[time 710] Re: [time 709] FTL propagations

Wed, 8 Sep 1999 06:48:15 EDT

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

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.

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.

The FTL propagation inside an LS in my context seems to
have different meanings from yours.

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."

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 }
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).

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?

My objective event horizon has evaporated. That is, if
I use either,

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



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