User blogs

The Double Rotation as Invariant of Motion in Quantum Mechanics (by Dainis Zeps)

Abstract: Quantum mechanics may loose its weirdness if systematically geometric algebra methods would be used more. Crucial aspect is to find laws of quantum mechanics be present in macroworld in the form of description of motions rather than objects. To help to reach this goal we suggest to use double rotation as one of the basic invariants in quantum mechanics. We suggest to consider geometric algebra as algebra of motion and double rotation specifically. http://prespacetime.com/index.php/pst/article/view/1

A Strategy for Proving Riemann Hypothesis (by Matti Pitkanen)

Abstract: Super-conformal invariance inspires a strategy for proving the Riemann hypothesis. The vanishing of the Riemann Zeta reduces to an orthogonality condition for the eigenfunctions of a non-Hermitian operator D+ having the zeros of Riemann Zeta as its eigenvalues. The construction of D+ is inspired by the conviction that Riemann Zeta is associated with a physical system allowing super-conformal transformations as its symmetries and second quantization in terms of the representations of the super-conformal algebra. The eigenfunctions of D+ are analogous to coherent states of a harmonic oscillator and in general they are not orthogonal to each other. The states orthogonal to a vacuum state (having a negative norm squared) correspond to the zeros of Riemann Zeta. The physical states having a positive norm squared correspond to the zeros of Riemann Zeta at the critical line. Riemann hypothesis follows both from the hermiticity and positive definiteness of the metric in the space of states corresponding to the zeros of Riemann Zeta function. Also conformal symmetry in appropriate sense implies Riemann hypothesis and after one year from the discovery of the basic idea it became clear that one can actually construct a twenty line long analytic argument for the correctness of the Riemann hypothesis using a standard argument from Lie group. http://prespacetime.com/index.php/pst/article/view/3

Space-time Geometry Translated into the Hegelian and Intuitionist Systems (by Stephen P. Smith)

Abstract: Kant noted the importance of spatial and temporal intuitions (synthetics) in geometric reasoning, but intuitions lend themselves to different interpretations and a more solid grounding may be sought in formality. In mathematics David Hilbert defended formality, while L. E. J. Brouwer cited intuitions that remain unencompassed by formality. In this paper, the conflict between formality and intuition is again investigated, and it is found to impact on our interpretations of space-time as translated into the language of geometry. It is argued that that language as a formal system works because of an auxiliary innateness that carries sentience, or feeling. Therefore, the formality is necessarily incomplete as sentience is beyond its reach. Specifically, it is argued that sentience is covertly connected to space-time geometry when axioms of congruency are stipulated, essentially hiding in the formality what is sense-certain. Accordingly, geometry is constructed from primitive intuitions represented by one-pointedness and route-invariance. Geometry is recognized as a two-sided language that permitted a Hegelian passage from Euclidean geometry to Riemannian geometry. The concepts of general relativity, quantum mechanics and entropy-irreversibility are found to be the consequences of linguistic type reasoning, and perceived conflicts (e.g., the puzzle of quantum gravity) are conflicts only within formal linguistic systems. Therefore, the conflicts do not survive beyond the synthetics because what is felt relates to inexplicable feeling, and because the question of synthesis returns only to Hegel’s absolute Notion. http://prespacetime.com/index.php/pst/article/view/4

Clifford Algebra and Dirac Equation for TE, TM in Waveguide (by Giuliano Bettini)

Abstract: Following Hestenes and others we explore the possibility that the electron is a (sort of) bound electromagnetic wave. To do this a waveguide analogy is considered. The E, H field components in waveguide satisfy the second-order Klein-Gordon equation. The question is whether a (first-order) Dirac equation is involved. Making use of Clifford Algebra, it is firstly shown that a spinor satisfying Dirac equation describes, through the relativistic energy impulse four-vector, the energy propagation of the electromagnetic field in a waveguide and in free space. At the same time automatically describes TE and TM modes (TEM in free space), each with Right or Left polarization. It is shown that this description with Dirac equation has been implicit in the waveguide theory at all times. The equivalence is embedded in the usual V and I mode description (See, e.g., S. Ramo, J. R. Whinnery, T. van Duzer, “Fields and Waves in Communication Electronics”, John Wiley [1994]). The Dirac equation for TE, TM modes opens new interesting interpretations. For example, the effect on of a gauge transformation with the electromagnetic gauge group generator (see, D. Hestenes, “Space-time structure of weak and electromagnetic interactions”, Found. Phys. 12, 153-168 [1982]) is readily interpreted as a modification of the TE, TM group velocity. This acts as the electromagnetic force on a charge, and requires two opposite sign of (fictitious) charges for TE or TM. Obviously, this suggests an analogy with electron, positron and possibly neutrino for the TEM. http://prespacetime.com/index.php/pst/article/view/5

Prespacetime Model of Elementary Particles, Four Forces & Consciousness (by Huping Hu, Maoxin Wu)

Abstract: A prespacetime model of elementary particles, four forces and consciousness has been formulated, which illustrates how the self-referential hierarchical spin structure of the prespacetime provides a foundation for creating, sustaining and causing evolution of elementary particles through matrixing processes embedded in said prespacetime. The prespacetime model reveals the creation, sustenance and evolution of fermions, bosons and spinless entities each comprised of an external wave function or external object and an internal wave function or internal object located respectively in an external world and an internal world of a dual-world universe. The prespacetime model provides a unified causal structure for weak interaction, strong interaction, electromagnetic interaction, gravitational interaction, quantum entanglement, consciousness and brain function. The prespacetime model provides a unique tool for teaching, demonstration, rendering, and experimentation related to subatomic and atomic structures and interactions, quantum entanglement generation, gravitational mechanisms in cosmology, structures and mechanisms of consciousness, and brain functions. http://prespacetime.com/index.php/pst/article/view/6

The Physical (Outer) Universe & the Inner Universe (by Dick W. Richardson)

Abstract: So, what is the physical universe? Well, it is all that stuff out there which is not me. What is the inner universe (and which is also big)? Well, it is all the bits which I am constructed of and the dynamics and inner dimensions of these bits. But the two are joined up in space and time, but not in Eternity. Without Time then Eternity would be pointless. Eternity can exist without time, but time cannot exist without eternity. To isolate these dimensions is to alienate Man from what he is and the physical universe from what it is. Nowhere in the physical universe will you find its causation. Nor will you find me or consciousness. We are visitors here. But you cannot see us. A part of me is in this world and my body is my space-time ship, but I AM not from the earth nor time and space. ONLY that which is constructed before time and space can go back beyond time and space from whence it came in its own ground of being, where I AM. Religions are not ready for mystics. Is physics ready for them? Some are. http://prespacetime.com/index.php/pst/article/view/2