Thoughts on the Origin of Mass

Michael  Anderson. B.Sc. (Chem Eng) Cape Town. AMP Harvard.

Summary

And in the end Einstein was only partly right, his equation should actually be E = m c2 

When I first became interested in particle physics back in the 60’s there were tables of particle products arising from proton collisions numbering hundreds, all unstable and decaying within very short times into electrons, positrons, neutrinos and gamma radiation. These particles were largely nameless with masses that ranged the full spectrum from electron size all the way up to nearly proton size. While some of these particles were neutral most had a charge of either +e or -e (where e represents the magnitude of charge on an electron) and this pattern seemed to indicate that there was a building block which somehow came together to produce the proton.

I was not able to reconcile my thinking with the standard model particularly with the fractional charge quarks and this unsatisfaction lead me to build my own model of the structure of matter. I also have never been able to accept the Big Bang Theory as in my view it was impossible to believe that with what we now see as the extent of our universe as much greater than we once thought, to believe that just once so very long ago an event of such magnitude could have occurred, never to have happened before or since was improbable in the last century and just as improbable today. So with these reservations I came to think that there must be another answer.

The treatise is in two parts, the first deals with the duality of electromagnetic radiation and the interface it has with mass. It provides some definitive conclusions which form the basis of the second which extends those conclusions further into the structure of matter itself.

Conclusions

In no particular order the conclusions I make are:

• Elementary particles of matter are indivisible particles of energy which appear and act as matter with the property of mass.
• Every quantum in an EMR energy wave has three significant variables namely energy, frequency, and charge and these three variables are related and unique to each combination and it is that uniqueness which defines the properties of the quantum.
• This means that in quantization of EMR, a single point charge pair is uniquely associated with a specific energy amount to define a quantum.
• An equally important conclusion is that if the relationship between those three variables in the EMR “wave” which is parent to the spawned “mass particles” is defined by the energy, then the three variables must be similarly related in those progeny particles
• Charge is the center of the issue and is an essential property of all matter
• It means that every elementary particle must have a charge which increases proportionally to the square root of the energy, In other words a particle without charge is not elementary and must be a combination of at least two elementary particles with opposite charges.
• The energy and mass in a positron is in every way identical to the energy and mass in an electron albeit their opposite charges. There is nothing anti about a positron. It is here that the secret of the structure of all matter lies, all particles are composed of only two elements, positrons and electrons and it is through the neutrino that this is made possible.
• Any particle that has no residual charge must be a composite particle with charges balanced, positive charges equal to negative charges, and this is made possible by a positron and an electron lining up to rotate in the same direction on a single axis.
• This results in the charge attraction being balanced by the magnetic repulsion, leaving the two opposite charges to create a neutral entity named a neutrino.
• There are two forms of neutrino, one in which the spins are aligned to both be clockwise, the second when the spins are both aligned anti
• The above difference causes the two forms to have very different magnetic properties, the one with two south poles, the second with two north poles.
• Although the absence of a residual charge makes neutrinos not able to interact with most matter, the unique magnetic structure causes them to be very attractive to each other making pairs or greater numbers of neutrinos to clump up.
• This is perhaps one of the reasons why it is so difficult to tie down the mass of a neutrino, sometimes its one other times two or more.
• This “clumping” is a possible origin of the apparent existence of quarks.
• A proton consists of multiple bundles of neutrinos held together by their unique attractiveness to each other topped off by a single positron leaving the entity with a single +e charge.

 

Part 1: What is going on with EMR.

As an amateur physicist I make no claim to be a great mathematician or have access to enormous facilities, but I do have a long and consuming interest in particle Physics. I have studied this subject from many angles with an accent more on the “how” than the “what”. This study has led me to answer some of my own questions and some of those answers, I believe, are unique and revealing. In this paper I try to explain my thoughts and give you, the reader, I hope, some serious food for thought and perhaps encouragement to use these ideas in some further research.

I began my journey of exploration when I tried to understand the “how” of Einstein’s famous E=mc² equation. It was clear to me that this meant that matter and energy are two forms of the same thing, that no matter can exist unless it is structured out of particles of energy. As simple as this fact is, it is hard to accept but accept it we must. Taken another way, perhaps we should say: “Elementary particles of matter are indivisible particles of energy which appear and act as matter with the property of mass.”

