The Scientific Revolution is ongoing:

You won't hear Bill Nye the science denier or Neil deGrasse Tyson talk about the proton radius problem, the Achilles Heal (sic) of The Standard Model.

**The Surfer, OM-IV**

Unified Physics of Haramein, Einstein, Rauscher, Planck, Euler, Simpson, and ALL

The Scientific Revolution is ongoing:

You won't hear Bill Nye the science denier or Neil deGrasse Tyson talk about the proton radius problem, the Achilles Heal (sic) of The Standard Model.

I like looking deeply into Nature.

**The present is an event horizon, a very interesting thing. It is the only place that life exists.**

The above image/link is of an Excel file showing that for n=4 case, the quantized angular momentum equation predicts the proton mass and disputed (muonic hydrogen) proton charge radius ($r_p=0.8412fm$).

The quantized angular momentum is calculated as shown on the previous post by using the de Broglie hypothesis, which amounts to assuming photonic (boson) energy with no rest mass, thus the equation for momentum applies:

$$p=m\nu={h\over\lambda}$$

and after solving for angular momentum, one gets

$$mr={nh\over2\pi c}$$

and for the $n=4$ case, the proton mass-radius product:

$$m_pr_p={2h\over\pi c}=4\ell m_{\ell}$$

All of the mass-energy of the proton is contained within a stable vortex in the aether of spherical radius, $r_p$. This is possible when one begins to examine the problem more completely as we have done previously, and that is to consider the vacuum energy density as Haramein has, and realize the proton is a stable oscillation in the Planckian aether, which is such high density, it behaves like a black hole and the photonic energy creates a path in 3D space where the aether flows or energetically vibrates.

Since the energy density of the vacuum is so high, the conditions for wormhole connected space are met, then the proton could be envisioned as an energetic vibration in the aether, and it is likely a stable vortex flow. There is much more implied by this view which will be examined in future posts.

The picture of the proton is then some 3D oscillation in the aether, thus perhaps the problem could be approached from aether dynamics and shown, in the limit, that the detailed solution approaches this post's approach, which is a lumped mass-radius idea coming from reductionist 1D-2D Cartesian physics approach rather than a whole 3D approach that includes interaction with the vacuum, i.e., resolution to the vacuum catastrophe.

The photon wavelength is:

$$\lambda={\pi\over 2}r_p$$

The photon frequency is:

$$f={2c\over \pi r_p}$$

The photon energy is:

$$E=hf={h2c\over \pi r_p}$$

Considering that this calculation results in the proton radius being 0.8412fm, and this is VERY close to the 2010 & 2013 muonic hydrogen proton radius experiments, I wonder why this hasn't been written about in the science journals or sites since it is simply the first thing one would look at if examining quantized angular momentum.

It is important to have derivations so as to avoid being accused of "cherry picking", lol. Being able to select the correct physics isn't necessarily "cherry picking", it could be skill, however, derivations are required and experimental data to check the theory.

Here's a diagram showing a hypothesized infinitesimal point mass at a radius r moving circularly at the speed of light. This is a diagram for the derivation - a real proton is more like described above and this diagram is a convenient way to represent some of the information about the proton that agrees with measurements.

Infinitesimal point mass

Infinitesimal point mass, $m_p$, representing the proton mass, circular motion at the speed of light, at the radius of the proton, $r_p$ distance from center. While this was simply a tool to derive the equation, the actual energy in the proton is the gamma/cosmic ray photon energy that is required to create a stable vortex in the aether. Still, this physical picture really gives one a sense of a very clearly defined boundary at the proton radius, $r_p$.

The energy itself is involved in a black whole like disturbance in the Planckian aether. I suspect the proper fluid dynamics or plasma dynamics (fluid-plasma dynamics? - high energy reactions seem to be showing evidence of a fluid dynamic rather than a gas dynamic) would result in solutions that would explain or somehow contain information in the derivation as to WHY the proton mass-radius is distributed according to quantized circular angular momentum for the n=4 case. Similarly using same possible future technique, one should be able to calculate the masses of all fundamental particles of the standard model.

The Lorentz factor $$\gamma (v)={1\over \sqrt{1-{v^2\over c^2}}}$$ is used in relativistic physics for showing how mass and length vary with speed relative to an observer. Mass is multiplied by the Lorentz factor, and length is divided by the Lorentz factor, for relativistic motion, thus the mass- length product is a constant in the direction of motion.

