**Hitoshi Kitada** (*hitoshi@kitada.com*)

*Wed, 8 Sep 1999 07:21:08 +0900*

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Dear Bill,

Bill <WDEshleman@aol.com> wrote:

Subject: [time 705] FTL propagations

[snip]

*> Hitoshi,
*

*>
*

*> You say in your paper that "The quantum mechanical
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*> phenomena between two local systems appear only
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*> when they are combined as a single local system. In
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*> the local system the interaction and forces propagate
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*> with infinite velocity or in other words, they are
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*> unobservable."
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*>
*

*> In my analysis of infinite products equal to 1/(1-x) there
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*> is a reason to infer that black holes, atoms, and the
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*> universe as a whole all have event horizons inside of
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*> which we cannot observe.
*

You seem to think LS as the region beyond the event horizon.

That is, black holes and atoms

*> have event horizons at 1/0.7035 * GM/c^2 = 1.4 * GM/c^2
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*> and the universe has an event horizon at,
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*> 0.7035 * c/2 * sqrt(3/pi/G/rho), where rho is the density
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*> of the universe. Interactions inside or beyond the
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*> event horizons are unobservable, but I have reservations
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*> as to whether Faster Than Light propagations occur in
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*> these regions, or whether they are necessary at all.
*

The FLT propagation inside an LS in my context seems to have different

meanings from yours.

*> Here is my reasoning:
*

*>
*

*> 1/(1-x) = prod{ [1+x^(2^n)]^(1/2^n) : n=0,infinity }
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*> * prod{ 1/[1-x^(2^n)]^(1/2^n) : n=1,infinity }
*

*> or,
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*> 1/(1-x) = A * B
*

*>
*

*> I am almost forced to admit that A is the objective part
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*> and B is the subjective part. Therefore to correct the
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*> observation we must simply remove the relativistic part
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*> to reveal what really happened. Now we have another
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*> candidate for the QM principle of objective change.
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*> Here are the candidates:
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*>
*

*> 1) Psi(t+dt) = (1+x) * Psi(t)
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*> 2) Psi(t+dt) = exp(x) * Psi(t)
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*> 3) Psi(t+dt) = prod{ [1+x^(2^n)]^(1/2^n) : n=0,infinity } * Psi(t),
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*> and the mixture of objective and subjective change,
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*> 4) Psi(t+dt) = Psi(t) / (1-x)
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*>
*

*> If we accept eq. 3 as a candidate for objective change,
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*> we notice first that it is the closest yet to eq. 2. Second,
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*> eq. 3 does not go to infinity when x = 1; eq. 3 evaluates
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*> to the value of 4 (not eq. 4) at x=1. That is,
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*> 4 = 2 * 2^(1/2) * 2^(1/4) * 2^(1/8) * 2^(1/16) * * *. While
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*> eq. 2 is 2.718... at x=1. Now, and here is the problem,
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*> eq. 3 does not converge for x > 1. I must conclude that
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*> a) either the propagation inside the event horizon is at the
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*> speed of light or b) that the speed of light inside the event
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*> horizon is actually zero and that communication between
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*> points is FTL due to the direct contact between
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*> incompressible matter points. I prefer b), but cannot
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*> exclude a).
*

If the region inside the event horizon could be objective in your sense and is

observable, it might be meaningful to wonder about FLT. Is your event horizon

transparent for the observer?

This may seem so academic and so

*> hypothetical as to be ignored, but at this time my main
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*> effort is for consistency not believability. The properties
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*> of my infinite products are so beautiful that I can't put them
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*> aside because of the concern that I may be correct. :-(
*

*>
*

*> Your positive feedback so far is greately appreciated,
*

*> but this is where I tend to loose people, because, if I am
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*> wrong, there no reason to keep "kicking a dead horse."
*

*> So, be critical, you may save me 20 years of work, after
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*> which I would only be in possession of a pure mathematical
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*> object having nothing to do with reality. Come to think of
*

*> it, that might not be so bad after all...
*

It would not be bad at all. Any physical thinking may be nonsense in the sense

that the final form would be mathematical tautology.

*>
*

*> Sincerely,
*

*>
*

*> Bill
*

*> http://members.tripod.com/~EshlemanW/
*

*>
*

*>
*

*>
*

*>
*

*>
*

Best wishes,

Hitoshi

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