# Angular aberration

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## Angular aberration |

**Angular aberration** describes the change in angles of light-rays due to the relative velocity of the emitter and observer.

## Contents

## Relativistic aberration

#### Exercise

Imagine that a body is between two parallel mirrors and giving off pulses of light. The light emitted at exactly 90 degrees to the mirrors is reflected exactly back to its origin. We'll imagine that a mask is placed over the object with two tiny holes that only allow light to be emitted in the "special" direction that allows light to retrace its path.

Now let's imagine how the same situation looks is we fly past the experiment at high speed, along a line parallel to the two mirrors. If we believe that we are stationary and the apparatus is moving, then the light needs to be reflected back to its moving source.^{[note 1]} But since the body moves a certain distance while the light is in flight, the transverse-aimed rays also have to be moving forwards by the same amount in order to be able to hit their target – if the body is moving at [math]v m/s[/math], then the parallel-aimed light *also* needs to be advancing at [math]v m/s[/math], and the rays seem to us to be aimed not at 90 degrees to the mirrors, but aimed slightly forwards.

#### The relativistic ellipse

If we calculate the necessary change in angle for every direction we end up with a **relativistic ellipse** diagram, and a general formulafor angle change which agrees wirh C19th emission theory, and also agrees with special relativity.

## Non-relativistic aberration

If the speed of light is absolutely fixed wrt the observer ("stationary absolute aether"), we can argue that the moving signal source will deposit its transverse rays in the stationary aether, and then move forwards, but the rays will be moving at c wrt the observer and should arrive with no angular aberration. However, from the emitter's point of view it would seem to be trailing these rays slightly behind it – they'd seem to be defelected rearwards by the dragging effect of the moving aether ("aether wind" / "aether drag"), so there is still a discrepancy between the apparent angles of the light-rays, as seen by the two observers. Since the nominally-transverse rays will now only be defected back along their same path in the *observer'*s frame, back to the original emitter's position (which has since moved) they will now miss the moving source. In order to compensate for aether drag, the emitter will need to aim their "transverse" rays slightly forwards in order to get them to reflect off the mirrors and hit the source, so if transverse angles are once again *defined* by the emitter as being those "aimed at an angle at which light returns to its source after reflecting off a perpendicular mirror"
, then *these* rays will again be seen to be angled forwards as measured by an observer who sees the apparatus as moving.

For theories in which there is a partial or complete" aether-dragging" effect, we expect intermediate effects ... but still a disagreement regarding the "actual" angles of rays.

## Theories that produce relativistic aberration

#### ... C19th "Ballistic emission theory"

- In the default C19th implementation of Newtonian optics, light is assumed to be emitted at c
_{EMITTER}, and to then continue indefinitely at this same speed. The entire system of light is therefore propagating through space with an offset of v m/s, with all lightrays seen by an observer to have an offset of v m/s in the direction of the emitter's motion.

#### ... special relativity

- In Einstein's 1905 special theory of relativity, the interpretation of what "really" happens in this situation is more complex, but the resulting angular aberration of the lightrays is precisely the same as it is under Newtonian theory. although both theories are relativistic (in that neither assumes an absolute preferred frame for the propagation of light), the frequency-shift associated with a deflection at a given angle is different for the two systems.

#### "acoustic" relativity

- In an acoustic model, the light is emitted at [math]c_{EMITTER}[/math], but received at [math]c_{OBSERVER}[/math]. The angular aberration effect is necessarily the same as BET and SR, but has different associated Doppler shifts to SR for a given angle-change.

## Notes

- ↑ This assumes that the moving observer is sufficiently far from the experiment for their own motion not to appreciably disturb how light propagates within the apparatus.