**[1]** This is a way of making an attempt to summarize or model the information of a proton since the 3D/4D (up to 8D???) superfluid or super-plasma dynamics equations are out of the scope of this presentation.

A quick check can be made by examining the two wikipedia pages linked here:

wikilink for mass

wikilink for length

Since the mass-length product is a key part of the equation for the proton mass-radius relationship, it may be informative to examine more deeply this product.

$$m_pr_p={2h\over{\pi c}}=4\ell m_{\ell}$$

By inspection, one can see that this equation is a form or a specific case of quantized angular momentum, such as that proposed in the Bohr model.

However, it could also be a solution to a stable vibration in the ether, like a black hole / white hole dual vortex pair.

Now, for investigative purposes, let's look at the math of treating the proton mass as a point mass at the end of a radius**[1]**, going at the speed of light, c, and look at the angular momentum:

Now, for investigative purposes, let's look at the math of treating the proton mass as a point mass at the end of a radius

- Using DeBroglie Hypothesis, $p=m\nu={h\over\lambda}$
- Future: examine with other cymatic or platonic hypotheses for $r\over\lambda$ solutions

Start with the equation for angular momentum:

$$L=m\nu r={hr\over\lambda}$$
Using the hypothesis that the proton is condensed light, a stable EM? vibration in the ether, thus $$\nu=c$$

$$L=m\nu r=mcr={hr\over\lambda}$$

$$mr={hr\over c\lambda}$$

Using the Bohr circular waveguide around a central point (integer number of wavelengths in a circumference), $$\lambda={2\pi r\over n}$$

$$mr={nh\over2\pi c}$$

For the $n=4$ case, why $n=4$ ? Tetrahedron is first 3D vibration??? Nonetheless, let $n=4$ because looking ahead, it is $n=4$ that is the stable proton "solution" to this energetic disturbance in the vacuum dynamics we call proton.

$$mr={2h\over\pi c}=4\ell m_{\ell}$$

Which is the proton mass-radius relationship. Note we are not saying that the proton is a little positively charge ball spinning at a radius r around a central point - this is just a way to keep track of the information of the proton, i.e., quantifying an aspect of an energetic disturbance in the aether, the math of which we'll have to look into later.

A star-tetrahedron, if free to rotate around a central point, draws out a sphere

and it is this energetic stably trapped photonic (EM) energy that is the proton:

A complete picture would include the surrounding disturbances in the aether, since nothing is isolated, but entangled.

Next, we'll look at how these ideas can be extended to replacing the strong force with quantum gravity, as Haramein did in: Quantum Gravity and the Holographic Mass and check to see if it makes any sense to go in this direction.

Image 1: Symbolic merging of our two main theories into one

Prior to solving a problem, it's best to define the problem. The problem I'm talking about is commonly known as the Grand Unified Theory:

Or the grand unification of physics. TOE - Theory Of Everything, etc.

Another way to say this is that all phenomena must be brought into a theory that is consistent with the main body of science we already have.

Yet another way, a way I like to say, is we need a theory that explains all aspects of nature and how nature behaves.

This then gets into defining what that means, and so on.

Yet another way to go about it is oversimplified, yet at the same time would be a BIG step, is to understand exactly what matter is. This, supposedly, is what the main search is behind the LHC and high energy particles physics. The idea of breaking matter down into smaller and smaller pieces to get a better understanding of what matter is. This has led to The Standard Model.

What I'm finding is it's best to step back and examine the problem some more.

This is where we have to leave behind preconceived belief systems about the nature of things while at the same time holding true to the scientific method.

What I've found as I go through this is that each step along the way EVERYTHING is already some agreed upon belief system. And it gets complicated fast. Perhaps this is the reason, to advance, many things were ignored to even begin to be able to build the technology we have today. However, at the same time, since we did not fully understand the nature of Nature, or the nature of what it is to truly be a fully developed human, then the argument starts to go towards philosophy or what is known as philosophy, which leads to another question: where have all the philosophers gone and why no longer is this an official profession?

So, it's a pretty big bite to take and attempt to discuss this in a simple post.

I'm going to have to address this some more in future posts, many future posts.

