Sunday, October 3, 2010

Creating Black Holes

Planck's Length is 1.6*10^-35 meters. That's .000000000000000000000000000000000016 meters. Very small. The significance of Planck's Length is the borderline between classical physics and physics of a more quantum flavor. Essentially, it is likely that any object that was that small would turn into a black hole.

Now, you can't just chop something into a particle that size, because there is no part of it that small; you cannot divide it into a smaller piece than its base piece.

You cannot compress it into being that small, as any thing you tried to use to compress anything  to this length would need a completely whole surface; the small imperfections would allow anything being compressed to shelter and be compressed only to the size of these molecular crevasses.

So, how can you turn something into a planck's length, creating a manafactured black hole?

Speed.

Special Relativity tells us that an accelerated object compresses along the axis of motion. There's even a simple equation for it;
Length of object at given velocity=(Length of object when resting)*√(1-v^2-c^2)
or
L'=L*√(1-V^2/C^2)

So, if you were too plug in Planck's Length as the resultant Length, you could find the speed necessary to compress any object to Planck's length; effectively you could find the speed you need to accelerate anything too to turn anything into a black hole. Let P=Planck's Length
P=L*√(1-V^2/C^2)
P^2=L^2*(1-V^2/C^2)
P^2=L^2-(V^2*L^2)/(C^2*L^2)
P^2+(V^2*L^2)/(C^2*L^2)=L^2
(V^2*L^2)/(C^2*L^2)=L^2-P^2
V^2*L^2=(L^2-P^2)(C^2*L^2)
V^2=((L^2-P^2)(C^2*L^2))/L^2

Just plug the length into that last equation, and you know how fast you need to accelerate that length into a black hole!

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