"Dr. V I Plankenstein" <PlankensteinC@stle.sci> wrote in message
news:68qdnZT-CJRWLLzbnZ2dnUVZ_hisnZ2d@comcast.com...
Hi fellows,
If anyone know about this idea?:
The distance can not get any quantity,and it includes
quantum of
distance.
Is this a physics question or a math question?
For math, the answer is no. For physics, the answer is maybe -
distances
less than Planck length are questionable.
Message was edited by: mathman
Unless you allow existential fuzzyness. For example, consider the interval
[0,1]. Now consider that each point be assigned a probability that the
point
exists, say 80:20 that the point exists for all points on [0,1].
You would expect this segment to behave as if it had a length of 4/5.
However, this does not seem quite sensible. You arrive at a notion of
"probabilitly of continuity" or "likelihood of continuity", and this is
something which is simply not found in the mathematical toolbox for some
reason, most likely because it sounds quite idiotic. Paradoxical.
Nonsensical.
Yet - we do know that there is this thing called Plancklength. And all the
little Plancklengths in the universe are _not_nailed_down_ .
So, you have a space which might reasonably be graduated like a ruler,
where
the graduations can slide around freely. Their location and orientation is
arbitrary, or indeterminate.
Suddenly, the idea of an existential gradient seems to make sense, that
length is probabilistic. Unfortunately it is extremely problematic
mathematically. In comparison to Real Analysis and elsewhere it seems
problematic, regardless, .....it might be possible somehow.
Here, the notion of partial randomness, and partial disorder can be used
to
try to model this "probabilistically existential gradient". We'll use
numbers of the form a + ~b, as discussed elsewhere on this group.
The number a is a nonrandom real, and ~b is a random real. The number ( a
+
~b ) is therefore a mixture of randomness and nonrandomness. This may
sound
as if we are contradicting Chaitin, that "given any number, there is no
way
to determine if that number is really random or not - no way to determine"
(paraphrased). However, we are not contardicting Chaitin, we are merely
exploiting the "existential indeterminacy" of the property of randomness
in
a novel way.
Omitting many details, we can skip forward to the fact that all of Real
Analysis could now be rewritten using numbers of the form ( a + ~b ),
where
b is null, in other words ( a + ~(null) ) = a , so that the random
component is null, and the result is just a nonrandom real. Such numbers
have a %100 probability of existing because they contain no uncertainty.
That have no uncertain component. Real Analysis now appears to be a
special
case of something much larger.
So, we can probably get away with making representations of such numbers,
similar to complex analysis. But many questions remain. For example, we'd
like to model the situation we mentioned earlier regarding the interval
[0,1] where each point has a certain probability of existing. We need to
do
the same thing with these numbers of the form ( a + ~b ). This does seem
possible somehow due to the presence of the random term ~b.
Now, I may sound like I'm full of *****, and I probably am.
But I'll say this - that if it works the way we want, then you will be
able
to bend space similar to the Lorentz transform (because length becomes
probabilistic), and you also get an explanation of the wave-particle
duality
due to the topological indeterminacy of the term ~b.
All of that from one number system and that aint bad. Assuming it works
.......
Lastly, I think that we may also have a means of showing that QM really is
incomplete, because QM does not address the issue of existential
indeterminacy - which it seems that it should. QM is not missing any
variables. Rather, it has been lacking a key concept - existential
indeterminacy.
For all of it's greatness and success, QM is lacking this very fundamental
concept relating to existence. Shrodingers Cat can be thought of as
something very much like the topological indeterminacy that we are using.
But the problem is that it must be accompanied by "existential
indeterminacy", and in QM this is not the case.
It _is_ the case algebra, even though noobody ever says so. Just to explain
this briefly - one more time.
The solution set to
0*x + 0*a = 0*x = 0*a = 0
can be considered indeterminately either continuous or discrete, because a
is a constant, and x is a variable. Constants are discrete valued, and
variables are continuous as logn as their domain is.
But the whole equation is reducible to the form 0 = 0 with no variables or
constants whatsoever, hence that there _is_no_solution_ is also a solution.
In effect, we cannot be sure if the solution set even exists.
In QM, we know that Shrodingers Cat may be both dead and alive at the same
time, but nobody ever said that the cat was both existing and not existing
at the same time indeterminately. But I think that is must be. I suspect
that topological indeterminacy cannot occur if unaccompanied by existential
indeterminacy, and this is something which may be provable / disprovable. It
seems that these must go together, that you cannot have topological
indetermiancy without existential indeterminacy, and vice versa. So, how can
that be proved ?
This "existential indeterminacy" also lies atthe heart of probability
theory, even though nobody cares to admit it. And the proof of that is quite
simple. If you are going to flip a coin, and you dont know whether it will
be heads or tails, then the outcome does not yet exist. To reiterate - the
outcome _does_not_yet_exist_ .
So, probability theory really is perhaps the best tool for doing QM, at
least initially. But analysis should work just fine as well as long as you
are working with the proper kind of number system, and ( a + ~b ) just might
do the trick because it is inherently probabilistic.
All that remains is to explain this number ( a + ~b ), and how it works. To
develop a kind of complex-like analysis based on that number. I think that
it is do-able.
Dr. Viktor Plankenstein
Cubiqa Emeritus Profundicum
- Rebuilding space, One plancklength at a time -
.