To begin to understand the implications of this concept we need to begin with the simplest and purest form of energy, Electromagnetic Radiation or EMR.

In 1850 Maxwell famously described EMR waves as oscillation of electric and magnetic fields.  Now an electric field is defined as “an electric property associated with each point in the space where a single or many charge/s is/are present” and an oscillation of those charges means they swing back and forth from positive to negative. We also know that magnetism exists only when a moving or changing charge is present. So the picture in all the textbooks show EMR as an electric wave oscillating from positive to negative while at right angles to it is the magnetic wave which swings polarity in phase with it.

The Interesting thing about the Maxwell model is that it depends on the energy moving. For the model to work the electric field must oscillate causing the magnetic field to swing polarity, which itself causes the next swing in the charge, and the energy goes along for the ride itself depending on and at the same time driving the magnitude of the fields themselves.

However, there is a problem with EMR. We know from work by Einstein and others it has both “wave” and “particle” characteristics. The exact mechanism of the transmission of these waves is not fully understood but the evidence that they are “quantized” is irrefutable. The individual quanta do not appear to be necessarily linked to each other as many lab experiments with very low intensity radiation and observations of distant astronomic objects have demonstrated the reception of individual quanta of energy arriving on occasions spaced apart by seconds or even longer. They have also shown irrefutably that those quanta of energy are of a unique magnitude linked specifically to the frequency of the wave with the energy growing larger as the frequency is higher.

The only variables affecting energy  in this picture are frequency and the electric field, and the only variable in the latter can be the density (or size) of charge   in that field, so we can say:

As  increases,  increases and  increases or mathematically

                                                                                                                                               Equ. 1.1

To determine the nature of those functions we go first the famous Feynman equation² which finds that the energy of an electron is given by    where all items on the denominator are constants for this purpose, so that they can be replaced by a single constant k.

In my own work I derived an expression of similar form but with different constants³, but it too related the energy  to the square of . We also know that the relationship between E and  is given by Planck’s equation⁴ as  . So we can rewrite Equ. 1.1 as:                 

                                                                                               Equ. 1.2

Moving to the alternative form of energy, namely mass, let us add Einstein’s equation into the mix to get:

                                               = mc ²                                                                                                  Equ. 1.3

Written another way,                                                               Equ. 1.4

The constant k can be evaluated by substituting the properties of an electron but as, for the purpose of this analysis, we are interested only in relative relationships, we can say:

                                              =                                                                       Equ. 1.5

The equation makes it clear that the sign of the charge is irrelevant, only it’s magnitude is important.

So what is this thing we call “charge”. In the macro world of matter, the answer is easy, it is the presence of a surplus of electrons for negative, and a deficit of them for positive. In space in EMR or in the micro world there are no electrons, so the real answer is we really don’t know, and because we really don’t know what a “charge” is, it is not possible to determine the size or number of individual charges that make up the “density” of the electric field that oscillates, and we certainly don’t know how many charges of what size makes up the total charge of a single quantum. However, if we want to really understand what is going on we need to bring it all down to that individual quantum where it must mean that it is the oscillation of a single charge or small group of charges that equal the size of that charge and the resulting magnetic effects that oscillation must cause to sustain the quantum on its travels.

To further understand this question, let’s look at the point we know that energy and matter are equivalent, the “creation” of an electron positron pair. In our natural world the simplest form of matter is an electron and it’s charge mate a positron. The sparking of these particles shows that they can also act as waves and indeed can experimentally be shown to be able to switch backwards and forwards between the two forms. High energy gamma waves under the right circumstances spark off an electron positron pair and if these entities recollide they disappear again and release gamma rays of equal total energy. This fact is a clear confirmation of the equivalence of the two forms of energy.

