Natural Science Forum / Physics / General Physics / July 2008

From Osher Doctorow

According to Special Relativity, mass become infinite when light speed
is approached because of the factor:

1) 1/sqrt(1 - v^2/c^2)

In Probable Causation/Influence (PI), however, the Probability that A
Causes/Influence B is:

2) P(A-->B) = 1 + P(AB) - P(A)

or its alternate version:

3) P ' (A-->B) = 1 + P(B) - P(A), with P(B) < = P(A

Here P(A), P(B), and P(AB) are all nonnegative from the definition of
probability.

But in the expression 1 - v^2/c^2 in (1), v^2/c^2 is also nonnegative,
so there is a missing term in the "probability representation," namely
either P(B) or P(AB).   Let's use P(B).  Notice, by the way, that v^2/
c^2 is between 0 and 1 by Einstein's postulate (whether it is true or
not), so it can indeed be taken mathematically as a probability under
rather general conditions.

Rewriting (1) with P(B) included gives:

4) 1/sqrt(1 + P(B) - v^2/c^2)

with P(B) not in general 0.   Notice what happens as v^2 --> c^2.  The
last term in the argument, v^2/c^2 --> 1 (from the left) so 1 - 1 = 0,
but P(B) is left in the argument, yielding:

5) 1/sqrt(P(B)) as v^2 --> c^2 (from the left)

Here P(B) is in general > 0 so 1/sqrt(P(B)) is finite (if P(B) is
constant, the former is a finite real number).  So mass does not
approach infinity, just as 1/sqrt(P(B)) does not in general approach
infinity.

Osher Doctorow