About an Anomaly that Breaks Relativity

Scientific Paper
Title	About an Anomaly that Breaks Relativity
Read in full	Link to paper
Author(s)	Helmut Hansen
Keywords	relativity, Paradigm, Mach's Principle, inertial compass, meta-ether, Nicolaus Cusanus, metaphysics
Published	2008
No. of pages	39

Read the full paper here

Abstract

The first step in scientific revolution or paradigm shift is the awareness of the existence of an anomaly. That means to see clearly that a specific fact cannot be explained by a universally accepted paradigm. Although relativity - one of the most driving paradigms of contemporary physics - is working efficiently in the most cases but there is one fact, which cannot be explained by it. This fact concerns a specific coincidence. Physicists have observed that the local inertial compass coincides with the frame of the most distant galaxies and quasars within the present measurement accuracy of 2.5 x 10-4 arcsec/year. In modern physics Machs Principle is the hypothesis most favoured to explain this fact. It maintains that the local inertial compass, f.e. Foucaults pendulum, is determined by all the masses in the Universe in such a way that the measured coincidence is given. As Machs Principle implies that not only gravity but all physics shall be formulated without any reference to an all-pervasive background like an ether, it is physically considered as the climax of relativity. But Machs Principle could never be formulated in a precise way. The above-mentioned coincidence is still unexplained. But it is not yet epistemologically recognized as an anomaly that breaks the relativistic paradigm. In this paper an argument is presented that could change the epistemological status of this fact tremendously. Actually this fact can be explained as the signature of an omnipresent and invisible entity.

Overview

The paper (headed in the PDF "About an Anomaly that challenges Relativity — Mach's Principle versus Principle of Radical-Non-Duality") takes a single well-attested observational fact and argues that it has been epistemologically misclassified. The fact is what Hermann Weyl called the "coincidence of the inertial compass and the stellar compass": a local inertial frame — Foucault's pendulum, a laser gyroscope — shows no rotation relative to the frame defined by the most distant galaxies and quasars, to a measured accuracy of 2.5 × 10⁻⁴ arcsec per year.

Hansen's argument proceeds in two moves. First, the historical one: Mach's principle is the only explanation modern physics offers for this coincidence, and it has never been made precise. Einstein worked on it for most of his life, found that general relativity does not satisfy it, and by 1954 told Felix Pirani that one should stop speaking of Mach's principle at all. Second, the constructive one: a coincidence between A and B can be explained either by A determining B, or by A and B sharing a common source. Mach's principle takes the first route; Hansen proposes the second, calling it the Principle of Radical Non-Duality. The common source is a transcendent, omnipresent entity he calls the One, or physically a "meta-ether" — and the observed inertial-stellar coincidence is, on his reading, its empirical signature.

The departure from the mainstream is thus not a new equation but a reversal of what counts as fundamental. Relativity treats the local inertial frame as something to be explained away by matter; Hansen treats its unconditioned character as a natural consequence of its being grounded in something outside the physical universe altogether. The paper is explicitly a work of metaphysics offered as physics, and says so.

The argument

Mach's principle as a history of failure

Hansen begins with Mach's 1883 motivation: Mach wanted to purge mechanics of unobservables, and the coincidence of the inertial and stellar compasses let him replace Newton's absolute space with something observable, "the frame of the fixed stars." Einstein gave this the status of a principle in his 1918 paper Prinzipielles zur allgemeinen Relativitätstheorie: "the G-field is without remainder determined by the masses of bodies."

But general relativity, Hansen notes, supplies a dynamic spacetime dependent on matter distribution without satisfying the demand that only relational properties between material objects appear. He quotes d'Inverno on the Newtonian alternative — "In Newtonian theory there is nothing a priori to predict this, it is simply a coincidence" — and assembles what he calls "voices of hope": Herbert Pfister in Foundations of Physics Letters (2004) calling the coincidence "the greatest wonder"; Trinh Xuan Thuan concluding that the pendulum's behaviour "forces us to conclude that there exists a sort of interaction totally different from those described by recognized physics"; Friedrich Hund calling it "uncanny." He also quotes, fairly, the deflationary reply, in a transcribed exchange from the Barbour–Pfister Mach's Principle volume in which Donald Lynden-Bell says the coincidence is "quite accurate, but no more accurate than one would expect."