To look in some more detail at the process of conversion of these high energy gamma rays into electron positron pair we find there is nothing new in this information, it is available from many sources. Gamma rays are high frequency high energy electromagnetic radiation (EMR). Clearly to produce a pair of particles, the energy of the gamma rays must be greater than the sum of the energies of the two particles. We know the rest energy of each of an electron and a positron is 0.511 MeV/c² so the energy of the Gamma rays must be greater than 1.022 MeV/c² from which we can deduce from Plancks law will have an frequency of greater than 2.47x10²⁰Hz. If such a ray were to pass close to a nucleus a pair of particles a positron and an electron are sparked off. If the two were to subsequently collide they would reverse the process and produce two identical gamma rays of total energy equal to 1.022 MeV/c² confirming that the energy of the gamma ray has indeed been converted into these two particles of matter and converted back again into two quanta of gamma radiation, but of necessity, each half the energy and frequency. Exactly what happens in the process of particle sparking is still not at all clear but the net effect is that if the energy and frequency (and by deduction, charge) of a quantum of EMR is greater than the level of 1.022MeV then certain circumstances can cause the spinning off of the negative half of the electric field to form the electron while the spinning off of the positive half forms the positron.

In the previous paragraph I used the word “Converted”. Perhaps if we used the word “Transformed” it would make it more clear that the two particles are still quanta of energy, now in the form of matter with the property of mass. In EMR it is clearly energy, in matter it still is energy now in the form of matter. Taking this view, it makes nonsense of the controversy as to whether a photon has mass. The word “photon” is simply an easy way of describing a “quantum of EMR” and as such it is energy which is at the same time mass in alternative form.

It Is interesting to note that the transformation described above is always precisely into a positron and an electron, it is never either two positrons or two electrons or indeed any other elementary “particle”. The other interesting fact is that the two appear together, not one after another. In fact, the conversion must be instantaneous, so if the quantum contained a multitude of charges that all swung back and forth in unison from positive to negative, then at the instant of conversion all the charges in the quantum must be one or the other and the production of both a particle with a positive charge and one with a negative charge would not be possible: it would have to be one or the other! This must mean that the positive side of the EMR wave must exist concurrently with the negative side meaning that EMR actually must be both charges rising and falling at the same time in phase with each other.

This may be difficult to visualize. I like to use the simulation of a ball of energy moving through empty space. As it does so it forces space to part as it passes through, causing space to become charged. Because of charge parity, the two sides of the split must be positive and negative of equal magnitude, that magnitude depending on the magnitude of the energy ball. Once the energy ball has passed the charges collapse and neutralize each other. Now replace the energy ball with a quantum of energy and you got it about right. Yes, you got it about right but you have also created the conundrum that puzzles us all. The magnitude of charge depends on the quantity of energy in the quantum, and that quantity of energy depends on the movement of the charge within the magnetic field which is itself created by the movement of that same charge.

However, this new model allows the charges to be always in balance, an equal number of positive charges as there are negative charges. As stated earlier, we don’t know if the charge of a quantum of EMR is a single point charge or a group of lesser charges that total to the magnitude of charge required, but logic would suggest that it is probably the former. Consider sunlight for example, it is made up of radiation of all frequencies and energies from low energy infra red through visible light to the ultra violet range and beyond, and yet individual quanta applicable to each and all those energies and frequencies coexist without interference. If the quanta were to be created by multiple charges as opposed to a single point charge, it would be impossible to separate one quantum from another in the stream. This strongly suggests that the actual mechanism is that each quantum of each individual frequency of the EMR is indeed a single matching pair of a positive and negative charge which remain linked to each other and only each other. Indeed it seems that this is a property of the quantization of EMR - each point charge pair is uniquely associated with a specific energy amount to define a quantum. The magnitude of the charge is not linear, double the energy only increases the charge by a factor of I.414.

 The conclusion I make from all this is that every quantum in an EMR energy wave has three significant variables namely energy, frequency, and charge and these three variables are related and unique to each combination and it is that uniqueness which defines the properties of the quantum.

An equally important conclusion is that if the relationship between those three variables in the EMR “wave” which is parent to the spawned “particles” is defined by the energy, then the three variables must be similarly related in those progeny particles. The two particles spawned each have half the energy of the wave from which they spawned and when they collide they produce not one quantum but two with energies now equal to that of each particle or half of that of the quantum in the original wave.

The above being true means that if that unique relationship is not present in a particle, one must conclude that the particle is not elementary and must be a combination of particles that do meet that criteria, because, very simply, there is no way they can form unless they do. This means also that a particle or indeed matter itself cannot exist without charge, and any particle that is neutral must have charge that is balanced positive and negative together.

