Neither a field nor a matter: The case of energy

Dominique-Marie Cabaret; Emmanuel Perrier; Ghislain-Marie Grange; Thierry Grandou

REVIEW 5 major objections 4 minor 64 references

Neither a field nor a matter: The case of energy

T0 review · 5 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read This paper argues that energy is neither a field nor a substance nor primary matter, but the act of a formal property: the activity through which quantum fields actualise into measurable particles and stable bodies.

desk verdict A clear Thomistic reading of QFT energy, but the central inference rests on a convention-dependent zero-energy vacuum claim and on the authors' own prior ontology. read the letter →

arxiv 2412.17858 v1 pith:A35QE6D6 submitted 2024-12-20 physics.gen-ph

Dominique-Marie Cabaret , Thierry Grandou , Ghislain-Marie Grange , Emmanuel Perrier This is my paper · ORCID

classification physics.gen-ph PACS 03.65.-w01.70.+w

keywords energyquantumfieldsactandpotencyprimarymattermass-energyequivalencevacuumfluctuationsconservationofphilosophyphysics

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Energy is usually treated as a measurable quantity or a substance that can be stored and transferred, but this paper argues that such descriptions miss what energy is. The authors claim that energy is neither a field, nor a thing, nor primary matter, but an act: specifically, the act of a formal property, the activity through which a quantum field's built-in capacities to propagate and interact are brought into measurable actuality. This matters because it turns 'what is energy?' from an open puzzle into a precise philosophical and physical claim with consequences across scales: energy is conserved because it is communicable, it is always the energy of something, and it is a primary datum of nature on the same footing as matter and the elementary fields. If the argument works, the elementary building blocks of the universe are not fields alone but fields together with their interactions, actualised by energy.

What carries the argument

The load-bearing machinery is the potency-act distinction applied to quantised fields. The authors take the zero-energy vacuum fluctuations of quantum fields as evidence that a field can exist as pure potential reality, deprived of actuality, and they take energy to be that which actualises a field's formal property into a measurable excitation. The covariant dispersion relation $E^2 = m^2 c^4 + p^2 c^2$ then carries the macroscopic half of the argument: because mass is a relativistic invariant, it functions as a first act fixed in a substance's definition, while the momentum-dependent term is a variable second act, so energy is genuinely dual in a stable body.

What would settle it

Measure whether empty spacetime itself carries a nonzero energy density that cannot be renormalised away by a constant counterterm. The paper's account predicts that quantum vacuum fluctuations are purely potential and carry zero energy, so a physically effective vacuum-energy density intrinsic to spacetime, for example a cosmological constant term that cannot be traced to energy received in any particular field, would show that energy can exist outside the actualisation of a formal property and would falsify the central claim.

Watch

Extended reading notes

Core claim

The central claim is that energy is the act of a formal property: it stands to a quantum field's capacity to propagate, receive, and interact as act stands to potency. On this account the seventeen elementary quantum fields are the first material realities, each a compound of primary matter and formal properties; energy is what actualises those formal properties into measured particles, and through chains of acts into stable substances with mass. The paper therefore denies that there is any pure energy or any reservoir of energy outside fields, and it distinguishes energy from mass: mass is an invariant, substance-determining first act, while transferable energy is a second act subject to variation. In the conclusion this is condensed into the statement that energy is not a thing but a necessary component of things, not a property but an actuality of a property, and what pulls matter out of potentiality.

Load-bearing premise

The argument stands on the earlier conclusion that the seventeen elementary quantum fields are the first material realities, each made of an undetermined primary matter plus definite formal properties; if instead fields are themselves patterns of energy, or if the notion of primary matter does not apply to quantum field theory, the distinction between a field and the energy that actualises it loses its ground.

