I read not too long ago that philosophy is dead, that science has completely usurped philosophy and therefore philosophy is no longer viable in science. If that is true, then I am a crackpot, and what I’m about to write is just because I don’t understand the complexities of the advanced mathematics. Let me take a shot at it anyway, even at the risk of being just another crackpot: 0=0, 1=1, 2=2 and ∞=∞.

Now I realize that the idea of infinity is a bit difficult to conceptualize, and Georg Cantor eventually drove himself nuts trying to prove a series of infinite sets, but whatever infinity is, it must by definition equal itself! This presents a significant philosophical logic problem for the definition of cosmic black holes for a variety of reasons. So let’s start with a common definition of what a black hole is and what’s inside. A black hole is are “area” in space where the gravitational strength is so strong that nothing can escape its grasp, not even light, whence the name black hole. Current theory holds that a black hole is caused (in adverse to created, which we won’t bother with) by a “singularity” at the center, which is a collection of matter and energy that has been crushed down to a single point of infinite density and infinite gravitational attraction, implying that they would have infinite mass.

There are at least two significant problems with using infinity in any definition of a black hole. The first, and perhaps most notable, is that if a black hole had infinite anything, especially gravity, it would instantaneously swallow the entire universe, and very probably every universe to infinity. Again, that may seem conceptually difficult to imagine, but gravity has no spatial limitations, and an infinite gravity source would pull in everything instantly. That is the problem with understanding what “infinite” or “infinitely” means.

If the entirety of existence in all universes being sucked out of existence in a time equal to zero is too much for you, let’s scale it down to something more reasonable. If the singularity at the center of a black hole is infinitely dense and has an infinite gravitational field, why are they different sizes? It is not because of observational distance. Black holes come in all sorts of different sizes, including what are called “super massive black holes” found at the center of many galaxies. If all black holes are powered by a singularity with an infinitely dense and infinite gravitational field, this would suggest from the definition that there are different values for infinity! While there is no way to calculate what infinity is, if it is part of mathematics then it must be equal to itself.

Therefore, the gravitational field of a singularity is not infinite, but a real number. Admittedly that value is unimaginably big, and will undoubtedly take Graham Notation to eventually calculate, but it is not infinite. Which leads us to a second problem, if the differences in sizes of black holes means they have different gravitational strengths, then the singularity at the center also are neither infinitely dense nor infinitely massive. Again, that does not mean they are not unimaginably dense and massive, just not infinitely.

Now if you’re a chemist and thought you dodged the bullet because I chose to pick on the astronomers, physicist and mathematicians, think again. The super-heavy elements, such as the Lanthanides and Actinides can only be formed (naturally) in the supernova of a giant star because of the immense pressures required to form these elements. However, even if a black hole is not infinitely dense, it is immeasurably dense, so as lighter elements pass over the event horizon and toward the center of the “singularity” they will ultimately be crushed into heavier and heavier elements. Again, this does not imply that the periodic table is therefore infinitely long, it does imply that the number of periods is an enormously larger real number than 8 or 9! Furthermore, due to the completely different gravitational environment they exist in, their half-life is likewise much longer. So inside of the event horizon and approaching the “singularity”, Flerovium’s half-life may go from 2.8 seconds to 2.8 million years. Admittedly that last point may be viewpoint dependent, since in theory time may cease to exist inside of the event horizon.

There will come a point when someone, like Steven Hawking, or Andrew Wiles or Ronald Graham will calculate the actual density, mass and gravity of a black hole of a given size, and from those calculations someone will calculate the maximum “heavy element” possible for that given size. Indeed, the center of a black hole may not be an infinitely dense singularity at all, but a single atom of a massively super heavy element. Perhaps it’s element number 3↑↑3 on the extended periodic table, which massive as it may be, is still a real number and not *infinitely* dense.

on July 6, 2012 at 9:41 pm |Stepanie Lourentzossehr gut, gerne mehr davon.

on July 20, 2012 at 9:36 pm |Leanna MeynExcellent read, I just passed this onto a friend who was doing some research on that. And he actually bought me lunch as I found it for him smile Therefore let me rephrase that: Thank you for lunch! “Remember It is 10 times harder to command the ear than to catch the eye.” by Duncan Maxwell Anderson.