The validity of this statement is critical to the understanding of elementary particles. It says that every elementary particle must have a charge which increases proportionally to the square root of the energy, In other words a particle without charge is not elementary and must be a combination of at least two elementary particles with opposite charges. As troublesome as this statement is, it is vital that a mechanism for how this can be must be found.

Another key conclusion this expression leads to is that it is impossible to differentiate between the energy related to a positive charge and that related to a negative charge, which while unsurprising in a mathematical context but may be critical in understanding the structure of matter. The energy and mass in a positron is in every way identical to the energy and mass in an electron albeit their opposite charges. There is nothing anti about a positron.

So a positron is not Anti-matter, it is simply matter transformed from the energy of a positive charge as an electron is matter transformed from the energy of a negative charge and other than the charge, the properties of that matter is identical. And perhaps this is why we don’t know where all the anti-matter in the universe is, because there isn’t any, it’s just all plain matter, and we cannot tell the difference.

Another conclusion could be that perhaps there are in fact only two elementary particles – The electron and the positron. All matter can be a  combination of those two entities if only they could coexist.

Perhaps we need to understand how negative charged matter particles can coexist with positive charged matter particles to find the answer, and perhaps the neutrino is that solution. In part 2 we will examine that possibility.

 

 Part 2: The Origin of Matter as we know it.

A few years ago I wrote a series of articles entitled the KISS theory of Everything, and sometimes I think that mantra, “Keep it Simple Stupid” has been forgotten when it comes to some aspects of physics. Just because strange things happen in quantum physics doesn’t mean that there are no explanations for some aspects of the quantum world and these should be investigated. For example, part one of this treatise showed that there is a simple probable explanation for how EMR is quantized. Admittedly not explaining the strange behavior of those quanta, but clearly this idea is worth critically pursuing.

So much of today’s high level particle physics relies on results from high energy colliders such as CERN but if one rejects the notion of the big bang as I do, those high energies were just not available in the early universe, that is not until the formation of the first stars. It is therefore imperative to examine other simpler explanations for the existence of matter as we now know it. It is in that spirit that I have developed my explanation for how it works and perhaps how it all began.

The main problem we have in understanding the universe is that we speak of charge as a thing, but we don’t really know what it is. But, as was clearly shown in part 1, charge is the center of the issue and, as I intend to show, is an essential property of all matter.

So, let us begin by surveying what we know about the particles of matter that make up our universe. We know that, on earth at least, all matter is composed of protons, neutrons and electrons. Protons and electrons are stable, while neutrons will decay to other particles unless they are in association with protons in a nucleus. Neither protons nor neutrons are considered elementary particles and are presumed to be composed of other smaller entities. There are myriads of other particles that are observed in cosmic rays and in decay products of radioactive materials, but a fact which I find interesting is that all the subatomic particles known have only 0, +1e or -1e charge (that is except the quarks which have supposed charges of less than +/-1e) and it just so happens that +1e is the charge of a single positron and -1e is the charge of a single electron.

It has to be conceded that there may be other elementary particles but I think the evidence is overwhelming that electrons and positrons are the prime candidates. The only matter we know that is produced from EMR are those two, and all other particles other than neutrinos quickly decay. The process of sparking these particles clearly shows a mechanism for converting energy into matter, and it would seem impossible, or at least improbable, that there was more than one mechanism for achieving what is indeed a most remarkable process. Also, there is the issue of the missing anti-matter. 

So, as we said in part 1, if charge is an essential part of mass, any particle that has no residual charge must be a composite particle with charges balanced, positive charges equal to negative charges, and as the only charges we find in free standing particles are +e and -e, we are led to the remarkable possible conclusion that all particles are composed of only two elements, positrons and electrons. Knowing that electrons and positrons cause each other to revert to EMR when they meet makes this a mammoth question.

So let us just say for a moment that it seems to be the only way it can be, so let us propose a possible mechanism

In the following discussion we must concede that we don’t know the structure of an electron or a positron and as we have already said, we don’t even really know what charge is, and we certainly don’t know with certainty if the charge in an electron (or positron) is a single point charge or a cloud of charge, so speaking of a spinning charge is in itself problematic. What we do know is that these entities have spin, have magnetic moment which in established science has been shown to only exist as a result of charge motion, and have mass which we know is energy in another form. These three properties suggest that a model of a spinning charge of some kind is at least a reasonable representation and an entity like that could have properties identical to all three.

