The detection of “the God particle” or Higgs boson , in 2012, was the culmination of theoretical and experimental efforts, carried out by thousands of scientists during half a century, in order to test and validate the “Standard Model” of particle Physics. 1
The Standard Model is the latest and most successful attempt to make sense of sub-nuclear phenomena, and in particular of the paraphernalia of strange new particles (muons, pions, kaons, mesons, neutrinos..) which were turning up during high energy collision experiments in particle accelerators.
The discovery of the Higgs Boson vindicated the “Standard Model” adding further experimental evidence in its favor.2
To be sure, the Higgs Boson was not the first “exotic” particle found in concordance with a theoretical prediction within a quantum field extension of quantum mechanics.
There were many other particles before it, including other bosons (W and Z ).
The first and most famous was Dirac’s positron which inaugurated the modern, post quantum mechanical, era of particle chase and of course “robotic fever” with Asimov’s positronic brain in his science fiction stories involving humanoid robots stories. 3
The Higgs Boson provided, in addition, a unique insight into an age long mystery regarding the origin of mass. In fact the Higgs field, of which the Higgs Boson is the particle manifestation, is thought to be responsible for the mechanism allowing particles to acquire mass i.e. the creation of the ordinary matter observed in this Universe.
Now, the mass is a concept invented by Physicists to represent the “property of inertia”, which is common to the behavior of all the “material” objects encountered in Nature. Concepts such as mass, particle, wave, time, space, charge, field, temperature arose from empirical observations. Each one of these concepts can be traced back to a direct perception of the phenomena whether in every day experience or in laboratory experiments.
It is useful for didactic reasons to trace back the development and evolution of these concepts in their historical context.
For the concept of mass which is our subject matter here, the appropriate approach for following its evolution is linear, the concept being gradually elucidated in consecutive steps mirroring our increased comprehension of the structure of matter.
So, what is mass?
Contents
Part A: The classical concept of mass
A1- Quantity of matter?
A2- Mass and weight
A3- Material and immaterial
A4- Lavoisier’s principle of conservation of Mass
A5- Newton’s Inertial and Gravitational Mass
A6- Classical particles and mass
Part B : The modern concept of mass
B1- Einstein’s Mass-Energy gambit
B2- Mass as internal energy
B3- Creation and annihilation of particles
B4- The quantum particles
B5- The Standard Model of elementary particles
– Fermions and Bosons
– The particles of the Standard Model
B6- Particles and Quantum fields
Part C: Higgs Boson and the origin of mass
Part A: The Classical concept of mass
A1- Quantity of matter ?
When we start learning physics in middle school, we are told that the mass of a body is a measure of « the quantity of matter » contained in that body.
This simple definition is thought to be safe enough, for a start.
Newton embedded this definition in the ‘Principia Mathematica’ in 1687, as the starting point of his mechanical model of the phenomena.
In definition I and in the language of that historical era, he states: 4
“The quantity of matter is the measure of the same, arising from the density and bulk conjointly..”
“ It is this quantity that I mean hereafter everywhere under the name of body or mass. And the same is known by the weight of each body; for it is proportional to the weight, as I have found by experiments on pendulums, very accurately made, which shall be shewn hereafter.”
However, this first definition does not tell us much about the nature of mass and matter, since, in a circular reasoning, matter is defined as that which possesses mass or density, which is mass per unit volume!
Nonetheless, this definition of mass proves to be useful.
It allows us to begin to carry experimental observations by distinguishing between two properties of a body, that are easily confused at that time (and age), namely, the mass of the object and the size or volume, that is the amount of space occupied by the object.
A2– Mass and weight:
The definition of mass as “quantity of matter” allows us also to distinguish between mass and weight.
Weight, unlike mass, is caused by the direct experience of the physical effort deployed to lift or hold an object. This experience is straightforward and unambiguous.
The “quantity” of matter by contrast does not have an independent empirical fingerprint since its is “known by the weight of the body, for it is proportional to the weight”, as Newton puts it.
Weight in Physics is a force which comes in two meanings:
- the “pushing” force exerted by an object on its support.
- the “pulling” force of gravitational attraction exerted by Earth on the body” .
This distinction between mass and weight does not seem evident at first glance, since mass is measured by its weight.
However, this distinction is confirmed by experimental evidence which shows that the weight of an object measured by the stretching of a spring (or dynamometer) varies with the location (latitude, altitude or different planet) since it depends on the acceleration of gravity, while its mass, measured by a balance, remains “apparently” unchanged.