Editorial extensions

If this is right

There is no such thing as pure energy: every instance of energy is energy received in, or possessed by, some quantum field or substance.
Mass and energy are not identical despite $E=mc^2$; mass keeps an invariant, substance-defining role, and a tiny but essential part of elementary mass has a different origin in the standard model's scalar sector.
An elementary quantum field cannot be switched off by removing its energy; its zero-energy vacuum fluctuations remain real but purely potential, so fields are not made of energy.
Energy is conserved because it is communicable between fields, never created or destroyed; the universe contains a finite, conserved energy rather than an infinite reservoir.
The elementary building blocks of the material universe are quantum fields together with their interaction diagrams, and energy is the component that projects their potential interactions into spacetime actuality.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A natural extension is to read the paper's claim as a specific prediction about vacuum energy: if energy always inheres in a formal property, then any observed cosmic acceleration due to vacuum energy would have to be attributed to energy received in some field, not to energy of empty spacetime itself.
The act-potency scheme could be tested by asking whether every measurable energy transfer in the standard model can be traced to a corresponding interaction vertex; the account would be embarrassed by a process in which energy changes form without any field-to-field vertex.
The distinction between first and second act suggests a reinterpretation of binding energy in nuclei and hadrons: the roughly 99% of hadronic mass that comes from gluon energy would be first-act mass of the composite, not stored second-act energy, which is a testable way to phrase the mass budget of ordinary matter.
If the scalar field responsible for elementary masses turned out to be composite rather than elementary, the paper's reliance on a fixed list of seventeen elementary fields would need revision, because the list of formal properties to be actualised would no longer be primitive.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

What you should know: this is a philosophy-of-physics paper, not a physics result, and its central argument is load-bearing fragile at exactly one technical point. The authors argue that energy is neither a field nor matter but the act of a formal property, and they support this by claiming that quantum fields can exist at zero energy, as shown by vacuum fluctuations. That claim is convention-dependent in flat-space QFT: normal-ordering sets H|0>=0, but adding a constant to the Hamiltonian changes no observable. The stress-test note is right about this. If the vacuum is assigned nonzero energy, the inference 'fields can persist without energy' collapses, and with it the act/potency distinction as derived here.

What the paper does well: it is honest, well-structured, and actually new in applying the authors' earlier act/potency ontology specifically to energy. The two indirect definitions—energy opposed to primary matter, energy as act of a formal property—are clearly stated and philosophically coherent. The physics it cites (E=mc2, Higgs mass, renormalization) is standard and mostly used correctly. The authors are transparent that the field ontology is taken from their own prior work [7,8], and the argument is internally consistent within that framework.

Soft spots beyond the vacuum issue: the ontology itself is imported whole from [7] and not defended here; one supporting reference is an in-preparation paper [20]; and the conclusion that the Universe contains finite, conserved energy is flagged in the text as a venture but then asserted in the conclusion without the caveat. These are proportional to the paper's nature as an interpretive essay, but they are real.

This paper does not change physics. It offers a metaphysical reading underdetermined by QFT at the crucial step. Still, it is a serious, readable contribution to the neo-Aristotelian philosophy of quantum fields, and it deserves a careful referee in a philosophy-of-physics venue. For a physics journal, I would not desk-reject, but the referee should be directed to the vacuum-energy normal-ordering problem specifically.

Referee Report

5 major / 4 minor

Summary. The paper proposes a metaphysical account of energy, arguing that energy is neither a substance, a field, nor primary matter, but rather the 'act of a formal property.' The argument proceeds in three steps. First, at the elementary scale, the authors recall that the elementary quantum fields (17 fields of the Standard Model) are the first material determinations, and that their associated particles are modes of actualisation of these fields. They use the mass-energy equivalence E=mc2, the Higgs mechanism, and the structure of interaction vertices to argue that energy is omnipresent but not a thing. Second, they argue that energy cannot be primary matter because quantum fields cannot be switched off by removing energy: even in the vacuum state the fields fluctuate, and in their reading these vacuum fluctuations occur at zero energy. Third, they translate this into the Aristotelian scheme of act and potency, defining energy as the actuality of formal properties, and conclude that the Universe contains a finite and conserved energy, with quantum fields as compounds of primary matter and formal properties, and elementary particles as their actualisations.

