[Deecart (OP)]

Can someone explain me why we talk about "light cone"  ?
Why the particular angle of the cone and so forth ?

[Dimensional]

Can someone explain me why we talk about "light cone"  ?
Why the particular angle of the cone and so forth ?

It would probably be a good idea to start a new thread about this.  But here is a good reference with some illustrations and definitions https://sites.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/spacetime/ .  If you know the basics, just scroll down about halfway to the light cone.

[Deecart (OP)]

Ok but light do not expand like that (some light cones).
It is more like this https://www.avionslegendaires.net/dossier/mur-du-son-et-bang-sonique/theorie-en-images/
Look at the image labeled 2.
You can verify if you have a "cone" or "circular expansion" using 2 detectors placed at the right place of the space (if light strike the first or the second detector at first (al last) you know the way light expand)

Furhermore i dont understand why in this document we are talking about 2D expansion of light when we know that light is expanding in 3D.

To see that structure, we imagine an event at which there is an explosion. Light will propagate out from it in an expanding spherical shell. In a two dimensional space, it will look like an expanding circle, as shown below.

After that we are reminded that we are not talking about light...
Ok...

To have a light cone, we do not need light to be present. The cones map out the trajectories light would take if light were to be present. Since it is just the possibilities that are mapped out, not necessarily the trajectories of actual light. Spacetime still has a light cone structure in the dark!

It is what we already known.
We talk about the expansion "of the possible action" (all SR is based onto).
But how do this "object" propagate ? (perhaps it is why we just talked about ligth, because if not it would be just nonsens ?)

To see how this works, pick any event "O" in the spacetime. The future light cone at O contains all the events in the spacetime that can be reached from O by future directed timelike or lightlike curves. If we make the usual assumption that all causal processes propagate at or less than the speed of light, we conclude that these are all the events that we can causally affect from O.

Now we think that "possible action" can be analog to light... but we dont even use the right expansion of light.
This is not science, more science fiction.

[Eternal Student]

Hi.

Je ne parle pas bien le français. Je suis vraiment désolé.  ↔  I don't speak French well, sorry.

Look at the image labeled 2.

   Je ne trouve pas d'image 2. Est-ce celle-ci ?    ↔   I couldn't find an image labelled 2.   Was it this one?


  Onde du Choc  ↔  "Shock wave"

Était-ce celui-ci ?   ↔  Was it this one?


  Mur du son  ↔  "Wall of sound"    but probably better translated as  "the sound barrier".


This is the usual sort of image presented for light cones:

[Image taken from Wikipedia article, in English:  https://en.wikipedia.org/wiki/Light_cone ]

An alternative discussion in French:   https://fr.wikipedia.org/wiki/C%C3%B4ne_de_lumi%C3%A8re

Furhermore i dont understand why in this document we are talking about 2D expansion of light when we know that light is expanding in 3D.

    We want a diagram in 3 -dimensions  BUT one of our available directions is taken up by the time axis.
    All we have left is then (at most) 2 other directions.     We show light as something expanding in a 2-dimensional space BUT we are aware that it's happening in 3-D space  - you just can't fit all the information on a simple diagram.
   ↔   Nous voulons un diagramme en 3 dimensions MAIS l'une des directions est le temps. Par conséquent, nous n'avons que 2 dimensions pour l'espace sur le schéma.

But how do this "object" propagate ? (perhaps it is why we just talked about ligth, because if not it would be just nonsens ?)

    If I've understood what you are saying then I think you have got it right and explained exactly why we're interested in light cones in your next quote:

The future light cone at O contains all the events in the spacetime that can be reached from O by future directed timelike or lightlike curves. If we make the usual assumption that all causal processes propagate at or less than the speed of light, we conclude that these are all the events that we can causally affect from O.

    We usually aren't interested in light.  We are interested in how everything else,  every sort of particle, might propagate.   We make the usual assumption that nothing travels faster than light,   so the future light cone shows the maximum (biggest) regions of spacetime that can be influenced by something that happened at a given event.  Meanwhile, the past light cone shows the biggest region of spacetime that could have influenced that given event.
   

Now we think that "possible action" can be analog to light...

    That is not essential.   All we assume is that no particle travels faster than light.

Best Wishes.