[Old Professer]

*Moreover, even if the particles did appear on the points of a lattice, there may still be a "handle" upon which gravity could act, because you cannot have a lattice that is free of multipole moments to all orders. The resulting non-uniformities may be of regular size, shape and spacing, but they'd exist. It all comes back to the fact that a particle, by definition, is itself a localized (read: non-uniform) concentration of energy.

By this definition there is no uniformity; it must all be an illusion.

[Physicist]

By this definition there is no uniformity; it must all be an illusion.

The gauge theories of particle physics suggest that there is a "natural" scale of order the Planck length. It is entirely possible that the objects we take to be pointlike are actually extended somehow over a scale equal to the Planck scale. (Many "theories of everything" such as superstring theories exploit this.) Back when the radius of the universe was of this order, I could imagine a state of true and perfect uniformity.