Significance. If the argument were successful, it would provide a coherent metaphysical interpretation of energy that connects contemporary quantum field theory with the Aristotelian notions of act and potency, and it would offer a principled way to distinguish energy from matter, mass, and fields. The paper is valuable in drawing attention to genuinely puzzling features of QFT, such as vacuum fluctuations, the non-switchability of quantum fields, and the distinction between mass and energy. The authors are explicit about their reliance on earlier work, and they engage seriously with philosophical sources. However, the central inference rests on a convention-dependent reading of vacuum energy, and the ontological premises are imported from previous papers without being defended here. The paper is therefore more suggestive than demonstrative in its current form.

major comments (5)

[Section II.C, footnote 9] The assertion that in the vacuum state the fields 'fluctuate into each others, each at zero energy' is presented as a physical fact, but in flat-space QFT the absolute zero of energy is a convention. The normal-ordered Hamiltonian is defined so that H|0>=0, and adding a constant c to H leaves all transition amplitudes, propagators, and S-matrix elements unchanged. Therefore the statement that a field can exist 'deprived of any amount of energy' (Section II.B.1) is not an empirical property of the vacuum but a chosen normalization. This step is load-bearing for the act/potency definition in Section IV.B, because without it the inference that fields are not made of energy has no ground.
[Sections II.A and II.C] The identification of elementary quantum fields as 'first determinations' composed of primary matter plus formal properties is imported from the authors' earlier paper [7] and related work [8], but the derivation is not summarized or defended in the present manuscript. The central distinction between energy and the field then rests on an external ontology. If that ontology is not granted, the conclusion that energy is the act of a formal property is not supported by the QFT material presented here. The paper should state which empirical facts constrain the notions of primary matter and formal properties, or provide an independent argument for these premises.
[Footnote 9 and Section IV.B] The claim that the mathematical formalism 'is able to testify' that fields exist at zero energy is supported by the in-preparation reference [20]. As [20] is not available, this is not checkable support for a load-bearing assertion. The paper should either present the argument in the present text or cite a published source for the claim that zero-energy vacuum fluctuations testify to the persistence of quantum fields without energy.
[Section IV.B.2 and Conclusion] The conclusion that 'the universe is filled with a finite and conserved energy' does not follow from the preceding discussion. The premise 'energy is always received in something and is thereby finite' is a metaphysical claim, not a physical derivation; the text itself concedes that whether the energy of the Universe is finite cannot be decided. As stated, the conclusion is ambiguous between a claim about individual energy receptions and a global physical assertion that would require empirical or theoretical support.
[Section III.A.1] The statement that 'no protocol ever would transform a cat into energy' is used to argue that mass acquires autonomy from energy at larger scales, but it is not derived from any physical law and is not precise as written, since a cat's rest mass energy is already a form of energy. The argument would need a precise criterion for when E=mc2 conversions are operational rather than conceptual, otherwise the claimed autonomy of mass is asserted rather than established.

minor comments (4)

[References, [20]] The reference [20] has a typo in its title: 'Classical and quantum pysics' should be 'Classical and quantum physics'.
[Section II.A] The phrase 'antis cosmological concepts' appears to be a typo; it should likely read 'ancient cosmological concepts'.
[Equation (11)] Equation (11) is described as 'covariant'; more precisely it is Lorentz-invariant, and the wording could be adjusted to avoid conflating covariance with invariance.
[Section III.A.1] The term 'impulsion' is used for three-momentum; since this is an unusual term in English, it should be defined or replaced with 'momentum' to avoid confusion.

Circularity Check

3 steps flagged · score 7.0 of 10

The central energy-as-act conclusion reduces a normal-ordering convention to a physical fact and imports the primary-matter/formal-property ontology from same-author prior work.

self definitional [Section II.C.1, footnote 9; applied in Section IV.B.1]
"An example of the latter is provided by the quantum fluctuations of the elementary fields' vacuum state, at nul energy, Pµ|0 >= 0. Though a physical reality, in effect, these fluctuations are not actual realities but pure potential realities [10], deprived of any amount of energy. … It follows from the positive character of energy that in the vacuum state of such systems, the various fields fluctuate into each others, each at zero energy: They exist at energy zero."

