Rethinking the relation between space, time, and matter

The Newtonian world-view is that of material objects, and light, embedded in three dimensional absolute physical space, and evolving through it in absolute time.

In special relativity, the world-view is that of objects and light and all electro-magnetic radiation evolving along world-lines in space-time. Space-time is absolute and causal, but spatial intervals and time intervals are no longer separately absolute.

In general relativity, the four dimensional space-time manifold is absolute and causal, but its geometry is determined by the distribution of matter and radiation.

In quantum theory, the background space-time is as given by general relativity, including a background distribution of classical matter and radiation, which co-exists with the curved 4D spacetime manifold. On this substrate, quantum systems [i.e. those with action order \hbar] evolve according to the rules of quantum theory. The time parameter in quantum theory is prescribed by the background space-time geometry.

If we get rid of the classical substrate of matter and radiation, and all systems now have action \hbar, we lose the absolute 4D classical space-time manifold and with it we lose its spacetime geometry. We also lose the distinction between matter-radiation and space-time. The universe is now made of atoms of space-time-matter (also known as aikyons). The action principle for an aikyon is shown in the attached screenshot. The action is measured in units of Planck's constant. The aikyon has an associated length scale L measured in units of Planck length, and it evolves in the absolute Connes time tau measured in units of Planck time.

The aikyon is described by a pair of dimensionless matrices Q_1 and Q_2 written on a sedenionic space, and this action is equivalent to three subsystems on an octonionic space [the three fermion generations]. Thus, although there is a space (octonionic space) there is no distinction between the space and the matter-radiation. The degrees of freedom that define the space are the same as those which define matter-radiation. This is unlike in any of the previous stages listed above. The length parameter is not free - it takes only a few discrete rational number values determined by the octonion algebra. This is a conformally invariant theory. The aikyon is so much like the string of string theory!

The universe is made from many copies of these aikyons. All the earlier stages listed above are supposedly emergent from here, including the standard model and its free parameters. Three right-handed sterile neutrinos are predicted.

Reference

https://arxiv.org/abs/2110.02062