A3– Material and immaterial:
In addition, this definition of mass allowed early scientists to distinguish between « matter » (i.e. all that has mass) and other natural phenomena, such as heat, sound, electricity, magnetism, or light which “appeared” at the time to be devoid of mass (immaterial, less tangible).
In fact, by the mid-19th century, “mass” was used as a main criterion in the classification of all natural phenomena under two broad areas: matter and radiation governed each by its set of laws, models and theories covering the whole physical domain.
In this classification, Classical Mechanics complemented by Thermodynamics, Statistical Mechanics and Chemistry, gave an adequate explanation for most of the “material” phenomena discovered at that time in their field of application, from the behavior of particles in a gas at the microscopic level to the motion of planets.
On the other hand, by the 1860s, all known electrical, magnetic and optical phenomena had been integrated in Maxwell’s electromagnetic wave-field theory.
Everything seems OK, until someone asks: But what is mass, really?
A4– Lavoisier’s principle of conservation of Mass
In Chemistry, the concept of mass is reduced to numbers (ratios) used to balance equations representing chemical reactions.
The basis of this “stoichiometry” is the principle of conservation of mass (only a first approximation as shown by the theory of Relativity), which states that during chemical or physical transformations, the total mass of the reactants is equal to that of the products i.e. remains constant; or in Lavoisier’s insightful words:
“Rien ne se perd, rien ne se crée. Tout se transforme”.5
The principle of conservation of mass is the basis of reaction Chemistry. Without it the chemical sciences fall apart. However it does not shed new light on the concept of mass.
The measurement of masses does not improve our understanding either, since measuring is in fact comparing a quantity to a reference (in this case the kilogram).
At the atomic level, the introduction of the atomic mass unit (u or au) helps only to reduce the number of zeros after the decimal point.
Actually, stating that the mass of the 12C isotope of Carbon is 12 u explains nothing more about the nature of mass. This is another way of saying that one mole of 12C atoms has a mass of 12 grams. 6
Since one mole contains an Avogadro number NA of atoms, the mass of the 12C atom is :
mC = 1.99×10-26kg.
A5- Newton’s Inertial and Gravitational Mass:
One must embark on the study of Newtonian Mechanics (classical), in order to obtain new insights on the concept of mass.
Here, Mass is encountered under two distinct aspects: inertial and gravitational.
The first aspect appears when we try to modify the motion of a body, the body “opposes” any change in its velocity (magnitude and direction).
This phenomenon is encapsulated in the 2nd Law of Newton which states that the force exerted on a body is given by the (rate of) variation of the momentum p = mv (or vice versa): 7
F = dp/dt [ 1 ]
The linear momentum is the measure of the inertia of the body, i.e. its resistance to change in its motion. The proportionality constant ( m ) is an intrinsic property of the body and is termed: Inertial mass.
The second aspect is revealed when we study the gravitational interaction between two bodies. The bodies attract each other with two equal and opposite forces according to Newton’s law of Universal Gravitation.
The common magnitude of the forces is proportional to the masses of the two bodies m and m’ , and inversely proportional to their separation (d) squared: 8
F = G.m.m’/d2 [ 2 ]
In this case, the mass describes the property of gravitational attraction of each body and is termed: Gravitational mass.
There was no theoretical justification for the two “masses” to be equal. However Newton postulated, intuitively, that they should be so. Experimental measurements of g (the acceleration of Earth’s gravity) and G (the Universal gravitational constant) showed later that he was completely right.
We know now from General Relativity and the Principle of Equivalence that the two masses are not only equal but also « identical ».
General relativity also shows that the inertia-gravity phenomenon is due to kinks in space-time?
The question is: does the mass produce the kink or is it the kink that produces the mass?
A6- Classical particles and mass
The physical Sciences assume that “particles” are the fundamental bricks of the universe, whose dynamical properties determine the observed phenomena.
In classical Mechanics, Newton describes material particles as “point-like”, hard, impenetrable, separate, countable, distinguishable and permanent “chunks of matter”, endowed with mass/inertia and moving in well defined trajectories mapped out by deterministic laws.
Newton’s concept of mass is closely bound to his concept of particle. He simply deduced the properties of the microscopic parts (particles) from the properties of macroscopic bodies, obtained by means of our senses .
For Newton mass or inertia is an intrinsic property of matter.