The premise that vacuum fluctuations are 'deprived of any amount of energy' is not an empirical fact but a convention of flat-space QFT: the Hamiltonian is normal-ordered so that H|0⟩=0, and adding a constant to H changes no transition amplitude or S-matrix element. The paper uses this formalism-dependent zero as the physical ground for saying that quantum fields 'can still be' without energy, and hence that energy is not the matter of fields but the act of a formal property. The conclusion is therefore a paraphrase of the normal-ordering input rather than a physical discovery.
self citation load bearing [Introduction; Section II.A; Section IV.B, footnote 17; Section V]
"Note that at several steps, this analysis relies on results which have been derived in the recent analysis of Reference [7], whereof its frequent mentions. … In [7], the very first determinations of our material World were identified as the 17 elementary quantum fields. … The matter of quantum fields is the primary matter such as identified in [7]."

The paper's central result—energy is not primary matter but the actuality of formal properties—presupposes the hylomorphic ontology of [7]: quantum fields are compounds of primary matter and formal properties, with primary matter as pure potency. Those are the same authors' prior conclusions, and they are not independently derived in this paper. Without that framework, the QFT facts about vacuum fluctuations and interactions do not by themselves yield the act/potency definition of energy. The conclusion is thus a re-description of the ontology supplied by the paper's own earlier citation.

1 more flagged steps

self citation load bearing [Footnote 9, reference [20]]
"It is remarquable (but not by chance [20]) that the mathematical formalism is able to testify of this."

The paper invokes an in-preparation same-author reference, [20], as the authority that the zero-energy vacuum is 'not by chance'—that is, that the normal-ordering zero of energy is physically meaningful and not an artifact. This is precisely the hinge on which the 'fields exist without energy' premise turns. Since [20] is unpublished and written by the same authors, the load-bearing support is an unverifiable self-citation rather than an independent check.

full rationale

This is not a case of a self-contained empirical derivation, so the usual external-benchmark criterion does not apply. The paper's survey of standard QFT facts—E=mc², interaction vertices, Higgs mass, Drell-Yan processes—is independent and not circular. The circularity is concentrated in the inference from the vacuum state to the energy-as-act conclusion. The 'zero energy' of the vacuum is fixed by normal-ordering convention; treating that convention as a physical absence of energy, and then defining energy as what actualizes fields, makes the conclusion follow by construction rather than from measurement. In addition, the primary-matter/formal-property framework is imported from the authors' own [7], and the significance of the zero-energy vacuum is referred to their in-preparation [20]. These self-citations are load-bearing because without them the QFT material does not determine the metaphysical conclusion. The score is therefore 7: substantial, but not total, circularity, since there is independent physical content in the paper's intermediate steps.

Assumptions & free parameters 0 free parameters · 6 assumptions · 3 invented entities

The paper contributes no free parameters; its load-bearing content is a set of metaphysical axioms, mostly taken from the authors' previous work.

assumptions (6)

domain assumption The Aristotelian-Thomistic act/potency distinction applies to quantum fields and elementary particles.
Introduced in Section I and used throughout III.A.2 and IV.B; the claim that energy is an act of a formal property depends on this metaphysics.
ad hoc to paper Elementary quantum fields are the first material realities, compounds of a unique primary matter and formal properties.
Taken from the authors' own prior paper [7], invoked in Sections II.A, II.C, and V; not demonstrated here.
domain assumption Quantum fields persist as real but purely potential realities at zero energy, with vacuum fluctuations satisfying P_mu|0> = 0.
Used in Section II.B.1 and footnote [9] to show fields are not made of energy; this is an interpretive reading of QFT conventions, not a uniquely established fact.
domain assumption The Higgs mechanism gives elementary particle masses an origin independent of energy, so mass is not reducible to energy.
In Section III.A and Fig. 5 the authors infer mass autonomy from the Higgs field; the inference is their interpretation.
domain assumption The divergences in perturbative QFT do not correspond to physical realities, so no physical entity has infinite energy.
Section IV.B.2 uses renormalization to conclude that energies are finite; the philosophical conclusion is not forced by the physics.
ad hoc to paper Energy is always received in something and is thereby finite; hence the Universe contains finite and conserved energy.
Section IV.B.2 and Conclusion; this is a speculative extrapolation from the act/potency framework, not a measured result.

