Mass mystery



Simple.   There are only 3 kinds of mass:

  1. “Newtonian” mass

  2. “relativistic” mass

  3. “quantum” mass


The origin of mass is one of the most intriguing mysteries of nature. What is it that makes one particle light and another heavy?

Some particles, such as the W boson (which carries the weak force) have so much mass they barely move, while others, like the photon, are entirely massless and zip around at the speed of light. The mass of fundamental particles – those that carry forces and build nuclei and atoms – is often explained by the way they move through the Higgs field that is thought to pervade all the space of the Universe. To some particles, such as the top quark, the Higgs field is like molasses: they get bogged down and become very heavy. To others, like the photon, the field is empty space: they fly through unimpeded and gain no weight at all.


Why Particles Have Mass ?   




Unfortunately, recently it has become clear that neither the Higgs field and its God particle, nor the Higgs mechanism is able to explain the existence of very small masses of neutrinos. The largest experiment ever to probe these mysterious particles could point the way to New Physics:



 ” The concept of mass, with the concept of gravitational mass identified with the concept of inertial mass, is quantified and defined by gravitational phenomenology. Therefore, on purely logical grounds, the concept of mass so defined cannot then be used in the theories of physics as an explanation of the very phenomenology used to define and quantify it.” — W.F. Heinrich,


In quantum physics we have de Broglie’s wave–particle duality. So, let’s change our perspective, and instead of conceptualising matter as made of particles, let’s look at it as being composed of waves. Do waves have mass?  Well, they do have energy.

The description of physical reality in terms of fields?

Due to our peculiar human sensory perception, we never see any waves of energy. Not true? We see water waves? We only see waves on water caused by waves of energy.

Due to our peculiar human sensory perception, we see waves of energy as solid  “matter”, but we never see solid matter as waves of energy. That is the reason why it is only natural for us to use the perceptual “particle” metaphor of de Broglie’s wave–particle duality. And here, I feel deeply convinced, we owe huge credit to Albert Einstein for his another ingenious suggestion expressed in his short paper, MAXWELL’S INFLUENCE ON THE EVOLUTION OF THE IDEA OF PHYSICAL REALITY, published on the 100th anniversary of Maxwell’s birth in: James Clerk Maxwell: A Commemoration Volume, Cambridge University Press 1931, that I am certain it is only in order to quote here in its entirety.

This is Albert Einstein at his best, the Philosopher-Scientist: 



The belief in an external world independent of the perceiving subject is the basis of all natural science. Since, however, sense perception only gives information of this external world or of “physical reality” indirectly, we can only grasp the latter by speculative means. It follows from this that our notions of physical reality can never be final. We must always be ready to change these notions — that is to say, the axiomatic basis of physics — in order to do justice to perceived facts in the most perfect way logically. Actually a glance at the development of physics shows that it has undergone far — reaching changes in the course of time.

The greatest change in the axiomatic basis of physics — in other words, of our conception of the structure of reality — since Newton laid the foundation of theoretical physics was brought about by Faraday’s and Maxwell’s work on electromagnetic phenomena. We will try in what follows to make this clearer, keeping both earlier and later developments in sight. According to Newton’s system, physical reality is characterized by the concepts of space, time, material point, and force (reciprocal action of material points). Physical events, in Newton’s view, are to be regarded as the motions, governed by fixed laws, of material points in space. The material point is our only mode of representing reality when dealing with changes taking place in it, the solitary representative of the real, in so far as the real is capable of change. Perceptible bodies are obviously responsible for the concept of the material point; people conceived it as an analogue of mobile bodies, stripping these of the characteristics of extension, form, orientation in space, and all “inward” qualities, leaving only inertia and translation and adding the concept of force. The material bodies, which had led psychologically to our formation of the concept of the “material point,” had now themselves to be regarded as systems of material points. It should be noted that this theoretical scheme is in essence an atomistic and mechanistic one. All happenings were to be interpreted purely mechanically — that is to say, simply as motions of material points according to Newton’s law of motion.