In “The rules of reasoning” at the beginning of Book III, Newton expounds the concept of material particles as follows:
“The extension, hardness, impenetrability, mobility, and vis inertiæ of the whole, result from the extension, hardness, impenetrability, mobility, and vires inertiæ of the parts;
and thence we conclude the least particles of all bodies to be also all extended, and hard and impenetrable, and moveable, and endowed with their proper vires inertia. And this is the foundation of all philosophy”. 9
This particle model was adopted by chemists and thermodynamists. However they soon discovered that most of the particles were composites made up of more than one atom, or chemical elements. Pure substances consisting of single atomic elements are rare in Nature. Most elements bond readily with each other forming compounds or molecules.
In addition, a new property of matter , the electric charge, was discovered. Physicists and chemists alike had to integrate this electric charge into their model of matter and attempt to imagine how it was bound to the mass of the particle.
These electric charges were found to be responsible for the electric and magnetic forces which held the atoms together and thus imparted the molecules with the additional internal degrees of freedom of rotation and vibration.
This gave rise to a more complex picture of the microscopic model of matter which was applied to the explanation of a variety of macroscopic mechanical, electrical and chemical properties and phenomena such as, changes of state, hardness, viscosity, conductivity, piezoelectricity, chemical structures and reactions etc..
This model of matter remained the consensus until the last decade of the 19thcentury.
Part B: The Modern concept of mass
B1- Einstein’s Mass-Energy gambit
In 1905, Einstein’s new theory of Special Relativity introduced a new aspect of mass. The theory showed that the mass (inertia) of a moving body increases with its speed according to the following equation:
m = γ.m0 [ 3 ]
Where, m is the mass of the moving object,
m0, its rest or proper mass (in the rest frame attached to the body),
c, the speed of light (electromagnetic waves) in vacuum,
and γ , the Lorentz factor.
γ is greater than 1 always, and tends to infinity as v tends to c. 10
One of the consequences of this equation is the famous equation of Einstein which links mass to energy: 11
E = m.c2 [ 4 ]
which applies to the rest mass m0 as follows:
E = m0.c2 [ 5 ]
This relation simply states that the rest or proper mass m0 i.e. the “quantity of matter”, can be completely converted into energy E and vice versa.
This means that Mass is in fact another word for Energy.
This prediction has been confirmed experimentally and provides of course the foundation of the atomic bomb and of nuclear power technologies.
Thus “Matter” became the last of a long list of phenomena that the concept of energy had gradually absorbed: kinetic energy or the energy of motion, potential energy with all its manifestations and “heat” or thermal energy.
Matter is another form or manifestation of energy, a specially structured (and condensed) form of energy!
B2- Mass as Internal Energy
What type of energy are we talking about?
From Thermodynamics we learn that a body or system of particles possesses internal energy, symbol U.
The first law of Thermodynamics, which is none other than the principle of conservation of mechanical energy extended to thermal interactions, is stated as follows:
ΔU = Q + W [6]
Where U is the total internal energy of the system, Q the Quantity of heat exchanged during thermal interactions and W the amount of Work deployed by the system during mechanical interactions.
The absolute value of U cannot be calculated from thermodynamic consideration i.e. we can measure (calculate) only its variation ΔU = Q + W, by measuring Q and W,
However with the relativistic mass–energy equation, and since energy is mass, we can measure in principle the rest mass mo of the object and thus calculate the total internal energy ( U = moc2) of a body.
Based on this, we can now attempt at proposing a first definition of mass as follows:
The (rest) mass of a body is a measure of the total internal energy of the body.
But what is meant by total internal energy of a body?
We will try to deal with this question in detail in later notes about energy and particles. However, we would like to propose the following preliminary definition, as a guide to the following discussions, contingent on reviewing it later:
The total internal energy of a body (system of interacting particles) is equal to the algebraic sum of:
a- The total kinetic and potential energies of the fundamental elementary particles of the system measured with respect to the center of mass.
And
b- added to it the rest energy (energy equivalent to the rest mass) of the particles, separated to infinity and at rest with respect to the center of mass.
However, this definition generates more questions, such like:
- What are the fundamental elementary particles?.
- How do these particles acquire their mass/energy/inertia?
- Do these fundamental elementary particles have an internal structure, i.e. internal energy other than their rest mass or do they materialize in whole chunks?
We shall attempt to answer these questions in the coming paragraphs below!
B3- Creation and annihilation of material particles
Einstein’s relationship (E = mc2) signifies that it is possible to convert matter into energy integrally. It also means that energy can be converted into mass (m = E/c2).
The first process is termed annihilation, the second, creation. The simple occurrence of the two processes of creation (from photons) and annihilation (into photons) of material particles shows that the distinction between mass and energy has become superfluous.
