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Science Forum Index » Physics Forum » What Happens if P(B) = 0, 1, or 1/4 When v^2/c^2 --> 1...
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| OsherD... |
 Posted: Wed Jul 09, 2008 6:33 pm |
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From Osher Doctorow
Look at:
1) 1/sqrt(1 + P(B) - v^2/c^2) (from a few posts back)
As v^2 --> c^2 (arrow indicates approaches from below), the quantity
in (1) approaches (from left):
2) 1/sqrt(P(B))
If P(B) = 0, then we have a situation where (1) approaches infinity:
3) For P(B) = 0, then (1) above --> infinity
If P(B) = 1, then we get:
4) For P(B) = 1, then (1) above --> 1, so mass remains unchanged as
v^2 --> c^2).
For P(B) = 1/4, we get:
5) For P(B) = 1/4, then (1) above --> 1/sqrt(1/4) = 1/(1/2) = 2, so
mass doubles as v^2 --> c^2.
Only the first scenario, (3), involves mass "approaching infinity".
The other two cases have mass remaining constant or mass doubling
respectively as v^2 --> c^2.
Now let's look at the physical interpretations of the cases P(B) = 0,
1, or 1/4.
For P(B) = 0, the probability of the event B (Probably) Caused by v^2/
c^2 in (1) is 0, which in probability theory means that B is either a
planar event or a planar section in 3-dimensional space or a curve or
curvilinear segment in 3 dimensional space or else an extremely rare
event in time or else doesn't occur or else is a point event. Notice
that these are lower dimensional events in 3 dimensional space or 1
dimensional time, or "infinitely thin/wide/thick events", etc.,
similarly to events in accord with the Holographic Principle of 't
Hooft.
For P(B) = 1, v^2/c^2 Causes an event B of probability 1, which is
roughly speaking a "certain" or "deterministic" event, although only
if we ignore random events of probability 0 (roughly speaking, very
rare events. No "contraction" or "expansion" of mass occurs for such
events, which from the Einsteinian view would be the typical
(deterministic) SR events.
For P(B) = 1/4, v^2/c^2 Causes an event B of probability 1/4, which
doubles mass as v^2/c^2 --> 1 from the left. That is, the limiting
mass doubles from the original mass. Events B of probability 1/4 =
0.25 are fairly low probability events, since probability 1/2 refers
to an event that is equally likely to occur or not occur, so events B
of probability 1/4 are 3 times as likely to not occur as to occur
(since 1/4 + 3/4 = 1, and in probability "not B" has probability 1 -
P(B) = 1 - 1/4 = 3/4). Roughly speaking, the probability of landing
on one face of a fair die (plural dice) tossed in the usual way is 1/6
since there are 6 faces, so a "4-faced" die would have probability
1/4.
Osher Doctorow |
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