that we're in a railway carriage that has a large mirror attached to
one of the
carriage's side-walls. We stand alongside this mirror, face-on, and
fire a light-beam directly at it. If the laws of physics appear to us
to be those of a "stationary" observer, we'll expect the beam to strike
the mirror at 90 degrees, leave the mirror at 90 degrees, and end up
being reflected straight back at the original light-source.
assume that this is what actually happens.
does this situation appear from the point of view of a second observer,
in a train moving along a second set of tracks parallel to
other observer is forced to agree with us that the light
source, bounces off the glass and ends up back at the source
again ... but from their perspective, the
source has moved
this time. They see the lightbeam to be emitted at
moving at an angle that takes it forwards to reach the moving mirror
and strike it a glancing blow, and then being reflected forwards to hit
the source again at its new position, B.
observer can argue that in order for the light to be able to
keep up with
us, it can't just be aimed sideways, it also has to
have a velocity
component parallel to the tracks, that exactly matches our velocity ...
The ray that we think is aimed at exactly 90
degrees appears to
the other observer to be aimed (and reflected) in a slightly different
direction. It seems to them that in order to hit the
source, our beam
must have been aimed at the mirror at an angle other than 90 degrees,
so that the reflected ray could point towards the source's future
argue that for the beam to hit its target, the lightsource must have
been tilted to point more towards the direction that we were
The condition that the second observer needs
the "transverse-aimed" ray to advance along the track at
the same rate as its source is enough for us to be able to work out the
angular deflection as a function of velocity.
"transverse-aimed" ray (aimed at an angle "A = 90 degrees"),
this gives us:
relationship can be written in various different ways, depending on
the scheme that we choose for labeling our angles).
"relativistic aberration" effect shows up in special
relativity [notes] , and
also in historical Newtonian ballistic
emission theory, which assumed that light was
thrown off at a set speed with respect to its emitter.
we want to generalise this result, and apply the same argument to any
rays that we emitted in other directions, we arrive at
This gives us the apparent angle-change for light emitted in any
direction. It can also be used to calculate a relativistic theory's Doppler
shift predictions, for any angle.
aberration generates two major results:
since light from a "moving" body has to appear to be tilted
to point more towards the direction that the body moves in, if
body emits a burst of light that it believes to be equally concentrated
in all directions, outsiders for whom that body is seen to be "moving"
will see a greater quantity of light to be emitted in the
forward direction, and a reduced quantity to be aimed
The body supplied more intense illumination to objects placed
ahead of it than behind it.
- Geometrical distortions: The
moving object's angles appear more "squashed together" at the front of
the object and more "splayed apart" at its rear. If we're looking at
the side of the object, the tilt of the rays, which makes it easier for
us to see the object's rear and more difficult for us to see its front,
might be interpreted as showing an image in which the object appears to
be partly rotated, with its nose tilted away from us (Terrell-Penrose
However, the "rotation" interpretation doesn't work so well for the
view seen by observers placed in front of (or behind) the object:
instead they see more (or less) of the surface than they would have if
there had been no relative motion.
arguments apply for how the moving observer sees their surroundings.
The surrounding universe can be taken as an "object"
been turned inside out to face us, and aberration effects tell us that
we should see our surrounding starfield to distorted when we
through it at high speed: The starfield should appear to us to be more
concentrated in the direction that we're moving in, and less
concentrated in the region that we're moving away from. Stars whose
positions we believe to be at exactly 90 degrees to
our position and direction of motion should be seen
by use to slightly ahead of us.
Not to be
aberration of light, which is about the annoying
tendency of glass lenses to focus different colours
at different places.
Bradley "… an Account of a New Discovered Motion of
the Fix'd Stars" Philosophical Transactions of the
Royal Society 637-660 (1728)
Einstein, " On the Electrodynamics of Moving Bodies
" (" Zur Elektrodynamik bewegter
Annalen der Physik 17 891-921 (1905)
Terrell "Invisibility of the Lorentz Contraction"
Physical Review 116 1041-1045 (1959)
Penrose, "The Apparent Shape of a Relativistically
Moving Sphere" Proc. Cambridge Phil. Soc. 55
137-139 "Research Notes", letter (1959)
starfields are discussed and illustrated in:
Scott and H.J. van Driel "Geometrical Appearances at
Relativistic Speeds" Am.J.Phys. 38 971-977
original material copyright © Eric Baird 2007/2008