A Particle Model of Our Spacetime: Origin of Gravity

We build a model of our spacetime by assuming new particles called "space quanta." In the ambient or bulk spacetime ${\cal S}^{D_{\rm amb}}$ ($D_{\rm amb} \ge 4$), a multitude of space quanta form a nearly three-dimensional object, whose continuum approximation is called the space 3-brane. The world volume ${\cal WV}_{\rm sq}$ of this space 3-brane is described by an embedding $f^A(x^\mu) \in {\cal S}^{D_{\rm amb}}$, which produces the induced metric $\gamma_{\mu \nu}$ on the world volume ${\cal WV}_{\rm sq}$. This emergent spacetime (${\cal WV}_{\rm sq}, \gamma_{\mu \nu}$) from the many space quanta is proposed as the particle model of our spacetime. To study our spacetime (${\cal WV}_{\rm sq}, \gamma_{\mu \nu}$), 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 (${\cal S}_{\rm GR}, {\bf g}_{\mu \nu}$) of General Relativity is, at least, a good approximation to the exact or true spacetime (${\cal WV}_{\rm sq}, \gamma_{\mu \nu}$) of our universe.