Hitoshi Kitada (hitoshi)
Fri, 9 Apr 1999 03:33:28 +0900
Dear Ben,
Thank you for your quite inpiring mail, which involves all what is
necessary for our present stage. Your paraphrasing and questions are
quite interesting and full of suggestive inspirations. After receiving
it on April 7, it has taken me rereading my papers, one night sleep and
some walking to resolve the problems you raised.
I first tried to understand your paraphrasing. I could understand it as
an English expression, but on the deepest level of my mind, it remained
unresolved. We usually do not think in time order in Japanese language.
There is just now for us. We do not have the past perfect tense in
native Japanese, nor the subjunctive mood. These were translated into
Japanese connecting past tense and some unnatural expressions as
Japanese. We live, as it were, in a world where all were changed, but
the whole remains the same.
I translated some of your paraphrasing into Japanese and found that tehy
do not include any tense, at least in the premise and conclusion. I
ordered your paraphrasing or your proof of the axiom of independence:
(1) there were a dependence between them
implies
(2) in order for this dependence to be known, the two systems would have
had to be observed interacting
implies
(3) they would not be two different local systems,
but
(4) two parts of the same local system.
The last two seem to constitute one sentence. It was decomposed just for
convenience.
The premise (1) was translated into Japanese:
(1') An observer O observes two local systems L1 and L2 as correlated.
The conclusion (4):
(4') The observer O observes some local system L that includes the
combined system (L1,L2) of L1 and L2.
Then I could understand your proof. It is in my thought one tautology:
(1') <-> (4').
Thus correct.
Your paraphrasing is quite subtle and clever. I have never thought of
such a paraphrasing. My Japanese and poor English did not give me such.
I next proceeded to the problems you raised. At first, they looked fatal,
but one day after, they have clear meaning that can be understood. In
doing so, I found one simple principle of observation:
What one sees when observing an LS depends on
which frame of reference one takes in the observation.
One extreme case is this: An observer O completely decomposes the
observed system L. In this case the observed system L is just a sum set
of single particles. Single particle does not have internal space
coordinate because it is 0 (zero) after the separation of its center of
mass. Thus it has no internal time and space, and there is only one
space-time coordinate (observer O's coordinate) that is available for
the observation. In this case, observer O observes L using O's space-
time as the reference-frame of observation. And the observed system L is
observed as a completely classical system of the particles inside L.
I assign value q=0 to this case.
Another extreme case is: An observer O observes L on the basis of the
space-time coordinate of the observed system L. In this case, the system
L behaves completely quantum-mechanically.
Tha value is q=1 for this case.
Thus observations are classified by the value q in the interval [0,1].
To q with 0<q<1 there correspond observations intermediate between
Classical and QM observations.
There may be other structures more suitable to classify observations,
but for the time being, let us assum this.
In understanding your problems, I compare them with Wheeler's quantum
eraser. I do not have access to this paper, so I just depend on the
description of your paper:
> In fact, according to (Wheeler, 1980), this even works if the choice is
> <b>delayed</b> -
>
> -
>
> then one has the phenomenon of the "quantum eraser." In other words, suppose
> one has a <b>machine</b> record which slit each particle passed through. If
> after a few hours one destroys the machine's records without having looked at
> them, and only <b>afterwards</b> looks at the plate, then result is the same
as
> if the information had never existed; the plate shows that the particles
> behaved like waves. But in the same scenario, if one looks at the machine's
> information before one erases it, the picture on the plate is quite different:
> it is consistent with whatever the machine said.<p>
I replace the observed particles by the system L=(L1,L2), a combined
system of two LS's L1 and L2, and denote the machine records by X, which
records some observation data about L for some value q1 in [0,1].
Then the observation here is
Case 1) When observer does never see X, the observation is that of L
with value q=1 (according to the description).
Case 2) When observer sees X and afterwards looks at L, the observation
is about the combined system L'=(L,X)=(L1,L2,X) with value q=q1
(probably, for "the picture on the plate is" "consistent with whatever
the machine said.")
Thus there is a difference in the observed object, and it is natural
there is difference in the results of observation.
Then I proceeded to your first problem:
> I start wondering here: What if the two local systems are observed together
> by some measuring
> apparatus, and the results are recorded on plate X but no one looks at
> them. Then the local systems are studied as if independent, using GR on
> their centers of mass, because they are separate local systems.
In this observation, the observed system is L=(L1,L2) bcause the
observer does not see X. (The "two local systems" are denoted by L1 and
L2.) The value q=0 in your case. We can take other values q.
> Then plate X is observed: Do the subsequent GR results become wrong because
> all of a sudden the
> axiom of independence is retroactively revoked??? Is there a paradox here?
> Don't the GR results
> get sucked into the subjectivity and multiple possible universes of the
> quantum domain?
At this stage, what the observer observes is the system L'=(L,X)=(L1,L2,
X), where X is the system of the plate X. The value q depends on
observer's choice of reference-frame.
Thus there is a difference in the observed object between the two
observations, and it is again natural to find difference in the observed
data, as well as in the value q accordingly to the reference-frame the
observer takes at each observation.
