In an excellent step forward for mainstream theoretical physics, the model of Loop Quantum Cosmology (LQC) presents a picture of a universe where singularities do not exist. LQC still holds that a Big Bang happened, but the Big Bang was not the beginning of existence itself, unlike conventional contemporary mainstream cosmology asserted. Rather, according to LQC, the Big Bang occurred after a prior “universe” collapsed and all the entities in it came to occupy an extremely small volume – but not an infinitely small one.

The New Scientist article, “Did our cosmos exist before the Big Bang?” by Anil Ananthaswamy, describes LQC in a manner accessible to the layman reader.

LQC, originated by Ashtekar, Singh, Pawlowski, and Bojowald, is a wonderful improvement in clarity and logical consistency over conventional cosmology. It also affirms many of the insights present in my treatise, A Rational Cosmology.

LQC does not treat “the universe” as all of existence; rather, it refers to the “present universe” as all of existence after the Big Bang, and to some “past universe” as all of existence prior to the Big Bang. Thus, LQC holds that there was not necessarily an act that created existence itself. This is a different definition of “universe” from the one I used in A Rational Cosmology (where I defined the “universe” as “everything that exists”). However, it is a definition that is logically consistent with what I have been saying all along: that existence itself could not have been created – although some subset of existence may have had a beginning.

According to Mr. Ananthaswamy’s article, here is a picture of existence that LQC would imply:

”If [LQC’s predictions are] verified, the big bang will give way to a big bounce and we will finally know the quantum structure of space-time. Instead of a universe that emerged from a point of infinite density, we will have one that recycles, possibly through an eternal series of expansions and contractions, with no beginning and no end.”  

While I am still somewhat skeptical that every entity in existence can act in this highly coordinated manner with respect to every other entity, this theory is at least logically conceivable, and if a plausible spontaneous-order mechanism for such coordination can be presented, I am willing to accept it. LQC eliminates two fatal flaws from mainstream contemporary cosmology:

(1) The idea that all of existence could have been created, instead of existence always existing. This is fundamentally a religious notion and not a scientific one; it implies creation ex nihilo and has no place in a rational worldview.

(2) The idea that the universe or “our present universe” at one time existed as a single point of infinite density – namely, a singularity. According to the article, “Bojowald’s major realisation was that unlike general relativity, the physics of LQC did not break down at the big bang. Cosmologists dread the singularity because at this point gravity becomes infinite, along with the temperature and density of the universe. As its equations cannot cope with such infinities, general relativity fails to describe what happens at the big bang. Bojowald’s work showed how to avoid the hated singularity, albeit mathematically… Singh and Pawlowski developed computer simulations of the universe according to LQC, and that’s when they saw the universe bounce. When they ran time backwards, instead of becoming infinitely dense at the big bang, the universe stopped collapsing and reversed direction. The big bang singularity had truly disappeared.”

I have been arguing these two points for over three years now, and have often been ridiculed by conventionally minded people for defying the scientific “consensus.” Well, it seems that there is no longer such a consensus and that the thrust of new scientific theory is in fact highly consistent with much, even if not all, of my philosophical writings on cosmology. Here are some excerpts from my treatise, precisely on these subjects. Keep in mind that the impossibility of creation ex nihilo and singularities were my primary objections to conventional Big Bang theory.

From Essay VII:

“Assuming that a singularity was a single entity, which exploded to result in the Big Bang, what caused the explosion? Explosion, like generic creation, is an action, and an action is a relationship of multiple entities that results in the alteration of said entities’ qualities.”

“…If the singularity were the only entity that existed, and had no component parts that could interact amongst each other, it could not have exploded, nor could it act in any way whatsoever!”

“…if the entity is some single, monolithic, component-less, indivisible thing, such as the Big Bang theory’s definition of a singularity, and it happens to have certain qualities at a given time (such as non-explosivity, for example), and no other entity exists to change these qualities, there is no way that these qualities can be changed! A thing is what it is, and cannot, especially if it lacks volition, spontaneously decide to become something else and assume a different totality of qualities.”

”If such a component-less entity as a singularity were left entirely unto itself, nothing could have influenced a change in its quality of non-explosivity, and it could not have exploded. Without any mechanism to induce an alteration in its qualities, it would have remained just what it was, a singularity.”

From Essay XIV:

“if the quality ‘matter’ exists in an entity, it must have a real manifestation; this manifestation is volume. If the quality ‘matter’ and the quality ‘volume’ did not coexist and were not inextricably connected, we would encounter absurdities.”

