Okay, tlet me know where I trip up:(adsbygoogle = window.adsbygoogle || []).push({});

The everyday concept of "distance" allows an event to occur in only one place at one time and nowhere else.

But because of the interval metric's signature (it has both positive and negative terms), the definition of four-dimensional distance implies that there is zero distance between a point in space-time and an an infinite number of other points called the "null cone."

My understanding is that the four-distance is called a "pseudo metric" because it is not transitive. That is, if the 3-distance distance A to B is nonzero and the 3-distance B to C is nonzero, the four-distance between A and C may be zero even if A and C are separated in both time and space (in equal amounts).

To clarify, I mean that an event at (3-dimensional) location A at time t also exists at a different spatial location B at time t+n, because if you add the same number to both the space and time coordinates of A, the value of the metric (the distance AB) remains unchanged.

Is that correct?

If so, it would seem to imply that a point mass which winks into existence for an instant at time t, continues to exist in future times, but in multiple locations. Specifically, as time unfolds, the event, (which happened in the past) continues to exist in the future as a sphere expanding outwards at c, and in fact, this is what the four-dimensional null cone looks like in three dimensions.

...and is THAT correct?

So when the null cone of this mass event intersects (passes through) a different event (say, a human at exactly 5 pm), the absolute distance between the instantaneous mass event and that human is zero (momentarily).

Is that correct too?

If so, then isn't the passage of the null cone through the human identical to (i.e., just another name for) the gravity wave produced by the instantaneous mass event?

To give a concrete example, this appears to mean that when you feel the tug of the Moon's gravity, what you're feeling is the physical moon itself touching you, but in the past.

If all this is true, I think it has very interesting and possibly important implications which involve my other question (in another message thread) about mass being a condition of space.

But I want to know if I made a mistake in my understanding before I point them out.

Thank you,

-- faye

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# Mass and the interval metric

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