Hansen also records how the fact has sharpened. Mach's version was vague — "the fixed stars." Modernly, the stars of the Milky Way, the Local Group and even the Local Supercluster are excluded; a drift of the pendulum's plane is observable relative to each. Only on scales beyond these does alignment obtain. He reproduces Pfister's list of accuracies: 10⁻⁸ of the Earth's rotation for laser gyroscopes, 10⁻⁹ for VLBI and GPS terrestrial frames, 0.02 milliarcsec/year for the dynamical solar reference, 0.25 milliarcsec/year for the Hipparcos galactic frame.

The methodological turn and the Threshold Area

Since the One is by hypothesis transcendent, no fact can be found in it. Hansen's "methodological turn" is therefore to stop trying to describe the One and instead look for its imprint in the visible universe — "this is the only place, where the scientific method can be applied, because only here experimental data can be expected."

This leads to what he calls the Threshold Area: the region of the physical universe closest to the limit of the One, where the "epistemological distance" is least and yet empirical data still exist. He is candid about the obstacle that produced the idea: if the foundation is genuinely omnipresent, no point of the universe is preferred, and so no point offers a non-trivial proof of it. The Threshold Area is his way out of that impasse.

Cusanus and the coincidence of the Smallest and the Largest

The decisive borrowing is from Nicolaus Cusanus (1401–1464) and the doctrine of the coincidentia oppositorum in De docta ignorantia (1440): "since the absolutely Maximum is all, that which can be, it is altogether actual… the Minimum coincides with the Maximum."

Hansen argues this identifies which differences must be dissolved. For the One to be invisible, the universe must contain no difference more extreme than the one it fails to dissolve — and the most extreme difference available is that between the Smallest and the Largest. He gives the reason an omnipresent entity requires exactly this coincidence: to be omnipresent, something must both contain all things (hence be the Largest) and be contained in all things (hence be the Smallest). Dissolving the difference between the two extremes seals off the last level ground, so that the One "is everywhere in the Universe but no one can see it." The resulting empirical prediction — that there must be a corresponding coincidence between the smallest and largest scales in the physical universe — he calls "Cusanus' conjecture," and claims it as "the first physical prediction of a Modern Metaphysics."

The identification then follows: the local inertial compass is the smallest-scale realization of an inertial frame (valid, in GR, in an infinitely small region, and tied to the equivalence principle, itself a factual coincidence verified to a few parts in a trillion); the frame of the most distant galaxies and quasars is the largest-scale one. Their observed coincidence is the empirical counterpart of Cusanus' coincidence of Minimum and Maximum.

Hansen is careful to flag the weak leg. The inertial character of the distant frame is established only approximately: inflationary cosmology permits a residual rotation of order 10⁻⁸⁰ to 10⁻¹³¹ radians per year, "which is in agreement with experiment," and the measured null result "could be a random error that shrouds a null result." He argues only that exact non-rotation is not excluded.

Boundary conditions, the inertial frame, and the elementary matrix

Hansen turns Einstein's own difficulty into support. Einstein disliked the inertial frame precisely because it "acts itself, but which cannot be acted upon," an "epistemological defect" he tried to remove; in his last lecture (Palmer Physical Laboratory, 14 April 1954) he compared it to "God Almighty," unaffected by anything else, and explained the failure of the Machian programme: "If you give up space, you have an enormous number of distances, and unhandy consistency relations." For Hansen, the unconditioned character of the inertial frame is not a defect but exactly what one expects of something grounded in the unconditioned.

Technically, he says, the Principle of Radical Non-Duality is a boundary condition at infinity: the universe must be infinite and Euclidean at infinity, because the straight line of the inertial frame presupposes Euclidean geometry. He quotes Einstein's 1922 rejection of that hypothesis on the ground that it demands the vanishing of the Riemann tensor at infinity — twenty independent conditions against ten curvature components — "certainly unsatisfactory to postulate such a far-reaching limitation without any physical basis for it." Hansen offers the One as that basis, an external rather than internal cause of the boundary conditions, and cites Goenner's observation that whether one discards Mach's principle or builds an alternative theory depends on which belief is stronger.

