In classical physics, the direction from which light appears to arrive is the same in all inertial frames. However, in special relativity, the observed direction of incoming light depends on the relative motion between the observer and the source. This phenomenon is known as relativistic aberration.
Relativistic aberration is the apparent shift in the angle of incoming light due to the motion of the observer. It becomes significant when the observer is moving at a velocity comparable to the speed of light. This effect is not merely a visual illusion—it has measurable consequences in astrophysics, particularly in observations of jets, pulsars, and quasars.
✅ Aberration relates angles of light between frames.
✅ The formula:
cosθ=1+βcosθ′cosθ′+β.
✅ Radiation is compressed into a ∼1/γ cone in the observer frame.
✅ Crucial for understanding relativistic jets, AGN, GRBs, pulsar winds.
Example Calculation
Suppose an AGN accretion disk emits photons isotropically in its rest frame.
Consider a region of the disk moving at v=0.95c (inner disk) relative to the observer.
We wish to compute the apparent angleθ in the observer frame for photons emitted at θ′=90∘ in the disk frame (i.e. photons emitted transverse to the disk motion).
Compute γ:
γ=1−(0.95)21≈3.20.
Therfore, we know from the 1/γ approximation that the radiatino will be beamed forward at an angle of
γ1=0.3125rad.
We can check this result by using the full aberration formula
cosθ=1+βcosθ′cosθ′+β,
which for an angle θ′=0, is reduced to
cosθ=β=0.95.
Solving for θ:
θ=cos−1(0.95)≈0.3176rad.
Interpretation:
A photon emitted sideways (90∘) in the accretion disk frame is observed at ∼18∘ in the observer frame — strongly beamed forward.
The disk appears brighter on its approaching side, with radiation compressed into a cone of angular width ∼1/γ≈18∘.
High-velocity regions of the disk (v∼0.95c) beam their radiation forward.
Even photons emitted sideways in the disk frame appear at small angles ∼1/γ in the observer frame.
This effect contributes to the brightness asymmetry of relativistic disks.