The most unsatisfactory side of this system (apart from the difficulties involved in the concept of “absolute space” which have been raised once more quite recently) lay in its description of light, which Newton also conceived, in accordance with his system, as composed of material points. Even at that time the question, What in that case becomes of the material points of which light is composed, when the light is absorbed?, was already a burning one. Moreover, it is unsatisfactory in any case to introduce into the discussion material points of quite a different sort, which had to be postulated for the purpose of representing ponderable matter and light respectively. Later on, electrical corpuscles were added to these, making a third kind,’ again with completely different characteristics. It was, further, a fundamental weakness that the forces of reciprocal action, by which events are determined, had to be assumed hypothetically in a perfectly arbitrary way. Yet this conception of the real accomplished much: how came it that people felt themselves’ impelled to forsake it?

In order to put his system into mathematical form at all, Newton had to devise the concept of differential quotients and propound the laws of motion in the form of total differential equations — perhaps the greatest advance in thought that a single individual was ever privileged to make. Partial differential equations were not necessary for this purpose, nor did Newton make any systematic use of them; but they were necessary for the formulation of the mechanics of deformable bodies; this is connected with the fact that in these problems the question of how bodies are supposed to be constructed out of material points was of no importance to begin with.

Thus the partial differential equation entered theoretical physics as a handmaid, but has gradually become mistress. This began in the nineteenth century when the wave theory of light established itself under the pressure of observed fact. Light in empty space was explained as a matter of vibrations of the Aether, and it seemed idle at that stage, of course, to look upon the latter as a conglomeration of material points. Here for the first time the partial differential equation appeared as the natural expression of the primary realities of physics. In a particular department of theoretical physics the continuous field thus appeared side by side with the material point as the representative of physical reality. This dualism remains even today, disturbing as it must be to every orderly mind.

If the idea of physical reality had ceased to be purely atomic, it still remained for the time being purely mechanistic; people still tried to explain all events as the motion of inert masses; indeed no other way of looking at things seemed conceivable. Then came the great change, which will be associated for all time with the names of Faraday, Maxwell, and Hertz. The lion’s share in this revolution fell to Maxwell. He showed that the whole of what was then known about light and electromagnetic phenomena was expressed in his well known double system of differential equations, in which the electric and the magnetic fields appear as the dependent variables. Maxwell did, indeed, try to explain, or justify, these equations by the intellectual construction of a mechanical model.

But he made use of several such constructions at the same time and took none of them really seriously, so that the equations alone appeared as the essential thing and the field strengths as the ultimate entities, not to be reduced to anything else. By the turn of the century the conception of the electromagnetic field as an ultimate entity had been generally accepted and serious thinkers had abandoned the belief in the justification, or the possibility, of a mechanical explanation of Maxwell’s equations. Before long they were, on the contrary, actually trying to explain material points and their inertia on field theory lines with the help of Maxwell’s theory, an attempt which did not, however, meet with complete success.

Neglecting the important individual results which Maxwell’s life work produced in important departments of physics, and concentrating on the changes wrought by him in our conception of the nature of physical reality, we may say this: before Maxwell people conceived of physical reality — in so far as it is supposed to represent events in nature — as material points, whose changes consist exclusively of motions, which are subject to total differential equations. After Maxwell they conceived physical reality as represented by continuous fields, not mechanically explicable, which are subject to partial differential equations. This change in the conception of reality is the most profound and fruitful one that has come to physics since Newton; but it has at the same time to be admitted that the program has by no means been completely carried out yet. The successful systems of physics which have been evolved since rather represent compromises between these two schemes, which for that very reason bear a provisional, logically incomplete character, although they may have achieved great advances in certain particulars.

The first of these that calls for mention is Lorentz’s theory of electrons, in which the field and the electrical corpuscles appear side by side as elements of equal value for the comprehension of reality. Next come the special and general theories of relativity which, though based entirely on ideas connected with the field theory, have so far been unable to avoid the independent introduction of material points and total differential equations.

