Holborn was born in Weende, Göttingen, the son of Louis and Louise née Oelsen.
He then taught mathematics and physics while also serving as an assistant to Ernst Christian Julius Schering at the Göttingen geomagnetic observatory (Gaußschen Erdmagnetischen Observatorium).
In 1890 he joined the Physikalisch-Technische Reichsanstalt, working there with Hermann von Helmholtz at Charlottenberg and designed a torsion magnetometer in 1903 in collaboration with F.W.G.
This optical pyrometer involved matching colours of an object heated with known reference filament until it becomes invisible.
Another pyrometer of the same kind was independently developed and patented by Everett Fleet Morse in the US.