If you took all of time and made a timeline out of it, then you take all of space or all locations that would be relative to the context. You take one spot on each of those things and that would be your particular “random moment” you would reference. It’s basically like saying, “anytime, anywhere”. Of course, it’s taking into account that the point in space and time would be relative to the subject matter. For instance, let’s say you’re talking about human interaction, and the saying comes up, they’re clearly not talking about the planet Jupiter in 5,000 B.C.E., in this case they likely mean a single point in time and space where two humans have interacted, typically in the past as well, but not always. The point in time and space is inferred based upon what other information is being talked about. Sometimes, they will be literally talking about all space and all time, other times, they will mean a time in the past, or a space on or near Earth where s human being would exist or something else relative to the topic. It could mean a random place and time or one chosen by the dictator of the explanation, as well.

Its usage dependent. But I get the feeling you mean a mathematical point in space time. Its a dimensionless point. Exactly 0 meters in every dimension. It doesn’t have a size. So if you pick a point in space of 1, 1, 1 it has 0 volume. There is no radius because the location is 1.00000….. on each axis. Its not spread over an area. It’s not even a plank length size point, because a plank length still covers an area.

If you don’t mean the mathematical point, its generally determined by the scope of the measurement and precision required. A point in space for a satellite could be a cubic meter or a cubic kilometer. Depends on how accurate they want to be.

It’s not something physical, it’s a location (and time), like being able to give the GPS coordinates for it. The coordinates for this point on the Earth’s surface are: x, y. It is now date/time t.

So basically whoever’s talking about “a single point” is trying to tell you where to look, in an abstract way. What you may find there when you look (atoms, etc.), that’s something else. Like “my boat is at these GPS coordinates” or “it’s just open ocean nothing there at these GPS coordinates”.

When physicists talk about idealized particles, they sometimes call them “point particles” or “pointlike particles.” These are not necessarily real things; they are basically a way to say, “imagine you had a particle that took up no space whatsoever, but had other properties.” So you could imagine what the math of a pointlike particle that had only an electric charge would be. It is a simplifying abstraction that basically says, “for the point of this discussion, I am assuming that this particle has no size or volume.” There may be reasons to imagine that certain fundamental particles, like electrons or quarks, are actually pointlike particles. But whether they are or aren’t isn’t really necessary for a lot of the equations, so assuming they are makes the math a lot easier.

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