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REVIEW 3 major objections 4 minor 185 references

General Relativity, Mental Causation, and Energy Conservation

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Pith's one-line read General relativity tends to exclude Cartesian mental causation: a scalar mental field must be constant, hence zero.

desk verdict A clean scalar-field no-go result from the generalized Bianchi identities, with an honest but unproven extension to multi-component mental-influence fields. read the letter →

arxiv 1909.01083 v1 pith:YBLHI76N submitted 2019-08-20 physics.hist-ph physics.pop-ph

J. Brian Pitts This is my paper · ORCID
classification physics.hist-phphysics.pop-ph
keywords GeneralRelativitymentalcausationCartesiandualismgeneralizedBianchiidentitiesgravitationalenergyconservationlawsNoether'stheoreminteractionism
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

For three centuries the conservation of energy has been used to argue that an immaterial mind cannot move the body. Some recent authors have replied that general relativity changes the story, because gravitational energy is not localizable and local conservation laws fail. This paper argues the opposite: general relativity actively resists external mental influences rather than inviting them. Modelling the mind's influence as a scalar field $\Psi$ that enters the total action without field equations of its own, the generalized Bianchi identities imply $(\delta S/\delta \Psi)\,\partial_\mu \Psi = 0$, so wherever the mind acts the field is forced to be constant; with the boundary condition $\Psi = 0$ outside brains, $\Psi$ is identically zero. The exclusion is finite—roughly five scalar components can saturate the identities—so the argument is a new objection to the simplest Cartesian models, and it counts in favour of taking gravitational energy-momentum conservation seriously.

What carries the argument

The load-bearing device is the generalized Bianchi identity, the differential expression of the action's invariance under arbitrary coordinate transformations, applied to fields that do not obey the principle of least action. After the gravitational and matter field equations are used, the remaining terms tie the variational derivative of the action with respect to $\Psi^A$ to the gradient and transformation coefficients of $\Psi^A$. For a single scalar $\Psi$ this collapses to $(\delta S/\delta \Psi)\,\partial_\mu \Psi = 0$, a constraint that either forces $\Psi$ to be constant or imposes $\delta S/\delta \Psi = 0$ as a hidden equation of motion. The same four identities can be saturated by a sufficiently large collection of fields, which is why the argument's strength depends on the component count of the mental model.

What would settle it

A decisive check is to search for a counterexample: a single scalar non-variational field $\Psi$ with $\partial_\mu \Psi \neq 0$ in some brain-sized region, satisfying the generalized Bianchi identities and the Einstein-matter field equations. The paper's toy wave-equation model claims no such solution exists with $\Psi = 0$ outside the region, so exhibiting one, analytically or numerically, would overturn the central claim.

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Extended reading notes

Core claim

The central claim is that the generalized Bianchi identities arising from diffeomorphism invariance turn general relativity into an obstacle to Cartesian mental causation. For an action $S[g_{\mu\nu}, u, \Psi^A]$ in which the mental influence $\Psi^A$ is a non-variational field—one for which one does not impose $\delta S/\delta \Psi^A = 0$—coordinate invariance yields $\delta S/\delta \Psi^A\,\partial_\mu \Psi^A + \partial_\nu [C^{A\nu}_\mu(\Psi,g)\,\delta S/\delta \Psi^A] = 0$. For a single scalar or pseudoscalar field the second term vanishes and the identity reduces to $(\delta S/\delta \Psi)\,\partial_\mu \Psi = 0$. Since the soul is supposed to act where $\partial_\mu \Psi \neq 0$, the only consistent option is that $\delta S/\delta \Psi = 0$ there, which is just the Euler-Lagrange equation one deliberately did not assume; otherwise $\Psi$ must be constant everywhere, and the boundary condition $\Psi = 0$ outside brains makes it vanish identically. Thus, contrary to the claim that general relativity's non-conservation of gravitational energy opens a loophole for dualism, general relativity excludes the simplest implementation of mental causation.

Load-bearing premise

The argument assumes the mind's influence is a local classical field with a definite coordinate-transformation behaviour, entering the action with finitely many derivatives and having no equation of motion of its own; if the influence is nonlocal, not field-like, or composed of enough components, the Bianchi-identity constraint weakens or disappears.

Editorial extensions

If this is right

  • The common claim that general relativity's failure to localize gravitational energy makes room for mind-body interaction is reversed: in the simplest scalar model there is no room at all.
  • The generalized Bianchi identities give a coordinate-invariant route to the conservation objection, independent of the contested pseudotensor formalism for gravitational energy.
  • Because roughly five scalar components can saturate the four Bianchi identities, the new objection is not a general refutation of interactionism; its force depends on how many fields a soul model employs.
  • If the identities are taken as evidence that general relativity conserves energy-momentum in infinitely many formal senses, then realism about gravitational energy-momentum gains support, and conserved-quantity theories of causation recover their standard examples.

