Suppose an instrument at one location emits a signal. Two seconds later, a station far away records an alarm.
Could the first event have caused the second?
The answer does not come from the words before and after. It depends on how far apart the events are, how much time separates them, and whether any influence could have crossed that distance in time. Relativity gives us a diagram for answering exactly that question: the light cone.
A light cone is often introduced as a picture of the rule that nothing travels faster than light. That is true, but it puts the emphasis in the wrong place. The deeper use of the diagram is to show which events can be causally connected. The speed of light matters because it marks the boundary of possible influence.
In relativity, an event is something that happens at a particular place and time: a detector clicks, a lamp turns on, a message arrives. A light-cone diagram begins by choosing one such event as its reference point.
Now imagine that the event emits a flash. As time passes, the light moves outward in every spatial direction. In ordinary three-dimensional space, the expanding wavefront would be a sphere.
A basic spacetime diagram suppresses two spatial dimensions and shows only one horizontal direction, with time running vertically. The expanding light therefore appears as two diagonal lines. If we include both the future and the past of the chosen event, those lines form the familiar double cone.
En acoustique, on entend la montée de la fréquence quand une ambulance arrive et sa descente quand elle s’éloigne. En relativité, l’effet Doppler s’applique à la lumière, pas au son, et la formule classique ne suffit plus.
Pour un émetteur et un récepteur s’éloignant ou se rapprochant selon la ligne de visée : $$ \frac{\lambda_{\text{obs}}}{\lambda_{\text{em}}} = \sqrt{\frac{1 + \beta}{1 - \beta}}, \quad \beta = \frac{v}{c}. $$ En termes de fréquences : $$ \nu_{\text{obs}} = \nu_{\text{em}}\, \sqrt{\frac{1 - \beta}{1 + \beta}}. $$
Exemple astronomique : Une planète en orbite à 30 km/s provoque un décalage d’environ 0,01 nm sur une raie de fer, suffisant pour sa détection.
L’aberration modifie l’angle \(\theta\) entre un rayon lumineux et la direction du mouvement. Si \(\theta\) est mesuré par la source et \(\theta'\) par l’observateur : $$ \cos\theta' = \frac{\cos\theta - \beta} {1 - \beta\,\cos\theta}. $$
