## What Happens When Things Go Near the Speed of Light? Advanced Analysis: Deriving the formula for g

### Use the mathematical form of the plot to derive g - understanding the constant.

 Bin Number Mean Decay Length (s) Mean Decay Time (s) Constant (s2) 1 5.25320 E-12 5.26699 E-12 1.4506 E-25 2 1.19318 E-11 1.19523 E-11 4.8848 E-25 3 1.11187 E-11 1.11317 E-11 2.8949 E-25 4 1.15704 E-11 1.15802 E-11 2.2665 E-25 5 1.39178 E-11 1.39267 E-11 2.4884 E-25 6 1.36513 E-11 1.36582 E-11 1.8982 E-25 7 1.69185 E-11 1.69254 E-11 2.3194 E-25 8 1.49663 E-11 1.49713 E-11 1.5090 E-25 9 1.58498 E-11 1.58543 E-11 1.4128 E-25 10 2.00322 E-11 2.00369 E-11 1.8855 E-25 11 1.34427 E-11 1.34454 E-11 7.3301 E-26 12 1.86430 E-11 1.86463 E-11 1.2226 E-25 13 1.89248 E-11 1.89277 E-11 1.0975 E-25 14 1.56065 E-11 1.56086 E-11 6.5556 E-26 15 2.04128 E-11 2.04153 E-11 1.0281 E-25 16 2.51898 E-11 2.51925 E-11 1.3855 E-25 17 3.89694 E-11 3.89732 E-11 2.9565 E-25 18 2.52780 E-11 2.52802 E-11 1.1208 E-25
Since the units of the constant are seconds squared, the value represented by the constant is some time (or distance) squared. In other words, the constant can be represented by:
constant = (another number)2

What does another number turn out to be? Well, it has units of time or distance (s). What does the form of the hyperbolic equation tell us about the number?

The hyperbola is:

time2 - space2 = constant
or
time2 - space2 = another number2

What happens when space = 0?

time2 - 02 = another number2
or
time = another number

Keep going!