# What is the Universal Scaling Law and Scale Symmetry?

## Schwarzschild as a Scale

Black holes are a pretty well-accepted theory, despite no direct confirmation (yet). The mound of evidence makes any alternatives incredibly unlikely, and it all started with the Schwarzschild solution to Einstein’s Field Equations from relativity. Other solutions to the field equations, such as the Kerr-Newman, give better descriptions of black holes, but can these results be applied to other objects? The answer appears to be a surprising yes, and the results are astounding.

The first part of the analogy lies in the main way we detect black holes: X-rays. Our singularities usually have a companion object that feeds the black hole, and as the matter falls in it gets accelerated and emits X-rays. When we find X-rays being emitted from an otherwise unexciting region of space, we have reason to believe it is a black hole. Can we then apply black hole equations to other X-ray emitters and glean useful information? You betcha, and it arises from the Schwarzschild radius. This is a way to relate the mass of an object to its radius, and it's defined as R­s = (2Gm­­s/c2), where R­s is the Schwarzschild radius (beyond which lies the singularity), G is the gravitational constant, c is the speed of light, and m­­s is the mass of the object. Applying this to different black hole solutions such as stellar, intermediate, and supermassive black holes yielded an interesting result for Nassim Haramein and E.A. Rauscher when they noticed that the radius and angular frequencies, when plotted, followed a nice negative slope. It was as if a scaling law held for these objects, but was it indicative of something more? After applying Schwarzschild conditions to other objects like atoms and the Universe, they too seemed to fall onto this nice linear line where as the radius increased, the frequency decreased. But it gets cooler. When we take a look at the distances between points on the graph and find their ratio…it’s pretty close to the golden ratio! Somehow, this number which appears all throughout nature mysteriously, has managed to sneak its way through to black holes, and maybe the Universe itself. Is it a matter of coincidence, or a sign of something deeper? If the scaling law is true, then it implies that a “vacuum state polarization” can lead us to “an event horizon topological space-time manifold,” or that we can describe objects in space-time as having the geometrical properties of black holes, but on different scales. Does this scaling law imply that all matter follows black hole dynamics and is just different versions of it? (Haramein)

Maybe we can gleam information about the scaling law if we examine one of its wildest claims: the Schwarzschild proton. The authors took the black hole mechanics and applied it to the known size of a proton and found that the vacuum energy supplying the formation of a proton would yield a ratio of the radius to a mass of about 56 duodecillion (that’s 40 zeros!), which happens to be near the ratio of the gravitational force to the strong force. Did the authors just discover that one of the four fundamental forces is, in fact, a manifestation of gravity? If this is true, then gravity is a result of a quantum process and so a unification of relativity and quantum mechanics has been achieved. Which would be a big deal, to put it lightly. But how much does vacuum energy really play into the formation of black holes if this is true? (Haramein)

## Is It Widely Accepted?

It is important to note that this scaling theory isn’t well received by the science community. The scaling law and its consequences don’t explain aspects of physics that are well understood, such as electrons and neutrons, nor does it offer a rationale for the other forces left unaccounted for. Some of the analogies are even taken into doubt, especially because it seems at times that different branches of physics are meshed together without regard for reasonability (Bobathon “Physics,” Bob “Reappearing”).

## A Different Theory of Scale: Scale Symmetry

Instead, when theories of scale are talked about, one example that does have potential is scale symmetry or the idea that mass and lengths are not inherently properties of reality but depend on the interactions with particles. This seems strange because mass and distances do change when things interact, but in this case, particles don’t inherently possess these qualities but instead have their normal properties such as charge and spin. When the particles are engaging with each other, that’s when mass and charge arise. It’s the moment that scale symmetry breaks, implying that nature is indifferent to the mass and length (Wolchover).

This theory was developed by William Bardeem as an alternative to supersymmetry, the idea that particles have massive counterparts. Supersymmetry was appealing because it helped resolve many mysteries in particle physics such as dark matter. But supersymmetry failed to explain a consequence of the Standard Model of particle physics. According to it, quantum mechanical means would force particles that the Higgs boson interacted with to achieve high masses. Very high. To the point that they would reach the Planck mass range, which is 20-25 orders of magnitude larger than anything currently known. Sure, supersymmetry does provide us with more massive particles but is still short by 15-20 orders of magnitude. And no supersymmetric particles have been spotted, and there is no sign from the data we have that they will be (Ibid).

## The Supporting Evidence

Bardeem was able to show that “spontaneous scale symmetry breaking” could take many aspects of particle physics into account including the mass of the (then hypothetical) Higgs boson and these Planck mass particles. Because the interaction of particles generates mass, scale symmetry would allow a jump of sorts form the Standard Model particles to the Planck mass ones (Ibid).

We may even have evidence that scale symmetry is real. This process is thought to happen with nucleons such as protons and neutrons. Both are composed of subatomic particles called quarks, and mass research has shown that those quarks, along with their binding energy, only contribute about 1% of the mass of the nucleon. Where is the rest of the mass? It’s from the particles colliding with each other and thus emerges from the symmetry breaking (Ibid).

So there you have it. Two different ways of thinking about fundamental quantities of reality. Both are unproven but offer interesting possibilities. Keep in mind that science is always subject to revision. If Haramein’s theory can overcome those aforementioned hurdles, it may be worth reexamining. And if scale symmetry ends up not passing the test, then we would need to rethink that as well. Science should be objective. Let’s try to keep it that way.

## Works Cited

Bobathon. “The Physics of the Schwarzschild Proton.” Azureworld.blogspot.com. 26 Mar. 2010. Web. 10 Dec. 2018.

---. “The reappearing Nassem Haramein posts, and an update on his science claims.” Azureworld.blogspot.com. 13 Oct. 2017. Web. 10 Dec. 2018.

Haramein, Nassem et al. “Scale Unification – A Universal Scaling Law for Organized Matter.” Proceedings of the Unified Theories Conference 2008. Preprint.

Wolchover, Natalie. “At Multiverse Impasse, a New Theory of Scale.” Quantamagazine.com. Quanta, 18 Aug. 2014. Web. 11 Dec. 2018.