It's just like the Lorentz Tranform or any other of the laws of Relativity. Things can get very massive and/or time can slow way down, but ultimately there's not a "problem" (i.e. mathematical failure requiring the theory to be extended) until the speed of light is reached, as an asymptotic limit.
But you're raising a good point that maybe Lorentz is pointing to 'non-integer dimensionality' where even enough mass crammed into a small enough space causes the "new maths" to begin to noticeably take hold. Like I said I see Lorentz as a way to transform dimensionality from N-D to (N +/- 1)D, but in a continuous and 'differentiable' way.
In super simplistic terms Lorentz is a "compression" function where one dimension of space is compressed perfectly flat, which is the mathematical equivalent of removing that dimension from the 'degrees of freedom' of the system.
But you're raising a good point that maybe Lorentz is pointing to 'non-integer dimensionality' where even enough mass crammed into a small enough space causes the "new maths" to begin to noticeably take hold. Like I said I see Lorentz as a way to transform dimensionality from N-D to (N +/- 1)D, but in a continuous and 'differentiable' way.
In super simplistic terms Lorentz is a "compression" function where one dimension of space is compressed perfectly flat, which is the mathematical equivalent of removing that dimension from the 'degrees of freedom' of the system.