That's false. It also has little or nothing to do with the question of whether particles are point-like or not.
Actually its not false, and has everything to do with the question of spatio and temporal distances, between zero-dimensional objects. Correctly stated, space and time are one entity. If time on the geometric level does not exist as current theory holds, then the dimensions of space do not exist linearly at all. Instead, we have a quantized space and time which remain fundamentally true, whilst, the geometry of space is not necesserily dependant on it. As i said early;
Now, according to physicist Fotini Markopoulou, the problems of time in a geometric sense is synonymous with the emergence of space itself - which is geometry. It absolutely requires no time whatsoever. He continues to say, ''By making the geometry not fundamental, we are able to make a distinctionbetween the geometric and the fundamental time, which opens up the possibility that, while the geometric time is a symmetry, the fundamental time is real.''
Concerning time, this imaginary dimension, which is not meaning it is ethereal in anyway without proof, takes off this spacetime triangle making the four-dimensional manifold of spacetime what it is, and what unifying them means. The math which described this was a new geometry:
[latex]s^2=-(c\Delta t)^2+(\Delta x)^2+(\Delta y)^2+(\Delta z)^2[/latex]
This equation is a Cartesian Coordinate of spacetime. In a Minkowskian Row Vector Notation in a bilinear form can be given as: [latex]V=(0,0,0,1)[/latex]. The Row Value of the Matrix is given as:
[latex]\eta=\begin{pmatrix}-1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{pmatrix}[/latex]
This makes a smooth manifold consistent of time and space as single entities.
Now, if we are to take relativity seriously, then the problems markopoulou mentions can we replace ''time'' with the equally problems of the geometry of real space. The timelessness of the geometry of space means that only the quantization holds any relevence or importance. The Wheeler-de Witt equation is [latex]\hat{H}\psi>=0[/latex] where the right hand side of the equation is the quantity of time, which is zero. This is how the timelessness is involved on large scales. Going back to the original question, ''space between two pointlike objects'' actually would mean we are to believe that a mass collection of zero-dimensional particles can make three-dimensional objects, using space. Geometry at the fundamental level does not exist, and any space between two zero dimensional particles is not very rewarding. The matter still does not make a three dimensional self. It's only an illusion if this be the case.