Amira Val Baker writes an informative article on the proton radius:

Zero Point (0,0) NO DARK MATTER, NO DARK ENERGY: $\Omega_\Lambda$ vs. $\Omega_m$ Universal Reality is pointed out here: No Dark Matter, No Dark Energy |

- List of failure to find dark matter/energy articles 2016
- http://phys.org/news/2016-12-dark-gamma-ray-background.html
- https://www.sciencenews.org/article/latest-dark-matter-searches-leave-scientists-empty-handed
- http://phys.org/news/2016-07-scientists-invisible-dark.html

While there is little to no evidence to support dark matter and dark energy, legacy scientists and legacy science still go after these topics with great vigor, investment, publications, and all the fanfare that goes along with the concensous legacy scientific method.

The image above highlights the area with a red dot where our universe lies. Legacy science claims it's somewhere in the center of the ovals. This video goes over legacy science's stance:

@ 9:30 The Red Zero Point IS Hyperbolic Black Hole Dynamic Driven SpaceTime!

Legacy science is useful for understanding the fundementals, however, it takes different thinking to solve the unsolved problems than what created them.

The Haramein-Rauscher soultion to Einstein's field equations combined with their other work at https://hiup.org/publications and course work at Resonance Academy and all the many hours of lectures/videos over many decades revisit the fundamentals of the two main science theories

- Cosmology: Einstein (et al), General Relativity (GR)
- Quantum: Planck (et al), The Standard Model (SM)

and gives great insight into how Nature truly behaves (superfluid like aether, tetrahedral structure, holographic, connected, alive/conscious - blueprint for life IS in the vacuum).

Perhaps more time should be invested in comparing the results of legacy analysis of Dark Matter and Dark Energy plots $\Omega_\Lambda$ vs. $\Omega_m$, comparing to GR using Torque and Coriolis, to determine a similar plot to $\Omega_\Lambda$ vs. $\Omega_m$ however, using Torque and Coriolis. Considering that the legacy science isn't whole, often it is better to invest the time in the ideas that work rather than working with a failed theory - however, it can be instructive. Anyway, we move on, as this blog is to point out viable scientific and consciousness ideas that address science and the long unsolved physics problems (I consider physics to be all encompassing, including consciusness as well. Complete physics includes ALL).

While the Dark Matter and Dark Energy failure is ongoing, not enough effort/publicity is placed on the geometric nature of the structure of the Universe:

- Pay site, gaia.com, David Wilcock assembles the knowledge into a coherent presentation:
- https://www.gaia.com/video/193-octahedral-universe
- https://www.gaia.com/video/194-galactic-geometry-part-1
- https://www.gaia.com/video/195-galactic-geometry-part-2
- https://www.gaia.com/video/196-galactic-geometry-part-3

red square nebula MWC 922 |

Pinwheel galaxy M101 has square arms like our milky way |

Hexagonal galaxy http://www.caelumobservatory.com/obs/m61.html |

More galaxy images here: (many have geometric shape, about > 80%)

Sacred geometry example (phi-spiral implosion / resonance - cymatics) |

Dual-tours black hole dynamics driven aether - simplified. Actual pattern more complex. |

Someone's been attempting to tell us... |

Anyway, what I'm saying is there is much evidence to support a geometric universe, overwhelming evidence. There are galaxies of all types of geometric shapes, and it is fits well with the ancient sacred geometry teachings.

My best guess on how our Universe behaves is a combination of Haramein-Rauscher with The Electric Universe (Maxwell or EM theory added to GR, which it already is if one decides to focus on those terms) and Platonic nested phi-ratioed sacred geometries - it's holofractal, Hermetic, as above, so below. A superfluid aether is needed to be added back to advance the physics.

What I would look out for in 2017 and the future is the resolution of the proton radius problem:

- https://www.jlab.org/prad/collaboration.html <-- PRad at JLab
- more later...

and how as this problem is resolved that insight is gained into the vacuum (vacuum catastrophe) which will lead right to the fundamental structure of the Universe and resolve Dark Matter and Energy and explain Galaxtic structure and star speed profiles and much more (gravitational control and energy/matter from/into the vacuum).

We are on the cusp of great revelations.

If the vacuum is indeed mutable and degradable as was explored, then it might be possible to do/extract work on/from the vacuum, and thereby be possible to push off of the quantum vacuum and preserve the laws of conservation of energy and conservation of momentum. It is proposed that the tapered RF test article pushes off of quantum vacuum fluctuations, and the thruster generates a volumetric body force and moves in one direction while a wake is established in the quantum vacuum that moves in the other direction.

