WDEshleman@aol.com
Thu, 9 Sep 1999 03:58:53 EDT
In a message dated 9/8/99 2:58:25 PM Eastern Daylight Time,
hitoshi@kitada.com writes
> Dear Bill,
>
> Before going further, let me ask a question on your paper:
>
> A Many-Worlds Wave-Object paradigm for
> Quantum Inertia and Quantum Gravity
>
> in your web page.
>
> In page02a, you wrote
>
> "Everett's interpretation demands the continuous and deterministic change
of
> the state function (psi), of an isolated system, with time according to a
> wave
> equation d psi/d t = x psi, where x is a linear operator. Letting (psi_0)
be
> the present state, then psi = psi_0 + x psi =psi_0/(1-x) predicts all
future
> states; or equivalently,
>
> psi 1
> ----- = ---- "
> psi_0 1-x
>
> Here you seem to think that the solution of the differential equation
>
> d psi/d t = x psi, with initial condition psi(0) = psi_0 (0)
>
> is
>
> psi(t) = psi_0 / (1-x). (1)
>
> My mathematics however tells the solution is
>
> psi(t) = exp(tx) psi_0, (2)
>
> if x is a time independent operator.
>
> I wonder how you derived (1).
>
>
> Best wishes,
> Hitoshi
Hitoshi,
It will probably come as no surprise to you that I have,
up until a week ago, been under the impression that
relativity is the "real" way things change. I have been
assuming that the deflection of light near the limb of
our sun is the "reality" that we must accept as the
objective way things change. This was more than a
belief, it was a state of mind. In short, you have
convinced me that exactly the opposite is in truth
more consistent.
That is, that relativity is a description of subjective
change and that QM and general change in our
environment dictate that the objective change is
really controlled by the exponential function (or
something very close to it).
In fact, after our discussions of change, I came
down with some mysterious ailments (clamy hands
and sleeplessness) and I did not immediately
realize that my world was not falling apart, but
that I must simply accept that my notions of
objective and subjective in relation to physics
had become reversed. This realization is what
recovered my health and helped me understand
that the "paradigm shift" of my thought placed
my paper in a subjective realm, not an inconsistent
realm. To my credit, I did not resist this reversal
very long.
That page02a was included after someone
requested that I make at least one assumption
to get readers on track. That is, 1/(1-x) is not
a solution of the PDE of change, but a require-
ment for the relativistic change that we actually
observe. Your orthogonalization of QM and
relativity is the concept that I hope will get me
back on the track of a consistent extension of
my mathematics from cosmology to QM.
Please respond to my questions concerning
Faster That Light propagations as to its being
objective or subjective, or such.
Sincersly,
Bill
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