The point is the difference of the observed objects and the reference-
frames, and the argument holds also for the case that L' is observed
before the observation of L.
The second problem:
> I am also puzzling over Axiom 6. Here we have 2 local systems and one is
> observing the other.
> The observing system is somehow seeing the observed system ~not~ as an
> object, a center of
> mass, but rather as an internal subjective universe, and it is translating
> the entities seen in the
> observed system's internal subjective universe using relativity... (using
> relativistic calculations
> based on the two systems' centers of mass and their relative motions). The
> question is, what
> determines whether I see you as a center of mass or as an internal
> subjective universe, a Euclidean
> quantum space. (In philosophical terms, this reminds me of Buber's
> distinction between
> I-It and I-Thou interactions.)
What determines what an observer sees is the observer's choice of the
reference-frame. This is expressed by the parameter q ranging over [0,1].
I then reconsidered the first problem, if it could be used to see the
future.
If the observation of L'=(L,X)=(L1,L2,X) in the future could affect the
present "retroactively" as you say, then the influence from the future
would have been already at the present time. Then comparing the data of
the observation of L=(L1,L2) with other observations of the similar
situation but without the future observation of L'=(L,X), couldn't one
catch if the observation of L'=(L,X) will be done in some future?
In Wheeler's quantum eraser, what affects the future is whether the
observer observes L'=(L1,L2,X) or not. In this case, it seems that the
observer of L'=(L1,L2,X) must be the same as the future observer of L'=
(L1,L2,X).
There is a difference in the observed systems between the first problem
and Wheeler's case: In the former, the observed system is L'=(L1,L2,X)
in the future and is L=(L1,L2) at present. In Wheeler's case, it is L'=
(L1,L2,X) always, but the data X will be erased after the observer sees
it. Then it "seems" for us to be able to regard that the observed system
is L=(L1,L2) (?), and this "may" be identified with the first problem
with time order reversed, if the observer of L of the first problem is
the same as the future observer of L'.
Or it may be possible to assume the observer "knows" the existence of
the plate X but does never see it until the future observation of L'.
Then is the situation the same as Wheeler's case just with time reversed?
This then might be able to be used to predict the future in some way:
An observer O is informed that the plate X records some data about his
objects L1 and L2, but does not see it. He makes observation of L=(L1,L2)
. Then he is planned to walk a corrider to the point where the corrider
forks into two directions. Beforehand another person brought the plate X
at the end of one of the two branched corriders. Wheter or not he
(observer O) sees the plate X depends on his choice which corrider he
takes. If he knows that his observation of L is the same as the data
that he will see the plate X, then he knows that he chooses the correct
corrider where the plate X is at the end, whichever way he takes. Or if
he knows his observation does not coincide with those data, he knows he
chooses the wrong way in advance... Just a dream... :)
> In closing, I have a suggestion of "how to proceed from here." I think we
> should try to formulate
> your theory in purely logical format, as much as is possible. This would
> serve several purposes
>
> 1) it would make clearer what has to be done to extend the theory to
> account for weak and strong forces
For me or general Japanese, strong nuclear force is the one that
realized the atom bomb, and as the people who has ever experienced it
whatever the reason or justice is, we dislike the bomb. We do not or
never use the word "hate" usually, although we have Japanese
correspondent. But our mind seems to "hate" it unconsciously. This might
be one of my reasons that I did not try to study the strong force. But
if the time comes, it might be included in my schedule.
> 2) it would make clearer the mapping between your theory and my
> psychological theory of perception and consciousness
Your description of Wheeler's quantum eraser seems to indicate that "
consciousness" has its own power. It is the power of grouping objects.
We have here a clear correspondence between your theory and mine. This
would be the core of the mapping.
> 3) it would make clear why the paradoxes I mentioned above are not really
> paradoxes (unless they are ;)
I expect the above-mentioned would be an answer.
>
> A first step would perhaps be for you to give a precise statement of your
> axioms and theorems
> in WORDS only.
English is quite a different language than Japanese, and the cultures
behind them are too. I have been thinking time is the core of your
culture. I feel I see this in your paraphrasing of the axiom of
independence. You think in chronological order, while we think
everything is at present. Maybe this is why you think the universe began
by Big Bang, while I think it is stationary. This might be just a
difference in custom of thinking. As you say below, it seems better for
us to proceed to the direction that does not relate with this point.
Best wishes,
Hitoshi
I started trying to do this, but figured you would be
> better at it. Given this,
> the second step will be to try to replace the words with the most general
> mathematical/logical
> constructs that make the axioms/theorems true. At worst, this effort would
> result in us understanding
> your theory better ;)
>
> One more thing. I think that the Big Bang dispute is not that relevant,
> because there is no reason to
> believe the universe is infinite. I think the whole universe is finite.
> Who says the universe doesn't
> have a local time, then? And who says a system can't observe itself?
> Maybe the universe observes
> itself. The infinite degrees of freedom of your hypothesized Universe is
> just a mathematical approximation.
> The Big Bang is a product of strong nuclear forces I believe (?), and this
> issue needs to be revisited once
> it is clear how your approach accounts for the strong force.
>
>
> ben
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