What is the Universal Scaling Law and Scale Symmetry?

Updated on November 9, 2019
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Leonard Kelley holds a bachelor's in physics with a minor in mathematics. He loves the academic world and strives to constantly explore it.


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 is 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 then 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 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)

The Scaling Law.
The Scaling Law. | Source

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”).

Bobathon has done an excellent job countering many of the claims and explaining their shortcomings, but let’s talk about a few of them here. Haramein’s Schwarzschild proton has issues too. If it has the radius required of it to have black hole analogies, then the mass would be 8.85 * 1011 kg. A kilogram on Earth weighs about 2.2 pounds, so this proton would weigh about 2 trillion pounds. This is not even reasonable and as it turns out the radius Haramein used isn’t that of a photon but a Compton wavelength of the proton. Different, not analogous. But it gets better. Black holes undergo Hawking radiation because of virtual particles forming near the event horizon and having one of the pair fall in while the other flies away. But on the scale of a Schwarzschild proton this would be a tight space for so much Hawking radiation to occur, leading to lots of heat that produces power. A lot. As in 455 million Watts. And the observed amount seen from a proton? Zippo. How about the steadiness of orbiting protons? Practically non-existent for our special protons because according to relativity objects release gravitational waves as they spin, robbing them of momentum and causing them to fall into each other “within a few trillionths of a trillionth of a second.” Hopefully, the message is quite clear: The original work didn’t take its consequences into account but instead focused on aspects that reinforced themselves, and even then the results had issues. In short, the work hasn’t been peer-reviewed and given a positive reaction (Bobathon “Physics”).

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).

A Scale Table.
A Scale Table. | Source

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% 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 then 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.

© 2019 Leonard Kelley


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    • 1701TheOriginal profile imageAUTHOR

      Leonard Kelley 

      2 months ago

      Jay, that is what further research has shown me, too. His idea is interesting, but realistically not too deep.

    • profile image


      2 months ago

      Nassim Haramein is not a scientist but rather a huckster, selling astrological hookum and magic crystals to gullible new-age devotees. His work has been widely debunked by physicists. He doesn't submit to peer-review because he knows hie work would be immediately trashed in the community. He acts like a new age guru, selling snake oil and "access" to his "inner circle." Run, run away as fast as you can.


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