Is spacetime really doomed?

Abstract

For many years now it has become conventional ([E. Witten, Phys. Today 49 (1996) 24; D. Gross, Einstein and the quest for a unified theory, in Einstein for the 21st Century: His Legacy in Science, Art, and Modern Culture, eds. P. L. Galison, G. Holton and S. S. Schweber (Princeton University Press, 2008), pp. 287–297; N. Arkani-Hamed, Spacetime is doomed (2010)]) for theorists to argue that “spacetime is doomed”, with the difficulties in finding a quantum theory of gravity implying the necessity of basing a fundamental theory on something quite different than usual notions of spacetime geometry. But what is this spacetime geometry that is doomed? In this paper, we will explore how our understanding of 4-dimensional geometry has evolved since Einstein, leading to new ideas about such geometry which may not be doomed at all.

An $E_8 \otimes E_8$ Unification of the Standard Model with Pre-Gravitation, on an Exceptional Lie algebra - Valued Space

“…We have Cl(8) ∼ = Cl(9) 0 , therefore the three generations of fermions discussed in [25] are related to spinors that we will now create from Cl (9). Another interesting thing to note is that Cl(9) spinors will be 2x2 matrices with octonionic entries, therefore we will show shortly how our previous work on three generations from J 3 (O) and Gresnigt's construction [25] are related to three generations via triality.…”

“…The other four exceptional groups F 4 , E 6 , E 7 , E 8 have their corresponding Lie algebras arising as composition Lie algebras over R ⊗ O, C ⊗ O, H ⊗ O and O ⊗ O, respectively [4]. Furthermore, the division algebras relate to the Lorentz group in higher dimensional spacetimes, as follows: SL(2, R) ∼ = SO(1, 2), SL(2, C) ∼ = SO(1, 3), SL(2, H) ∼ = SO (1,5), SL(2, O) ∼ = SO (1,9). There hence arises the possibly that 10D spacetime is of importance to the unified theory.…”

“…The unbroken U(1) grav has recently been suggested as a possible fifth force which might explain the phenomenology of Milgrom's MOND (Modified Newtonion Dynamics) [6]. There is evidence in the literature, for instance in the works of Ashtekar [7], and of Woit [8,9], that general relativity can be treated as a Yang-Mills gauge theory of SU(2) R symmetry. Our ongoing investigations attempt to put general relativity and the weak interaction on the same footing, except that they have opposite parity.…”

An $E_8 \otimes E_8$ Unification of the Standard Model with Pre-Gravitation, on an Exceptional Lie algebra - Valued Space

“…The other four exceptional groups F 4 , E 6 , E 7 , E 8 have their corresponding Lie algebras arising as composition Lie algebras over R ⊗ O, C ⊗ O, H ⊗ O and O ⊗ O, respectively [4]. Furthermore, the division algebras relate to the Lorentz group in higher dimensional spacetimes, as follows: 9). There hence arises the possibly that 10D spacetime is of importance to the unified theory.…”

Clifford algebra Cl(0,6) approach to beyond the standard model and naturalness problems

“…We would like to highlight the fact that both the local Lorentz symmetry and the extended lefthanded weak symmetry are Spin(1, 3), hinting at an interesting duality between Lorentz gravity and weak interactions. Historically, there have been various attempts [166][167][168][169] trying to explore the possible connection between the gravitational and weak interactions.…”