  Radiation reaction describes the effective force experienced by an
accelerated charge due to radiation emission. Quantum effects dominate charge
dynamics and radiation production[1][2] for charges accelerated by fields with
strengths approaching the Schwinger field,
$\mathbf{E_{sch}=}$\textbf{\SI[detect-weight]{1.3e18}{\volt\per\metre}[3]. Such
fields exist in extreme astrophysical environments such as pulsar
magnetospheres[4], may be accessed by high-power laser systems[5-7], dense
particle beams interacting with plasma[8], crystals[9], and at the interaction
point of next generation particle colliders[10]. Classical radiation reaction
theories do not limit the frequency of radiation emitted by accelerating
charges and omit stochastic effects inherent in photon emission[11], thus
demanding a quantum treatment. Two quantum radiation reaction models, the
quantum-continuous[12] and quantum-stochastic[13] models, correct the former
issue, while only the quantum-stochastic model incorporates stochasticity[12].
Such models are of fundamental importance, providing insight into the effect of
the electron self-force on its dynamics in electromagnetic fields. The
difficulty of accessing conditions where quantum effects dominate inhibited
previous efforts to observe quantum radiation reaction in charged particle
dynamics with high significance. We report the first direct, high significance
$(>5{\sigma})$ observation of strong-field radiation reaction on charged
particles. Furthermore, we obtain strong evidence favouring the quantum
radiation reaction models, which perform equivalently, over the classical
model. Robust model comparison was facilitated by a novel Bayesian framework
which inferred collision parameters. This framework has widespread utility for
experiments where parameters governing lepton-laser collisions cannot be
directly measured, including those using conventional accelerators.
