• # Question: Since space and time are the same is it that whatever happens at different positions in space should take place at different time? If what I think is correct consider an electric dipole, the charges are at different positions in space then, can there be electrostatic attraction between the charges even if they are individually present in different time?

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Asked by rajathjackson to Dave, David, Jack on 26 Jun 2013.
• Jack Miller answered on 26 Jun 2013:

Hi Rajath,

You’re sort of right, in that there’s no such thing as a simultaneous event. It is impossible to say in an absolute sense whether two distinct events occur at the same time if those events are separated in space, such as a car crash in London and another in New York. The question of whether the events are simultaneous is relative: in some reference frames the two accidents may happen at the same time, in other frames (in a different state of motion relative to the events) the crash in London may occur first, and in still other frames the New York crash may occur first. However, if the two events are causally connected (“event A causes event B”), the causal order is preserved (i.e., “event A precedes event B”) in all frames of reference.

This is, I think, pretty damn cool!

— Jack

• David Freeborn answered on 26 Jun 2013:

Yes,

You’re exactly right. Suppose we have a charge at a particular point in space and time, and then the charge vanishes (this is a thought experiment, not something that is physically possible). The electrostatic field will linger even after the charge has vanished. The field will slowly vanish at the speed of the electromagnetic field (which is the speed of light). What is happening is that the electric charge can generate an electric field in both space and time.

We see the same effect in General Relativity: in fact this is precisely what separates it from Newtonian gravity. When we move a mass, the space-time metric doesn’t immediately settle back into place: it moves back into place at the speed of light: c. So a mass generates a “gravitational field” in space and time by bending both the space and time around it.

That reveals something really important, a really profound point I have seen a lot of physicists misunderstand. Newton believed that space and time should be closely related, but his theory of gravity is not symmetric between space and time. Einstein’s relativity is said to have a “deeper symmetry” than Newton’s gravity.

I hope that explains what you were asking. This is a really important and fascinating principle.