What has so far prevented us from decrypting quantum mechanics is the Cookie Cutter Paradigm, according to which the world's synchronic multiplicity derives from surfaces that carve up space in the manner of three-dimensional cookie cutters. This insidious notion is shown to be rooted in our neurophysiological make-up. An effort is made to liberate the physical world from this innate fallacy.
What has so far prevented us from decrypting quantum mechanics is the Cookie Cutter Paradigm, according to which the world's synchronic multiplicity derives from surfaces that carve up space in the manner of three-dimensional cookie cutters. This insidious notion is shown to be rooted in our neurophysiological make-up. An effort is made to liberate the physical world from this innate fallacy.
The problem of understanding quantum mechanics is in large measure the problem of finding appropriate ways of thinking about the spatial and temporal aspects of the physical world. The standard, substantival, set-theoretic conception of space is inconsistent with quantum mechanics, and so is the doctrine of local realism, the principle of local causality, and the mathematical physicist's golden calf, determinism. The said problem is made intractable by our obtruding onto the physical world a theoretical framework that is more detailed than the physical world. This framework portraits space and time as infinitely and intrinsically differentiated, whereas the physical world is only finitely differentiated spacewise and timewise, namely to the extent that spatiotemporal relations and distinctions are warranted by facts. This has the following consequences: (i) The contingent properties of the physical world, including the times at which they are possessed, are indefinite and extrinsic. (ii) We cannot think of reality as being built "from the bottom up", out of locally instantiated physical properties. Instead we must conceive of the physical world as being built "from the top down": By entering into a multitude of spatial relations with itself, "existence itself" takes on both the aspect of a spatially differentiated world and the aspect of a multiplicity of formless relata, the fundamental particles. At the root of our interpretational difficulties is the "cookie cutter paradigm", according to which the world's synchronic multiplicity is founded on the introduction of surfaces that carve up space in the manner of three-dimensional cookie cutters. The neurophysiological underpinnings of this insidious notion are discussed.
Conceptual spaces can be barriers to understanding. Our classical understanding is hard to escape, with its precepts even being imposed on QM “behaviours”. Interpretation is also an artifact of methodology; a problem already noted in parapsychology. In physics, consciousness—some sort of awareness centre —is thought to have anomalous physical effects in the world, but there is no consensus on the claim, thus making consciousness as ambiguous as psi. A broader understanding of the causes and relations inherent in the world, at all levels, requires pluralistic and holistic thinking; this is the approach taken in synchronicity theory. If the psi function is essentially synchronistic and aided by consciousness, then consciousness has a grander role yet to be discovered. Jung states that synchronicity occurs when archetypes are constellated (activated); they act as bridges, so that synchronicity is an experience in consciousness where we witness the unity of mind and matter.
We introduce the cookie-cutter lifting procedure: a systematic method for determining whether a quantum algorithm requires magic (non-stabiliser resources) or whether its speedup is purely Clifford-level. The procedure writes any classical algorithm as an Origami ISA programme at the classical (β=0) level and identifies whether the quantum lifting requires the TWIST opcode—the ISA marker for non-Clifford C₃-level gates. Applied to Shor's algorithm (N=15, a=7): the ISA trace LABEL→FLIP→FLOP(U_f)→FLIP(QFT) has mana=0 along the pre-measurement branch; for this instance the period r=4 divides the register size 2ⁿ=16 exactly, so the QFT output is a stabiliser state on the zero-measurement branch. The speedup comes from exponential-weight stabiliser generators compressed by coherent cancellation, with no magic required on that branch. Applied to non-abelian hidden shift over D_N: mana=0 before the non-abelian QFT and mana>0 after, for all N≥3; the abelian cases D₁≅ℤ₂ and D₂=ℤ₂×ℤ₂ are the Clifford exceptions. The TWIST opcode fires because non-abelian D_N (N≥3) have 2-dimensional irreducible representations whose Fourier blocks lie outside C₂. We identify the eigenphase spectrum of the NAQFT as a basis-independent replacement for T-count. The results reveal two roads to quantum advantage: Clifford complexity (Shor) and magic (non-abelian hidden shift). Part of the Origami ISA series. Companion papers: 10.5281/zenodo.20955514 (ISA as PROP), 10.5281/zenodo.20956674 (nine normal forms), 10.5281/zenodo.20956685 (three-tier resource theory). Keywords: shor, clifford, lifting, qft, hidden-subgroup, naqft, twist, magic, mana, eigenphase, origami-isa, cookie-cutter, dihedral-group, stabiliser, wigner-function
It is well recognized that two of the foundational theories of modern physics, relativity and quantum mechanics, are inconsistent. Efforts to overcome this through intensive pursuit of unifying theoretical frameworks or improvements in experimental precision as pursued by Robertson-Mansouri-Sexl and Standard-Model-Extension test theory protocols, have so far proven unsuccessful. Nonetheless, empirical evidence deriving from investigations inspired by the twentieth-century 'EPR' polemic, can now claim to have identified 'locality' and 'separability' as notions integral to special relativity theory inconsistent with quantum mechanics and experimental evidence supporting it. Following intimations of J.S. Bell, L. Smolin, Maudlin and others, the history and philosophy of science are engaged as research tools to uncover the origins of the assumptions underlying such incompatibility. In particular, known but prevalent fallacies and the deprecation of processes as described by Whitehead, together with recent insights into the functional distinctions between representative models and explanatory theories, are engaged. Analysis of the evolution of optical and electromagnetic theorizing is then suggested to demonstrate that the choice of a mechanically compatible model of electromagnetic radiation, as has conventionally underwritten development of the light-speed postulate of special relativity, is inappropriate. Pursuing options made available within a multiple models idealization of optical and electromagnetic phenomena, replacement of the sponsoring model by a nonlocal and non-separable wavefront process of radiation of the form advanced by Fresnel and Kirchhoff on the basis of Huygens' principle, suggests the possibility of reformulation of relativity theory without incurring such conflicts. However, choice of a wavefront electrodynamic model including the extinction theorem of Ewald and Oseen, equally suggests possible theory reformulation without necessitating a four-dimensional construct of space and time or postulating an absolute constancy of light-speed in vacuum. Such a constancy can in turn be considered as demonstrating an innate limitation on empirical observation resulting from the loss of relative velocity information during electromagnetic transmission due to the memorylessness of the Markov propagation process of refraction together with information flow discontinuity resulting from dielectric boundary extinction events. Such characteristics are shown to be applicable to electromagnetic radiation of all frequencies. Further, from a wavefront reformulated hypothesis of inertial relative motion, it appears possible to demonstrate that the Galilean principle of relativity can be preserved. However, Lorentz invariance would then require reinterpretation wherein the Lorentz transform group would be deemed to quantify the degree of information distortion inherently experienced by any empirical enquiry into electrodynamics involving relative motion.