【NO.46】Phenomena Related to Electric Charge，and Remembering Nobel Laureate T. D. Lee

The concept of mass explained by the Higgs mechanism is able to include all concepts of mass, inertial mass, gravitational mass, mechanical mass, electromagnetic mass [1], kinematic mass, static mass, longitudinal mass, transverse mass [2], bare mass ...... ? Is it the Higgs field that leads to the mass-energy equation? How are coupling relationships established? Do the Couplings Transfer Energy-Momentum?

Although there are many different sub-concepts of mass, a distinguishing feature is that the mass of an object is not reflected, recognisable, or measurable when it is not interacting. We can think of all mass as a property of resistance that only presents itself when an object's state of motion changes^§. The so-called "rest mass" can only be regarded as a representation of the amount of static energy, and not vice versa.

Thus, it is clear that masses are essentially the same, differing only in size and form^*. This also implies that no matter how many differences there are in the occasions of interaction, as long as the required dimension is the same, they are the same mass. In this way, the Equivalence Principle in GR need not be regarded as a specific condition.

However, mass is not constant, and the magnitude of an object's mass in SR changes according to the Lorentz transformation. This predicts that the mass of an object is related to the increase or decrease in the energy of the object and is bounded by the speed of light.

Higgs physics suggests [3] that the mass of bosons is given by the Higgs mechanism [4]; that the mass of fermions is also given by the Higgs field [10], although this is still an open question [5]; and that Higgs particles themselves give their own mass [3], although this is not a clear-cut conclusion either [6].The Higgs field is a scalar field that pervades space, and is the same as the other elementary particle fields, electron fields, quark fields, etc., co-existing in the vacuum^**. They all appear to have the same status, except for the Higgs mechanism.

However, the current Higgs mechanism has some obvious explanation missing.

1) Why does the Higgs field selectively couple to bosons? I.e., how does the Higgs field recognise the bosons W^±, Z and γ, g, all of which have energy and perform the same function, and to which the Higgs field selectively assigns mass, or not.

2) The magnitude of the coupling coefficient of the Higgs field determines the mass size of the fermions [10]. Then, the mass hierarchy of the three generations of fermions is determined by the Higgs field^¶.Why should the particles all have different couplings coefficients g_j to the Higgs field? and where do these values come from[7][8]? Before there is mass, fermions have exactly the same quantum number and they are indistinguishable [9]^†. How does the Higgs field recognise these particles? The obvious requirement is that they must have additional parameters, or other physical quantities that do not present . At the same time, The action of the Higgs field on the positive and negative particles (e+,e-; q+,q-; ) is identical. And how does it ignore this difference?

3) If the Higgs field is not coupled to fermions, can fermions really travel at the speed of light like photons without stopping? According to the mass-energy equation E=mc², are all particles energy before there is mass（or none）? So the coupling of the Higgs field is to energy, do they have to exchange energy between them? What is the energy transfer relation here, E=mc²? If m=0 now, is E fully converted to the raw energy of the particle?

4) If the significance of the existence of inertial mass for fermions, W^± can be explained, what is the significance of the Higgs Boson possessing inertial mass itself?Does it really implies the existence of a 'fifth force', mediated by the exchange of Higgs bosons [8]?

5) The shape of the Higgs potential V(Ø) expresses the relationship between the potential and the field strength , V(Ø) ~ Ø [10] ^‡ . Ø is hidden in the vacuum ††. How do different Ø present themselves at a given spatial location? Do they interact with other particles in one way?

6) How does the mathematical explanation of the Higgs mechanism map reasonably to physical reality? Must the Higgs potential be an external field? ^‡‡ Wouldn't it be better if it were the field of the particle itself? [12] Is the Higgs mechanism for mass completely excludes the relation between mass and spin ?[15]

7) Not all mass is caused by Higgs [10], and potential energy (binding energy) gives mass as well. In this case, is mass still consistent? Doesn't mass become a variable?

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Supplement: Can mass have multiple origins? （2024.9.26）

“The Higgs does seem to be the source of the mass of elementary particles, e.g., the electron; but it is responsible for < 2% of the mass of more complex things, like the proton. The mass of the vast bulk of visible material in the Universe has a different source.”[1] “the Higgs boson is almost irrelevant to the origin of the proton mass. ”[2]

Mass is an important particle property. If mass has surprisingly multiple origins, how do we explain their relationship? Do they produce the same results by similar mechanisms, or completely different ones? Do they all rely on external fields? Is the mass-energy equation, m=E/c^2, a clue to determining the uniform origin of mass? Can a mechanism that does not provide energy provide mass?

