Is mass an emergent property?

[C C]

[...] Understood or not .. Higgs doesn't help with the General Relativity equivalence of mass and energy.

The latter arguably pertains to the mass and binding energy of atoms or nuclei, whereas Higgs purely gives mass to elementary particles. One rebellious paper (at very bottom), however, does seem to revert back to focusing on individual particles rather than the adhesive agencies of the nucleus, for the equivalence (lamenting the introduction of the Higgs field).

How the Higgs Field (Actually) Gives Mass to Elementary Particles
https://www.quantamagazine.org/how-the-h...-20240903/

EXCERPTS: A common approach has been to tell a tall tale. [...] portraying the Higgs field as akin to molasses, a thicket, a crowd of people or an expanse of snow. However, all such stories conflict with what we physicists teach in the very first weeks of first-year university courses. [...] In truth, the Higgs field has nothing to do with motion or slowing. Instead, its story is all about vibration.

[...] A stationary electron, much like the vibration of a guitar string, is a standing wave that vibrates with a preferred frequency, known as its resonant frequency. [...] Most of the universe’s fields have resonant frequencies. In a sense, the cosmos loosely resembles a musical instrument; both have characteristic frequencies at which they most readily vibrate.

[...] While the Higgs tall tales suggest that mass arises from the slowing of elementary particles by a molasses-like substance, the truth is that a stronger Higgs field makes the elementary particles vibrate at higher frequencies, thus raising their masses.
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Binding energy
https://www.geeksforgeeks.org/physics/binding-energy/

EXCERPTS: Binding Energy is defined as the energy required to hold together the constituents of a system, such as the particles within an atomic nucleus or the electrons surrounding an atomic nucleus. Understanding binding energy is crucial for comprehending the stability, structure, and behaviour of atoms, molecules, and nuclei.

Binding energy specifically refers to the amount of energy needed to disassemble a nucleus into its individual protons and neutrons. The binding energy of nuclei is a positive value because every nucleus needs net energy to isolate them into neutrons and protons. Binding energy is applicable to atoms and ions bound together in crystals.

The binding energy of a nucleus arises from the interactions between many constituent particles. [...] Another formula that can be used to calculate the binding energy is: E = mc2
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Nuclear binding energy
https://en.wikipedia.org/wiki/Nuclear_binding_energy

EXCERPT: The mass of an atomic nucleus is less than the sum of the individual masses of the free constituent protons and neutrons. The difference in mass can be calculated by the Einstein equation, E = mc2, where E is the nuclear binding energy, c is the speed of light, and m is the difference in mass. This "missing mass" is known as the mass defect, and represents the energy that was released when the nucleus was formed.

The term "nuclear binding energy" may also refer to the energy balance in processes in which the nucleus splits into fragments composed of more than one nucleon. If new binding energy is available when light nuclei fuse (nuclear fusion), or when heavy nuclei split (nuclear fission), either process can result in release of this binding energy. This energy may be made available as nuclear energy and can be used to produce electricity, as in nuclear power, or in a nuclear weapon. When a large nucleus splits into pieces, excess energy is emitted as gamma rays and the kinetic energy of various ejected particles (nuclear fission products).
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Mass-Energy Equivalence Versus Higgs Mechanism
https://sciencepublishinggroup.com/artic...8070401.11

ABSTRACT: In Einstein Relativity mass of a given particle is related to the amount of the energy that is incorporated in the particle. Relation between mass m of the particle and energy E of the particle is expressed in famous formula E=mc2. Higgs mechanism open in physics new view on mass of the elementary particles, namely, that a given field which has appeared after Big Bang has given mass to the elementary particles. From the view of mass-energy equivalence, Higgs mechanism view on mass has several drawbacks. Furthermore Higgs boson is an artificially man made flux of energy with extremely small lifetime and does represent a direct prove for the existence of Higgs field.

[confused2]

Many thanks CC.

With a lot of help from Pi AI I've put together (hopefully) some insight into the Standard model which is (I think) pretty much where we are now .. also roughly where we were in the 1970s. .. we get to mass at the end ..
[Various people on the 'net have tried to teach me most of the maths .. and failed dismally .. so I see and I don't see]
Part of the point of doing this is to illustrate that photons (for example) look like they've escaped from a mathematical zoo .. if not a mathematical Island of Dr. Moreau.

The Standard Model of particle physics is built on quantum field theory (QFT), with its core math rooted in:
Gauge symmetry (based on the group SU(3) \times SU(2) \times U(1)) — dictating how particles interact via forces
^^^ just hang in with 'symmetry' .. how hard can that be? (Very)
Lagrangian formalism — a single equation (the Lagrangian density) encodes all particles and interactions
Relativistic quantum mechanics — combining special relativity and quantum theory via the Dirac and Klein-Gordon equations
Renormalization — a technique to handle infinities in calculations and make precise predictions
It’s a highly mathematical framework, tested to extraordinary precision — but it doesn’t include gravity, which is why physicists seek deeper theories.

Of which I figger the worst/best most beautiful part is..