Read More: http://arc.aiaa.org/doi/10.2514/1.B36120

see 10. Discussion for more detail of the explanation. Uses pilot wave theory and Bohm's arguements. Basically, adding back the aether to physics and saying one can push of the vacuum, just like I said in my earlier post:

So, once the underlying physics is better understood, gradients in the vacuum can be optimsed for greater thrust and energy extraction. It just a matter of time before the mainstream catches up and helps to develop the theory and bridge it into engineering from that theory. Much work has already been done by the alternative community.

More later. New things are coming. Great things. A Connected Universe.

We are proud to announce that Sir Patrick Stewart, known for his role as Star Trek: The Next Generation's Captain Jean-Luc Picard, is the narrator of The Connected Universe, a groundbreaking feature film documentary by Malcom Carter.
Watch the newly updated trailer featuring the voice of Patrick Stewart and get tickets to the premier in L.A. on Monday 9/26/2016 –> http://getconnected.resonance.is
"The Connected Universe” explores the interconnection of all things in the Universe. It inspires people to see the world differently. There is no better guide on this journey of exploration than Sir Patrick Stewart. Known for boldly exploring the galaxy in Star Trek, he is also revered as a Royal Shakespearean actor who has taken an inner journey of extraordinary depth. This intertwining of both science and humanity creates a unique narrative to explore connection.
Nassim Haramein • Resonance Science Foundation - Français • Resonance Science Foundation - Hispana • Resonance Science Foundation - Português • Collective Evolution • Unify • Thrive • Spirit Science • Universe Explorers • Physics-Astronomy • Resonance Science Foundation - 中文 • Cosmometry

Spatiotemporal optical vortices, or STOVs (thin, gray ringlike objects), are newly described three-dimensional light structures that strongly resemble smoke rings.

Read more at: http://phys.org/news/2016-09-physicists-laser.html#jCp

Interesting.

Remember my past post about smoke rings:

Different, however, related concepts.

Considering that the aether is a superfluid of immense density, something moving through it will leave vortices. The concept is important, and this photonic vortex may be supporting this concept.

And light or photons, being electro-magnetic radiation is itself an othogoanl votrex of E and M radiation, which is a relativistic projection of a single field, just looks like two fields due to motion (Feynman mentions this in his reds rags, buried in there somewhere: http://www.feynmanlectures.caltech.edu/II_01.html).

As above, so below:

Nature behaves in ways not yet captured by mainstream science. They're getting closer...

This is how it's done.

So, you're wondering, "hey, exactly how are you going to crank out these equations people have been looking for for likely hundreds of years over the next few months?" Well, just like I said way back in the beginning of the blog, we'll do it the old fashioned way, and that is step by step.

Alternative method:

We can now calculate, from first principles and fundamental Planck units, the mass of blackholes, protons, and electrons. (link to post about new electron holographic solution)

The proton actually is a fundamental particle as well. The Standard Model considers that the proton is composed of quarks, thus not fundamental.

So, now, what about all of the other fundamental particles? Can we also calculate their masses and predict all their masses correctly, and predict masses of other unknown particles?

For all the success of The Standard Model, it is incomplete, and, while it works very well for some things (QED, QCD, etc), it has issues.

Anyway, we can now calculate the mass of one of the elementary particles in the table above, the electron. It seems then like the muon or tau particle would be the appropriate particle to target next to see if we can calculate its mass, and perhaps along the way determine or demonstrate exactly what works and what does not work with "The Standard Model" way of looking at things.

For now, we will list the masses of the first three leptons:

electron mass | |

Value | 9.109 383 56 x 10^{-31} kg |

Standard uncertainty | 0.000 000 11 x 10^{-31} kg |

Relative standard uncertainty | 1.2 x 10^{-8} |

Concise form | 9.109 383 56(11) x 10^{-31} kg |

muon mass | |

Value | 1.883 531 594 x 10^{-28} kg |

Standard uncertainty | 0.000 000 048 x 10^{-28} kg |

Relative standard uncertainty | 2.5 x 10^{-8} |

Concise form | 1.883 531 594(48) x 10^{-28} kg |

tau mass | |

Value | 3.167 47 x 10^{-27} kg |

Standard uncertainty | 0.000 29 x 10^{-27} kg |

Relative standard uncertainty | 9.0 x 10^{-5} |

Concise form | 3.167 47(29) x 10^{-27} kg |

And their relative mass ratios:

muon-electron mass ratio | |

Value | 206.768 2826 |

tau-electron mass ratio | |

Value | 3477.15 |

tau-muon mass ratio | |

Value | 16.8167 |

Since the muon and tau are simply more energetic electrons, it seems like if these were actual particles, we should be able to find an equation that predicts their masses based upon first principles and fundamental Planck constants.

