Comment by kstrauser

I think this is where the math breaks down:

> you’d really need perfect incompressibility such that pushing one end of the rod would propagate the pressure wave to other end instantaneously

I.e. by pushing an abstraction of "perfect incompressibility" and "instantenous propagation of pressure waves" to the point stops corresponding to reality. Those ideas are descriptive simplifications, abstracting away the underlying process of matter / fields interacting sequentially, an interaction that propagates at the speed of light.

It's the same kind of thing like assumption that array access is O(1). It is, until the array gets so large the process of finding the right place in memory becomes visibly O(n).

Or, on a more basic level, arithmetic on numbers seems to be O(1) with respect to the values of the numbers. Almost all programming practices and popular algorithms depend on that assumption, but it only holds for numbers that the hardware can process in one go. Adding 64-bit numbers is constant-time. Adding 64000-bit numbers isn't.

> Maybe a string of singularities lined up and touching (hey, there’s your 0!) without tearing spacetime apart?

At that point it's starting to sound less like a rigid rod and more like changing spacetime itself so that the two locations are closer together. :p

Force cannot transmit through the material faster than the speed of sound and because fundamentally at a subatomic level, mechanical force is the interaction of electromagnetic and gravitational fields between molecules, the speed of sound cannot exceed the speed of light in a material. The rod will compress or physics breaks down. Solid particles are an abstraction.