What Happens When Things Go Near the Speed of Light?

Advanced Analysis: Deriving the formula for g


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Use the mathematical form of the plot to derive g - converting units.

Remember the equation of the hyperbola:

time2 - space2 = constant
For the first data point, the equation becomes

(5.26699x10-12 s)2 - (5.25320x10-12 s)2 = constant

1.4506x10-25 s2 = constant

The values of the constant for all data points range from 6.5556x10-26 to 4.8848x10-25.

Every entry in the table, like all data, has some intrinsic, unavoidable error. Each value of the constant calculated from the entries is error-prone as well. Taking the average of many points helps to minimize these errors.

The range of the calculated values for the constant may seem large until you realize that the values are all within a power of ten. The numbers have an average of

1.8450x10-25 ± 1.0248x10-25 s2.

Keep going!
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

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Last Updated: February 10, 1999
http://www-ed.fnal.gov/data/phy_sci/relativity/unitsmgb3.shtml