  Accreting black holes are responsible for producing the fastest, most
powerful outflows of matter in the Universe. The formation process of powerful
jets close to black holes is poorly understood, and the conditions leading to
jet formation are currently hotly debated. In this paper, we report an
unambiguous empirical correlation between the properties of the plasma close to
the black hole and the particle acceleration properties within jets launched
from the central regions of accreting stellar-mass and supermassive black
holes. In these sources the emission of the plasma near the black hole is
characterized by a power law at X-ray energies during times when the jets are
produced. We find that the photon index of this power law, which gives
information on the underlying particle distribution, correlates with the
characteristic break frequency in the jet spectrum, which is dependent on
magnetohydrodynamical processes in the outflow. The observed range in break
frequencies varies by five orders of magnitude, in sources that span nine
orders of magnitude in black hole mass, revealing a similarity of jet
properties over a large range of black hole masses powering these jets. This
correlation demonstrates that the internal properties of the jet rely most
critically on the conditions of the plasma close to the black hole, rather than
other parameters such as the black hole mass or spin, and will provide a
benchmark that should be reproduced by the jet formation models.