The two processes are depicted by the Feynman diagram shown in Figure 1. In order for the annihilation and creation of particles to occur, the system must obey the fundamental conservation laws involving: energy/mass, linear momentum, angular momentum or spin, electric charge and in many cases parity.12
Both processes have been demonstrated experimentally.13a,b
The two processes are also thought to have occurred during the early stages of the universe. The particle creation process was dominant during the first 100 seconds of the Universe, and is thought in combination with the Higgs mechanism to be responsible for the existence of matter?.
Experiments in particle accelerators showed that, in collision between highly accelerated particles, new particles were created possessing masses orders of magnitude larger than the combined mass of the colliding particles.
For example in high energy electron-positron collisions W bosons pair ( mass: 80.385 GeV/c2 × 2), Z bosons (mass: 91.188 GeV/c2), and quarks were produced, via processes similar to the one depicted in The Feynman Diagram of Figure I. (See reference 22 for the conversion of the masses into SI unit kg).
By comparison the rest mass of the electron-positron pair is only : 0.511 MeV/c2 x2 !
It is clear that these particles were created from the kinetic energy of the colliding particles and not from “debris” of the colliding leptons or light particles.
Furthermore, it must be noted that, mass being energy and vice-versa, means that the dividing line between material and immaterial phenomena, matter and radiation, particle and wave-field has become blurred. The relativistic model of particles suggests that particles are not “permanent chunks of matter” but bundles of energies which exist as ephemeral entities.
This new relativistic picture of material particles as ephemeral bundles of energy found further confirmation and clarification as new discoveries in nuclear and sub-nuclear physics kept pouring in throughout the twentieth and twenty-first centuries.
As we shall see next, a very complex picture of the sub-nuclear world emerged gradually and which was finally resolved (as we hope ) with the “Standard Model of particle Physics”.
B4- The Quantum particles
Indeed, as things progressed new discoveries unfolded.
By the end of the 19th century, several experimental discoveries took place in rapid succession revealing new surprising features of the subatomic world:
anode rays or protons (Goldstein, 1885), natural radioactivity and α, β, γ emission (Becquerel, 1895), X-rays (Roentgen, 1897), cathode rays or electrons (Thomson, 1897).
The atoms were found to have internal structure: each atomic element consists of an equal number of negatively charged electrons, and positively charged protons (e+), in addition to the uncharged neutrons. 14
These three subatomic particles, electron, proton and neutron were identified, for a while, as the “fundamental elementary particles” of matter.
Not for long!
Neutrons and protons turned out to be made up of constituent particles termed quarks and gluons; however, empirical evidence for the existence of the elusive quarks and gluons as free separate entities could not be obtained. Quarks and gluons play a central role in the “Standard Model” of particle physics and their existence and properties are inferred from high energy collision experiments in particle accelerators. 15
Additional particles of one kind or another started popping out in high energy experiments, that were being carried out with more and more powerful particle accelerators (muons, pions, kaons, mesons, neutrinos..).
Furthermore, it had been discovered early on that the particles possessed an additional degree of freedom i.e. the spin; This was demonstrated in 1922 in the Stern-Gerlach experiment which showed that electrons possessed an intrinsic magnetic moment termed spin which could take only two values: + ℏ/2 and – ℏ/2. 16
Later on, it was discovered that all “elementary particles” possessed a spin.
That’s not all !.
The most baffling discovery was, that “quantum particles” were not particles, after all. They possessed a fundamental property normally associated with wave characteristics: the property of phase .
De Broglie proposed in 1923 that all material particles possessed a wavelike nature and postulated that the wavelength was inversely proportional to the linear momentum of the particle (λ=h/p) , thus generalizing the Planck-Einstein hypothesis to all particles.
The de Broglie hypothesis is now an established fact confirmed repeatedly in various experiments. 17-18
This means that he use of the term “particle” to refer to “quantum entities” conveys a misleading picture. The term “particle”, and the picture associated with it, are borrowed from our coarse perception of the macroscopic world around us, a perception which is embedded in the fabric of the classical models of Reality.
It is inadequate for communicating the meaning of the particle concept in quantum theories. even when associated with the term quantum.
The “quantum” particles are not particles in any normally accepted sense. The phase property allows the superposition, interference, overlapping and entanglement of the “particles”, phenomena normally encountered with mechanical and electromagnetic waves observed in the classical domain. They are wave-particles or “wavicles”.
