Is it possible to apply the rules that govern four dimensional
space-time geometry and combine them with the rules that govern the fractional dimensions of fractals?
BTW, is time a fractional dimension?
After all, one can go in any direction in space, but can only go
foreward in time at a uniform rate.
Einstein’s full field equations describing the relation between energy density and the geometry of the space time are not to be taken lightly they are horrendously nasty non-linear differential equations that are just plain bad for the human mind.
For the truly mad here is most of the original work in English.
Can it be done in general people have modified them but you are in for a world of hurt without some serious silicon and a whole raft of Maths. Not to mention the proof you would need to justify the modifications.
Further warning Fractional dimensions, are not always easy to differentiate in.
Time is a measure of change, change tends towards lower Energy states this is at a global level non-reversible, and thus the geometry of the universe slopes down towards a minimum energy level condition, this slope is what we call time. No fractionalisation for these reasons is necessary