Could someone explain to me why space/time must be curved. The few examples given in most books do not convince me of its necessity. My opinion is not fixed on this matter. I just need to understand it better first.
Here is what I see wrong withe the examples commonly given.
First a short story.
A long, long time ago, in a universe far far away, there was two planets.
The planet called De Sitter, and the plant Euclid. They share a common history and differ only in their view of the universe.
The planet De Sitter claimed that space was curved, and the shortest path between two points was a curve called a Geodesic line.
The planet Euclid claimed that only the yardstick used to measure space was curved, and the shortest distance between two points is a straight line.
Both have spacecraft that can travel at the speed of light. Planet De Sitter issues a challenge to a space race to decide this once and for all, the loser must stop space travel. Planet Euclid picks the course for the race. It is through a corridor of densely packed stars and planets. Planet De Sitter is pleased with the choice, as gravity and curved space is on their side.
Both ships can travel forward at the speed of light, but they are not the same design. The Euclid ships are equipped with powerful maneuvering thrusters all around. Their computer system uses relativity to calculate the gravitational pull in any direction on the ship, and the gravity is opposed by maneuvering thrusters so that the ship maintains a straight line through space.
The Euclidean ship wins the race hands down because the De Sitter ship must follow a curved, snake like course in the race.
End of story.
The yardstick we use to measure space is itself bent and distorted by gravity as shown by Einstein. But this is not proof that space/time is curved.
The Red Shift is evidence that the universe is expanding, but not proof that space/time is curved.
Let us look at the now famous balloon example, with a twist.
Place the balloon in a vacuum chamber and fill the balloon with hydrogen gas. As you decrease the air density around the balloon, it expands. Atoms within the balloon move away from each other as it tries to keep a uniform density within the balloon. Dots on the balloon will move away from each other also. Yet all this happens within a defined 3 dimensions plus time.
The greater density within our universe causes it to expand into the vacuum around it, while all the energy/matter within it seeks a uniform distribution, just like the gas within our balloon. We see everything moving away from us, even though we are not at the center.
The warping of space is RELATIVE to our frame of referance. If our frame of referance is a rubber yardstick that bends (light), then we percieve that space is bent also. But if we know how much our yardstick is bent, we can correct for it.