Reading between the lines

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

  • We infer that the same generic obstruction applies to any non-variational classical field used to model special divine action, angelic action, or psychokinesis, since only the action's coordinate invariance and the non-variational status of the field enter the derivation.
  • We infer that the field-redefinition inequivalence shown in the paper carries a practical moral for future models: the geometric-object type of $\Psi^A$ (scalar, weight-1 density, contravariant vector, spinor, etc.) is physically consequential and must be specified before testing a candidate model against the Bianchi identities.
  • We infer that a quantum-field-theoretic treatment could sidestep the classical conclusion, because quantum fields are not required to satisfy their classical field equations pointwise; testing this would require formulating a non-variational quantum coupling carefully, which the paper does not do.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. This paper argues that General Relativity, contrary to a tradition that takes the non-localizability of gravitational energy to remove conservation constraints, makes Cartesian mental causation harder rather than easier. The author models the mind's influence as a non-variational classical field Ψ^A added to the total action S[g,u,Ψ], derives the generalized Bianchi identities (Eq. (3)), and shows that in the single-scalar case the identities force ∂_μΨ = 0 whenever δS/δΨ is not a constant, so with the boundary condition Ψ = 0 outside brains the influence vanishes identically. The paper further argues that this result supports realism about gravitational energy and helps conserved-quantity theories of causation, and it discusses the scope of the objection for theistic and nontheistic dualism.

Significance. The single-scalar no-go result is a genuine, self-contained derivation and a useful contribution: it bypasses the pseudotensor controversy by using tensorial Bianchi identities, and it gives a concrete answer to Carroll's rhetorical question in the simplest case. The derivation is not circular; it starts from general covariance and the field equations and derives a constraint that was not assumed. The analysis of field-redefinition inequivalence in §6.1 is also illuminating. The paper is less successful in its broader claim that GR 'tends to exclude' Cartesian mental causation: the step from four identities to a verdict about arbitrary multi-component fields is only a crude function-counting heuristic, not a theorem. If the conclusion is appropriately weakened, the result remains significant for the philosophy of mind and for debates about gravitational energy.

major comments (3)
  1. [Section 6, Eqs. (3)-(5) and the following paragraph] The paper's central conclusion is not supported for multi-component fields. The derivation yields only the four identities in Eq. (3); the argument that 'roughly five' scalar fields let the soul win is explicitly said to be 'admittedly crude and merely plausible'. Because the identity itself contains δS/δΨ^A for each component, the number of components changes the equations, so the existence of a local, generally covariant action with a sacrificial set of fields that saturates the identities while a fifth field acts on matter has not been demonstrated. This gap is load-bearing, since the abstract's 'tends to exclude' claim is broader than the proven scalar no-go.
  2. [Section 6, Eqs. (1)-(3)] The derivation assumes that the mental influence is represented by a local classical field with definite transformation properties and, crucially, no equation of motion of its own: one does not impose δS/δΨ = 0. That assumption is essential but is not defended against the alternatives. If mental causation is nonlocal, not field-like, or if Ψ itself has a dynamical equation, Eq. (3) need not hold. The paper should state clearly that the no-go theorem applies to this specific modeling class, rather than to Cartesian mental causation as such.
  3. [Abstract and Section 1.1] The phrase 'General Relativity tends to exclude Cartesian mental causation' overstates what is proven. The rigorous result is established for a single scalar or pseudoscalar field; the multi-component case is left open by the paper's own admission. Please either provide a worked example of a multi-component model and analyze its Bianchi constraints, or rephrase the central claim as a conditional no-go for simple local field models.
minor comments (4)
  1. [Section 6.1, Eq. (10)] Calling the trace of Einstein's equations '10% of Einstein's equations' is imprecise; the trace is one independent functional direction among ten, so the percentage remark is confusing and should be rewritten.
  2. [Section 6, equation display with strikethrough] The notation δS/δΨ (gµν,u,Ψ ✟✟✟∂µΨ) uses a strikethrough that is not defined anywhere; please use standard notation, for example writing explicitly that the expression is independent of ∂μΨ.
  3. [General] The paper relies on the companion paper (Pitts 2019a) for Noether's converse and for the failure of the Leibnizian objection; the manuscript should state explicitly which results are assumed from that paper and which are established here.
  4. [General] There are several typographical and OCR artifacts in the preprint text, such as 'u ndermining' and 'conser- vation'; please proofread the final version carefully.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation: the generalized-Bianchi no-go is self-contained; the only self-citations are peripheral, not load-bearing.

