Chromosomes in the eukaryotic nucleus are highly compacted. However, for many functional processes, including transcription initiation, the 3D pair-wise motion of distal chromosomal elements, such as enhancers and promoters, is essential and necessitates dynamic fluidity. Therefore, the interplay of chromosome organization and dynamics is crucial for gene regulation. Here, we use a live imaging assay to simultaneously measure the positions of pairs of enhancers and promoters and their transcriptional output in the developing fly embryo while systematically varying the genomic separation between these two DNA loci. We develop a comprehensive data analysis pipeline to extract the two-point correlations, giving insight into the underlying polymer physics of the system. We identify a striking combination of static and dynamic exponents suggesting a combination of fractal globule organization with ideal chain subdiffusive dynamics. These combined features cause an anomalous scaling of polymer relaxation times with genomic separation. We demonstrate how these relaxation times set the time-scale for functional transcriptional encounters, suggesting that such encounters are much less dependent on genomic separation than predicted by existing polymer models. These findings have crucial implications for the spatiotemporal organization of the cell nucleus, including the dynamics of long-range focal contacts and enhancer-promoter interactions.