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In another forum, I read this question: On page 31 of the book Gravitation there a image in which various events are symbolized by a black dot, absorption of a photon, emission of a photon, collision between particles,etc. What can be said (for example) of the particle -before- it collides with the other particles? The particle is moving freely in the spacetime, but it hasn't yet collided with the other particle, so at moment there is not been any event... How is the state of this particle defined? Someone did this answer: An idea behind the GR, although not always explicit, is that the events constitute a kind of and therefore given an event there will be a neighborhood of events. This allows for use spacetime coordinates as continuous variables.

Could you explain me better?

Níckolas Alves
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luca andreoli
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    Link to forum page? – Qmechanic May 31 '23 at 16:41
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    "but it hasn't yet collided with the other particle, so at moment there is not been any event" - In GR, the term "event" does not denote "something that happened that is of interest to us" as in everyday language. "Event" is simply a technical term for a point in 4D spacetime (described by 3 spatial coordinates + 1 time coordinate). Every point (x, y, z, t) in spacetime is an "event" - doesn't matter if there's anything happening there, or if there's any object there or not, etc. – Filip Milovanović May 31 '23 at 20:35

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An event is a point in spacetime, a specific time and place. It is not a physical process. A physical process, like the emission of a photon, happens at some event. But the event itself is the time and place, not the physical process.

Similarly, in geometry a point is a place. You may put a dot at a point, but the dot is not the point and there are an infinite number of other points in a small neighborhood of the point with the dot.

Likewise, a physical process may be used to identify some event, but there is another event at the same place but just a little earlier, and another event at the same time but just a little to the right. The events form a continuum, even if the physical processes are discrete

Dale
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Writing our book (Kopeikin et al. 2011), we suggested the following definition of event:

Let us consider a physical process taking place within a sufficiently small volume of space and a sufficiently short period of time. One assumes that it is possible to reduce the actual physical process to its limiting content by shrinking the volume and the time interval to zero. This brings to life an idealised notion of event, an often used abstraction of a physical phenomenon taking place at one point in space and at one instant of time. Examples of the events are a photon’s emission or absorption, a collision of two elementary particles, a meteorite’s burst in planetary atmosphere, etc. The event is mathematically identified with a point, and the physical world is considered as consisting of a continuous set of points modeling its underlying mathematical structure. The set of events is further equipped with additional mathematical paraphernalia which convert it into a well explored mathematical object called manifold.

I regret that we did not mention what some call "The Third Postulate of Special Relativity", the principle of invariance of coincidences. Tacitly implied since Einstein's times, this principle was spelled out explicitly by David Mermin in his book "Space and Time in Special Relativity":

When one observer says two events coincide in space and time, so will all other observers.

The principle defines an important aspect of the notion of event. For more on this, see this discussion.

Now, you are asking: "What can be said (for example) of the particle before it collides with the other particles?" In my opinion, this question is answered by the fact that a particle is always interacting with virtual particles. In this sense, an event is happening to the particle at each point of its trajectory.

Michael_1812
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  • That is the classical definition of event, but it is completely wrong for quantum phenomena and one should not mix classical and quantum event structure in one sentence or even one paragraph IMHO. "Events" in quantum mechanics are processes that have infinite duration. They either start at infinity and are finished at a specific (and often arbitrary) moment in time or they start at some moment and last for infinity. This is not easily dealt with in the language of classical physics. In quantum field theory it is generally represented with scattering of plane waves from infinity to infinity. – FlatterMann May 31 '23 at 23:06
  • @FlatterMann Does this apply also to a creation and annihilation of a virtual pair? – Michael_1812 May 31 '23 at 23:12
  • I (or better the detectors that I have helped to build) have measured a lot of quanta over the years. Not one of them was virtual. They were all irreversible energy exchanges between one volume of the physical vacuum and another. The only place where I have ever seen virtual particles are the pages of theory books and papers. No offense, but as an experimentalist I can't afford to mistake mathematical terms in a perturbation series (that may or may not even converge) for a physical phenomenon that is so real that it can kill me in seconds if I step into an actual particle beam. – FlatterMann May 31 '23 at 23:15