Finally he sketches quantification: the Smallest and Largest become R = 0 and R = ∞, from which the universe must be infinite; and by the same logic a pair 0 and ∞ for velocity, so that "if we have trust in the existence of the One, or the Meta-Ether, then we have unavoidably to assert the velocity of v = ∞ as somehow meaningful." Omnipresent action requires instantaneous connection of separated points, which special relativity forbids; hence, he concludes, relativity is incomplete rather than false — the velocity range between c and ∞ is simply left out. He refers this to his Mandala structure, developed in Do Space and Time have an Archetypal Design?, in which relativistic spacetime is "perfectly embedded" in a larger metaphysical picture. A closing section draws theological consequences: because invisibility is here the result of a conception rather than of a personal act, the traditional picture of God is replaced by "a completely impersonal cause" open to everyone.

Assessment

The paper's first half is its best, and it is genuinely useful. Hansen has done real work assembling the observational record of the inertial-stellar coincidence, with the accuracies and sources properly cited from Pfister, and he correctly resists the common conflation of the fact (a measured null rotation) with the explanation (Mach's principle) — physicists do frequently speak as though naming the principle disposed of the observation. His account of the historical arc is accurate: Einstein did adopt Machian language in 1918, general relativity does not satisfy Mach's principle in any strong formulation, and Einstein did eventually recommend abandoning the term. Presenting Lynden-Bell's dismissal alongside Pfister's wonder, rather than suppressing it, is to his credit. And the observation that the local inertial frame retains an unconditioned, act-but-not-acted-upon character in GR is a real feature of the theory and a fair thing to press on.

The trouble is that the explanatory move does no work. The Principle of Radical Non-Duality is claimed as simpler than Mach's principle by Occam's razor, but simplicity of statement is not the relevant measure; what matters is whether the hypothesis constrains anything. "Cusanus' conjecture" predicts that some coincidence between smallest and largest scales exists — it does not predict which quantities, at what magnitude, with what residual. Any coincidence found would confirm it, and none could refute it, since the One is stipulated to be beyond every scientific access. Hansen states this candidly ("we cannot, in principle, point to anything"), but a hypothesis with that property cannot then be credited with an empirical signature.

The identification itself is also strained. The "local inertial compass" is small in the sense of being defined in a locally flat neighbourhood; the distant quasar frame is large in the sense of being far away. Neither is the Smallest or the Largest in Cusanus' sense, and the paper supplies no argument that a limit taken for the size of a coordinate patch is the same kind of extremum as a limit of spatial extent. Calling the equivalence principle "a factual coincidence" and hence "a sub-principle of the more general principle of radical non-duality" is verbal rather than derivational: the equivalence principle is a statement about the equality of two measurable masses, tested by Eötvös-type experiments, and nothing about its structure follows from Cusanus.

Three further problems bear on the physics. First, the paper's most-cited alternative explanation of the coincidence goes unrebutted: McCrea's argument, which Hansen fairly quotes in a footnote, that because the relative angular drift of two very distant objects is bounded by c divided by their distance, a sufficiently remote set of objects automatically constitutes a rigid reference direction — so the coincidence may be geometrically unremarkable. That deserved a reply in the body of the paper and does not get one. Second, the appeal to a residual rotation of 10⁻⁸⁰ to 10⁻¹³¹ rad/yr cuts against the argument rather than for it: those figures are so far below any conceivable measurement that they cannot distinguish exact from approximate inertiality, which is what Hansen's reading requires. Third, the demand for v = ∞ conflicts directly with measurement — the arrival-time coincidence of the gravitational waves and the gamma-ray burst from the neutron-star merger GW170817 constrains the propagation speed of gravity to within about one part in 10¹⁵ of c, which is hard to reconcile with an omnipresent instantaneous connection, and no mechanism is offered by which the ∞-sector would remain unobservable.

Finally, there is a category question the paper raises and does not settle. Hansen wants metaphysics to become "a physical discipline like atomic physics" while granting that its object cannot in principle be measured. The Verifiability Principle he sets out to defeat is not defeated by pointing to a fact in the visible world and declaring it a shadow; it would be defeated by a statement about the One from which some observation follows that would not follow otherwise. The paper does not produce one. What it does produce — a careful dossier on a real and underdiscussed observational coincidence, and a lucid account of why Mach's principle never worked — is worth having on its own, independently of the metaphysics built on top of it.

See also

• Helmut Hansen
• Do Space and Time have an Archetypal Design?
• About the Dual Parametrization of c
• The Hidden Face of c, or The True Meaning of the Kennedy-Thorndike Experiment
• Is Special Relativity a Decidable Theory?
• Elementarmatrix 3.0
• Von der Entdeckung Gottes am Rande des Universums
• Albert Einstein
• General Relativity
• Special Relativity
• Aether