There is no Such Thing as Actual Infinities
First, some house keeping. Before we discuss the specifics of the 5 salient features, let us deal with Steinhardt's first objection - the general fact that the whole Big Bang Theory is based on a singularity, something that is so fundamentally flawed, that when scientists encounter singularities in any other theories, they abandon the theories, because they know they have made a mistake in formulating them. However, in the case of the Big Bang, not only did they not abandon the mistaken theory, but by adding band-aid proposals like Inflation to try and overcome its shortcomings, they are doubling down, on their initial failures! So, before we get into the specifics, we must deal with why singularities are proof of a lack of critical thinking.
Actual Infinities Do NOT Exist
The Big Bang has always been a sketchy idea. Probably, most of you, when you first heard the idea, thought it was rather strange. Mathematically, it's a singularity. That means it's a mistake, or a problem when we solve the equations going backwards in time. We reach a point where temperatures and densities become infinite! Normally, when we encounter a singularity, when solving equations, we know there's something wrong with the theory that we're extrapolating. And that's true here!" Paul Steinhardt - Time to TAke the 'Big Bang' Out of the Big Bang Theory? (3:28 - 3:59)
This is a significant point. But, one that is thoroughly inconvenient for Big Bang theorists. It seems when scientists come across facts that should spell the end of their theories, they just opt to ignore them. All scientists agree that singularities represent the breakdown of a potential theory's utility, as they are the point at which the whole working model falls apart. Yet, as it relates to Big Bang cosmology, scientists plow ahead and make more assumptions based on what they know is impossible. For instance, when Alan Guth speaks about infinite temperatures being the necessary conditions to allow for exotic forms of matter, it is like building castles in the air. Instead of stopping once they realize they have reached an impasse, a singularity, they instead use the singularity to propose even more metaphysical theories.
In his excellent article about the nonsensical idea of infinite entities Steve Patterson explains logically, why infinite quantities and entities cannot exist. The essay is entitled Infinite Things Do Not Exist. Here are a few highlights:
Much to my surprise, a fairly basic logical error is rooted at the very foundations of modern mathematics. The error is now ubiquitous; it’s become an unquestioned premise in mathematical reasoning. As with most unquestioned premises, it’s become dogma, and the vast majority of professional mathematicians accept the error as truth. The mistake is simple. It is a self-contradictory concept: The existence of actually infinite things" Steve Patterson - Infinite Things Do Not Exist
Surprise is the operative word, but if you understand that academia has been overtaken by Intellectuals, surprise is the last thing you should be at the lack of critical thinking that undergirds the technical aspects of most of contemporary life. When your focus is not on excellence, but on achieving a certain standard of living, rigour and integrity are the first casualties. This is the effect of Intellectualism, and it's deviant brethren - Credentialism.
As I will demonstrate, this concept is incoherent – no different than the concept of square circles or married bachelors. Upon simple examination, it will become clear why there cannot be “actually infinite” distances, densities, forces, numbers, lines, circles, sets, or anything else" Steve Patterson - Infinite Things Do Not Exist
Patterson doesn't make empty assertions. He goes on to offer proofs of the illogical nature of infinities by applying the concept to real world issues and showing the resulting contradictions. He starts by defining the term infinite,
First of all, we have to define our terms. 'Infinity' or 'infinite' means 'without end', 'never-completed', or 'without boundaries'. An infinite distance can never be covered – by definition of what we mean by 'infinite'. There is no 'end' to an infinite series – if the series ends, it’s finite by definition" Steve Patterson - Infinite Things Do Not Exist
He then goes on to contrast that definition with the one for actual,
By the term 'actual', I mean 'fully-realized', 'completed', or 'totally encapsulated.' And here we find the elementary error in the conception of an 'actual infinite'. I realize my refutation would appear impressive and profound were it complex. If it were some difficult, abstract chain of reasoning disproving a century of mathematical thinking – that would surely impress people. But alas, the refutation is not complex. It’s outrageously simple. So simple, it is anti-climactic" Steve Patterson - Infinite Things Do Not Exist
Everyone should be comfortable with his reasoning so far. What is of equal interest is the psychology of resolving such questions. He is quite right that many people would prefer complicated arguments, but the truth is often very simple. And, establishing it, is just a matter of clear thinking and a logical application of the facts. This is true, with his arguments against the existence of infinities, and it is true regarding the fact that the Big Bang is metaphysical conjecture, and has nothing to do with physical reality. We now come to the crux of his argument:
'Infinity' is, by its definition, never fully encapsulated. 'Actual' is, by its definition, totally encapsulated. What is 'infinite' is never fully realized, by its definition. What is 'actual' is fully realized, by its definition. What is 'infinite' has no boundaries. What is 'actual' has boundaries. Therefore, an 'actual infinite' is a simple contradiction in terms – no different than 'a square circle'. If this isn’t intuitively obvious, I will give a few examples, then explain why in a purely logical sense infinite things cannot exist" Steve Patterson - Infinite Things Do Not Exist
Let us review just one of the examples he gives:
Consider a clear example. Try to imagine a circle with an infinite radius. The radius isn’t really big – it’s actually infinite. Is this possible? ... What is the curvature of a circle with an infinite radius? Take any segment of your infinite circle. Does that segment [differ] in any way from a straight line – i.e. does it have any curvature whatsoever? The answer must be “no”, if the radius is actually infinite. After all, if the circle has any curvature at all, the circle would eventually be completed, and therefore finite. Thus, we arrive at an explicit contradiction: a circle with an infinite radius is a straight line" Steve Patterson - Infinite Things Do Not Exist
The reasoning is clear, but resistance to this logic arises from what he says is an "unexpected place: mathematics." However, any such resistance is the result of a clear lack of critical thinking. Here is his answer to such illogical objections:
Now, I am sure somebody will object by saying, 'The circle isn’t actually a straight line. It simpl[y] converges with a straight line.' This is only half-true, and it’s the subject of my earlier piece on calculus. 'Convergence' is a waffle word. Only one of two possibilities is true: either the circle fully converges – i.e. becomes identical with – a straight line, or it gets “ever-so-close-but-not-quite”. If it never becomes identical, then it has a curvature and is therefore finite. There is no third option" Steve Patterson - Infinite Things Do Not Exist
That is simple, logical reasoning at its best. Why don't mathematicians apply it? Regarding concepts like infinities, Patterson points out that mathematicians and physicists are part of the problem. They promote them, so as not to be forced to abandon their ill thought-out theories and models of the world. Patterson's reasoning on the an infinite circle, applies to all the so-called infinite properties in the primeval atom of the Big Bang. Quantities such as infinite density, infinite temperature, infinite curvature and so on, can never actually be realized. They never existed, or can exist! For instance, what does infinite temperature mean? No actual temperature can be infinite. Another problem is that, by definition, infinite quantities can never decrease to non-infinite levels. Something that was infinitely hot could never cool to 3000 Kelvin as is claimed for the early universe, because half of infinity is ... infinity! and no matter how many times you half an infinity, the answer will always remain infinity. This is why on a previous page I said the you can never close the gap with infinite temperatures to achieve equilibrium. Because it takes an infinite number of steps to do and would thus be impossible to achieve.
Also consider that cosmologists who are frustrated by the evidence pointing to that the Earth is at the center of the universe, say its only an illusion. The universe is infinite and an infinite universe doesn't have a center! They then invoke the discredited notions of Isotropy and Homogeneity to claim that every other location in the universe has the same perspective, and thinks that they are at the center of the universe. Clearly this is unreasonable and another example of a "simple contradiction in terms" because the same people acknowledge that nothing exists outside of the boundaries of the Mighty CMB and that it encapsulates the universe. Since the CMB is finite, how can it "encapsulate" an infinite universe. Thus we can safely conclude that there are no infinite properties: be they infinite temperatures, densities, measurements, or any other variable! Further, infinite values can never decrease to non-infinite values. Patterson makes some other good points, but the ones we have already highlighted are sufficient for our discussion. For those who are religiously inclined, let me test your comprehension: is God infinite or finite? Let me leave you with that. Under the subheading Logic and Identity Patterson generalizes his findings to their most non-specific form so that they can be applied to anything, not just circles. I would encourage you to read his blog, if you need more proof of the impossibility of actual infinities. In truth, only ethers are infinite, because, just like infinity - they also don't exist! We now return to Steinhardt's discussion of the 5 "apparent salient features" of the Mighty CMB.