From Essay XV:

“A singularity conceived of as a sole point containing mass, but mass without volume, i.e., a point-entity, is a contradiction in terms.”

In the words of Ayn Rand, “an error made on your own is safer than ten truths accepted on faith, because the first leaves you the means to correct it, but the second destroys your capacity to distinguish truth from error.” (“Introduction,” The Virtue of Selfishness) In the true spirit of the individualism that Rand advocates, I held to my own reasoning and my own understanding of cosmology, in spite of what the prevailing consensus among the laymen and scientists of my time was. I did not take any understanding on faith, irrespective of how prestigious or “indisputable” the theory endorsing it was. In this issue at least, future scientists will likely agree that I was right after all.

Sincerely,

Gennady Stolyarov II

The Rational Argumentator

A Journal for Western Man

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What is an Entity? A Topological Definition

G. Stolyarov II

Issue CLXXVII - November 15, 2008

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Much of my work in A Rational Cosmology depends on a threefold distinction among existents.

Existents are either entities, qualities, or relationships, and each of these designations is mutually exclusive. I have been asked, however, what counts as an entity. In “Entities and Spatial Continuity,” I provided an explanation of one of the necessary qualities of an entity, which I called spatial continuity. Here is how I described that quality:

“Every entity — homogeneous or heterogeneous — must have continuity among all of its parts. The test for spatial continuity is this: is it conceivable for one to trace a path from any point on the entity to any other point without any part of that path entering a region of “space-as-absence,” i.e., a region where the entity does not exist? If such a path is conceivable — no matter whether one’ s current level of technological advancement actually permits one to trace it — the entity is continuous and is affirmed in this ubiquitous quality.”

Having studied topology over the past several months, I was pleased to discover that a topological equivalent of my concept of spatial continuity exists. It is called path-connectedness.

Here is how James R. Munkres defines a path and path-connectedness in Chapter 24 of the Second Edition of his book, Topology:

Path: “Given points x and y of the space X, a path in X from x to y is a continuous map

f: [a, b] → X of some closed interval in the real line into X, such that f(a) = x and f(b) = y.”

Path Connectedness: “A space X is path connected if every pair of points of X can be joined by a path in X.”

A path-connected space is one in which any two points can be joined by a continuous function – a path – that never strays outside the space. To say that every entity is spatially continuous (as per my definition) is the same as saying that every entity is path-connected.

There is more that can be said about the ubiquitous qualities of entities by invoking the topological property of compactness. Compactness has a formal definition pertaining to every open cover of a space possessing a finite subcover, but for our purposes here, we need only to consider the Heine-Borel Theorem, which states that every closed and bounded subspace of an n-dimensional space of real numbers (Rⁿ) is compact.

I argue in A Rational Cosmology that all entities are three-dimensional subspaces of R³ and that every entity has a finite nonzero volume and finite dimensions of length, width, and height, which means that every entity is bounded. Of course, every entity also includes its own boundary and so is closed in topological terms. Therefore, every entity is compact.

Therefore, we can use topology to concisely state the ubiquitous qualities of entities:

1) Every entity is a three-dimensional subspace of R³.

2) Every entity is path-connected.

3) Every entity is closed and bounded – and therefore compact.

4) Every entity exhibits the quality of matter (i.e., every entity is material). This is not a topological property, because topology only addresses spaces and not matter. However, Chapter XIV of A Rational Cosmology addresses my definition of matter in an accessible and concise fashion.

Any existent that meets the above four qualities is an entity; any presumed existent that does not is either not a genuine existent in itself or is a quality or relationship.

­­___________

G. Stolyarov II is a science fiction novelist, independent philosophical essayist, poet, amateur mathematician, composer, contributor to Enter Stage Right, Le Quebecois Libre, Rebirth of Reason, and the Ludwig von Mises Institute, Senior Writer for The Liberal Institute, former weekly columnist for GrasstopsUSA.com, and Editor-in-Chief of The Rational Argumentator, a magazine championing the principles of reason, rights, and progress. Mr. Stolyarov also publishes his articles on Helium.com and Associated Content to assist the spread of rational ideas. His newest science fiction novel is Eden against the Colossus. His latest non-fiction treatise is A Rational Cosmology. His most recent play is Implied Consent. You can also view his YouTube Videos. Mr. Stolyarov can be contacted at gennadystolyarovii@yahoo.com.

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