|MadSci Network: Physics|
Space-time can be curved. It is curved by mass (or energy) - this being the source of gravity. To warp it very much, a huge amount of mass would be required - this is what happens in a Black Hole. If you drew a circle on a flat piece of paper, and measured the radius and the circumference, you would hope to find that radius = circumference / 2*pi. What if you were not aware of height, but lived on the Earth. You could draw the equator - a circle. The radius should be measured from the centre of the Earth. But being unaware of the fdirection 'down', you would measure the radius from the North Pole. This would be much larger than the actual radius. When you divided the equator (your circumference) by 2*pi, you would find that your measured radius was much bigger than your expected radius. There is an excess radius because the Earth's surface - your space - is bent. The surface area of a sphere is A=4*pi*(r^2). If you measured the surface Area, you would expect to predict the radius, r=sqrt(A/(4pi)). ...unless, that is, our space-time is warped. In this case, there may be an excess radius. Excess Radius = Predicted Radius - Measured Radius = GM/(3c^2), where G is Newton's Gravitational Constant, c is the speed of light, and M is the mass inside the sphere (assumed to be evenly distributed). G/3c^2 has a value of about 2.5*10^-29 cetimetres per gram, so for each gram, there is an excess radius of about 2.5*10^-29 cm. As you can see, a lot of energy is needed to warp space-time by a large amount. I suggest you read 'Hyperspace' by Michio Kaku for a godd account of this area, or perhaps 'Six Not-So-Easy Pieces' by Feynman, whose explanation of General Relativity I have just given you.
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