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CODATA Proton Charge Radius; The History Of This Fundamental Measurement. 

By Dr. Inés Urdaneta / Physicist at Resonance Science Foundation

It’s been almost two years since the charge radius of the proton was finally confirmed experimentally by a September 2019 study from Eric Hessels, of York University in Canada, and his colleagues.  

In his 2013 paper entitled Quantum gravity and the holographic mass, Nassim Haramein had anticipated this value, by proposing a generalized holographic model that enables us to compute the now-confirmed value for the proton charge radius, which was then adjusted by the CODATA (Committee on Data for Science and Technology) to that same value in 2018. This all is part of the so-called Proton Puzzle, which we will address in this article.  

Since the nucleus of a hydrogen atom consists of a single proton and this atom has only one electron, hydrogen is a suitable platform for determining the proton’s intrinsic properties, such as the proton charge radius, which is the spatial extent of the distribution of the proton’s charge. The established proton charge radius rp found by experimental techniques performed before 2010 (such as elastic electron–proton scattering and hydrogen spectroscopy) produced the mean value of rp = 0.8768±0.0069×10−13 cm. Another way of expressing this value is: rp = 0.8768 femtometers (1 fm is 10--13 cm, or 13 zeros after the decimal point) with an uncertainty of 0.0069×10−13 cm. This was the CODATA recommended value for the proton charge radius until 2018, when it was updated to a value in agreement with the one predicted by the generalized holographic model.  


Image: from Dipangkar Dutta's presentation. Mississippi State University

As explained in this Nature article, according to quantum mechanics, there is small probability that the electron will be found inside the region of the proton (let’s recall that protons and electrons are not solid balls). When inside, the electron is less strongly influenced by the proton’s electric charge than it would otherwise be. This effect slightly weakens the binding of the electron to the proton and causes a tiny shift in the energy of the electron state with respect to other electronic states. The high precision achieved both by experiments and by the theory of quantum electrodynamics allows the proton radius to be extracted from measurements of this energy shift. 

In 2010, Randolf Pohl, of the Max Planck Institute of Quantum Optics in Garching, Germany, and his colleagues measured a highly accurate value of the proton radius using spectroscopy of muonic hydrogen; a form of hydrogen in which the electron is replaced by a heavier version of the particle called a muon, whose much higher mass causes it to orbit 207 times closer to the hydrogen nucleus than the electron, increasing the probability of the moun being inside the proton and making it much more sensitive to the size of the proton. Since the associated energy shift is about 8 million times larger for muonic hydrogen than for regular hydrogen, and since muons and electrons have the same electrical charge, we would have expected an increase in the accuracy of the already known value for the proton radius. The community was confused when it obtained a radius that was 4% smaller than the previously accepted one, which is a huge difference at that scale. 

The disagreement was known as the proton radius puzzle and it opened the possibility that protons interact differently with muons and electrons, an anomaly that would contradict the standard model of particle physics and would require new physics to explain why and under what conditions the proton might behave differently.


Figure 1 (taken from Nature article) : Values for the proton radius expressed in femtometres (1 fm = 10exp(-13) cm). The data points are values for the proton radius obtained over the past decade, including the latest results, from Bezginov (from Hessels group) et al. 4 and Xiong et al., with uncertainties indicated by the error bars. The data were obtained using three different measurement techniques: electron–proton scattering, spectroscopy of ordinary hydrogen, and spectroscopy of an exotic type of hydrogen called muonic hydrogen. The error bars for the two data points associated with muonic-hydrogen spectroscopy are too small to be depicted in this figure. The bands denote the values adopted by the Committee on Data for Science and Technology (CODATA) in 2014 (0.8751(61)×10exp(−13) cm) and in 2018 (see 

Three years later, on January 25, 2013, the journal Science reported results from Aldo Antognini et al. on the measurements of the charge radius of the proton. The team was able to obtain measurements with 1.7 times more precision than the 2010 muonic hydrogen result from Pohl et al., while also confirming the earlier findings. Antognini’s team reported 0.84087(39) fm ( = 0.84087(39)×10−13 cm) for the charge radius.

At this time in 2013, Haramein was publishing his article “Quantum gravity and the holographic mass.” Antognini's latest results for the proton charge radius had just been released, casting serious doubts on the theoretical value predicted by the standard model. Using Antognini’s value, the generalized holographic model prediction of the proton radius is rp = 0.841263(28)×10−13 cm.  which is within 1 standard deviation (written as 1 σ and being 0.00037×10−13cm) of that experimental result. The predicted value falls inside the accuracy of the experiment. 

Then, a September 2019 study by Eric Hessels of York University in Canada and his colleagues confirmed with spectroscopy measurements that the proton radius of muonic and electronic hydrogen are the same. They performed a measurement analogous to that of Pohl and his coauthors, but for the electronic hydrogen this time, which required experimental strategies to reach parts-per-million accuracy. The authors developed an experimental method based on a technique used in atomic clocks and has many technical advantages over other approaches, including eliminating systematic uncertainties, filtering environmental noise, and the simplicity of the shape of the spectral signal. This allowed Hessels et al. to carry out a meticulous study of systematic uncertainties and to extract a precise value for the proton radius, obtaining rp = 0.833 ± 0.010 femtometres (1 fm is 10--13 cm), consistent with the value from Pohl’s team.  


