About the Dual Parametrization of c

Scientific Paper
Title	About the Dual Parametrization of c
Read in full	Link to paper
Author(s)	Helmut Hansen
Keywords	wave-particle-dualism, fundamental constant, light, special relativity, ether drift
Published	2010
Journal	Proceedings of the NPA
Volume	8
No. of pages	13
Pages	186-198

Read the full paper here

Abstract

The unification of relativity and quantum mechanics is the main problem of modern physics. It is still unsolved. The root of this problem could perhaps be the relativistic postulate of the invariance of the speed of light. In countless experiments it was found that the speed of light does not depend neither on the velocity of the light source (c₁) nor on the velocity of the observer (c₂), but in special relativity this dual constancy of light (c₁, c₂) is not understood well. In Einstein's theory these two parameters c₁ and c₂ are simply supposed as two fundamental principles of nature. In this paper it is shown how this dual constancy of light (c₁, c₂) could be considered as an expression of the quantum mechanical wave-particle-dualism. This quantum-mechanical interpretation implies not only a dual parametrization of c, but the existence of a sort of ether (probably the vacuum) as well. As the result of the dual parametrization of c an etherdrift is predicted, that is significantly smaller than all the values which were expected in previous times. Even if the velocity of Earth of approx. 390 km/s with respect to the cosmic microwave background is taken, the observable ether drift would only be of D = 0.0003 km/s.

Overview

Helmut Hansen presented this paper at the 2010 NPA conference in Long Beach. Its starting observation is a genuine one, and it is the thing worth taking from the paper: the constancy of c is really two separate empirical statements, not one. The first, c₁, is that the measured speed of light does not depend on the motion of the source; the second, c₂, is that it does not depend on the motion of the observer. Special relativity treats them as a single postulate and describes them, in Hansen's phrase, with "one geometrical face". He argues they have two.

Hansen's framework is what he calls the Physics of Mandala, and its foundation is explicitly metaphysical. He posits an invisible, absolute, omnipresent medium — "the ONE" in philosophy, the Meta-Ether in physics, "probably the vacuum". A "Principle of Radical Non-Duality", set out in an earlier paper, requires that not c but v = ∞ be the ultimate limiting speed. Applying that principle to special relativity yields a spacetime whose diagram is a mandala: a circle and a square interlocked. The quarter circle encodes c₁; the square encodes c₂. Both, Hansen finds, carry Lorentz-invariant structure, but by two different mathematical routes. Special relativity, on this reading, "erased essential lines of a fundamental blueprint of the universe (i.e. the square)" and so lost a real distinction between source motion and observer motion — a distinction which, because it is the signature of a medium, ought to be measurable as a very small ether drift.

The argument

Epstein's space-propertime diagrams

Hansen's geometrical language is borrowed from Lewis Carroll Epstein's Relativity Visualized, whose premise is that "everything is always moving at the speed of light" and only the direction of that motion through spacetime can change. A clock forced through space diverts speed from its passage through time, which is why moving clocks run slow; at v = c the clock stops ticking and stops ageing. The relation is x² + y² = 1 with c = 1, and Hansen takes over Epstein's diagrams but reinterprets their axes as absolute space and time, S_A and T_A, since the Meta-Ether is by definition absolute.

Within this geometry he singles out the speed 1/√2 c ≈ 0.707c, which he names the Gödel-Point and which sits at 45° in the Epstein diagram. Its Lorentz factor is γ = √2, and the ratio of the square's vector to the quarter circle's vector at that angle is also 1.414… — the coincidence he takes as evidence that the mandala carries a Lorentz-invariant structure of its own.

Two Lorentz transformations

The paper's technical core is Table 1, which lists two transformations at the Gödel-Point:

Transformation	S-vector	T-vector	γ
L1	1.414…	1	1.414…
L2	1	0.707…	1.414…

Both give the same Lorentz factor, "but the mathematical machinery behind is different." That difference — invisible to any measurement that only checks γ — is what Hansen claims distinguishes his theory from special relativity, and it is what he proposes to test.

The rewritten history

Hansen's historical claim is that the Michelson-Morley experiment of 1887 tested only length contraction, i.e. the neutralisation of the space-line S_L, and that the time-line T_L was untested until Kennedy and Thorndike in 1932 — by which date special relativity was already established, so their null result was read as a second confirmation of c₁ rather than as the discovery of c₂. "This is one of the most fatal mistakes that was ever made in physics." He faults Einstein for solving the wrong contradiction: the real one was not between Galileo's relativity and the constancy of light, but between the two classical theories of light, emission theory and Maxwell's wave theory. That contradiction, he says, was quantum-mechanical in nature and simply could not be resolved in 1905; wave-particle dualism, available only from 1925, dissolves it by making the two aspects complementary rather than exclusive. He notes with approval Einstein's own 1909 Salzburg remark that a future theory of light would be "a sort of fusion of the wave and of the emission theory".

