Some Rectifiable Inconsistencies and Related Problems in Einstein's General Relativity
| Scientific Paper | |
|---|---|
| Title | Some Rectifiable Inconsistencies and Related Problems in Einstein's General Relativity |
| Read in full | Link to paper |
| Author(s) | Chung Y Lo |
| Keywords | General Relativity, Einstein, Equivalence Principle, Special Relativity, particle physics |
| Published | 2009 |
| No. of pages | 14 |
Read the full paper here
Abstract
Einstein's accurate predictions created a faith that makes a critical analysis of general relativity over due. Since his field equation has no dynamic solutions, the observational confirmations have been exaggerated. Einstein's covariance principle has been proven to be invalid. This error comes from Einstein's theory of measurement that adapts the mathematical notion of distance in Riemanian geometry as if valid in physics, and his supporting arguments are actually based on invalid applications of special relativity. However, such a theory of measurement was not used in Einstein's predictions. Nevertheless, Einstein's equivalence principle plays a crucial role in rectifying the shortcomings of his theory, and the Maxwell-Newton Approximation is proven as independently valid for massive sources. Then, general relativity leads to the discovery of the charge-mass interaction that would explain the space-probe pioneer anomaly discovered by NASA. Thus, unification of gravitation and electromagnetism is proven necessary. Moreover, since the photons must include gravitational energy, particle physics would not be clearly understood without gravity.
Overview
This 2009 report from the Applied and Pure Research Institute (APRI-TH-PHY-008-04) is a critique of General Relativity written from inside the theory rather than against it. Lo does not argue that Einstein was wrong about gravitation; he argues that Einstein's theory is "not a self-consistent theory", that two distinct pieces of it — the covariance principle and the theory of measurement — are defective, and that both can be removed without damaging the predictions everyone cites as confirmations. The paper's title is deliberate: the inconsistencies are described as rectifiable. Lo's repeated position is that "Einstein is still a great theorist" and that the rectified theory is stronger than the received one.
The departure from the mainstream account lies in what Lo takes to be established. Textbook relativity treats general covariance as a foundational principle and treats the metric as directly giving physical distances and times. Lo rejects both. He holds that Einstein's field equation "has no dynamic solutions", that the covariance principle is inconsistent with Einstein's own requirement on weak gravity, and that the local notion of distance is fixed instead by a Euclidean-like structure compatible with actual measurement. He further claims that the three classic confirmations are less secure than advertised, that Einstein's equivalence principle — properly stated, and in his view misstated in every textbook — is the tool that repairs the theory, and that the resulting framework points toward a charge–mass interaction and hence toward unification of gravitation and electromagnetism.
The argument
Issues with the three observational confirmations
Lo takes the standard tests one at a time. The gravitational redshift, he argues, was derived from Einstein's 1911 preliminary assumption of equivalence between acceleration and Newtonian gravity — an assumption he holds to be inconsistent with the 1916 equivalence principle, citing Fock's result that no metric is consistent with Newtonian uniform gravity. His conclusion is careful: the redshift "can be derived from an invalid theory", though it also follows from the 1916 principle, so the observation does not discriminate.
For the perihelion of Mercury, Lo revives Gullstrand's objection to the Nobel Committee that Einstein's equation may admit no solution to the two-body problem — which, he notes, is why the 1921 prize was awarded for the photo-electric effect instead. He claims this suspicion has been confirmed, the equation having no physical two-body solution, so that agreement with the perihelion "only suggests that his theory would be on the right track" and that for dynamic cases the equation "needs to be improved with modifications".
For the deflection of light (Gravitational Lensing), Lo quotes Einstein's remark that the first-order result "is not influenced by our arbitrary choice of a system of coordinates". He accepts that the second-order deflection is gauge invariant in the impact parameter b, but argues that this conceals a failure: the shortest distance r0 differs from gauge to gauge, while r0 is precisely the quantity carrying Einstein's first-order formula. When a Royal Society editorial replied that only b is measurable and r0 "just an arbitrary label", Lo treats that as evasion — an argument that has "not reached the expected maturity in logic".
What survives: the Maxwell–Newton approximation
Against these losses Lo sets one positive result. The Maxwell–Newton approximation is, he claims, independently valid as the first-order approximation for gravity due to massive sources, following directly from the equivalence principle rather than from the field equation. On this basis the binary-pulsar radiation data can be explained, light bending is validly derived, and Einstein's notion of weak gravity is vindicated. He draws a sharp consequence: because this approximation follows from the equivalence principle alone, "strictly speaking, Einstein's field equation has not been confirmed". He also reports that the approximation implies gravitational coupling constants of different signs, contradicting the assumption of a unique coupling sign.
The equivalence principle as Einstein stated it
Appendix A is the paper's most sustained textual argument. Lo reproduces Einstein's own statement from The Meaning of Relativity (p. 57) and insists that its content is the Einstein–Minkowski condition: that the local frame reached by an appropriate physical acceleration must be Minkowski. He then catalogues what he regards as corruptions of it — Pauli's version, which reduces the principle to the mathematical existence of locally constant coordinates; Misner, Thorne and Wheeler's local-Lorentz-frame formulation, which he says yields an incorrect local time for the Earth in the solar system; Wald's and Ohanian & Ruffini's reduction of it to the equality of inertial and gravitational mass; and Thorne's charge that the principle ignores tidal forces, which Lo answers with Einstein's letter to Rehtz stating that the principle "does not assert that every gravitational field ... can be produced by acceleration of the coordinate system". He also quotes Einstein to Laue that a gravitational field is marked by non-vanishing field strength, not by non-vanishing curvature — which he needs, because it licenses the geodesic equation as the equation of motion under gravity alone.
