MadSci Network: Physics

Re: Why can't we warp the space time continuum??

Date: Sun Nov 12 10:13:36 2000
Posted By: Dan Mayer, Post-doc/Fellow, Mathematics and Theoretical and Particle Physics, I am currently out of work.
Area of science: Physics
ID: 968551309.Ph

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 

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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