On pages 159 + 161 in his book [Ref.#1], Sternglass describes the structure of the pi-meson and the mu-meson.  {Hint:  they have very similar structures}

Note:  While I know that the standard model does not consider the “muon” to be a “meson”, I write “mu-meson” instead of “muon” to emphasize my belief that the standard model is, (to say it politely), not quite right about how it explains the structure of the muon.  Specifically, there is evidence that the muon is not a fundamental particle. 

Because the so called muons do not interact strongly with ordinary matter, like pi-mesons do, the folks who built the standard model decided, many years ago, with no clue to its actual structure, that it’s not a meson.  However, one can easily explain why “muons” behave differently:  it’s because they are fermions, while pi-mesons are bosons.


A quick look at the schematic diagrams on pages 159 and 161 in Sternglass’s book [Ref.#1] shows that, according to his model, the pi-meson and the mu-meson have almost exactly the same structure.  Copies of the same schematic diagrams appear in Figures 2 and 3 (near the end of the paper) in one of Sternglass’s 1964-papers, available at:

{Note that if you input the link into your browser, a summary of the paper comes up, but if you input the link a second time, then you get the entire paper !!  At least that’s how my computer works}

Regarding the mesons:  one can use the image of a child riding on a “merry-go-round” in a play ground to describe Sternglass’s idea for the difference between a pi-meson and a mu-meson:  if the child just simply sits on the merry-go-round as it spins, well, that’s a mu-meson.  If he or she gets “excited” and stands up and runs, in a direction against the rotation of the merry-go-round, as I did many times as a child, well, that’s a pi-meson.  Sternglass says that the pi-meson is an “excited state” of the mu-meson, and in fact calls the little rascal a “mu-meson” instead of a “muon.”

Physicists know that a pi-meson will, after approx. a hundred-millionth of a second, experience a process called “decay”, producing a mu-meson and a neutrino.  The neutrino flies away at light-speed, carrying away some energy, and also carrying away some angular momentum.  So the mu-meson’s angular momentum is half of a Planck-unit less than that of a pi-meson.  {Note that one can google the term “Planck unit” if one needs to}  It’s mass is also less, because the energy which the neutrino carried away is equivalent to mass, according to Einstein’s famous E = mc2. 

Recently I became aware of the work of a gentleman who has taken Dr. Sternglass’s model as a starting-point to describe a possible structure for the so called “tau particle” — which the standard model also regards as a fundamental particle.  Ray Fleming’s descriptions are so clear and articulate that I will quote him, below.

Alternatively, you might want to look at his paper [Ref.#41] directly:  here is a link to it:

“Summary … Ernest Sternglass determined that a neutral meson, the π 0 [i.e., the uncharged pi-meson], could be modeled as a relativistic electron-positron pair, and later determined that the muon could be modeled as an electron rotating around a similar electron-positron pair. The author noticed that there is a second higher-energy orbital solution not previously published by Sternglass where the electron-positron pair orbits around the electron’s center. A simple computation shows that the mass-energy of this second solution is consistent with the tau particle. Based on these models the mu and tau leptons are not fundamental particles as described in currently popular theories but are instead two excited meta-stable states of an electron and an electron-positron pair.

“Background … In 1961 Ernest Sternglass published a paper titled “Relativistic electron-pair systems and the structure of neutral mesons” [Physical Review Journal, 1 July 1961] in which he described a relativistic Bohr-Sommerfeld model of an electron-positron pair. He was able to show that when the pair was in a relativistic equilibrium condition, where the inertia pulling the two particles apart was equal to the electrostatic attraction, the pair had mass-energy and a half-life consistent with a neutral meson, the neutral pion (π 0 )  [see Ref.1, below].  In his book Before the Big Bang: Origins of the Universe Sternglass recounts how he performed his initial mathematical derivation in the presence of and with encouragement from Richard Feynman  [see Ref.2, below].  Sternglass went on to extend his theory and describe all the known particles of the day  [see Ref.3, below].  One of the more interesting is the muon, as today it is considered to be a fundamental particle classified as a lepton within the scope of the standard model. The other leptons, the electron and tauon, are also considered to be fundamental, rather than composed of other particles. Sternglass, however, published a rather compelling model for the muon in 1965  [see Ref.3 below].  Given the simplicity of the model it seems likely that the muon is not fundamental.”

At this point you might want to click-on a link to the paper, as there are some excellent schematic diagrams in it: 

“Figure 1 … The Sternglass model for the Muon. The solid arrows indicate the direction of each particle’s magnetic moment. The open arrows indicate the direction of the angular momenta. (Figure by Sternglass from reference 3, [below]).

“The mass calculation [for the muon-mass] required a sum of 6 contributions  [Ref.3, below].  The first two contributions are the mass of the excited pion, 275 x Me x c^2, and the mass of the electron, 1 x Me … From that is subtracted [the mass equivalent to] the potential energy of the system -274 x Me … Next [the mass equivalent to] the kinetic energy of the orbiting electron, (1/α -1) x Me = 136 x Me, is added, with α being the fine structure constant. Additionally there is relativistic precession of the system as viewed from a laboratory frame of reference, which introduces an additional 68.75 x Me … Lastly he considered the wave mechanical binding energy between the electron and pion leading to a small correction term of –0.014 x Me … This calculation yields the sum of 206.7 x Me.

“Conclusion … This paper shows that it is simple to model the tau particle using the Sternglass theory, and the mass calculated from this model is very close to the accepted value. The Sternglass theory can now account for both the mu and tau particles, so it seems that the standard model, in which they are both fundamental particles, is incorrect. The Sternglass theory also provides a simple physical model for the neutral pion, which is favorable when compared to the irrational quark π 0 model. Based on this result there should be more in-depth investigations made of the Sternglass theory.”

Ref.1:  Sternglass, E. J., “Relativistic electron-pair systems and the structure of neutral mesons”, Phys. Rev., 123, 391 (1961);

Ref.2:  Sternglass,E.J., Before the Big Bang: Origins of the Universe, 1997, Four Walls Eight Windows Publishing (1997);

Ref.3:  Sternglass, E. J., “Electron-positron model for the charged mesons and pion resonances”, Il Nuovo Cimento, 1 Gennaio, Volume 35, Issue 1, pp 227-260 (1965); 

Many thanks to Ray Fleming for permission to quote from his paper.

Sincerely,  Mark Creek-water Dorazio, ApE (amateur-physics-enthusiast),  Princeton, New Jersey, USA,  3-March-2016

########### << END OF CHAPTER 16 >> ###########



  1. Pingback: book-title: VISUALIZE-ING “QUARKs” — sub-title: Essays re the Work of DR. ERNEST STERNGLASS + DR. MENAHEM SIMHONY | markcreekwater

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