A Particle Model of Our Spacetime: Origin of Gravity

Abstract

We build a model of our spacetime by assuming new particles called "space quanta." In the ambient or bulk spacetime ${\mathcal{S}}^{D_{\mathrm{amb}}}$ ($D_{\mathrm{amb}}\ge 4$), a multitude of space quanta form a nearly three-dimensional object, whose continuum approximation is called the space 3-brane. The world volume ${\mathcal{W}\mathcal{V}}_{\mathrm{sq}}$ of this space 3-brane is described by an embedding $f^A(x^{\mu })\in {\mathcal{S}}^{D_{\mathrm{amb}}}$, which produces the induced metric ${\gamma }_{\mu \nu }$ on the world volume ${\mathcal{W}\mathcal{V}}_{\mathrm{sq}}$. This emergent spacetime (${\mathcal{W}\mathcal{V}}_{\mathrm{sq}},{\gamma }_{\mu \nu }$) from the many space quanta is proposed as the particle model of our spacetime. To study our spacetime (${\mathcal{W}\mathcal{V}}_{\mathrm{sq}},{\gamma }_{\mu \nu }$), we construct what we call the Aim-At-Target (AAT) method, which introduces an action for a 4D metric $g_{\mu \nu }$. This metric action from the AAT method can lead to General Relativity at low enough energies. The spacetime (${\mathcal{S}}_{\mathrm{GR}},{\mathbf{g}}_{\mu \nu }$) of General Relativity is, at least, a good approximation to the exact or true spacetime (${\mathcal{W}\mathcal{V}}_{\mathrm{sq}},{\gamma }_{\mu \nu }$) of our universe.

39 pages, 1 figure; minor changes and references added