Gauge theory .. (we should be able to sit in the bath and figger this bit out for ourselves .. it's so simple and OBVIOUS [not to me though]) a framework where the laws of physics stay the same under certain continuous transformations (called gauge symmetries).
For example, in electromagnetism, the physics doesn’t change if you shift the electric and magnetic potentials in a specific way — that’s a U(1) gauge symmetry. [Obviously! (fkn not)]
The key idea: require symmetry → force emerges.
When you demand that a theory is invariant under such local transformations, you MUST introduce force-carrying particles (like photons) to preserve the symmetry.[MUST! Jeez ]
In the Standard Model:
U(1) → electromagnetism (photon)[Heard of them]
SU(2) → weak force (W and Z bosons)
SU(3) → strong force (gluons)
So gauge symmetry isn’t just math — it’s the reason forces exist in the first place.[That's why I said it was obvious]

This traces back to Noether’s Theorem!
Emmy Noether proved that every continuous symmetry in a physical system corresponds to a conserved quantity. For example:
Time symmetry → energy conservation
Spatial symmetry → momentum conservation
Gauge symmetry takes this further: when you make those symmetries local (i.e., they can vary from point to point in spacetime), the requirement to preserve them forces the existence of force fields — and their associated particles.
Noether’s deep insight is the foundation: symmetry isn’t just beautiful, it builds the universe.

Finally .. MASS..

Photons (and gluons) are force carriers for unbroken gauge symmetries (U(1) and SU(3)), so they MUST be massless — otherwise the symmetry breaks.
W and Z bosons (weak force) get mass via the Higgs mechanism — the symmetry is spontaneously broken, allowing them to be heavy.
Electrons and other fermions get mass through Yukawa couplings to the Higgs field — but the strength of that coupling is arbitrary in the model, so their masses are set by experiment.
Edit..
So far as I can make out .. the problem is gravity and mass warping spacetime when there shouldn't even be any spacetime to warp.

[Syne]

The Higgs boson supposedly gets it's mass from interacting with its own field. That seems like a "it is because it is" explanation.

While the Higgs mechanism is mathematically consistent, it feels like "special pleading" because it requires a set of rules that apply only to the Higgs and to nothing else in the universe.

This is the biggest red flag. Because the Higgs interacts with itself and everything else, quantum mechanics says its mass should naturally rocket up to the Planck mass (quadrillions of times heavier than it is).

To keep the Higgs at its measured mass (125GeV), the math requires a near-miraculous cancellation of numbers to about 30 decimal places.
Physicists call this "Naturalness." Relying on such a specific, "just-so" number feels like the definition of special pleading—as if the universe is rigged to make the math work.
- Google AI

[confused2]

^^^ At the time the Higgs Boson was detected there were mutterings about 'predicted mass' .. does Google have any idea what those predictions were based on?

[Syne]

The Standard Model limited the range of the Higgs mass prior to discovery.

[confused2]

The Standard Model limited the range of the Higgs mass prior to discovery.

I liked the way it had an opinion .. it seems to have lost its edge..

To keep the Higgs at its measured mass (125GeV), the math requires a near-miraculous cancellation of numbers to about 30 decimal places.

AIs will be AIs.

[confused2]

Mass–energy equivalence .. what is it.. why.. and can we derive it ..

From https://poe.com/Assistant
My query:

"Please provide a short self-contained derivation of mass–energy equivalence using Einstein’s 1905 emission thought experiment — suitable for lecture notes."

I think we can do this if anyone wants to .. step by step .. line by line .. even word by word .. it isn't as bad as it looks.

Setup and assumptions

In inertial frame S a body is initially at rest and emits two light pulses of equal energy L/2 in opposite x-directions. Total emitted energy in S is L, and the body remains at rest in S after emission.
Light carries momentum p = E/c (magnitude).
Consider another inertial frame S' moving at speed v relative to S in the +x direction. Quantities in S' are primed. Use the relativistic Doppler energy transform for light:
E' = γ E (1 − β cos θ), where β = v/c, γ = 1/√(1 − β^2).
Apply conservation of energy and momentum in S'.
Photon energies and momenta in S'

In S, photons A and B have E_A = E_B = L/2 and propagate at θ = 0 (to +x) and θ = π (to −x), respectively.
Transform to S':
E'_A = γ (L/2) (1 − β), E'_B = γ (L/2) (1 + β).
Total radiated energy: E'_rad = E'_A + E'_B = γ L.
Photon momenta in S' (along x): p'_A = +E'_A/c, p'_B = −E'_B/c. Hence
p'_rad = p'_A + p'_B = γ (L/2c)[(1 − β) − (1 + β)] = −γ (L β / c).
Bookkeeping for the emitting body in S'

Let the body’s mass before emission be m and after emission m − Δm. In S' its initial velocity is −v; after emission it changes by a small δv (we assume L ≪ mc^2 so Δm and δv are small).
Conservation of energy in S':
γ m c^2 = γ_f (m − Δm) c^2 + E'_rad = γ_f (m − Δm) c^2 + γ L.
Conservation of momentum in S' (x-direction):
γ m (−v) = γ_f (m − Δm) v_f + p'_rad,
where v_f = −v + δv and γ_f ≈ γ + (dγ/dv)δv.
Linearize to first order in small quantities (Δm, δv). Expansions give (after straightforward algebra)
(i) γ^2 m v δv = Δm c^2 − L,
(ii) γ^2 m δv + v Δm = L v / c^2.

Eliminate δv: multiply (ii) by v and subtract (i) (or substitute (i) into (ii) after algebra), yielding
Δm (c^2 + v^2) = L (c^2 + v^2)/c^2.

Hence
Δm = L / c^2.

Conclusion
When a body (measured in its rest frame S) emits energy L, its mass decreases by Δm = L/c^2. Equivalently, adding energy ΔE to a body increases its inertial mass by ΔE/c^2. This result follows from Lorentz transformation of light energy (Doppler shift) plus conservation of energy and momentum, and is frame-independent.

Remark (one-line interpretation)
The argument shows that rest energy E0 associated with mass m satisfies E0 = m c^2, so energy and mass are equivalent with conversion factor c^2.

[Syne]

The mass-energy equivalence mirrors the equivalence principle for gravity and acceleration.