invented entities (3)

primary matter as pure potency
purpose: Conceptual substrate of quantum fields that is distinct from energy; used to deny that fields are made of energy.
Introduced from [7] and reused in II.C and V; no measurable or falsifiable counterpart.
formal properties of quantum fields
purpose: The capacities to interact and propagate that energy actualizes; includes interaction vertices 'encrypted in the fields' nature'.
Section II.A and IV.B; these are metaphysical re-descriptions of physical structure, with no separate testable handle.
energy as act of a formal property
purpose: The central new characterization of energy, distinguishing it from matter, mass, and fields.
Section IV.B.1; a philosophical definition not derived from new equations or experiments.

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Cite this review

Pith. "Pith review of Neither a field nor a matter: The case of energy." pith.science (2026). https://pith.science/paper/A35QE6D6

@misc{pith2026241217858,
  author       = {Pith},
  title        = {Pith review of: Neither a field nor a matter: The case of energy},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/A35QE6D6}},
  note         = {Machine review of arXiv:2412.17858}
}

read the original abstract

Energy is no doubt an intuitive concept. Following a previous analysis on the nature of elementary particles and associated elementary quantum fields, the peculiar status and role of energy is scrutinised further at elementary and larger scales. Energy physical characterisation shows that it is a primordial component of reality highlighting the quantum fields natural tendencies to interact, the elementary particles natural tendency to constitute complex bodies and every material thing natural tendency to actualise and be active. Energy therefore is a primordial notion in need of a proper assessment.

Figures

Figures reproduced from arXiv: 2412.17858 by the authors.

**Figure 2.** At the strong interaction vertex, with coupling [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** A quark and an anti-quark annihilate into a virtual photon [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: A virtual gluon G, with 4-momentum K such that K2 ≥ 4m2 e , fluctuates into a quark loop which connects to a virtual photon γ ⋆ (K), ultimately decaying into an electron/positron pair. Four-momenta conservation is checked at each vertex of interaction. 1. A ‘pure energ…

**Figure 5.** Figure 5: The fusion of 2 gluons, through a top quark (t) triangle, emitting a Higgs particle [PITH_FULL_IMAGE:figures/full_fig_p020_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

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They don’t in general and in particular in the Standard Model of particle physics whose fundamental principle, dynamical, is that of local gauge invariance

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The Higgs field is scalar and this only, is an issue in itself: Do scalar fields really exist as elementary ones? Some authors have recently suggested that the Higgs field, of mass 125 GeV , would enjoy a further resonance at some 700 GeV , which would seriously question its supposed elementarity [28]

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The discovery of the Higgs boson at CERN in 2012 is perhaps the most dramatic example of the utility of the Drell-Yan mechanism [17]

This process was used to design the experiments at CERN that discovered the W and Z bosons and was crucial in the discovery of the top quark at Fermilab. The discovery of the Higgs boson at CERN in 2012 is perhaps the most dramatic example of the utility of the Drell-Yan mechanism [17]. 11 Figure 4: A virtual gluon G, with 4-momentum K such that K2 ≥ 4m2 ...

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2 and offices, to manufacture products, and to send astronauts into space

For him [Man], the end of things and their principles are invincibly hidden in an impenetrable secret. 2 and offices, to manufacture products, and to send astronauts into space. That is, several different forms of energy can be noticed, such as light, heat, motion, the electrical, chemical and gravitational forms, and a convenient classification for the p...

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Commutators are defined by [ a, b] = ab − ba and anti-commutators by {a, b} = ab + ba. 5 balls in effect, that is the elementary particles associated to the quantum fields (1) or (2) are, and are in order to : They are in order to compose into the more substantial realities of the hadronic matter, and itself, to compose into atom’s nuclei at a later stage...

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Now, the quantum fields themselves may be redefined [10], in particular through the un- avoidable renormalisation algorithm

In gauge theories, interactions may be described in ways which differ from (6), the so-called minimal coupling. Now, the quantum fields themselves may be redefined [10], in particular through the un- avoidable renormalisation algorithm. The point is that all of these technical steps preserve the observ- able/measurable quantities the quantum theories give...

