is everyone?—why haven’t we seen any? The resolution is simple: Just because something exists doesn’t mean we’re likely to experience it. There are (I suspect) infinitely many intelligent civilizations, but they’re spaced far enough apart so that the distance between them is too great for them to traverse. After all, we’re intelligent, but how far in the universe have we managed to travel? (Not very far.) It may even be that infinitely many do make contact with each other. But perhaps it’s only two in a thousand, which means we’re unlikely to be one of them.

Astronomer Heinrich Wilhelm Olbers (1758–1840) argues that the universe could not be infinite, that there could not be infinitely many stars, for, if there were, with stars thus at all points in the visual field, the night sky would appear to us as a continuous wall of light.

            In reply, imagine this: Our (finite) universe expands tenfold; the same (billions of) stars move proportionately farther away; but one average star is added at the fringe. The starlight would dim. Hence, it’s not true, as Olbers’s argument implies, that the existence of some sufficiently larger number of stars would necessarily cause the night sky to blaze, because a circumstance is possible wherein the greater the number of stars, the darker it is. . . .

In his May 2003 Scientific American article titled “Parallel Universes” (page 44, in the section, Level II: Other Postinflation Bubbles), Max Tegmark writes:

If the Level I Multiverse was hard to stomach, try imagining an infinite set of distinct Level I multiverses, some perhaps with different spacetime dimensionality and different physical constants. Those other multiverses—which constitute a Level II multiverse—are predicted by the currently popular theory of chaotic eternal inflation.

      Inflation is an extension of the big bang theory and ties up many of the loose ends of that theory, such as why the universe is so big, so uniform, and so flat. A rapid stretching of space long ago can explain all these and other attributes in one fell swoop. . . . Such stretching is predicted by a wide class of theories of elementary particles, and all available evidence bears it out. The phrase “chaotic eternal” refers to what happens on the very largest scales. Space as a whole is stretching and will continue doing so forever, but some regions of space stop stretching and form distinct bubbles, like gas pockets in a loaf of rising bread. Infinitely many such bubbles emerge. Each is an embryonic Level I multiverse: infinite in size and filled with matter deposited by the energy field that drove inflation. (My emphases.)

             A major flaw in Tegmark’s conception is that, again, you can’t get an infinitely large universe out of a big bang.

            Similarly, an infinite universe cannot be bubble-shaped (spherical): Again, a sphere has a surface and a diameter, the span of two (opposite) points on the sphere’s surface. Because the distance between those (between any) two points is finite, the sphere’s diameter is finite, and therefore so too is its volume. . . .

            Apropos, what would it mean for an infinite universe to expand or contract? Expansion or contraction entails pushing boundaries outward or pulling them inward. But an infinite universe has no boundaries. Where would it “contract” or “expand” to? . . .