In addition, the position of the quantum particle is described by a continuous wave function which gives the probability density of the particle’s position. The quantum particles therefore lose the precise localization, in contrast to classical particle
The location of the particle thus its mass/energy is smeared over a extended volume of space e.g the whole atomic volume for atomic electrons and the whole nuclear volume for nucleons.
This is akin to the mass distribution over the whole space associated with potential (or interaction) energy between particles in classical physics. In this case the energy/mass is not a property of of a specific particle but of the system.
Thus, the quantum entities manifest themselves as intangible bundles of mass/energy which may pop into being or vanish under appropriate conditions. They are entangled, interpenetrating, indiscernible, ephemeral entities. The “particle” properties of inertia, charge and the mysterious spin, are detected as “splashes” of energy on phosphorescent screens or as whimsical tracks in a cloud chamber.
Mass seems to have lost its age long status as a fundamental intrinsic property of the particles and becomes a consequence of the interaction of the particles with the environment. In fact the standard model defines the particles themselves in terms of excitation states of quantum fields in which the mass /inertia/energy is borrowed by interaction with the Higgs field as we shall see next.
B5- The Standard Model of elementary particles
Fermions and Bosons
In 1928, Dirac developed a relativistic quantum theory of the electron thereby extending the Schrödinger – Heisenberg non-relativistic model to conform with the Principle of covariance. 19
Dirac’s theory described two new fundamental features of the microscopic world i.e the particle’s spin or intrinsic magnetic moment and antimatter (creation and annihilation of electron -positron pair)). It also showed that the collective behavior of the particles is related to their spin.
Accordingly, all particles may be classified in two groups:
– Fermions such as electrons, quarks and other elementary and composite particles which possess a half integer spin.
– Bosons such as photons and other elementary and composite particles which possess an integer spin.
The theory showed that Fermions are described by anti-symmetric wave functions and therefore obey the Fermi-Dirac statistics (hence Fermions) which forbids two particles from belonging to the same quantum state i.e. to possess the same dynamical properties.
On the other hand photons and other Bosons are described by symmetric wave functions and therefore obey the Bose-Einstein Statistics ( hence Bosons) which allows an unlimited number of particles of the same kind to be in the same quantum state. 20
The impact of the symmetry of the wave function of the particles on the properties and behavior of macroscopic bodies (large collections of interacting particles ) has been discussed in a previous blog (https://particlemysteries.wordpress.com/2023/09/04/the-quantum-interface-with-reality/).
Indeed, the electrical, magnetic, optical , spectral, mechanical and thermodynamic properties of the solid state among other things are a direct result of the quantum wave properties of their constituent fermions i.e. electrons.
The fermionic nature of the electrons is responsible for the periodic potential and energy band structure of crystals and for the existence of the Fermi energy which plays a central role in defining their semi-conducting behaviour, which is the essential component of many modern technologies (electronics, optoelectronics, photovoltaics, energy storage, communication, information technologies..).
On the other hand, Bose-Einstein Condensation (BEC) is a collective quantum phase change underwent by bosons at low temperature, in which all the particles”condense” in the same quantum state giving rise to some amazing macroscopic quantum mechanical properties such as, coherence , interference, zero viscosity, zero resistivity and tunneling through walls and barriers.
Finally, it is important to point out that Dirac’s equation provided the prototype which laid the foundation for the subsequent quantum field theories QED (Quantum Electron Dynamics), QFD (Quantum Flavor Dynamics) and QCD (Quantum Chromodynamics ), which where ultimately integrated in the Standard Model.
The particles of the Standard Model
The Standard model, as expected groups the elementary particles in the two main classes presented above, fermions and bosons (figure 2):
– The Fermions include the 6 quarks and the 6 leptons.
Fermions are termed material particles. The actual number of elementary fermions is 48 in total, by taking into account all the antiparticles and the quarks three colors.
– The Bosons include the photon, the gluons (8 including colors), and the W– , W+ and Z bosons.
Bosons are also termed quasi-particles: they are force carriers mediating fundamental interactions. There are 12 elementary bosons in total in the standard model, in addition to the Higgs Boson.
Figure 2 below shows the elementary particles of the standard model.21
It also lists the “intrinsic” properties of the particles i.e. mass, charge and spin.22
B6- Particles and quantum fields.
We now presume that the physical phenomena occurring in Nature can be traced back to 4 fundamental forces driving the interactions between the particles.