Does mass obey the superposition principle? Is it a scalar superposition or a vector superposition? Is it a linear or nonlinear superposition? Let us consider a process in which u, d quarks combine to form a proton p. In the early stages of the evolution of the universe, nothing else in particular existed. u and d automatically combine to form p in such a scenario, like a pair of lovers meeting to form a family. The family is a more stable structure, and the ‘quality’ of life of the family (In Chinese, quality and mass are one word, 质量) has increased. The increased ‘quality’ does not come from outside, but from the union itself.

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§ Mass is usually thought of as resisting a change in the "state" of matter, but what is the "state"? Why does it resist change? Why can it resist change? My personal reference answer is here [12]: Mass originates from damping the superluminal intent of a spinning light ring and as a result is the fundamental property that distinguishes fermions from bosons.

* Mass is somewhat similar to energy in that it exists in various forms, but the two are fundamentally different.

** Physics doesn't know what parameters to use to describe these fields and doesn't seem to be interested.

‡ “One of the most important open questions in Higgs physics is whether the potential written in that equation is the one chosen by nature. ”[8]

‡‡ "Central to all of Higgs physics is the Higgs potential."[8] C. N. Yang[13]: "Symmetry breaking with the introduction of a field will not be the last theory, although for the time being it is a good theory, like Fermi's theory of beta decay." Expresses his scepticism about the Higgs mechanism.

† With no Higgs field, the electron and electron neutrino would be identical particles, and the W and Z particles, and in fact all standard model fermions, would be massless. [9]

†† The vacuum seems to be the all-powerful vacuum, and physics assigns many functions to the vacuum [14].

¶ The hierarchies among fermion masses and mixing angles, however, remain unexplained.[11]

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[1] Thomson, J. J. (1881). XXXIII. On the electric and magnetic effects produced by the motion of electrified bodies. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 11(68), 229-249.

[2] Abraham, M. (1902). Principles of the Dynamics of the Electron (Translated by D. H. Delphenich). Physikalische Zeitschrift 4(1b), 57-62.

[3] Ellis, J. (2013). Higgs physics. arXiv preprint arXiv:1312.5672.

This is question I asked myself a long time ago, and In fact, with the use of complex numbers, based on most beautiful equation of mathematics, in 1991, I found a way to deduce all fundamental equations of physics, based in a concept I called a Basic Systemic Unit, based on Euler's relation, that has the most remarkable property to remain the same with those operation that represent change, I mean derivation and integration. One of most important aspect of this treatment, is that due to that metric based on the BSU, in which both totalities of time and space are differentiated by that symbol that Descartes called imaginary, I mean

which in fact is a symbol to differentiate two different orders of reality or totalities, in this case Time and Space. In that metric of the BSU, the part affected by the symbol "i" has to do with Space and is affected by the Sine that has two solutions

Sine(Theta) = Sine(Theta)

Sine(-Theta) = -Sine(Theta)

while that part not affected by "i", or else Time, is affected by the Cosine function that has just one solution

Cos(Theta) = Cos(Theta)

Cos(-Theta) = Cos(Theta)

This fact is the reason of that great incompatibility between GR and QM, as in GR based on Tensor Analysis, Time is reduced to a Space dimension, so it is symmetric just as Space, and can take both signs, so it is possible to conceive travel to the past or to the future, just as space, in which if we have a point of reference, it is possible to travel in any direction.

The BSU is a system in the complex plane, not a trajectory, whose state must be determined in such a way that we must have relations between both totalities, of Time and Space, or the contrary we will have the Uncertainty Principle.

For those interested in how this great incompatibility between GR and QM that has produced the so called the Crisis of Physics, in my paper

‘How big is the proton?"[1] We can similarly ask, “How big is the electron?” “How big is the photon?” CODATA gives the answer [2], proton rms charge radius r_p=8.41 x10^-16m; classical electron radius, r_e=2.81x10^-15m [6]. However, over a century after its discovery, the proton still keeps physicists busy understanding its basic properties, its radius, mass, stability and the origin of its spin [1][4][7]. Physics still believes that there is a ‘proton-radius puzzle’ [3][4], and does not consider that the size of a photon is related to its wavelength.

