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A Minkowski diagram is a two-dimensional graphical depiction of a portion of a (suitably selected) region of flat spacetime, and thus of a corresponding set of events, such that (among additional properties)

  • each distinct (point-)event is depicted as a distinct point of the graph, and

  • each segment of a world line contained in the spacetime region being depicted is depicted as segment of a line in the graph.

As far as a certain (segment of a) world line consist exclusively of events in which a certain "material point" (such as an electron, or an atom) took part (event by event generally together with varying others), the corresponding line segment in a Minkowski diagramm can be labelled accordingly;

  • for instance with the specific symbol of the particle type (such as the symbol "$e$" being associated to the world line of a particular electron in one of Minkowski's original diagrams: "Fig. 4";

  • or more abstractly, by generic distinctive letters (in particular by capital letters, following Einstein's use of denoting distinct individual participants by "$A$", "$B$", etc.) as shown in some of these pictures, or here as well.

A certain point of a Minkoski diagram which is supposed to depict the specific event in which, say, both the participant identified as "$A$" and the participant identified as "$Q$" took part together, would therefore uniquely and conveniently labelled as "$\varepsilon_{(AQ)}$", for instance. (Examples of this particular notation seem rare, however.)

Now, consider the specific case of a Minkowski diagram with line segment "$A$" depicting the world line of a certain atom, and line segment "$Q$" depicting the world line of a certain electron, and the point labelled "$\varepsilon_{(AQ)}$" depicting a collision event in which both the referenced atom and the referenced electron took part; and which involved the collisional excitation of the atom (i.e. the excitation strictly only of this atom, but certainly not of this electron).

My question:

In a Minkoski diagram having two line segments labelled "$A$" depicting the world line of a certain atom, and "$Q$" depicting the world line of a certain electron, where these two lines have a common point labelled "$\varepsilon_{(AQ)}$" which depicts specifically the collision event of the atom and the electron,
is there a graphic element which depicts specifically the collisional excitation of the atom ?

(Note however, that the collisional excitation of the atom in the collision event depicted as the point "$\varepsilon_{(AQ)}$" can in any case be symbolized as "$A_Q$"; distinct from the symbol "$Q_A$" symbolizing the specific indication of the electron in this same collision event.)

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  • $\begingroup$ For full disclosure: The OP question was submitted in attempting fulfillment of the suggestion in this comment, with particular attention to the underlying question. $\endgroup$
    – user12262
    Oct 25, 2023 at 22:24
  • $\begingroup$ Why not just call the resulting recoiling particle with a star (for example like $N\to N^*$), you can name these lines whatever you want and the collision and particle type are really immaterial to minkowski space. $\endgroup$
    – Triatticus
    Oct 26, 2023 at 1:08
  • $\begingroup$ @Triatticus: "[...] call the resulting recoiling particle with a star" -- Labeling the line segment which depicts the relevant world line segment (events in which the excited atom took part) with its designation which generally involves a star/asterisk symbol ? Sure, easy. However: OP is about depicting the collision excitation of the atom $A$ (and not of the electron $Q$!), without significant temporal or spatial extent itself; which I'd call "the atom's part of the collision event with the electron", IF this were admissable. $\endgroup$
    – user12262
    Oct 26, 2023 at 5:57
  • $\begingroup$ @Triatticus: "collision and particle type are really immaterial to minkowski space." -- Whether two specific lines of a Minkowski diagram have a point in common, or not, seems relevant, though. This point depicts the collison event. And we can show the relevant line segment and say "This depicts the world line of the excited atom". But which piece of the Minkowski diagram shows the collision excitation of the atom $A$ (and not of the electron $Q$!) ? If there is, then label it $A_Q$. ... And this may be relevant, too, for determining ratios of spacetime intervals in the first place, btw. $\endgroup$
    – user12262
    Oct 26, 2023 at 6:00
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    $\begingroup$ No what I'm saying is you are overthinking it, you can label lines whatever you please in a minkowski diagram, all a minkowski diagram does is chronicle what happens in spacetime in a given reference frame. If your particle becomes excited and recoils you can name it something completely different. The fact that it is a minkowski diagram doesn't care what you've labeled your before and after particle. $\endgroup$
    – Triatticus
    Oct 26, 2023 at 18:40

1 Answer 1

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No.
A Minkowski diagram which depicts the complete collision event $\varepsilon_{(AQ)}$ of atom $A$ and electron $Q$ as precisely and only as one point (without any temporal or spatial extent) does not offer any graphics element that would depict exclusively the collision excitation of the atom $A_Q$ (as the portion of event $\varepsilon_{(AQ)}$ attributable specificly to the atom, and not to the electron).

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