full rationale

The central derivation starts from an invariant action S[g,u,Ψ], deliberately avoids imposing δS/δΨ = 0, uses only the gravitational and matter field equations plus general covariance, and obtains Eq. (3) and its scalar specialization δS/δΨ ∂_μΨ = 0 (Eq. 5). This is a genuine mathematical consequence of the stated assumptions: the conclusion that Ψ is constant, and hence zero given the boundary condition Ψ = 0 outside brains, is not inserted into the premises. The boundary condition is an explicit input, but the nontrivial content is the derivation of constancy from the Bianchi identity; that is not a case of defining the result into existence. The paper's self-citations (Pitts 2019a, 2010, 2016a) provide historical framing, the converse Noether background, and an interpretive realism thesis, but none of them carries the Bianchi calculation or the scalar no-go result. The multi-component discussion is explicitly tentative—“this function-counting argument is admittedly crude and merely plausible”—so it is a stated limitation of scope rather than a prediction disguised as an input. No fitted parameters are renamed as predictions, no uniqueness theorem from the author's prior work is used to forbid alternatives, and no known result is merely relabeled. The core derivation is self-contained and does not reduce to its inputs by construction.

Assumptions & free parameters 1 free parameters · 6 assumptions · 1 invented entities

The central claim rests on a deliberately constructed toy model: a covariantly coupled, non-variational field Ψ with no equation of motion, plus the standard field equations for gravity and matter. The only hand-set parameter is the number of components of Ψ. No numerical fits or empirical data enter.

free parameters (1)
  • Number of components of the mental-influence field Ψ^A
    The strength of the Bianchi-identity constraint depends on how many field components the model assigns to the mind's influence. The paper shows N=1 fails, suggests N=5 may succeed, and admits the exact threshold is not derived. This is a hand-chosen modeling parameter rather than a measured quantity.
assumptions (6)
  • domain assumption The total action S[g,u,Ψ] is invariant under coordinate transformations up to a boundary term.
    Invoked in Section 6 to derive Eq. (1); this is the standard general-covariance assumption extended to the non-variational mental field Ψ.
  • ad hoc to paper The mind's influence Ψ enters as a local field with definite coordinate transformation properties and at most finitely many derivatives.
    Section 6 states this modeling choice explicitly; it is not derived from physics or neuroscience. It is the load-bearing premise for the scalar-field calculation.
  • ad hoc to paper Ψ has no equation of motion; one does not set δS/δΨ = 0.
    Section 6 says: 'Crucially, Ψ does not have any equations of motion from the principle of least action.' This distinguishes mental influence from ordinary matter fields.
  • domain assumption The gravitational and matter fields satisfy the principle of least action, δS/δgμν = 0 and δS/δu = 0.
    Used to drop the first two terms in Eq. (1); standard in classical field theory.
  • ad hoc to paper Boundary condition Ψ = 0 outside brains, so a constant Ψ must be zero everywhere.
    Introduced in Section 6 to convert spatio-temporal constancy into vanishing; without it a nonzero constant influence would remain.
  • standard math Noether's first and second theorems and the generalized Bianchi identities are valid in the given setting.
    The derivation relies on the standard relationship between coordinate invariance and differential identities; cited to Noether 1918 and Bergmann 1958.
invented entities (1)
  • Mental-influence field Ψ^A
    purpose: To provide a local classical-field model of Cartesian mental causation in the action S[g,u,Ψ].
    The paper invents Ψ as a toy-model device; no experimental signature is proposed, and the author treats it as a placeholder for whatever nonphysical influence a soul would exert.

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Cite this review

Pith. "Pith review of General Relativity, Mental Causation, and Energy Conservation." pith.science (2026). https://pith.science/paper/YBLHI76N

@misc{pith2026190901083,
  author       = {Pith},
  title        = {Pith review of: General Relativity, Mental Causation, and Energy Conservation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YBLHI76N}},
  note         = {Machine review of arXiv:1909.01083}
}
read the original abstract

The conservation of energy and momentum have been viewed as undermining Cartesian mental causation since the 1690s. Modern discussions of the topic tend to use mid-19th century physics, neglecting both locality and Noether's theorem and its converse. The relevance of General Relativity (GR) has rarely been considered. But a few authors have proposed that the non-localizability of gravitational energy and consequent lack of physically meaningful local conservation laws answers the conservation objection to mental causation: conservation already fails in GR, so there is nothing for minds to violate. This paper is motivated by two ideas. First, one might take seriously the fact that GR formally has an infinity of rigid symmetries of the action and hence, by Noether's first theorem, an infinity of conserved energies-momenta (thus answering Schr\"{o}dinger's 1918 false-negative objection). Second, Sean Carroll has asked (rhetorically) how one should modify the Dirac-Maxwell-Einstein equations to describe mental causation. This paper uses the generalized Bianchi identities to show that General Relativity tends to exclude, not facilitate, such Cartesian mental causation. In the simplest case, Cartesian mental influence must be spatio-temporally constant, and hence 0. The difficulty may diminish for more complicated models. Its persuasiveness is also affected by larger world-view considerations. The new general relativistic objection provides some support for realism about gravitational energy-momentum in GR (taking pseudotensor laws seriously). Such realism also answers an objection to theories of causation involving conserved quantities, because energies-momenta would be conserved even in GR.

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