When Albert Einstein first made public his field equations describing general relativity, he had not yet found the final solution to his equations. The solution was actually discovered a few months later, by a German physicist named Karl Schwarzschild, and with his contribution a complete description of gravity as an intrinsic property of the geometrical structure of space-time was put forth. But the solution, called “The Schwarzschild solution”, revealed a strange phenomenon in Einstein’s field equations in which the gravitational field became singular; certain variables increased to infinity and thus predicted the presence of bottomless curvature in the space-time manifold – they predicted singularity. The significance of this discovery was debated for decades, few people thought they would actually observe physical singularities in nature, and it was not until the latter half of the 20th century that the phenomenon was accepted as an inherent feature of general relativity. Today the existence of astrophysical singularities, or “black holes“, is widely accepted, and they represent a key component of modern cosmology. Although the solution proposed by Karl Schwarzschild describes infinite curvature in the space-time manifold it’s still frequently used in astrophysics with regard to areas of “flat” curvature – normal three-dimensional space. However, the areas of extreme space-time distortion and zero volume are much less understood and difficult to deal with when formulating physics.
The theory of General relativity defines specific criteria for the amount of mass/energy required within a given radius of space to form a black hole – the so-called Schwarzschild radius. We can imagine the Schwarzschild-radius as a sphere. The field equations state that any object compressed to a size smaller than this sphere will become so densely massive that it generates infinite curvature in the space-time manifold – a black hole (e.g. our own planet would have to be compressed to a radius equal to that of a ping-pong ball to attain such a density). This hypothetical region (termed r), where even light cannot escape gravity, defines the event horizon and it is expressed by the equation below, where G = the gravitational constant and m = mass and c = the speed of light. The equation simply describes the linear relationship between the mass and the radius of a black hole, based solely on the system’s mass.
In the fractal-holographic model, the proton of an atomic nucleus is described as a microscopic black hole instead of a limited particle. Protons are found absolutely everywhere in the universe, it is the basic building block of all matter, thus seeking to understand how the universe is connected it is crucial to understand the proton structure. In fact vacuum fluctuations make up 99.999% of the proton itself, so by utilizing the renormalized value for these fluctuations we may accurately calculate the amount of available vacuum energy within the proton volume itself, and thereby calculate whether there is sufficient available mass to meet the criteria for the Schwarzschild radius defining it as a black hole. The result of these calculations is striking: the proton volume contains an amount of energy equivalent to 4.98 x 1055 grams – exactly the same value of the total mass of the universe! Of course this is far more than required to be defined as a black hole. Not only can all protons in the universe be understood as tiny black holes but this auspicious correlation between the energy density of the proton and the mass of the universe indicates an underlying relationship between the two variables hitherto undiscovered. In fact, as we discuss elsewhere in this blog, this relationship is the first clue to the holographic nature of the cosmos.
But protons with a mass equivalent to hundreds of trillions of grams may seem paradoxical at first, especially considering that the mass of the universe is comprised of these very same protons and is itself believed to have as much mass (4.98 x 10⁵⁵ grams). Besides, measurements made in laboratories indicate the proton mass to be a mere 1.672621777 x 10-24 grams, an extremely small value, in great contrast to the mass of the Schwarzschild-proton. For this reason the proposition of such super-massive protons is still highly controversial and the apparent discongruity between mass values within the theory itself has been the basis for much criticism by the scientific community. Yet, the criticism stems from an incomplete understanding of the theory itself. If we integrate these findings with our knowledge of the holographic principle, we may understand that the proton mass cannot at all be isolated from the universe in which it appears, and only then can we also see the full range of these correlations.
To learn where all this ties up beautifully, proceed to Quantum Gravity and Holographic Mass.