Do Space and Time have an Archetypal Design?
| Scientific Paper | |
|---|---|
| Title | Do Space and Time have an Archetypal Design? |
| Read in full | Link to paper |
| Author(s) | Helmut Hansen |
| Keywords | Pauli, Einstein, Jung, Mandala, Metaphysics, Archetypes, Transcendence |
| Published | 2007 |
| Journal | Proceedings of the NPA |
| Volume | 4 |
| Number | 1 |
| No. of pages | 23 |
| Pages | 115 |
Read the full paper here
Abstract
The physicist Wolfgang Pauli (1900-58), one of the founder of quantum mechanics, was highly fascinated of Jungs archetypes. He conceived them as the underlying principles of the physical world. He even suggested a research program in order to explore the physical meaning of these archetypes. But this research program never became reality. This article gives an example how this research program could look like. It refers to a structure consisting of different circles and squares that are put together in a specific way; a structure, which is traditionally called a MANDALA. By making Einsteins special theory of relativity geometrically compatible with a transcendent background this archetypal structure surprisingly came up. As its speed limit is given by the speed of infinity, it includes the possibility to overcome special relativity theory (SRT).
Overview
Helmut Hansen's paper takes as its starting point a research programme Wolfgang Pauli proposed but never carried out: to look for the physical content of the Jungian archetypes, which Pauli regarded not as psychological curiosities but as "the underlying principles of the physical world". Hansen offers a worked example. The archetype he chooses is the Mandala — a figure built from circles and squares nested in a particular way — and he argues that this figure emerges unbidden when one tries to make Special Relativity geometrically compatible with an undetectable background medium, a "Meta-Ether". The paper is written as a popular overview rather than a formal derivation, and Hansen says so plainly in his closing remarks.
The physical claim beneath the imagery is specific and can be stated without reference to Jung at all. Hansen holds that Einstein, in solving the conflict between the invariance of light and Newtonian velocity addition, excluded more than logic required. To destroy absolute time it is enough to exclude signals of infinite speed; Einstein instead excluded the whole band from c to ∞. Hansen proposes a space-time picture whose only strictly forbidden velocity is v = ∞, in which all other superluminal speeds are excluded only "in parts", and which he claims is nonetheless Lorentz invariant. That structure, drawn out, is the Mandala. Its attraction for him is that it is non-local by construction and therefore might reconcile relativity with quantum entanglement — the tension he identifies as the central unsolved conceptual problem of modern physics.
The argument
The problem: is special relativity incomplete?
Hansen sets the scene with the SRT locality constraint — nothing faster than light, hence no influence between sufficiently distant events — against the non-local correlations of quantum theory. He recounts the 1935 Einstein–Podolsky–Rosen paper, Einstein's "spooky action-at-a-distance", his insistence that a theory predicting such correlations must be incomplete, and John Bell's 1964 theorem which made the local-hidden-variable alternative experimentally distinguishable. The measurements went against Einstein. Yet, Hansen stresses, "SRT works still perfectly as far as the experimental predictions are concerned. No failure so far is recognizable." Two successful theories rest on two different pictures of the universe, one local and one not, and reconciling them is the frontier.
An invisible ether as a boundary condition
Hansen's ether differs, he says, from other revivals: he assumes the ether is really invisible, which explains directly why every experiment to detect it failed. He then makes the move that gives the assumption teeth. Invisibility is not a vague or unfalsifiable property but "a highly restrictive physical condition". Borrowing Einstein's own metaphysical habit — the question he put to Ernst Straus, "whether God could have created the world differently; in other words, whether the demand for logical simplicity leaves any freedom at all" — Hansen substitutes the demand for invisibility for the demand for logical simplicity. A universe founded on something in principle unobservable must be organised "conspiratorially" so that the foundation cannot show itself, and that organisation should be specifiable and testable. His claimed translation of invisibility into physics is a single boundary condition: the universe's limiting speed must be v = ∞.
Einstein excluded too much
The core critique is put crisply. Einstein's insight, as he described it in his 1922 Kyoto talk after visiting Besso, was that time could not be absolute if the speed of light was really invariant. Hansen argues that because the problem and Einstein's solution have since been "mixed together", the problem itself "was never formulated in a precise and strict way". Formulate it strictly and one sees that "Einstein made time more relative than it was really necessary": an absolute time can only be given a physically serious definition by infinitely fast signals, so excluding v = ∞ alone already destroys absolute time and already resolves the contradiction with light's invariance. Excluding the entire superluminal range from c to ∞ is, on this reading, a blunter instrument than the problem called for.
Hansen supports the objection with Lorentz's 1913 Teyler Foundation lectures: "It should be noted that the daring assertion that one can never observe velocities larger than the velocity of light contains a hypothetical restriction of what is accessible to us, [a restriction] which cannot be accepted without some reservation." He notes that Lorentz fully commanded the theory's physics and mathematics and that the criticism carried no personal animus.
The Mandala space-time picture
Diagrams 1–3 contrast the Minkowski light-cone diagram, whose "everywhere" region is wholly excluded, with the Mandala figure, in which the excluded region is only slightly smaller in appearance but structurally different: "only one speed is definitely excluded: it is just the value of v = ∞, whereas all other superluminal speeds are only excluded in parts." In such a universe, Hansen argues, "God would have no choice since all possibilities that logic allows would be realised."
