Germ of a synthesis: space–time is spinorial, extra dimensions are time-like

Sparling, George

doi:10.1098/rspa.2007.1839

Cited by 16 publications

(18 citation statements)

References 47 publications

(39 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The first is a six-dimensional analogue of the half-Fourier transform introduced by Witten in [1] which relates objects on null momentum space to objects in twistor space. The second is the Ξ-transform introduced by Sparling in [36,37]. We find an analogue of the half-Fourier transform in six dimensions and extend the Ξ-transform to include fields of arbitrary spin.…”

Section: Introductionmentioning

confidence: 90%

“…This real approach simplifies matters significantly and allows one to exploit standard tools such as Fourier analysis. Sparling [36,37] referred to the k = 0 version of this transform as the Ξ-transform, and we will follow his terminology here. We will use Fourier analysis to identify the kernel of this map on twistor space and to extend it to the 'indirect' cases of weight k − 2).…”

Section: ξ and Half-fourier Transforms In Split Signaturementioning

confidence: 99%

“…However, the real momentum space light-cone is 5-dimensional whereas the real twistor space is 6-dimensional and we will find that this leads to new features in the correspondence as it can no longer be one to one. In this context, the transforms have been studied by Sparling [36,37] for the wave equation and homogeneities −2 and −4 who referred to them as the Ξ-transform. He discovered that the −4 case leads to solutions to the wave equation but the kernel of the map consists of those twistor functions F that are in the image of the conformally invariant wave operator 2 on twistor space, f = 2g for some g (recall that twistor space, being a quadric, is canonically a conformal manifold in six dimensions).…”

Section: ξ and Half-fourier Transforms In Split Signaturementioning

confidence: 99%

See 2 more Smart Citations

Conformal field theories in six-dimensional twistor space

Mason¹,

Reid-Edwards²,

Taghavi-Chabert

2012

Journal of Geometry and Physics

View full text Add to dashboard Cite

This article gives a study of the higher-dimensional Penrose transform between conformally invariant massless fields on space-time and cohomology classes on twistor space, where twistor space is defined to be the space of projective pure spinors of the conformal group. We focus on the 6-dimensional case in which twistor space is the six-quadric Q in CP 7 with a view to applications to the self-dual (0, 2)-theory. We show how spinor-helicity momentum eigenstates have canonically defined distributional representatives on twistor space (a story that we extend to arbitrary dimension). These give an elementary proof of the surjectivity of the Penrose transform. We give a direct construction of the twistor transform between the two different representations of massless fields on twistor space (H 2 and H 3 ) in which the H 3 s arise as obstructions to extending the H 2 s off Q into CP 7 . We also develop the theory of Sparling's 'Ξ-transform', the analogous totally real split signature story based now on real integral geometry where cohomology no longer plays a role. We extend Sparling's Ξ-transform to all helicities and homogeneities on twistor space and show that it maps kernels and cokernels of conformally invariant powers of the ultrahyperbolic wave operator on twistor space to conformally invariant massless fields on space-time. This is proved by developing the 6-dimensional analogue of the half-Fourier transform between functions on twistor space and momentum space. We give a treatment of the elementary conformally invariant Φ 3 amplitude on twistor space and finish with a discussion of conformal field theories in twistor space.

show abstract

Section: Introductionmentioning

confidence: 90%

Section: ξ and Half-fourier Transforms In Split Signaturementioning

confidence: 99%

Section: ξ and Half-fourier Transforms In Split Signaturementioning

confidence: 99%

See 1 more Smart Citation

Conformal field theories in six-dimensional twistor space

Mason¹,

Reid-Edwards²,

Taghavi-Chabert

2012

Journal of Geometry and Physics

View full text Add to dashboard Cite

show abstract

“…We are not the first to seriously consider the quantum world to have three time dimensions and three space dimensions, see for example [89][90][91][92][93][94][95][96][97][98][99] that also suggested there could be three time dimensions and three space dimensions (3+3). Still, this line of thought does not appear to have gained momentum and was principally discussed in the 1970s to 1980s, and is now partly forgotten.…”

Section: Energy Time Uncertainty Principlementioning

confidence: 99%

Re-thinking the Foundation of Physics and its Relation to Quantum Gravity and Quantum Probabilities: Unification of Gravity and Quantum Mechanics

Haug¹

2020

Preprint

View full text Add to dashboard Cite

In this paper we will show that standard physics to a large degree consists of derivatives of a deeper reality. This means standard physics is both overly complex and also incomplete. Modern physics has typically started from working with first understanding the surface of the world, that is typically the macroscopic world, and then forming theories about the atomic and subatomic world. And we did not have much of a choice, as the subatomic world is very hard to observe directly, if not impossible to observe directly at the deepest level. Despite the enormous success of modern physics, it is therefore no big surprise that we at some point have possibly taken a step in the wrong direction. We will claim that one such step came when one thought that the de Broglie wavelength represented a real matter wavelength. We will claim that the Compton wavelength is the real matter wavelength. Based on such a view we will see that many equations in modern physics are only derivatives of much simpler relations. Second, we will claim that in today’s physics one uses two different mass definitions, one mass definition that is complete or at least more complete, embedded in gravity equations without being aware of it, as it is concealed in GM, and the standard, but incomplete, kg mass definition in non-gravitational physics. First, when this is understood, and one uses the more complete mass definition that is embedded in gravity physics, not only in gravity physics, but in all of physics, then one has a chance to unify gravity and quantum mechanics. Our new theory shows that most physical phenomena when observed over a very short timescale are probabilistic for masses smaller than a Planck mass and dominated by determinism at or above Planck mass size. Our findings have many implications. For example, we show that the Heisenberg uncertainty principle is rooted in a foundation not valid for rest-mass particles, so the Heisenberg uncertainty principle can say nothing about rest-masses. When re-formulated based on a foundation compatible with a new momentum that is also compatible with rest-masses, we obtain a re-defined Heisenberg principle that seems to become a certainty principle in the special case of a Planck mass particle. Furthermore, we show that the Planck mass particle is linked to gravity and that we can easily detect the Planck scale from gravity observations. The Planck mass particle is unique as it only lasts the Planck time, and in that very short time period it can only be observed directly from itself, and it therefore closely linked to absolute rest.

show abstract

“…More precisely, the paper [7] asserts that the equation in a form of Let n, m ≥ 2. Inspired by [7,16,17], we here consider an ultrahyperbolic equation in u(x, y) := u(x 1 , ..., x n , y 1 , ..., y m ), which is associated with general geometry in the space variables y:…”

Section: Introduction and The Main Resultsmentioning

confidence: 99%