Geometrically the radius of a circle is clearly defined, and if an elementary particle is regarded as a energy packet, which is unquestionably the case, whether or not it can be described by a wavefunction, can its energy have a clear boundary like a geometrical shape? Obviously the classical electron radius is not a clear boundary conceptually in the field, because its electric field energy is always extending. When physics uses the term ‘charge radius’, what does it mean when mapped to geometry? If there is really a spherical charge [8][9], how is it maintained and formed^*?

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Notes:

^*“Now if we have a sphere of charge, the electrical forces are all repulsive and an electron would tend to fly apart. Because the system has unbalanced forces, we can get all kinds of errors in the laws relating energy and momentum.” [Feynman Lecture C28]

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According to the mass-energy equation [1], E = mc², the rest energy of an electron is contained in its mass. When the positive and negative electrons annihilate [2], e+ e- = γγ, their rest energy is converted to photon energy and the total energy is conserved. The electron also carries an electric charge and has electromagnetic energy. When an annihilation reaction occurs, the mass disappears and so does the charge, where does the energy of the charge go? If all energy is contained in the mass-energy equation, does this mean that charge and mass are closely related? Therefore, all mass is electromagnetic mass [3][4][5]. If electromagnetic mass is only a part of mass, then what kind of mass is produced by the Higgs mechanism?

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2025.1.31

One can continue to ask, if the charge contains energy, what form of energy is it? If it is the same as the electric field energy, then when all the energy of the charge is contained in the electric field outside of it, what should the ‘charge’ itself be? And if not, which implies that the charge contains two types of energy, how is the electric field energy bound to the charge energy?

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Reference's References

In electromagnetism the Coulomb force F=q1q2/r^2, the Lorentz force F=q(E+νxB), are computed treating spacetime as flat, and we are measuring what is actually a macroscopic phenomenon, not at the microscopic level. But this does not mean that the principle fails completely at the microscopic level.

Consider particles with mass such as electrons, which should have both electromagnetic and gravitational forces (we cannot rule out the validity of GR at tiny masses). Looking at an electron from the outside, it expresses electric field, magnetic moment, and mass. The Stern-Gerlach experiment fully expressed these covariates [1]. The electron involves only 4 factors, time t, space x, electric field E, and magnetic field H. We express the electron in the set e={Δt, Δx, ΔE, ΔH}, where the elements are all variables. This then implies that the external electromagnetic force, gravitational force, and mass, should all be able to be described by these components, since we can only act on the electron through these components.

Mass then could be exclusively electromagnetic mass [2][3], me={Δt, Δx, ΔE, ΔH}, regardless of the mechanism by which it is produced [4]. The electric field force can likewise be expressed only in terms of Fe=α{Δt, Δx, ΔE, ΔH}, and the gravitational force in terms of the set Fg=G{Δt, Δx}. Obviously, this is their simplest expression.

We need not consider what the electron is. It can be inferred from the set that its electric and gravitational forces overlap, since they share the same part of spacetime expression. This can also be seen by comparing Coulomb's law with Newton's law of gravity. As for neutral massive particles, they can be regarded as cancelling out the electromagnetic field [5] leaving only the Fg = G{Δt, Δx} part. In this way, the gravitational force is naturally unified to the electromagnetic force, and they are coupled together by the spacetime {Δt, Δx}, and automatically incorporated into the gauge field theory; the 'graviton' can be regarded as the spacetime product of the 'photon'. As for gravitational waves, they can be regarded as a part of space-time detached from accelerated motion, like electromagnetic waves radiated by accelerated electrons. This is exactly what Poincaré envisaged [6].

"After Einstein developed his theory of general relativity, in which a dynamical role was given to geometry, Herman Weyl conjectured that perhaps the scale of length would also be dynamical. He imagined a theory in which the scale of length, indeed the scale of all dimensional quantities, would vary from point to point in space and in time. His motivation was to unify gravity and electromagnetism, to find a geometrical origin for electrodynamics. [7, 8]" Wouldn't Weyl have been right if, instead of searching for a geometrical origin of electromagnetism, he had searched for an electromagnetic origin of gravity? Wouldn't electromagnetism be equally geometrical if one considered that the electromagnetic force Fe = α{Δt, Δx, E, H} is essentially the same as that resulting from variations of {Δt, Δx} therein?