Hansen reads the figure with an explicit dictionary: the inner circle corresponds to time, the outer square to space, and the whole structure is parametrised by the speed √2 c. He also finds a second, orthogonal branch alongside the ordinary relativistic function, whose limiting speed is v = ∞ and which therefore contains all superluminal velocities; he names it "Gödel's Trench". The two branches appear to touch at a sub-luminal speed, c/√2 ≈ 0.707 c, which he names "Gödel's Point" after a paper of Kurt Gödel's. This contact point is where he places his hope of reaching superluminal velocities — while conceding that direct acceleration past c remains impossible for the same reason as in Einstein's theory, since the fuel required diverges. He draws an explicit analogy to Dirac's equation, which had two solutions when only one class of particle was known, and whose second solution Dirac trusted enough to postulate the positron that Carl Anderson found in cosmic-ray cloud-chamber tracks two years later.
Epstein's diagram and Lorentz invariance
To connect the figure to relativity Hansen uses Lewis Carroll Epstein's Relativity Visualized (1981) and its space-proper-time diagram, whose organising idea is that "there is in fact only one speed: the speed of light" and that everything always moves at it, changing only its direction through space-time. A clock forced through space "diverts some of the speed it should use for travelling through time"; at c it stops ageing. The relation is simply x2 + y2 = 1 with c = 1, so an object with intermediate velocity 0.5 c ages 0.75 of a year per year (Diagram 4). Applying Epstein's construction at Gödel's Point returns a figure Hansen says is "easily recognizable as a natural part of the structure of the Mandala".
The key numerical claim follows. In SRT the Lorentz factor at v = c/√2 is γ = √2. In the Mandala, that speed sits at 45° in Epstein's geometrical language, and the ratio of the outer-square vector to the inner-circle vector at that angle is likewise γM = √2 with c = 1. Hansen takes this as evidence that the Mandala structure is Lorentz invariant, and offers that as its chief advantage over rival post-relativistic models: it explains "why special relativity is physically working so well", where "many alternative models, which like to go beyond special relativity, have a problem in explaining why the universe 'conspires' in such a way that it looks extremely relativistic."
Because the Mandala's limiting speed is infinite, Hansen expects non-locality to be a property of space and time themselves and not only of quantum systems: "It would be incomprehensible that nature acts differently if we change only our theoretical 'glasses'." He closes by noting the symmetry and beauty of the structure, and that Nobel laureate Karl Alex Müller cited the Dharmaraja Mandala — geometrically the same figure — as the inspiration behind his work on high-temperature superconductivity.
Assessment
The paper's most valuable move is one that survives detachment from its Jungian framing. Hansen puts his finger on a real logical looseness in the standard presentation of relativity's founding argument: the incompatibility of invariant light speed with absolute simultaneity is usually said to force the light cone, but strictly what it forces is the denial of instantaneous signalling. Whether the whole superluminal band must go with it, or only the limit point, is a genuine question about the strength of the premises rather than a crank's complaint, and Lorentz's 1913 reservation is quoted accurately and to the point. Equally sound is Hansen's diagnosis of what any post-relativistic model owes the reader: an explanation of why the world looks so exactly Lorentzian. Most ether revivals founder on precisely that, and Hansen is right to make it the criterion his own proposal must meet.
The difficulties are, however, severe, and Hansen is unusually candid about several of them, describing his own work as "a loose collection of some speculative ideas" and admitting that superluminal travel is "not yet verified neither physically nor mathematically". The central step — the claim that requiring an ether to be invisible implies a limiting speed of v = ∞ — is asserted, not derived; it is referred to a footnote and the reasoning behind it is never given in the paper. Since every subsequent conclusion depends on it, the argument's foundation is exactly the part the reader cannot inspect. Likewise the "details of this searching process" by which the boundary condition led to the Mandala are explicitly "not discussed here", so the figure arrives by fiat rather than by construction.
The Lorentz-invariance demonstration is thinner than its billing. What Hansen actually shows is that one ratio, taken at one angle, reproduces one value of γ. Lorentz invariance is a statement about the whole transformation group and about which quantities are preserved under it, not about agreement at a single point; a single coincidence at 45° cannot establish it. The identification of the inner circle with time, the outer square with space, and √2 c as the parametrising speed is a stipulated reading of a picture, and no independent reason is given why those correspondences and not others are the right ones. Because the dictionary is chosen rather than forced, the figure risks accommodating whatever is asked of it. The naming of "Gödel's Point" and "Gödel's Trench" after Gödel's rotating-universe work is likewise decorative rather than load-bearing — nothing in Gödel's solution is used.
Most importantly, the paper does not deliver what its motivating problem demands. Non-locality is announced as the goal, but no mechanism is offered by which the Mandala structure would generate the specific correlations that violate Bell's inequalities, and no quantitative prediction is made that could distinguish the picture from ordinary relativity. Since Hansen concedes that relativity's experimental record is unblemished and that his structure is engineered to reproduce it, the proposal at present has no observational consequence at all — the superluminal "spin-off" is offered as hope rather than as calculation. The appeal to beauty and symmetry that closes the paper ("it is hard to believe that nature does not follow it") is an aesthetic argument, and the Müller anecdote shows only that a mandala inspired a physicist, not that a mandala is a physical structure. Read as what it says it is — an illustration of the shape a Pauli-style research programme might take, and a sharp criticism of one over-strong step in relativity's founding argument — the paper is worth attention. Read as a physical theory, it has not yet begun.