January 20, 2012

The Light Limitation

I've been wondering why things can't go faster than light, and while practicing my Living Biography speech, I figured out the answer.  Here is Einstein's equation for velocity-corrected mass:

W = m * (1 / sqr(1 - (v ^ 2 / c ^ 2)) - 1)
where W is the velocity-corrected relative mass,
m is the original mass,
v is the velocity at which the object is moving (in miles per second),
c is the constant speed of light (186282.4 miles per second),
and sqr is a function that returns the square root of its input.

If an object with a mass of 274 is moving at 186292.4 miles per second, just a little faster than light...

W = 274 * (1 / sqr(1 - (186292.4 ^ 2 / 186282.4 ^ 2)) - 1)
W = 274 * (1 / sqr(1 - (34704858297.76 / 34701132549.76)) - 1)
W = 274 * (1 / sqr(1 - 1.0001073667550953108019300907397) - 1)
W = 274 * (1 / sqr(-0.000107366755095310801930090739)

"ERR: NONREAL ANS" is generated upon attempting to simplify the last line.  It is impossible to get a real answer for the square root of a negative number, hence an object moving at this speed cannot be sustained in this universe.  If you attempted to move at exactly the speed of light, you would end up dividing by zero (creating a theoretically infinite mass).

And there you have it!  The equation at the top of this post is a great thing to know and share with others at opportune moments.

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