LF12878DR
- A spacetime with fractal geometry may help in unifying the gravitational
force with quantum mechanics, and bridge a gap between the observed
reality and theories postulating that Nature is discrete.
One of the greatest worries of physicists are infinities: If we hope
that Nature be described by the language of mathematics, then we expect
that everything be described by a finite set of observable quantities.
However, things go wrong when trying to merge general relativity with
quantum mechanics, and infinities arise. The author of this research
argues that a cure to this problem is to replace ordinary geometry with
fractal geometry. While in the former case concepts such as volume and
dimension have an intuitive meaning, in the latter they experience
radical transformations. At very small distances a discrete spacetime
texture emerges, thus opening up the possibility that the continuum
geometry we observe at large scales is only an effect of a coarse
resolution. Also, the dimension of spacetime is predicted to change with
the probed scale (as in multifractals), to be noninteger and smaller
than four. This phenomenon of dimensional reduction can render field
theories finite.