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The λa stand for the 8 generators of the SU (3)-Lie algebra taken, here, in the so-called fundamental representation where quark fields ‘live’, a = 1, 2,

Repeated indices, a and µ, are summed upon and f runs over the full set of the 6 flavours of quark fields, u,d,s,c,b,t . The λa stand for the 8 generators of the SU (3)-Lie algebra taken, here, in the so-called fundamental representation where quark fields ‘live’, a = 1, 2, . . . ,8. 8 fermionic content : The 2nd generation comprising the quarks s and c, ...

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This means that E = mc2 is valid in a particular reference frame only (see p.21)

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To wit, The energy is not a thing, not a property as well as not a condition

A ‘pure energy’ ? This noticeable aspect of the photonic field excitations, mediated by so-called virtual photons (ordinarily denoted by the symbol γ⋆(k) in the scientific literature), shows up in this transversal way among the whole span of elementary particle interactions an...
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13 the lack of these interactions and propagations in the same way as act compares to potency

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If energy were primary matter In this subsection, things will be taken from a somewhat different point of view by examining the consequences which would follow from an identification of energy with primary matter. ▷ From the quantum fields’ immutability . Quantum fields reveal...
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Reviewed August 11, 2026 · model on record in the stance chip above.

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They don’t in general and in particular in the Standard Model of particle physics whose fundamental principle, dynamical, is that of local gauge invariance

work page

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The Higgs field is scalar and this only, is an issue in itself: Do scalar fields really exist as elementary ones? Some authors have recently suggested that the Higgs field, of mass 125 GeV , would enjoy a further resonance at some 700 GeV , which would seriously question its supposed elementarity [28]

work page

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The discovery of the Higgs boson at CERN in 2012 is perhaps the most dramatic example of the utility of the Drell-Yan mechanism [17]

This process was used to design the experiments at CERN that discovered the W and Z bosons and was crucial in the discovery of the top quark at Fermilab. The discovery of the Higgs boson at CERN in 2012 is perhaps the most dramatic example of the utility of the Drell-Yan mechanism [17]. 11 Figure 4: A virtual gluon G, with 4-momentum K such that K2 ≥ 4m2 ...

work page 2012

[4] [1]

2 and offices, to manufacture products, and to send astronauts into space

For him [Man], the end of things and their principles are invincibly hidden in an impenetrable secret. 2 and offices, to manufacture products, and to send astronauts into space. That is, several different forms of energy can be noticed, such as light, heat, motion, the electrical, chemical and gravitational forms, and a convenient classification for the p...

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[5] [2]

Commutators are defined by [ a, b] = ab − ba and anti-commutators by {a, b} = ab + ba. 5 balls in effect, that is the elementary particles associated to the quantum fields (1) or (2) are, and are in order to : They are in order to compose into the more substantial realities of the hadronic matter, and itself, to compose into atom’s nuclei at a later stage...

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[6] [3]

Now, the quantum fields themselves may be redefined [10], in particular through the un- avoidable renormalisation algorithm

In gauge theories, interactions may be described in ways which differ from (6), the so-called minimal coupling. Now, the quantum fields themselves may be redefined [10], in particular through the un- avoidable renormalisation algorithm. The point is that all of these technical steps preserve the observ- able/measurable quantities the quantum theories give...

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[7] [4]

The λa stand for the 8 generators of the SU (3)-Lie algebra taken, here, in the so-called fundamental representation where quark fields ‘live’, a = 1, 2,

Repeated indices, a and µ, are summed upon and f runs over the full set of the 6 flavours of quark fields, u,d,s,c,b,t . The λa stand for the 8 generators of the SU (3)-Lie algebra taken, here, in the so-called fundamental representation where quark fields ‘live’, a = 1, 2, . . . ,8. 8 fermionic content : The 2nd generation comprising the quarks s and c, ...

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[8] [5]

9 of energy and momentum within each interaction process

In spite of a few interesting insights, provided for instance by some Clifford algebraic considerations [12], these 3 generations are essentially taken to be a primary data of Nature. 9 of energy and momentum within each interaction process. This stands for a universal law, satisfied at any level of the physical reality, actual and potential, like vacuum ...

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