So conceding we don’t know exactly what a positron or electron actually is, we do know they both have charge, spin and magnetic moment. So let us say that the structure of both is a either a single charge or a group of charges in a kind of disk or even an orb of charges spinning sufficiently to create the magnetic moment. To help in this discussion I have introduced a descriptive notation as follows:

A Positron:           . Imagine a positive charge spinning in a circle oriented vertically to the page so that the axis of rotation is parallel to the line of type. The direction of rotation is shown by the arrow as anticlockwise when viewed from the right side. This will cause the magnetic field to point north to the right and obviously south to the left represented by the notation sn.

An Electron:         . Here the rotation the same but because the charge is negative, it makes the “current” in the opposite direction, hence the magnetic field is opposite also and is notated as ns.

So it happens that a positive and negative charge spinning in the same direction on the same axis would create opposing magnetic fields such that the charges would cause them to be attractive but the magnetic fields would be repulsive. This leads one to speculate that were it to be that the two entities with equal but opposite charges and identical spin happened to be generated in such a fashion as to be placed in such a position, would it not be just possible for the resulting combined entity to be stable and to become what I originally called one of the forms of a neutrino. If the particles move apart, the electrostatic force would tend to bring them back together while, if they move closer, the magnetic field would tend to push them apart again.

This situation, using the above notation when the spin is clockwise when viewed from the right could be represented as follows where the neutrino is represented by  :

                                                                       Eq 2.1

The very curious result is that the net result is an entity with two opposing magnetic fields with both ends pointing south. It is also interesting to see what happens when both entities are rotating in the reverse direction. This would be the result:

                                                                                                     Eq 2.2

So the surprising result is an entity identical in every respect except that here it is two north poles extending from the two ends. This suggests there are two forms of the neutrino, one  the other .

The big question is how could such a combination be stable? I believe the secret is in the fact that, with the spinning disc concept, the attractive force of the charge surrounds the repulsive force of the magnetism. It is speculation, I concede, but let’s just see where this leads!

Once we become comfortable with this concept we can begin to consider what may be the properties of this particle:

Spin: Clearly the  will have identical spin characteristics as the two sub components with the rider that there are two distinct variants, one where both are spinning clockwise, the second when both are spinning anticlockwise.

Magnetic moment: This will be interesting. As we noted above, there will be two versions, one where the two components are joined at the north poles, and a second when they are joined at the south poles, each dictated by the direction of spin. However the most interesting feature is that the first version will have two south poles, the second two north poles. This feature is important because, as we will see later, it is here that the secret of the structure of all matter lies.

Mass: The total mass is likely to be very close to, perhaps slightly less than the sum of the MeV/ masses of the two components, i.e. very close to 1.22 MeV/. The loss of mass would be consistent with the release of a small amount of energy as the two particles settle into their new structure as a single, if compound, entity.

Charge: Because  has both a positive and negative component with equal charge, the net result is zero charge. However, the particle will have a small electric dipole.

To now examine what these entities may do in the presence of others!

I found it useful to look at a pair of the two forms of   side by side with the magnetic poles added for emphasis:

S S

N N

Lets look a bit deeper. To begin, let us expand the neutrinos into their subcomponents, and I have added a second pair for illustrative purposes:

S S NN

N N S S

Here you can see that in parallel presentations, in every case the two like charges are adjacent and therefore repulsive but the magnetic poles are opposite providing a strong attraction. Also the two versions would be strongly attractive end to end enabling easy chain like association. (Is this perhaps the origin of the strong force of the standard model)

Seems to me this could form a lattice like structure:

S S N N S S NN S S N N

N N S S N N S S N N S S

S S N N S S N N S S N N

N N S S N N S S N N S S

 

The result is that while neutrinos may not interact with most matter as they have no net charge, they certainly will react to other neutrinos, easily pairing up between a north and a south, or even clumping up most frequently in multiple pairs. This clumping could result in entities as listed below

                              Number               Expected mass                  Compare with                   Est. Mass

                              1 pair                   2.44 MeV/                  Up Quark (u):              Appr. 2.2 MeV/

                        2 pair               4.88 MeV/              Down Quark (d):          Appr. 4.7 MeV/

Could be just coincidence, I think not.