Meanwhile, electron scattering measurements still consistently yielded a larger value for the proton radius. Therefore, a new experiment in which electrons were scattered off the protons in hydrogen gas, the Proton Radius (PRad) Experiment, was performed by Ashot Gasparian of North Carolina A&T State University and his colleagues at the Thomas Jefferson National Accelerator Facility in Virginia. The improved accuracy allowed them to measure rp = 0.831 ± 0.007 fm, which supports the value found by the two previous muonic hydrogen experiments. Additionally, their finding agrees with the revised value (announced in 2019) for the Rydberg constant, one of the most accurately measured fundamental constants in physics.

All these different experiments with electronic hydrogen have consistently yielded a smaller value for the proton radius, possibly resolving the mystery at the experimental level. For the standard model, however, this is not good news. 

In 2018, the CODATA commission actualized the proton radius to the one that is still recommended, which is rp = 0.8414 x 10-13 cm, with a standard uncertainty of 0.00019 x 10-13 cm. This adjustment occurred before the latest electronic hydrogen measurements of September 2019  (Hessel's rp = 0.833 x 10-13 cm), which totally validate the 2018 update.

As it says here, "the best measurement is the one using muonic hydrogen rp = 0.84087 fm (ANTOGNINI 2013), that is far more precise." Which is also the one closest to Haramein's prediction! 



Redefinition of the SI units

It is worth noting that the most accurate value for the Planck constant was announced in 2019. Measuring the Planck constant to a suitably high precision of ten parts per billion required decades of work by international teams across continents, which allowed this constant to be fixed at exactly 6.626070150 × 10−34 kgm2/s. 

Our RSF article from Nov. 2018  entitled From the Planck constant to the Kilogram is a complementary text for this subsection, as it gives a detailed description of the history of this redefinition. 

Since mass is linked to energy through Einstein's equation E = mc2, and energy is quantized through Planck's equation E = hf (f being the frequency), equating both energies allow mass to be expressed in terms of speed of light c, the frequency f and the Planck constant h, as m = h f /c2. This enables scientists to define mass in terms of Planck's constant h, which is an unchanging feature of the universe, instead of using a 130-year-old, platinum-iridium cylinder weighing 2.2 pounds (1 kilogram) that is sitting in a room in France as a reference or unit of mass. 

 Centenary Commemoration Stamp

The MKS units (Meter for distance, Kilogram for mass, and Seconds for time) of measure are now completely described in terms of vacuum and quantum regime properties, which are fundamental agents. The units of mass, time, and distance have unified around the Planck constant!

Having all units defined relative to the Planck constant, the only remaining issue is the limitation posed by the gravitational constant G upon which all Planck units depend. G is the constant with the lowest accuracy at 10-5 digits, while other constants have accuracies at least of 10-9. Therefore, the accuracy of G is a limiting factor.  Now that the Planck constant has been fixed to a more accurate value and now that the units of mass depend on it, the increase in the accuracy of G depends only on achieving the solution to quantum gravity, and that's where the generalized holographic model reaches its climax. We already have the complete solution to quantum gravity expressed in terms of our surface-to-volume ratio 𝝓, and it is beautiful!  

In our coming paper, entitled Scale invariant Unification of Forces, Fields, and Particles in a Quantum Vacuum Plasma, we will demonstrate the unification of all the units, constants, forces, and increase the accuracy of the Planck Units by calculating the gravitational constant G up to  10-12 digits of accuracy! 


RSF in Perspective

After all the above, the proton puzzle was solved, at least at the experimental level. The discrepancy with the former larger value for rp from 2010 and before was likely due to measurement errors. Nevertheless, most mainstream media claimed this smaller radius would not require new physics because it gave the same result in both electronic and muonic hydrogens. This statement is misleading. The standard model’s theoretical prediction at the time was off by 4%, so evidently, major modifications to the standard model were required. Additionally, let us not forget that it uses at least 17 adjusting parameters, while the generalized holographic model is a first principle calculation. Fortunately, the confirmation of the proton charge radius validates the Generalized Holographic Model!

The fact that Planck Units are no longer just the result of human convention makes them real universal constants. Any other advanced civilization would therefore find the same values for them. 

Redefining the SI units so that they derive from the fixation of the Plank constant, means they now depend on fundamental values from nature instead of human convention. Together with the fact that the Planck Spherical Unit (PSU) is necessary to achieve Quantum Gravity, this all implies that the PSU is not just related to a unit of measure... it IS a fundamental unit of the Universe. This is because the PSU is a real voxel or volume unit of space, directly related to the quantum of action or angular momentum h.  

The science course proposed by Resonance Academy, particularly in Module 7, addresses in detail all these fundamental aspects of the generalized holographic model. The reader can take this course for free, registering in this link Unified Science Course. 


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