What is meant by the curvature of spacetime?

Answer 1

The best analogy is to imagine a sheet of stretched rubber on which you put some marbles. The marbles will create indentations in the sheet. Planets and stars create the same indentation in space except they do so in three dimensions instead of 2.

Answer 2

Einstein postulated that all objects of mass bend space in their immediate vacinity, hence the universe, as a whole, bends space in it's immediate vacinity to a point where you can't travel out from the center in a straight line.

Even light bends due to the mass

With this BIAS influence it means you can NEVER be sure if you are travelling in a straight line or slight parabol.

Einstein postulated that if you left Earth in a space ship going in a straight line after eons you would return to the same spot without ever turning around.

If there was, for example, a black hole between US and a STAR at a close proximate to the LINE OF SIGHT, the black hole would bend the light and thus the position we think the star is in would be incorrect becuase of the BIAS shift caused by the black hole.

This, by the way, has been proven during eclipses of the sun

Stars near the edge were not exactly where they were supposed to be. Their LIGHT was bent by the gravity of the sun so they were off by seconds of an arc.

This also, it would seem, tends to make occultations a paradox. If a star is about to be eclipsed by the sun it vanishes sooner that it's position should because of the bending and it comes out later.

It is also possible that occulations may also have proved Einstein to be correct. If so, the ingress and egress should be milliseconds shorter than the distance travaelled required.

In other words a star moves from POINT A (ingress) to POINT B (egress) slightly faster than it should for the diameter of the disk, but were talking milliseconds here.

It also means we must take that into account when judging a diameter based on occultations. We could be off, in the case of the sun, by hundreds of miles on for Jupiter by several miles.

Think of the UNIVERSE as a HAMMOCK made of mesh cord. Put a base ball in the center. You will see the weight (graity) of the ball stretches the cords and makes them bend.

Now do this in three dimensions instead of two.

Now do this in four dimensions instead of three.

Time and space are altered around gravity wells.

Now, imagine 100 trillion gravity wells in the universe

Imagine an expanding, near circular universe and the gravity wells created by it on the space outside of it's even hornizion.

The gravity well event horizon preceeds the mass, partical or light of the mass by a fraction.

Now imagaine a universe with nothing (which don't exist, but I said imagine).

It is the hammock made of cords.

Now imagine somehwere, anywhere, a gravity well starts to grow. It pulls against all the cords, drawing them closer to it and streatching out the cords near the tie down points.

Now imaging that gravity well getting SO powerfull it deforms all of space (the hammock) then it explodes and puts out pebbles that each form gravity wells along the fabric of the haommock in a spherical patter moving outward from the center.

The deformity of the uiverse relaxes and starts to return to the shape it was in before the gravity well, but not totally because it has little gravity wells all over the place.

Answer 3

To get a feel for "curvature of spacetime", imagine that you are walking on a road in a broad valley. Ahead of you appears to be an undersized small town. Before you continue, you investigate by first walking around it in a circle. You come back to your original spot after walking less than a mile. Then you proceed into the town. After a while, you realize that you've walked a mile, and you're now in the center of the town. But everybody knows that the circumference of a circle is longer than its radius! But in curved spacetime, this bizarre outcome is possible. Because it no longer obeys the "Euclidean metric", it's considered as an example of non-Euclidean geometry, where numerous other violations of Euclidean geometry could occur, such as the angles of a triangle adding up to more than 180 degrees (Reimannian), or less than 180 degrees (Lobachevskian). These particular geometries have been named in honor of the 19th century mathematicians who first studied non-Euclidean geometries.