So you see where this is leading, we start to get a couple of 1 pair structures with a two pair structure, and instead of fanciful gluons, they clump up with multiple additional neutrinos (probably in pairs)  assisted by their natural magnetic attraction (just like the strong force) and after about 900 are collected, are cemented by an the addition of a single extra positron, and we have a proton. I agree that none of this explains why we have to get to 900 or so neutrinos for the stabilizing force of the extra positron to create a proton, and no other intermediate structure appears to exist and be stable. But nor can we really explain how three quarks of dubious mass, but certainly less than about 10% of the mass of a proton, with countless gluons also of dubious mass suddenly get together to create the most essential building block of all matter, the proton.

Although neutrinos have been known to exist for almost a century, little is definitively known about them. This is because they have no residual charge which makes them difficult to detect and manage. There has even been questions about their mass, and current estimates give them a very small amount. Clearly I do not accept that assertion. The findings in part 1 make it clear that the conversion of energy from it’s form in EMR to it’s form as mass takes place precisely at the level of energy in a positron or electron, i.e. precisely 0.5109989 MeV/. To me this is very significant! We cannot possibly believe that the matter in a neutrino is different to the matter in electrons or positrons because when other larger particles such as protons are broken up, positrons, electrons, neutrinos and EMR are the products, so it seems they must be all made of the same stuff, energy in one form or another. While an electron or positron imagined as a charge spinning in its own magnetic field may be too simple a picture, it certainly is a reasonable approximation and provides a basis for calculation of their properties. So if mass is in fact a material which exists because a specific charge spins within the magnetic field it creates itself, a particle without charge is not possible, and a neutral particle must have balanced charge, i.e. an equal number or magnitude of opposite charges.

We likely will never be able to really know what the structure of an electron or positron actually is and the nature of a neutrino is even more likely to elude us due to its elusive nature, but I cannot escape the conclusion that matter cannot exist without all three of the necessary components energy, charge and spin and the only way this can be is for every elementary particle to have charge, balanced or not.

The mechanism I have proposed may not be wholly correct, but I stand by the principle that matter created by a negative charge is identical in every way except the charge as matter created by a positive charge. When the two exist together we cannot tell the difference. And in this process, neutrinos appear to be the key.

So if neutrinos are the key, how could they have got there. In the theory of quantum physics it implies that “there never is nothing” In the darkest loneliest coldest place in deep space there is always quantum foam, entities emerging from space only to recollide and disappear. Mostly the entities recollide and disappear, but it is conceivable that every now and again two entities of precisely the required intrinsic energy to be a positron and an electron, and are positioned precisely parallel and instead of disappearing a new particle emerged, a neutrino. Over millennia neutrinos of one form or another began to permeate space in enormous banks (which we know are still there today.) Much more possible than the Big Bang!

It would seem to me a real possibility that these banks of neutrinos could gather in greater and greater clouds eventually so thick that clumps could form so large that for some undisclosed reason we’re just large enough to be the structure of a proton held together by a process by which a single neutrino split leaving the proton with a positive charge and the released electron circling forever around it to form the original stable gas of the universe namely hydrogen.

I know that the initial reaction to this suggestion is that positrons and electrons cannot exist together because they annihilate each other but what if this is not the case in this specific condition. In the early work on the collision between protons and other massive bodies the resultant products were a multitude of particles which had an equal multitude of different masses but all were unstable and all degraded further with the final result being only electrons positrons neutrinos and EMR perhaps those larger particles were just combinations of neutrinos gradually disintegrating.

And perhaps after all, matter is not as complicated as we thought.

References

1. From the Big Bang to Quarks – Have we lost our way. Michael Anderon Vantage Press, 1996.
2. Feynman Lectures. https://www.feynmanlectures.caltech.edu/II_28.html
3. From the Big Bang to Quarks – Have we lost our way. Michael Anderon Vantage Press, 1996.p71
4. Planck’s law https://en.wikipedia.org/wiki/Planck%27s_law

As most of the references used in this paper were seeking specific data available from multiple sources so no specific references are listed. Indeed most information was accessed using ChatGTP.

 

 

Copyright Michael Anderson 2023.