Time travel and relativity theory have always been explained to me with the following quote-
“Space is curved”
as if this statement alone would somehow automatically make the counter-intuitive concepts behind time travel crystal clear to me.
What does this saying mean? I can understand how a 1-D or 2-D object can be curved, but how can 3-D space be curved?? Or is it just some sort of analogy???
Thanks.
“Space is flat. Einstein was curved.”
And remember kids: “186,000 miles per second. Not just a good idea – It’s the Law.”
If you were a 2-dimensional critter living on, say, a sphere, you could tell that it was a curved surface by drawing a triangle. You find that the angles don’t add up to 180 degrees, you conclude that your space is curved. No need to travel in the 3rd dimension to find out.
Same thing for us. Construct a huge triangle around the sun. Measure the angles. If they don’t add up to 180 degrees, space is curved.
Of course, no one has ever done this. But in GR it is actually spacetime that is curved. So light traveling past the sun should be slightly bent by the curvature. This can be checked, by carefully measuring the positions of stars near the sun during an eclipse. The results agree with the GR predictions, hence spacetime is curved.
Time travel comes in when you imagine a piece of paper bent back onto itself so that it touches itself. If you could jump from one sheet to the next you would find yourself at a point very distant from your original position, measured the long way around. By analogy, we can imagine doing the same thing to spacetime, and jumping to a point very distant in space or time from where we are now. According to GR, this is possible, but we don’t know if such situations actually arise in our universe.
Well, you can think of spacetime as being curved in a higher dimension (the same as the 2D surface of a sphere is curved in the third dimension). In this way, you could potentially “cut corners” by jumping into a higher dimension. For example, consider a 2D creature on a 2D surface. If the surface were bent back onto itself somehow, then this could create a short-cut for the 2D creature to leap onto a very distant (in two dimensions) part of the surface.
Similarly, it seems to us that gravity bends light (as can be seen in “gravitational lensing” caused by distant black holes), whereas in fact the light beams are travelling in straight lines through curved spacetime (mass distorts spacetime, hence gravity). It’s like the route an aeroplane takes to fly from, say, London to Chicago - a “straight line” over the globe’s surface actually looks like a sine curve (or roughly so) on a flat map.
I’ll leave the final word to Douglas Adams:
woo… bit of an identical simulpost there…
A location in space is described by a set of numbers called coordinates. Just like on an ordinary sheet of graph paper, the distance from some starting point is described as so many units to the right or left and so many units up or down. Or a location on a map is described by longitude and latitude.
In space an object can be described as at a location in three space coordinates at a certain time. And it turns out that the space and time coordinates are interdependent. That is, if you change to a different reference point or velocity, you have to describe the position by a different set of coordinates and the old space coordinates alter the new time coordinate and the old time coordinate alters the new space coordinates. The old and new space and time coordinates are interdependent with a change in reference points.
It turns out that in order to describe the motions of objects in space and time in the vicinity of objects having mass, it is necessary to use a curved set of lines on the graph of space and time, so space is described as “curved.”
This is sort of sketchy and hurried and my detailed expertise in this area is limited. But this is the general idea of curved space.