The 4 fundamental mechanical interactions between the particles in the Universe are labeled as follows:
a- gravitational, b- electromagnetic, c- weak nuclear and d- strong nuclear.
a- The gravitational interaction occurs between all known particles since it is due to the property of mass/inertia/gravity that they all possess. This interaction is described by Einstein’s general relativity or by Newton’s Universal gravitation in the limit of weak fields. It is observed , among other things, in the motion of planets and stars and felt as weight on the earth’s surface.
There is no working (accepted) quantum gravitation theory as yet. Attempts at constructing such a model using elementary strings and membranes have not been successful until now. But that ‘s another story!
b- The electromagnetic interaction occurs between charged particles only (electrons, protons…).
All interactions (phenomena) encountered in everyday life are electromagnetic in nature except those of gravitational origin.
In the quantum field version of Maxwell’s classical electromagnetic theory, termed QED (Quantum Electrodynamics), the EM field and the electron field are quantized. The photons which are bosons are the force carrier of the electromagnetic field between electron-positron pairs which are themselves excitations in the quantized electron field.
During interaction the field exchanges energy in terms of photons or electron-positron pairs. The processes are called creation and annihilation of particles.
QED, as noted before, served as a prototype for the quantum field theories of the weak (QFD) and strong (QCD) interactions.
c- The weak nuclear interaction acts between leptons (light particles, such as electrons).
The weak interaction acts within the nucleons causing a quark to flip. This leads occasionally to the transformation of a neutron into a proton (or vice versa), accompanied by a release of beta radiation (electrons, or positrons).
During the process the nucleus may become unstable and disintegrate releasing energy, resulting in nuclear fission.
There are 3 force carriers for the weak interaction: the W– , W+ and Z bosons.
In the Standard model the weak and electromagnetic forces result from a single interaction termed electroweak interaction.
The strong nuclear interaction acts between quarks, and between nucleons (protons and neutrons and is thus effectively restricted to the nucleus.
It acts between quarks, binding them together to produce protons ( two up quarks one down, uud) and neutrons ( one, two down, udd) and other less stable hadrons (heavy particles) and mesons (intermediate mass particles). It also acts between neutrons, between protons and between protons and neutrons, binding them together to form the nucleus and counteracting the repulsive electromagnetic potential between protons.
The bosonic force carriers for the strong interaction are called gluons. There are 8 gluons differing by what scientists termed colors (they have nothing to do with visual impressions).
Unlike the gravitational and electromagnetic forces which diminish in intensity with distance, the gluonic strong force increases rapidly with quark separation, thus confining the quarks to the nucleons and the nucleons to the nucleus. The potential energy of the gluonic bond is therefore positive, not unlike the potential energy of a stretched elastic spring.
Thus, both the strong and electroweak interactions are described by the standard model in terms of quantum fields. The fields interact via their bosonic particles exchange. The bosons become carriers of the force deployed by the quantum fields during interaction.
The exchange of bosons is equivalent to the exchange of energy, linear momentum and angular momentum (spin). The interactions obey the conservation laws.
The Standard model is in fact a theory of “almost everything”. It covers all natural phenomena except gravity. All electrical, magnetic and optical phenomena, including the properties of materials and all of chemistry, in addition to all atomic nuclear and sub-nuclear observations are contained in the symbols of the standard model equation.
Part C- Higgs Boson and the origin of mass
The standard model succeeded in unifying three of the four fundamental interactions in the Universe, namely the weak, the strong and the electromagnetic interactions. It has provided testable predictions which were confirmed experimentally.
In addition to the quantum fields associated with the three fundamental interactions, the Standard model introduced a fourth quantum field which was termed Higgs field in reference to one of its author . 23
The Higgs field is a special type of an energy field pervading all space. It was proposed initially in the context of the electron -weak theory (QFT) to account for the mass of the W and Z bosons which would have been otherwise massless. The interaction of the particles with Higgs field is mediated by yet another boson, the Higgs boson.
The Higgs boson has 2 peculiar features:
- it is extremely massive (126 GeV/c2; in terms of mass/energy),
- it has a spin equal to zero (all the other bosons have a spin of one) .
In the case of QFT, the interaction of the force carriers (photon, W+, W+ and Z bosons) with the Higgs boson plays two roles:
a- it breaks the symmetry between the, as yet, unified weak and electromagnetic quantum fields, therefore rendering them independent.
b- it imparts mass/inertia to the weak carriers, W and Z and to the electron-positron pairs with only the photon remaining massless.
Mass in this case appears as increased sluggishness or resistance to acceleration i.e. inertia, which manifests itself in the short range effect of the weak interaction as it remains confined to the nucleons.