The last and most successful creation of theoretical physics, namely quantum mechanics, differs fundamentally from both the schemes which we will for the sake of brevity call the Newtonian and the Maxwellian. For the quantities which figure in its laws make no claim to describe physical reality itself, but only the probabilities of the occurrence of a physical reality that we have in view. Dirac, to whom, in my opinion, we owe the most perfect exposition, logically, of this theory, rightly points out that it would probably be difficult, for example, to give a theoretical description of a photon such as would give enough information to enable one to decide whether it will pass a polarizer placed (obliquely) in its way or not.

I am still inclined to the view that physicists will not in the long run content themselves with that sort of indirect description of the real, even if the theory can eventually be adapted to the postulate of general relativity in a satisfactory manner. We shall then, I feel sure, have to return to the attempt to carry out the program which may be described properly as the Maxwellian — namely:

the description of physical reality in terms of fields,

which satisfy partial differential equations without singularities.

Albert Einstein,  1931


Figure 30_08_02a


 “ Before Maxwell, people conceived of physical reality — in so far as it is supposed to represent events in nature — as material points, whose changes consist exclusively of motions. After Maxwell they conceived physical reality as represented by continuous fields, not mechanically explicable. The conception of the electromagnetic field as an ultimate entity had been generally accepted, and serious thinkers had abandoned the belief in the possibility of a mechanical explanation of Maxwell’s equations. Before long they were, on the contrary, actually trying to explain material points and their inertia in terms of field theory. This change in the conception of reality is the most profound and fruitful one that has come to physics since Newton; but it has at the same time to be admitted that the program has by no means been completely carried out yet. The successful systems of physics which have been evolved since rather represent compromises between these two schemes, which for that very reason bear a provisional, logically incomplete character. 

In the light of the above wisdom, let’s ask: What if mass of elementary particle, or of a body of matter, were to be understood, in the most general sense, as its total combined energy divided by the square of the speed of light. There would be, essentially, not much else to “mass” other than the total combined energy, but energy in a form of waves, not particles.


But since we want to change our perspective, and instead of conceptualizing matter as made of particles, look at it as being composed of waves, and waves have no mass, then we need to answer the question: How such “mass” seems to be localised in this picture? If everything is made of waves, and waves neither have mass, nor are they local, then in such a picture, what would be this “mass” that seems to be localised?

Perhaps, such “mass” could be a result of particular interactions among all, or some of various waves spanning the Universe, and being, in the most general sense, something like a local interference pattern. That would also be helpful in explaining how such local interference pattern can exhibit inertia — inertia resulting from mass, in the most general sense, being like a “standing” local interference pattern on a standing wave.

That would bear close resemblance to the idea of the Higgs field, where the mass of an elementary particle is not its inherent property, but rather a result of its interaction with the Higgs field.

 ” The present systems of physics, which have been evolved since Maxwell, represent compromises between the two schemes of waves and particles, which for that very reason bear a provisional, logically incomplete character.”

In order to explain the existence of mass of elementary particles, suddenly we need a field! Not only do we need a field, but we need the Higgs field which existence, until recently, was neither needed, nor discovered. Indeed, Higgs field clearly seems to have a provisional and logically incomplete character, as opposed to my postulate.

The most important implication of this postulate would be that such “mass”, or more precisely its inertia, neither being an inherent property of matter, nor depending on some additional, specialized field that perfectly and homogeneously fills the entire Universe in addition to everything else in it, could be increased, decreased, completely nullified, or even made “negative”, as a result of physically influencing the “interference pattern” that constitute it.