To do this, we will have to look more deeply into the muon and tau particles. We are having great success so far at applying Haramein's Holographic Solution, and the approach will either solve for the masses of these other particles, or explain what is wrong with The Standard Model.

Since this work is too large to fit in the margin of this post, we'll do it over the next few posts, and months, until some resolution is made.

The writing is already on the wall that The Standard Model has missed the boat, while at the same time MISSING a whole lot of things that really matter.

That's all for now.

The writing is already on the wall that The Standard Model has missed the boat, while at the same time MISSING a whole lot of things that really matter.

That's all for now.

Using Haramein's The Electron and the Holographic Mass Solution:

$$\mu={m_p\over m_e}={2\phi m_{\ell}\over {\phi_em_{\ell}/2\alpha}}=4\alpha{\phi\over\phi_e}=4\alpha{a_0\over r_p}=1836.15267...$$

Compare to:

$$\mu={\alpha^2\over{\pi r_pR_{\infty}}}=1836.15267...$$

$\mu=$ proton to electron mass ratio

$m_p=$ mass of proton

Compare to:

$$\mu={\alpha^2\over{\pi r_pR_{\infty}}}=1836.15267...$$

$\mu=$ proton to electron mass ratio

$m_p=$ mass of proton

$m_e=$ mass of electron

$\phi={\eta\over R}$ Holographic ratio for proton

$\phi={\eta\over R}$ Holographic ratio for proton

$\phi_e={\eta_e\over R_e}$ Holographic ratio for electron

$m_{\ell}=$ Planck mass

$a_0=$ Bohr radius

$r_p=$ proton radius (muonic hydrogen proton radius)

$R_{\infty}=$ Rydberg constant

$m_{\ell}=$ Planck mass

$a_0=$ Bohr radius

$r_p=$ proton radius (muonic hydrogen proton radius)

$R_{\infty}=$ Rydberg constant

Google calculator link and results snapshot:

((4 * fine-structure constant * hbar) / (m_e * c * fine-structure constant)) / (((4 * hbar) / c) / m_p) =

1 836.15267

CODATA value for proton-electron mass ratio:

http://physics.nist.gov/cgi-bin/cuu/Value?mpsme

proton-electron mass ratio | |

Value | 1836.152 673 89 |

Standard uncertainty | 0.000 000 17 |

Relative standard uncertainty | 9.5 x 10^{-11} |

Concise form | 1836.152 673 89(17) |

There remain a few issues to be ironed out as Haramein's paper, The Electron and the Holographic Mass Solution, reports the proton to electron mass ratio as:

$$\mu={m_p\over m_e}={2\phi m_{\ell}\over {\phi_em_{\ell}/2\alpha}}=4\alpha{\phi\over\phi_e}=1836.942579077855...$$

So, the work continues to understand this difference...

This result, the 1836.94259077855... above, is calculated using the CODATA value for $\alpha$, the 2013 muonic hydrogen charge radius in the $phi$ calculation, and $phi_e=6.108458512E-25$ . See Google Drive Excel File for calculations.

More in upcoming post: Another Equation for Proton to Electron Mass Ratio!!! #2

Sword of Science - SoS

Let's examine the expression for the electron mass and go through the exercise of how to put numbers to the equations and compare the results to CODATA measurements and previous mainstream theoretical predictions and analysis.

$$m_e={1 \over 2\alpha}\phi_e m_\ell$$

$m_e=$ mass of the electron

$m_\ell=$ Planck mass

$\phi_e={\eta_e\over R_e}=$ electron Holographic ratio

$\eta_e=$ Surface entropy

$R_e=$ Volume entropy

$\alpha=$ fine-structure constant

The subscript "e", for electron, is to emphasize that the $\eta_e$ and $R_e$ are to be calculated for the electron, using the confined electron's Bohr hydrogen radius atomic volume and the surface area to calculate $\eta$ and $R$.

