Can density be infinite?

First photo
of a black hole

Einstein’s general theory of relativity allows for the existence of objects with infinite density (singularities). There are two types:

1.      Black holes, accumulations of matter in a null volume, either at the center of a galaxy, or as the result of a supernova explosion.

2.      The universe, at its initial moment (the Big Bang).

A star like the sun is in equilibrium because the gravitational attraction, which tends to make it contract, is equal to the expansion caused by the nuclear reactions taking place inside the star. When a star much larger than the sun exhausts its nuclear fuel (first hydrogen, then helium, then other elements), as there are no longer nuclear reactions to stop the contraction, the star implodes. When the implosion rebounds, the star throws large quantities of matter into space: a supernova explosion, which for some time makes the star brighter than a whole galaxy. But there is always a remainder of matter, which gives rise to a new type of object.

Is time infinite?

S.Augustin, by Louis Comfort Tiffany
Lightner Museum

Since ancient times, man has been interested in the enigma of time. Even though we all experience time, time is an enigma. As St. Augustine said in his Confessions (B.XI C.XIV): What is time? If no one asks me, I know; if I want to explain it to a questioner, I don’t know.

As I said in another post, the explanations devised to solve the enigma of time are of two types: those that consider it cyclical, with or without multiple repetitions, which would allow the passage of time to be represented geometrically by a circle, and those that consider it linear, which represent it by a straight line. In turn, this last case is divided into several: one can accept, or not, that time had a beginning; and one can accept, or not, that there will be a final moment of time. Combining these two alternatives, we have four different cases. So in total there are six possibilities, which we will analyze next in the light of modern cosmology:

Is space infinite?

Georg Cantor

According to Georg Cantor, one of the first to study the concept of infinity in depth, there is not just one concept of infinity, but three different ones. Let's see how he expresses it:

The actual infinite arises in three contexts: first when it is realized in the most complete form, in a fully independent other-worldly being, in Deo, where I call it the Absolute Infinite or simply Absolute; second when it occurs in the contingent, created world; third when the mind grasps it in abstracto as a mathematical magnitude, number, or order type. I wish to make a sharp contrast between the Absolute and what I call the Transfinite, that is, the actual infinities of the last two sorts, which are clearly limited, subject to further increase, and thus related to the finite. (Georg Cantor, Gesammelte Abhandlungen, Springer, 1980. Translation taken from Rudy Rucker, Infinity and the Mind, Princeton University Press, 2004).

The origin of eukaryotes

John Maynard Smith

As I have said several times in this blog, the theory of evolution is now well established. However, it is far from explaining everything. Many mysteries still remain. I listed some of them in a previous post. A book by J. Maynard Smith and E. Szathmáry, The Major Transitions in Evolution (Oxford University Press, 1995), describes them in more detail.

One of these problems refers to the changes of level that have taken place in the history of life, which I made the central idea of ​​my book The Fifth Level of Evolution. As its title implies, during evolution, things have not happened in an orderly or stable manner. At various points, there were changes of state (similar to those in physics) where evolution passed a critical point that made it possible to reach higher levels and opened up huge new fields in the configuration space. These points are the following:

Paul Davies, popularizer of science

Paul Davies

Paul Davies came to the fore among scientists who devote time to popular science with his 1992 book The Mind of God, written in response to Stephen Hawking’s final words in his popular best-seller A Brief History of Time. In another post I talked about another of his popular books, The Eerie Silence. Here I am going to discuss two other books he has written.

The Last Three Minutes (1994): This book on popular science is a little behind the times, as it predates the standard cosmological model, but explains well the state of cosmology when the book was published, and many of the things it says are still valid. It says something very interesting: that the Big Bang theory by Lemaître (whom Davies does not name) should have been accepted long before its two surprisingly accurate predictions gave it a boost in the sixties, because there is another argument supporting it, that scientists of the 19th century should have noticed, but didn’t: If the universe were infinitely old, it would have died by now. It is evident that something that moves to a stop at a finite rate cannot have existed from all eternity. By the way, there is an error in this paragraph: Davies ignores the difference between what is eternal and everlasting, which was solved fifteen centuries ago by Boethius. And there is a major flaw when he says that the radius of the visible universe is 15 billion light-years, because he does not take into account the expansion of the universe. The correct radius is about 43 billion light-years.

Science Cannot Prove That God Does Not Exist

In several posts, I have pointed out that it is impossible for science to prove that God exists, just as it is impossible to prove that God does not exist. The reason is that the object of scientific inquiry is the material world, and God is not part of that world and is therefore beyond the reach of science.

In a previous post, I criticized a book that attempted to do the former, from the perspective of believers. In this post, I will criticize another book that attempts to do the latter, from the atheist perspective. It is M-E: The God Within, by Joseph R. Abrahamson.

Although the author claims to rely on the principles of logic and the scientific method, he makes significant errors that indicate his lack of in-depth knowledge of these disciplines. The argument he presents as proof that God does not exist, although not explicitly stated in the book, can be deduced from reading it and can be summarized as follows:

Phantoms in the Universe?

The Standard Cosmological Model has introduced in physics two new concepts that didn't exist before:

• Dark matter: It seems to be five times more abundant than ordinary matter, but we don't know what it is, what it's made of. We only know that it appears to be affected by gravity, and so far, its existence has been concluded in two different ways: a) By analyzing the rotational motion of galaxies, which seems to require that there is more mass in them than what we can see. b) By studying the cosmic microwave background radiation, which has served as the basis for adjusting the standard cosmological model.
• Dark energy: We have no idea what it is. Some speak of a fifth fundamental interaction (or force), the quintessence, which would join the four we know: gravitational, electromagnetic, strong, and weak. Others offer different explanations, none of which have received experimental confirmation. The hypothesis of its existence is supported by two observations: a) Analyzing the expansion rate of the universe, after the 1998 discovery that this rate is accelerating. b) By studying the cosmic microwave background radiation, which has served as the basis for adjusting the standard cosmological model.