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What is the formal definition of an event? According to Wikipedia, "an event is a point in spacetime (that is, a specific place and time) and the physical situation or occurrence associated with it." This definition seems too large because it includes even points where no identifiable process is happening.

On the other hand, what about particle-fields interaction:

  • a comet passing through the gravitation field of the Sun
  • a collision between two particles where one particle is entering the field of another particle and then bouncing off in a parabolic worldline (deceleration & acceleration).

In both cases a field is continuously acting on an object, thus the event itself seems to be somewhat continuous.

Can someone provide a formal definition which is taking into account particle-fields interaction? Do continuous events exist?

Edit: The Wikipedia definition (which also might be found in textbooks) is inacceptable for a particular reason: Events (such as a particle collision) have somewhat observer-independent character, i.e.all observers agree on the fact that an event happened, even if they disagree on the time & the simultaneity of the event. In contrast, we cannot say that observers agree on any "point in spacetime".

=> A sufficient answer would be a good reference for what @By Symmetry wrote.

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    $\begingroup$ An event is indeed a point in spacetime i.e. $(t,x,y,z)$. The phrase continuous event is an oxymoron. We get continuous processes when the events are points on a differentiable manifold so we can use calculus to trace how trajectories link sets of points. $\endgroup$
    – John Rennie
    Commented Nov 26, 2015 at 17:50
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    $\begingroup$ The point of the definition of an event is not to capture the meaning of the word event in natural language, its that we needed a name for a point in 4d space-time that was distinct from the name for a point in 3d space, in order to avoid endlessly having to clarify which one we were talking about. "Event" seemed like a good name for the purpose. $\endgroup$
    – By Symmetry
    Commented Nov 26, 2015 at 18:53
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    $\begingroup$ So what name would we have to give to "points of interaction of worldlines" (= events in natural language)? $\endgroup$
    – Moonraker
    Commented Nov 26, 2015 at 19:41

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When you talk about a point in space, you're talking about a specific set of $(x, y, z)$ coordinates. Of course there's no use to talking about a point in space unless something is happening there,

e.g. $(0, 6, 0)$ is the cannonball's starting location".

An event is the same idea in $3+1D$ spacetime- it's a specific set of $(t, x, y, z)$ coordinates. That's all. For example, "$(0, 0, 6, 0)$ is the cannonball at the start of its motion", or "at $(6, 1, 5, 3)$, the comet was experiencing X gravitational force from the sun".

So "continuous events" not only don't exist, it doesn't even make sense to talk about continuous vs discrete events.

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I might be wrong but I interpret your question as : if actual measurements of physical events are extended in both space (such as a macroscopic clock), and time, why do we interpret them as happening instantaneously and located at a single point in space?. In this sense, an event is an idealization that is exact only in the limit when it can be thought of occurring at a zero dimensional location and at a specific time, as opposed to a time interval measurement and some finite space volume. This mathematical idealization of defining processes as occurring at a singular spacetime point is still a very useful concept to work the details of a theory, even if, in practice, events are not exactly ideal.

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