Let's do $\eta$, the surface entropy first:

$$\eta=\eta_e$$

$$\eta_e={A_{e-surface}\over A_{eq}}$$

$$A_{e-surface}=4\pi {a_{0}}^2$$

$$A_{eq-PSU}=\pi {r_{\ell}}^2$$

$a_0=$ Bohr hydrogen radius - distance electron is away from proton center
$r_{\ell}$ is the Planck radius of the PSU

$r_{\ell}={\ell\over 2}$

$\ell=$ Planck length

$r_{\ell}={\ell\over 2}$

$\ell=$ Planck length

$A_{e-surface}$ is the surface area of a sphere of radius $a_0$, the Bohr radius.

$A_{eq-PSU}$ is the equatorial cross-sectional area of the Planck Spherical Unit (PSU).

$$\eta=\eta_e={4\pi {a_{0}}^2\over \pi {r_{\ell}}^2}$$

$R_e$, the volume entropy is next:

$$R_e={V_e\over V_{PSU}}$$

$$R_e={{4\over3}\pi a_0^3\over {4\over3}\pi r_{\ell}^3}={a_0^3\over r_{\ell}^3}$$

And finally:

$$\phi_e={\eta_e\over R_e}$$

$$\phi_e={4r_{\ell}\over a_0}$$

$$m_e={{1\over2\alpha}\phi_em_{\ell}}$$

Google link for m_e - mass of electron

CODATA Link to M_e electron mass

Check!!! Another success of Haramein's holographic approach.

Some further simplifications/reductions:

$$m_e={{1\over2\alpha}{4r_{\ell}\over a_0}m_{\ell}}$$

**The Surfer, OM-IV**

$$\eta=\eta_e={4\pi {a_{0}}^2\over \pi {r_{\ell}}^2}$$

$R_e$, the volume entropy is next:

$$R_e={V_e\over V_{PSU}}$$

$$R_e={{4\over3}\pi a_0^3\over {4\over3}\pi r_{\ell}^3}={a_0^3\over r_{\ell}^3}$$

And finally:

$$\phi_e={\eta_e\over R_e}$$

$$\phi_e={4r_{\ell}\over a_0}$$

$$m_e={{1\over2\alpha}\phi_em_{\ell}}$$

$$m_e={{1\over2\alpha}{4r_{\ell}\over a_0}m_{\ell}}$$

Google calculator expression:

https://www.google.com/search?q=hbar%3D&oq=hbar%3D&aqs=chrome..69i57.3102j0j8&sourceid=chrome&ie=UTF-8#q=(1%2F(2*(fine-structure+constant))*4*(sqrt(hbar*G%2Fc%5E3)%2F2%2F(hbar%2F(m_e*c*(fine-structure+constant)))*sqrt(hbar*c%2FG)%3D

Google calculator expression:

https://www.google.com/search?q=hbar%3D&oq=hbar%3D&aqs=chrome..69i57.3102j0j8&sourceid=chrome&ie=UTF-8#q=(1%2F(2*(fine-structure+constant))*4*(sqrt(hbar*G%2Fc%5E3)%2F2%2F(hbar%2F(m_e*c*(fine-structure+constant)))*sqrt(hbar*c%2FG)%3D

Google link for m_e - mass of electron

electron mass =

9.10938356 × 10^{-31} kilograms

CODATA Link to M_e electron mass

electron mass | |

Value | 9.109 383 56 x 10^{-31} kg |

Standard uncertainty | 0.000 000 11 x 10^{-31} kg |

Relative standard uncertainty | 1.2 x 10^{-8} |

Concise form | 9.109 383 56(11) x 10^{-31} kg |

Check!!! Another success of Haramein's holographic approach.

Some further simplifications/reductions:

$$m_e={{1\over2\alpha}{4r_{\ell}\over a_0}m_{\ell}}$$

$$m_e={\ell m_{\ell}\over\alpha a_0}$$

$$\ell=\sqrt{\hbar G \over c^3}$$

https://en.wikipedia.org/wiki/Bohr_radius

$$m_{\ell}=\sqrt{\hbar c\over G}$$

$${\ell}m_{\ell}={\hbar\over c}$$

$${\ell}m_{\ell}={\hbar\over c}$$

$$m_e={\hbar\over c\alpha a_0}$$

$$a_0={\hbar\over m_ec\alpha}$$

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