*WDEshleman@aol.com*

*Wed, 8 Sep 1999 06:48:15 EDT*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**stephen p. king: "[time 711] Re: [time 708] Time operator => Ensembles of clocks?"**Previous message:**Hitoshi Kitada: "[time 709] Re: [time 705] FTL propagations"**In reply to:**WDEshleman@aol.com: "[time 705] FTL propagations"**Next in thread:**Hitoshi Kitada: "[time 715] Re: [time 710] Re: [time 709] FTL propagations"

[WDE]

Hitoshi,

You say in your paper that "The quantum mechanical

phenomena between two local systems appear only

when they are combined as a single local system. In

the local system the interaction and forces propagate

with infinite velocity or in other words, they are

unobservable."

In my analysis of infinite products equal to 1/(1-x) there

is a reason to infer that black holes, atoms, and the

universe as a whole all have event horizons inside of

which we cannot observe.

[HK]

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

[WDE]

Yes, but there are also local systems of the type you suggest;

that is, local systems inside the local system we observe from.

Each of the many local systems that are inside our observation

local system is either a large collection of matter points (fermions)

or a small collection of matter points. The largest and densest

collection of matter points is the black hole that, although it is in

our local system (the galaxy or universe), it is on the other side of

an event horizon and is in a way unobservable to us. In the same

way, atomic nuclei are each on the other side of their own event

horizon. Between these event horizons are local systems of grains

of dust on up to local systems of stars and galaxies; i.e., the local

system of our universe. The event horizons are constructions of

subjective observations extrapolated to locations we will never get

to observe directly. In the same sense, the universe must itself

be confined to a subjective event horizon so that there must exist

other local systems (universes, galaxies, black holes, stars,

grains of sand, molecules, atoms, etc.) that are really beyond the

event horizon of our universe local system. I know that you will

agree that there are many local systems open to our observation

in our own universe, and I will argue that there are many local

systems in the objective sense of many-worlds.

[WDE]

That is, black holes and atoms

have event horizons at 1/0.7035 * GM/c^2 = 1.4 * GM/c^2

and the universe has an event horizon at,

0.7035 * c/2 * sqrt(3/pi/G/rho), where rho is the density

of the universe. Interactions inside or beyond the

event horizons are unobservable, but I have reservations

as to whether Faster Than Light propagations occur in

these regions, or whether they are necessary at all.

[HK]

The FTL propagation inside an LS in my context seems to

have different meanings from yours.

[WDE]

My meaning is not mine at all. If it was, I would be smart. My

meaning is that of many-worlds made compatible with your local

systems. The event horizons are what I previously believed to be

objective structures generated by my mathematics, but I am

happy to see them as limitations of subjective observation

predicted by my mathematics. FTL communication is not

necessary in many-worlds, but I'll consider subjective FTL though.

Is that what you mean? Here is the Everett idea as explained

by M. C. Price:

"Many-worlds is local and deterministic. Local measurements

split local systems (including observers) in a subjectively random

fashion; distant systems are only split when the causally transmitted

effects of the local interactions reach them. We have not assumed any

non-local FTL effects, yet we have reproduced the standard predictions

of QM."

[WDE]

Here is my reasoning:

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

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

or,

1/(1-x) = A * B

I am almost forced to admit that A is the objective part

and B is the subjective part. Therefore to correct the

observation we must simply remove the relativistic part

to reveal what really happened. Now we have another

candidate for the QM principle of objective change.

Here are the candidates:

1) Psi(t+dt) = (1+x) * Psi(t)

2) Psi(t+dt) = exp(x) * Psi(t)

3) Psi(t+dt) = prod{ [1+x^(2^n)]^(1/2^n) : n=0,infinity } * Psi(t),

and the mixture of objective and subjective change,

4) Psi(t+dt) = Psi(t) / (1-x)

If we accept eq. 3 as a candidate for objective change,

we notice first that it is the closest yet to eq. 2. Second,

eq. 3 does not go to infinity when x = 1; eq. 3 evaluates

to the value of 4 (not eq. 4) at x=1. That is,

4 = 2 * 2^(1/2) * 2^(1/4) * 2^(1/8) * 2^(1/16) * * *. While

eq. 2 is 2.718... at x=1. Now, and here is the problem,

eq. 3 does not converge for x > 1. I must conclude that

a) either the propagation inside the event horizon is at the

speed of light or b) that the speed of light inside the event

horizon is actually zero and that communication between

points is FTL due to the direct contact between

incompressible matter points. I prefer b), but cannot

exclude a).

[HK]

If the region inside the event horizon could be objective in

your sense and is observable, it might be meaningful to wonder

about FTL. Is your event horizon transparent for the observer?

[WDE]

My objective event horizon has evaporated. That is, if

I use either,

Psi(t+dt) = exp(x) * Psi(t),

or,

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

it is not there anymore. The way I analyze 1/(1-x) depends

on the mathematical fact that it is defined for x only up to

x=0.7035. Above x=0.7035 it cannot calculate orbital

motion due to the lack of an inverse procedure to give

position and velocity in the region up to what I called the

event horizon. Anyway, if FTL is subjective, FTL might

as well be observed even if it is not happening. Is FTL

in your context, merely subjective? Is the constant

c in a vacuum, subjective, and FTL objective?

Sincerely,

Bill

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

**Next message:**stephen p. king: "[time 711] Re: [time 708] Time operator => Ensembles of clocks?"**Previous message:**Hitoshi Kitada: "[time 709] Re: [time 705] FTL propagations"**In reply to:**WDEshleman@aol.com: "[time 705] FTL propagations"**Next in thread:**Hitoshi Kitada: "[time 715] Re: [time 710] Re: [time 709] FTL propagations"

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