The physical proposal that follows is stated compactly: since a classical wave's speed is fixed by the medium and is therefore independent of the source, and since physicists "have never taken into account that the particle-like aspect of light could also be determined by this medium", c₂ should be re-read as independence of the source too. In the Michelson-Morley and Kennedy-Thorndike geometries the observer sits at the source (v_O = v_L), so both readings fit the data equally; only historical accident, Hansen says, made the relativistic one canonical.

The predicted drift

Because a medium makes source motion and observer motion asymmetric, the mandala's two entangled patterns should differ by a quantity Hansen writes D(x), "the visible signature of the existence of the Meta-Ether". Its magnitude depends on the absolute velocity, which he takes from Smoot, Gorenstein and Muller's 1977 detection of cosmic blackbody anisotropy — 390 km/s toward Leo, their own "new ether drift". For that velocity he reports D_LEO = 0.0003 km/s, "almost indistinguishable from a null result", and smaller than any classical interferometer residual.

Beyond the Gödel-Point

A final section argues that the wave-like aspect of light has a speed scale limited to 1/√2 c, beyond which it enters a superluminal, relativistically space-like sector running from c to ∞. Hansen offers this as a home for quantum entanglement's space-like correlations, and points out that the observed superluminal jets — 3C 273 at up to ~9.6c — require a minimum true speed of exactly 1/√2 c. He closes by comparing his dual parametrisation to doubly special relativity, and disarmingly concedes: "The statements that I have presented here are still largely my personal opinion. All the results of my considerations have not yet been checked by others."

Assessment

The paper's opening distinction is worth keeping. It is true that source-independence and observer-independence are logically separate propositions, that they were established by different experiments decades apart, and that popular expositions — Hansen catches Richard Feynman doing it in The Character of Physical Law — routinely credit Michelson-Morley with a result that only Kennedy-Thorndike established. His account of Lorentz's local time as a heuristic device rejected on grounds of ad-hocery rather than of evidence is also accurate history, and his reading of the whole episode as one where an aesthetic criterion (Occam's razor) decided between empirically equivalent theories is a fair one, made in good faith and without rancour. So is his final admission that none of it has been checked.

But the paper does not deliver a theory. The Meta-Ether, the ONE, the Principle of Radical Non-Duality and the requirement that v = ∞ be the limiting speed are all imported from earlier work and asserted here, not derived; the mandala's status as "a physically meaningful blueprint of the universe" rests on its beauty and on an archetypal argument from Pauli and Jung, which is not a physical criterion. Nothing in the paper explains why an interlocked circle and square should be the geometry of spacetime rather than one diagram among many that can be drawn.

More seriously, the single quantitative result — D_LEO = 0.0003 km/s — is unreproducible from what is given. Hansen says that "to determine all these differences quantitatively only simple trigonometric functions are necessary", but no formula for D(x) appears anywhere in the paper, and no statement of which observable the drift is supposed to modulate, or at what order in v/c. Without that, the prediction cannot be compared against the modern repetitions of Michelson-Morley — the cryogenic optical and microwave resonator experiments that now bound directional anisotropy in c at the 10⁻¹⁷–10⁻¹⁸ level — and cannot be falsified. That is the opposite of what a paper claiming to distinguish itself experimentally from special relativity needs.

There is also an internal tension in the treatment of interferometer residuals. Hansen invokes Múnera's re-analysis to argue that Michelson-Morley and its successors "never were null", and offers his own theory as a possible explanation. But the residuals in that literature are of order several km/s, four orders of magnitude larger than his own predicted 0.0003 km/s. His prediction cannot account for them; if anything it is in tension with them. Similarly, the 3C 273 argument does not work in his favour: the threshold speed 1/√2 c for apparent superluminal motion is a direct consequence of the relativistic beaming formula for apparent transverse velocity, so it is a result derived from special relativity rather than a coincidence pointing beyond it. The Pioneer anomaly cited from his 2009 paper has since been accounted for by anisotropic thermal recoil from the spacecraft's own radioisotope generators (Turyshev and co-workers, 2012), removing that support as well.

Finally, the two Lorentz transformations of Table 1 are, on the paper's own showing, empirically identical in γ — Hansen concedes that Einstein's theory "describes the dual constancy of light almost perfectly – at least from a purely experimental point of view". A difference in "the mathematical machinery behind" that produces no different number is a difference of interpretation, and the paper stops before turning it into physics.

A note for readers going to the PDF: text extraction from this document silently drops square-root signs and infinity symbols, so "1/ 2 c" should read 1/√2 c and "v = " should read v = ∞. The extracted figures for Epstein's time components (0.9375 and 0.75 for v = 0.25c and 0.5c) are 1 − v² rather than the √(1 − v²) that the paper's own x² + y² = 1 requires; whether that is the author's slip or another dropped radical cannot be settled from the extraction.

See also

• Helmut Hansen
• Special Relativity
• Lorentz Transformation
• Michelson-Morley Experiment
• Aether
• Speed of Light
• Length Contraction
• Time Dilation
• Simultaneity
• Emission Theory
• Hendrik Lorentz
• Albert Einstein
• Hector A Munera
• Cosmic Microwave Background