Science > Physics > Quantum Gravity Via Expansion-Contraction 21.3: Strange Role of Intersection
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Science > Physics |
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"OsherD" |
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09 Sep 2006 08:45:02 AM |
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Quantum Gravity Via Expansion-Contraction 21.3: Strange Role of Intersection |
From Osher Doctorow
In the expression:
1) p --> pt --> t --> ts --> s
where p is Probable Causation/Influence (PI), t is time, s is space or
spatial variable, pt and ts correspond to intersection, the role of
intersection seems surprising if not strange. I'll try to explain it
physically.
Consider in general for two sets A, B, the expression:
2) A --> AB --> B
Let's back up and ask whether we could regard B as being defined at
first by AB and then expanded into B rather than assuming that B is
defined at the "beginning" when considering the leftmost expression A.
In mathematical language, could we regard B as "indeterminate" until
made "determinate" by AB and later "expanded" to B? The answer is
arguably "yes", although we don't have to assume any flow of time here
despite the description, just a "flow of information/knowledge", except
possibly in AB --> B (see below).
To understand how this is possible, notice that AB can be regarded as
selecting a subset of A which is then labelled AB. Certainly AB, which
is described in words as the intersection of A and B (seeming to imply
the "existence" of B separately from A, but not quite), is a subset of
A and so AB selects a subset of A which is then labelled AB. The same
holds if we use the "mathematical" definition of AB as {w: w is an
element of A and w is an element of B}, which despite the word
"mathematical" is again a definition in words, since there is no
difference in the result when we regard the definition of AB as "select
a subset of A which is then labelled AB".
At the "stage" of selecting AB, we "implicitly" are defining B to equal
AB. Recall that if B is a subset of A, then AB = B from set theory.
However, in AB --> B of (2), B is not necessarily equal to AB, as the
corresponding expression in logic a ^ b --> b indicates for a, b
propositions and ^ conjunction ("and") and --> the logical conditional
("if...then") or implication (a "implies" b). So we can regard B as an
extension or expansion of AB obtained by adding to AB a set of elements
in the complement (part of the Universe outside) of AB and labelling
the whole thing B. It seems plausible that physically this takes time
to do, but mathematically it can be regarded as arguably instantaneous
if we're willing to regard information/knowledge as changing or
increasing whether or not time is involved.
Osher Doctorow
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| User: "Dr. Moria" |
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| Title: Re: Quantum Gravity Via Expansion-Contraction 21.3: Strange Role of Intersection |
09 Sep 2006 11:08:59 PM |
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"OsherD" <> wrote in message
news:1157809502.053532.161750@m73g2000cwd.googlegroups.com...
From Osher Doctorow
In the expression:
1) p --> pt --> t --> ts --> s
what does p --> pt mean ?
What does the operator --> mean ?
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| User: "OsherD" |
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| Title: Re: Quantum Gravity Via Expansion-Contraction 21.3: Strange Role of Intersection |
09 Sep 2006 09:11:36 AM |
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From Osher Doctorow
Physically, these ideas indicate a revolution in both mathematics and
physics. Up to now, the main place that objects are regarded as
"created" or "destroyed" in physics is in creation/annihilation
operators, which lack considerable intuition. But to regard sets as
changing is to regard events themselves as changing, as readers very
familiar with probability know (an event is a type of set) and by
extension other objects.
The new ideas enable us to propose physically that Probable
Influence/Causation creates time which creates space, possibly
"instantaneously" in an intuitive sense, with intersections as
intermediate "states". Ultimately, we may turn the quest for rapid
spatial travel into a problem of creating space between us on earth and
us near our destination, or "annihilating" space between us on earth
and our destination elsewhere.
If you ask a typical full professor of mathematics whether sets change
or not, the reply will probably be "no". Mathematics in itself does
not require any "identity" in different states of the same object, or
even the notion of the "same" object, a fiction which is maintained by
the common practice in probability of labelling different states of an
object X in time as X_t1, X_t2, etc. The typical mathematical
professor will say, if asked what X is in X_t1 and X_t2, that X is "the
same thing in a sense", but if pressed further will argue to the effect
that everything in incorporated into different variables or expressions
X_t1, X_t2, etc., at different times, and that the question of the
identity of some object X in these different expressions is either
philosophical or physical. Of course, physicists pass the buck back
to mathematics or philosophy.
It doesn't require much of an extension of the "classical" notion of
sets to define a "changing set". If A is a set, just define A_1 as
whatever is left of A or is added to A together with what is left of A
at time t1 (or label it A_t1), and similarly for other times. If
nothing is left of A at some time t_n or t_infinity or t_final, we can
regard A as being "annihilated" at that time. Reversing the reasoning,
we can regard A as being "created" at time t1 or as having existed
forever up to and including time t1, etc.
I am talking about axiom/definitional changes here, just as valuable
arguably as the geometric change from the parallel postulate that
generated Non-Euclidean geometry. The resistance to such changes is of
course "historic".
Osher Doctorow
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