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References

Physics states that ‘symmetry dictates interaction’ [1][2]; Invariance, symmetry, and conservation are usually approximately the same concepts [3], and the objects of conservation are usually discrete. The basic conservation of energy corresponds to the energy quantum e = hν, the basic conservation of momentum to the momentum quantum P =h/λ, the conservation of charge to the integer charge e, the conservation of the spin number to ℏ/2, the conservation of the particle number to the lepton number, the baryon number [4], and so on.

1) Does Noether's theorem impose a limit on the continuity of energy and momentum [5]?

2) If we regard these discretisations as representing different energy forms, do the symmetries likewise convert when the energy forms convert?

3) Assuming that an abstract energy remains constant in all cases, should there likewise be any symmetries that remain constant all the time to support symmetry evolution?

4) Should these different discretisations have a common origin? If so, how are the relationships between them constructed? Or through what channels are they related?

5) Particle number conservation are all additive and empirical postulates [4], should there be theoretical support behind them?

6) Symmetries are classified into external and internal symmetries [6]; external symmetries are concerned with spacetime coordinate transformations and internal symmetries are concerned with gauge invariance. If they are united, how are inner space symmetries related to external space symmetries?

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References：

[1] Yang, C. N. (1996). Symmetry and physics. Proceedings of the American Philosophical Society, 140(3), 267-288.

[2] Gross, D. J. (1992). Gauge theory-past, present, and future? Chinese Journal of Physics, 30(7), 955-972.

The possible combinations of "limits" and "boundaries" in nature are [1]: 1) "limited and bounded'; 2) “limited and unbounded”; 3) "unlimited and bounded”; 4) “unlimited and unbounded”. Here the object of "limit”can be geometric size, matter, energy, etc., and the object of “boundary”can be regarded as space-time boundary. We need to pay attention to two points here, first, what is the 'space-time boundary'; second, the static 'boundary' and dynamic 'boundary' of the essential difference. For the first point, usually the boundary of space can only be constituted by geometric points, lines and surfaces [2], which ensures that there is no indeterminate space on both sides of the boundary. If set time is the boundary in another dimension, the endpoints of such a boundary are zero-dimensional if they exist at all. For the second point, the Koch snowflake, a fractal curve, is often used in mathematics to express 'infinite perimeter, finite area', which presupposes that the 'boundary' is dynamically progressing infinitely. But once it is stationary at a fixed N(≠∞) [3], it becomes 'limited and bounded’.

‘Symmetry dictates interaction’is a motto of modern physics [4]. Symmetry is in some sense invariance. Coordinate symmetry reflects energy conservation, momentum conservation [5]; charge conservation reflects gauge invariance [6] ....... If time Displacement invariance, and space Displacement invariance, are globally applicable to any individual, do they thereby determine that the entire universe must be unconditionally time Displacement and space Displacement symmetric? Does this dictate that the entire universe must be unbounded in time and space? If there are boundaries to the universe, how can symmetry be maintained at such special places as boundaries? If the universe is anything like "limited and unbounded" [7], how does it support the finiteness of space if conservation of momentum applies globally, when the universe is viewed as a whole object? If conservation of energy is globally applicable, how does it support the finiteness of time? Either way we have to deal with some kind of 'boundary' violation. And if time is cyclic, then the universe must form an 'Ouroboros' [8]. Therefore, if the laws of nature are required to apply globally, it is impossible to face any 'boundary'.

Suppose a finite set, whatever its nature, can we always assign it a centre, as with a tangible entity, we can define its centroid, centre of mass, center of gravity, and so on. Can a finite universe then avoid the existence of a centre? If there is a centre, the universe must have boundaries. At this point, are the time and space boundaries symmetrical? And if we assume that the universe is, infinite in space, infinite in time, and infinite in energy, what would be the catastrophe for our cosmology, or would it be a convenient and useful gateway for research?

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Notes

* It has been said that the universe is limited and unbounded similar to the surface of the Earth, where clearly no boundaries are defined.

** Multiverse theories are receiving more and more attention, and it is more appropriate to think of them as subuniverses within an entire universe.

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References