The Size of Muons and Protons

Morton Spears’ calculations on the relative sizes of neutrons, protons and electrons leave us with two separate ways to describe the size of particles. We can describe them in terms of inertial mass, or we can describe them in terms of particle quanta.

However, particle quanta don’t exist freely in nature. They might not exist at all. But if they do exist, they are so reactive that they immediately assemble into electrons and positrons.

Particle quanta are in other words theoretical entities useful in calculations, but not necessarily real in physical terms. They are abstractions, not to be taken too seriously.

Fundamental particles vs. assemblies

Our theory doesn’t operate with the 16+ different types of fundamental particles that the standard model uses. Instead, we have 3. They are the electron, the positron and the neutrino.  All other particles are assemblies of electrons and positrons.

Of these, electrons and positrons combine readily into photons, which is why we don’t see a lot of positrons in nature.

Protons are also assemblies. But these form slowly over time. No-one has ever produced a proton from radiation in a lab. Only the opposite is routinely done. Namely, smashing them to bits in high energy accelerators.

Nuclear binding energy

It should be noted that Morton Spears’ calculations are less exact than he made them seem. He ignores binding energy. His numbers are based on a best fit. There’s substantial room for error. However, we can nevertheless rely on his calculations. We can use them as our starting point, and refine them as we look more closely into the structure of protons.

From previous calculations, we can start off with the following values, rounded off purposely to fit our theory:

• A proton is 1833 times more massive than an electron
• A proton consists of 366 electrons and 367 positrons; a total of 733
• 60% of the mass of a proton is in the form of binding energy

Particle fragments

Particle fragments produced in collisions are subassemblies that can tell us something about the structures they came from, but they are not fundamental. From this, we can conclude that muons, created by smashing protons together, aren’t fundamental particles. They are subassemblies.

High energy particles that enters Earth’s atmosphere in the form of cosmic radiation are smashed to bits by atoms that they crash into. This produces a great number of muons that constantly bombard us. These particles are naturally occurring and easy to detect. A cloud chamber will reveal their existence.

However, these particles are no more fundamental to protons than smashed brick walls are fundamental to brick walls. Fragments of wall contain bricks and mortar, which are fundamental, but the fragments are not fundamental themselves. Likewise, muons are made of electrons and positrons that are fundamental to matter, but this doesn’t make muons fundamental.

Size of muons

With this in mind, we can make some calculations related to the size of muons relative to protons. Wikipedia tells us that muons are roughly 207 times more massive than an electron. If we relate this number directly to the mass of the proton, we get 1833/207 = 8.86. However, muons are proton fragments. There’s binding energy in the proton which isn’t in the fragments. The fragments retain some binding energy, so we’re not down 60%. It’s more likely to be something like 40%. Rounding down from 8.86 to 6 is therefore reasonable.

From this, we can conclude that 1 smashed proton should produce no more than 6 muons.

Size of pions

When we look closer at how muons are formed, we learn that they are not directly produced from protons. There’s an intermediate stage. Protons are first broken into pions, and pions subsequently decay into muons.

Pions are 1.32 times as massive as a muon. With a muon roughly 207 times as massive as an electron, we get that the pion is about 273 times as massive as an electron. We can now repeat the above calculation to find how many pions we can get from a proton: 1833/273 = 6.71.

Given that 1 pion decays into 1 muon and 1 neutrino, and some binding energy is lost in the transaction, we get once more that one proton produces 6 muons. So, our two calculations confirm each other.

Unstable fragments

Pions and muons are fragments, originating from protons. They are therefore unstable. They fall apart. However, they don’t explode into a myriad of electrons and positrons, as we might suspect from our model. They fall apart in stages, with each stage producing a few fragments.

In the case of muons, they break into an electron or a positron, an electron neutrino and a muon neutrino. The neutrinos carry away a small part of the muon’s mass while the electron or positron, as the case may be, carries away the majority of the muon’s mass.

This doesn’t add up with our theory because a proton consists of 366 electrons and 367 positrons. Distributed over 6 muons, we end up with about 61 electrons and 61 positrons for each muon. We must therefore propose some alternative explanation for what has been observed and measured trough experiments.

Photons created from electron-positron annihilation

The alternative explanation is that we are in fact observing a myriad of electrons and positrons in the form of photons, produced through electron-positron annihilation. They’re just not included in standard calculations.

Instead of electron-positron annihilation, standard theory introduces the concept of bremsstrahlung. This is photon radiation that’s taken out of the overall equation when considering how muons and pions decay. However, if we include this radiation as part of our equations, we end up with a lot of photons. Maybe as many as 60 per muon. The missing electrons and positrons can thus be accounted for.

With this alternative interpretation of the phenomenon of bremsstrahlung, we’re still able to defend our theory.