The rotating disk and Einstein's theory of measurement
Appendix B is the technical core. Lo re-derives Einstein's rotating-disk argument, the source of the claim that the ratio of circumference to diameter exceeds π. Working with a local free-fall space L* attached to a particle at rest in the rotating frame K′, he writes the Lorentz relations between L* and the inertial frame K and recovers the familiar contraction and dilation expressions with factor [1 − (ωr/c)2]−1/2. His objection is to the integration that follows: the contracted element belongs to a local space L* that depends on t and θ, and the various L* at different θ are "under different accelerations", so summing them "would not make sense as distance in K′".
He then does what he says Einstein should have done — transforms to the rotating frame following Landau and Lifshitz, obtains the metric ds2 = (c2 − ω2r2)dt2 − 2ωr2dθ′dt − dr2 − r2dθ′2 − dz′2, checks that it gives the expected force mv2/r′ on a resting particle, and re-expresses it in the local time t′ of the rotating frame. The transformation c dt′ = c dt − (ωr/c)r dθ′[1 − (ωr/c)2]−1 is, he stresses, not integrable: θ′ and θ′ ± 2π are the same position but would not give the same t′. Since r = r′ and r dθ = r′dθ′, the rotating frame retains a Euclidean-like structure and "Einstein's claim of U/D > π is not valid". Lo's verdict on the wider theory is that "some claims of Einstein appear to be valid because he made two mistakes that cancel each other", and that the resulting theory of measurement — quoted from Einstein, that coordinate differences "cannot be directly measured by the unit measuring-rod" — is the point Whitehead had already rejected as unacceptable in physics.
Photons, E = mc2, and unification
The closing argument extends the critique to particle physics. Lo denies that general relativity is confined to macroscopic phenomena. If the photon consisted of electromagnetic energy alone, he argues, one could not reconcile that with the decay of the neutral pion into two photons, since on his account electromagnetic energy is not equivalent to mass. He therefore concludes that photons "must include non-electromagnetic energy" — gravitational energy — that Einstein's proof of E = mc2 is incomplete and the relation only conditionally valid, and that gravity cannot be ignored in particle physics. The same line leads to the charge–mass interaction he offers as an explanation of NASA's Pioneer spacecraft anomaly, and hence to the claim that unification of gravitation and electromagnetism is not optional but "proven necessary".
Assessment
The genuinely valuable part of this paper is its close reading. Lo works from Einstein's own words — the 1916 statement of the equivalence principle, the letters to Laue and Rehtz, the rotating-disk passage — and shows convincingly that the textbook formulations are not paraphrases of them. The observation that Pauli's version replaces a physical acceleration with a mere coordinate transformation is a real distinction, and the point that Einstein explicitly denied the field of a material point could be transformed away is a fair correction to loose popular statements. His separation of the theory of measurement from the predictions is also a clean and testable historical claim: the deflection formula and the perihelion formula are written in terms of quantities defined on a Euclidean-like background, so in that narrow sense he is right that the measurement doctrine does no work in the calculations. The revival of Whitehead's and Gullstrand's objections, largely forgotten, is a service to the historical record.
The difficulties are equally clear. First, most of the load-bearing claims are not established here but referred to Lo's own earlier papers: that Einstein's equation has no dynamic solutions, that no physical two-body solution exists, that the coupling constants have different signs, that the charge–mass interaction exists at all. A reader of this paper alone is asked to accept these on citation. The charge–mass interaction, the Pioneer explanation, and the incompleteness of E = mc2 occupy a few sentences each and are asserted rather than derived; no coupling strength, no magnitude for the anomalous acceleration, and no comparison with the measured Pioneer deceleration is given, so the proposal cannot be checked. Second, the pion argument as stated is too quick — the π0 → 2γ decay is normally read as showing exactly that electromagnetic energy carries the pion's mass, and Lo does not engage that reading. Third, the paper is uneven in tone; extended passages assess the "logical maturity" of named editors and societies rather than their arguments, which weakens rather than strengthens a case that stands or falls on the rotating-disk algebra.
That algebra is the strongest section, and it deserves to be judged on its merits: the non-integrability of the time transformation around the rotating disk is a real feature, well known in the literature on rotating frames and the Sagnac effect, and Lo's insistence that a sum of intervals belonging to differently-accelerated local frames is not a length in K′ is a substantive objection rather than a rhetorical one. But it does not by itself dispose of the wider theory of measurement, since the disk is a special case chosen because its free-fall local frames are Minkowskian; Lo does not show that the same cancellation of errors occurs in the static spherically-symmetric case where the theory is normally tested. Nor does the paper address the measurements that most directly probe metric time, such as the Hafele–Keating and GPS clock-rate comparisons, or the Shapiro time delay — any of which a claim about what clocks and rods really measure must eventually confront. Finally, there is an internal tension the paper does not resolve: Lo rejects the covariance principle while retaining the equivalence principle and the geodesic equation, but does not spell out what replaces general covariance as the constraint that fixes an acceptable field equation, leaving the promised "valid field equation for the dynamic case" as acknowledged unfinished business — as he himself concedes in the conclusions.