The mass/energy/inertia is transferred from the vacuum energy (referred to as “dark energy” for some obscure reason!) which resides in empty space.
The success of the Higgs mechanism, in explaining the symmetry breaking of the electroweak fields and of the masses of their particles, prompted its extension to the strong interaction, in an attempt to unify all three fundamental interactions in a single theoretical model, a Grand Unified Theory or GUT.
The strong field particles i.e the quarks are fermions and behave somewhat like electrons, while its force carriers , the gluons, are bosons with no charge or rest mass and behave like the photons.
At present, the Higgs mechanism is able to account, in principle, for the masses of all the elementary particles of the Standard Model. The predictions of the model regarding these particles and their properties have been validated experimentally.24
.
Epilogue
We have presented a brief survey of the gradual elucidation of the concept of mass.
We learned a few things about the physical world as we chased the concept of mass. And we know more about mass and matter than we did at the start.
Let’s summarize the knowledge that we have gleaned about mass:
The mass m of an object is a physical quantity which measures its inertial-gravitational effect.
b- The mass depends on the frame of reference; it increases with velocity: m = γ m0
c- The mass can be converted into energy and vice versa; E = m.c2
d- The rest mass/energy E0 = m0.c2 is equal to the total internal energy of the body.
e-Taking the body as a system of interacting elementary particles i.e. electrons and quarks, the internal energy is calculated as the algebraic sum of all the kinetic and potential energies of these particles in addition to their rest mass/energy.
f- Quantum particles are bundles of energy which can be annihilated or created in conformity with the conservation laws.
g- The mass of elementary matter particles i.e leptons and quarks is not a fundamental intrinsic property of the particle but a consequence of their interaction with the Higgs quantum field.
We learned also that concepts in the physical sciences are a shorthand used to describe a natural phenomenon. However, concepts evolve and acquire gradually a more refined meaning as scientific knowledge increases. Their content changes, becoming more abstract and more mathematical in accordance to the expansion of our scientific knowledge. Moreover, these concepts become at some stage intertwined: for example the concept of mass with that of energy, energy with time, time with entropy, field and wave with particle and so on.
(first published, may 25, 2021; revised and extended, December 2023)
Images
a- Feynman diagram of gluon radiation:
The massive quark – antiquark pair is generated from the high kinetic energy electron-positron pair colliding in the accelerator. In the process the antiquark radiates a gluon g, represented by the green helix.
https://en.wikipedia.org/wiki/Feynman_diagram#
b- The standard model of particle physics:
The number of elementary particles is actually 61 (13 bosons and 48 fermions) if we include the anti-particles and all the colors and flavors of gluons and quarks.
https://en.wikipedia.org/wiki/Standard_Model
Notes and References
1- “Higgs boson”
https://en.wikipedia.org/wiki/Higgs_boson
2- “Standard Model”
https://en.wikipedia.org/wiki/Standard_Model
3- Dirac, P. A. M. (1928). “The Quantum Theory of the Electron”. Proceedings of the Royal Society of London A. 117 (778): 610–24.
Dirac integrated the theory of relativity in the quantum mechanical wave-field equation, thus rendering the electron theory Lorentz invariant. In doing so he obtained two valid solutions instead of one. The second solution was later interpreted as predicting the existence of the positron (e+) the antiparticle of the electron.
4- Isaac Newton (1687). The Mathematical Principles of Natural Philosophy, Book I: Definitions. Translated by Andrew Motte, (1846), MacMillan, On Line Library.
5- Nothing is lost, nothing is created. Everything is transformed “
Note that this statement is strictly true even today if we apply it to the the mass-energy of the isolated system, considering that all forms of energy represents masses and vice-versa.
6- “2019 redefinition of the SI base units”
https://en.wikipedia.org/wiki/2019_redefinition_of_the_SI_base_units
7- Isaac Newton (1687). Principia, Book I : Laws of Motion.
Law II: “The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.”
8- Issac Newton (1687). Principia, Book III : Force of gravity..
Proposition VII. Theorem VII.
“that there is a power of gravity tending to all bodies, proportional to the several quantities of matter which they contain.”
Corollary 2:
“The force of gravity towards the several equal particles of any body is reciprocally as the square of the distance of places from the particles”
9- Isaac Newton (1686), The Mathematical Principles .
“Moreover, that the divided but contiguous particles of bodies may be separated from one another, is matter of observation; and, in the particles that remain undivided, our minds are able to distinguish yet lesser parts, as is mathematically demonstrated. But whether the parts so distinguished, and not yet divided, may by the powers of Nature, be actually divided and separated from one another, we cannot certainly determine.