The hypothesis that the Sun may carry a negative electric charge was proposed by Australian physicist, Prof. V.A.Bailey at first in 1960 for the explanation of the maximum energy found for a primary cosmic ray particle and other astronomical phenomena. According to the electrogravitic theory by B.V.Ivanov, it can be seen that stars, like the Sun, can have their mass generated by its electric charge:


 ” Until now, negative matter has not been found to exist in natural form. However, since E=mc², negative matter may be created in a laboratory using negative energies. Previous studies showed that effective negative inertia exists for neutrons and also for electrons in short transient time intervals. We present two possibilities to create stationary, charged negative effective masses that could be used to test self-propulsion effect. It is based on the assumption that Weber’s electrodynamics is correct predicting a negative mass regime for electrons inside a highly charged dielectric sphere. The other possibility is using asymmetric charge distributions that could be realized using electrets. With proper geometry and charge densities, negative mass regimes are derived, which could lead to negative energies many orders of magnitude larger than those obtained from the Casimir effect. Based on these concepts, a negative matter, and therefore antigravity, could be realized in a laboratory environment.” — Propellantless Propulsion with Negative Matter Generated by Electric Charges


 ” It followed from the special theory of relativity that mass and energy are both but different manifestations of the same thing, a somewhat unfamiliar conception for the average mind.” — Albert Einstein

 ” Even masses at rest have an energy inherent to them. You’ve learned about all types of energies, including mechanical energy, chemical energy, electrical energy, as well as kinetic energy. These are all energies inherent to moving or reacting objects, and these forms of energy can be used to do work, such as run an engine, power a light bulb, or grind grain into flour. But even plain, old, regular mass at rest has energy inherent to it: a tremendous amount of energy. This carries with it a tremendous implication: that gravitation, which works between any two masses in the Universe in Newton’s picture, should also work based off of energy, which is equivalent to mass.”  Ethan Siegel

Mass should be treated on the same footing as energy and momentum

What is the meaning of mass? This is an important question in the history of physics. Newton is probably the first one to give a scientific concept of mass. In his 1687 work “Mathematical Principles of Natural Philosophy”, he thought “mass” is “the quantity of matter”. He found that for any two objects, the ratio for their inertia and the ratio for their weight are the same. This implies that the inertia mass and the mass associated with weight are equal. Then, people could measure the mass of a body by determining its weight.

Furthermore, Newton proposed that the weight of an object is just a measure of the gravitational force for that object. This then implies that the inertia mass and the gravitational mass are the same thing.

Today, one can measure mass using several distinct phenomena. This makes some theorists to speculate that mass could have different meanings:

  • Inertial mass (which measures an object’s resistance to being accelerated by a force)
  • Active gravitational mass (which measures the gravitational force exerted by an object)
  • Passive gravitational mass (which measures the gravitational force exerted on an object in a known gravitational field)
  • Energy-mass (which measures the total amount of energy contained within a body)

In this work, we think there is only one “mass”; it is a measure of the energy of the particle. Such an interpretation is consistent with Einstein’s view that mass can be interpreted as “a reservoir of energy”. We show here that, in the classical limit, such an energy-related mass will automatically appear in the equation of motion as an inertial mass. Also, in Section 10 of this work, we showed that the gravitation law can be interpreted as energy-attracting-energy; it only gives an appearance of mass-attracting-mass. The perception of “gravitational mass” can be regarded as an illusion.

In Newtonian mechanics, the mass is regarded as an intrinsic property of an object. Why?

From human observation, it is very easy to see that any object is made up of “matter”. Such matter could be a piece of rock, a sheet of metal, or a piece of wood. Each of these matters has a certain weight. From a long time ago, people thought that such weight must come from the “mass” of the object. An object with more mass would have more weight. Thus, it is very natural for ancient people to think that the mass is an intrinsic property of an object.

In this work, we propose that a particle is an excitation wave of the vacuum, and, particle properties including energy, momentum and mass can all be treated on the same footing. This proposal is mainly based on the phenomenon of wave-particle duality, namely, a particle has both wave and corpuscular properties. We suggest that, like the energy and momentum, mass has a corresponding meaning in the wave view. We show that the equation of motion in classical mechanics is only an approximation under the condition that the “moving energy” of a particle is much smaller than its “resting energy”.

Based on this wave model, we think mass is not more intrinsic than energy and momentum. The main reasons are: 








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