Yet, had we the proof of but one experiment that any undivided particle, in breaking a hard and solid body, suffered a division, we might by virtue of this rule conclude that the undivided as well as the divided particles may be divided and actually separated to infinity.”
10- The Lorentz factor is given by :
γ = (1 – v2/c2) -1/2 , where c is the speed of light in vacuum.
Relativistic effects are perceptible at very high relative velocities
for v= 30,000km/s (one tenth of the speed of light), γ = 1.005.
11- Albert Einstein, (1905). “Does the Inertia of a body depend on its energy content?“. Annalen der Physik. 18, 639-641.
https://cdn2.hubspot.net/hubfs/232514/Einstein%20E=mc2%20(pp172-174).pdf
The fundamental law of relativistic dynamics states the following:
E2 – p2 c2 = m02 c4
Two limiting cases:
for p = 0 (or v = 0) we have : E = m0.c2 or equation [5]
For the photon case, m0 = 0, we have E = pc = hc/ λ = hν
12- There are also conservation laws which are partially valid relating to certain properties of elementary sub-nuclear particles. They are not universal and hold under certain conditions and for certain processes. For example “strangeness” , one of the quark’s flavor is conserved in strong interactions but not in weak interactions.
13- a- see for example, Pike, O, J. et al. (2014). ‘A photon–photon collider in a vacuum hohlraum’. Nature: Photonics, 18 May.
b- Wikipedia: “Electron – positron annihilation”.
https://en.wikipedia.org/wiki/Electron%E2%80%93positron_annihilation
14- It was also discovered that atoms were mostly empty space (apart from the force fields holding them together), with most of their mass, consisting of protons and neutrons (~ 99.9%), concentrated in a central nucleus and occupying a vanishing small fraction of the atomic volume (~10-14).
15- To know more about quarks: https://en.wikipedia.org/wiki/Quark
For a list of particles: https://en.wikipedia.org/wiki/Particle_physics#Bosons
16-For the Stern-Gerlach experiment:
https://en.wikipedia.org/wiki/Stern%E2%80%93Gerlach_experiment#History
17- C. Davisson, L. H. Germer: Diffraction of Electrons by A Crystal of Nickel, Physical Review 30/6, 705–40 (1927).
The first direct experimental confirmation of the de Broglie hypothesis by Davisson and Germer. They bombarded the surface of a Nickel crystal with low energy electrons (E=54Kev). The electrons, back scattered off the crystal, formed concentric rings with a wide bright center, akin to Newton’s rings obtained with electromagnetic waves.
Electrons behaved like waves. The measured wavelength of 1.65 A0 compared well with the theoretical value (1.67 A0) calculated from De Broglie’s formula.
18- Tonomura A., Endo J., Matsuda T., Kawasaki T., and Ezawa H. “Demonstration of single electron build-up of an interference pattern”, Am. J. Phys. 57: 117 (1989)
19- P. A. M. Dirac (1928). “The Quantum Theory of the Electron”.
Proc. R. Soc. Lond. A 1928 117.
20- For background and details, see my blog : “ The Quantum interface with reality”
21- The standard model of particle physics:
The number of elementary particles is actually 61 (13 bosons and 48 fermions) if we include the anti-particles and all the varieties of gluons, leptons and quarks.
https://en.wikipedia.org/wiki/Standard_Model
22- The masses are quoted in units of energy: 1 GeV/c2 = 1.78266192×10−27 kg. In general, the masses of all hadrons are of the order of 1 GeV/c2, which makes the GeV/c2 a convenient unit of mass for particle physics:
The charges are quoted as a fraction of the “elementary charge”. Fractional charges are in fact theoretical and have not been detected experimentally.
23- “Higgs Field” , Wikipedia
https://simple.wikipedia.org/wiki/Higgs_field
And references therein.
24- A number of questions marks remain, however concerning the Higgs discovery.
There is only one source of information the CERN. No other research entity has the capacity to produce the collision energies necessary for the detection of the 125 gigawatt Higgs boson.There is no way to verify the claims with an independent source!
A new CEPC (Circular Electron Positron Collider) is being built by China. It is projected to come on line in 2030. The CEPC will be able to generate a much larger number of Higgs events allowing a more detailed analysis of the particle.
https://en.wikipedia.org/wiki/Circular_Electron_Positron_Collider
The God particle and other mysteries 