**Stephen P. King** (*stephenk1@home.com*)

*Tue, 06 Apr 1999 23:48:43 -0400*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Ben Goertzel: "[time 198] local systems, measurement, etc."**Previous message:**Hitoshi Kitada: "[time 196] Re: [time 193] Re: [time 192] one more addition to Re: Prugovecki's time"**In reply to:**Stephen P. King: "[time 187] Re: one more addition to Re: Prugovecki's time"

Dear Hitoshi,

Hitoshi Kitada wrote:

*>
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*> Dear Stephen,
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*>
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*> Just on technical points...
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snip

*> > There is also the matter of "equivalence classes".
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*>
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*> Equivalence classes is the notion that the freshmen have to learn at first
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*> when they enter a university. It is one of indispensable knowledges for anyone
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*> who wants to learn something about math and nature.
*

Equivalence classes play a major role in Peter's work. We will, I

suppose, get to them in time. :)

*> Prugovecki writes on
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*> > pg. 447:
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*> > "...the generic element of \H is not a single function, but rather an
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*> > equivalence class of almost everywhere (in the Lebesgue sense) equal
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*> > functions, which are such that one can change the value of any one of
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*> > these functions \Psi(x) at any given point x without leaving the
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*> > equivalence class -namely, in physical terms, without changing the
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*> > quantum state vector. "
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*> >
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*> > I had stated in [time 188]:
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*> > > Yes, Peter and I discussed this for a while. It appears that the
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*> > > subject-object relation is symmetrical. There is a wonderful thing that
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*> > > happens when we consider an LS as a subject as a singleton set A and the
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*> > > other LSs that it is near to as the singleton's complement A^c. If we
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*> > > think of A^c as a finite number of LSs that can somehow be reduced to a
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*> > > singleton by some particular observation by A, by symmetry, would we not
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*> > > expect that A becomes many neighboring yet distinct LSs? As one fuses,
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*> > > the other fissions, many -> one | one-> many ... Does this make sense?
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*> > > There exists a mathematical way of saying this but I do not remember it
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*> > > now. :(
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*> >
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*> > It is the fact that I am not stating explicitly the "mathematical way
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*> > of saying this" that, I think, is the reason I am just making noise
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*> > here... :( The role of equivalence classes is very important!
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*>
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*> Yes, it is so important that one usually does not refer to the usage of it,
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*> i.e. people frequently use it without mentioning...
*

I am only now finding this out. :) One last thing about subject-object

symmetry; an exact symmetry of the pair is a very special case, the case

where uncertainty is zero, I think. I was mistaken in thinking it to be

a generic situation.

I just wish to understand how we formulate the Equivalence Principle

[(EP) : an observer X in free fall in a gravitational field experiences

no differences from that of an unaccelerated observer X'], the caveat is

that this only holds in conventional GR within an infinitesimal

neighborhood of X, due to the tidal forces ("Weyl tensor" in Penrose's

explanation). I think that there is something strange necessary to

quantize this, since infinitesimal ("sharp") quantities are not in

general allowed by QM's uncertainty. But since you define the

uncertainty in a different manner than usual, maybe, just maybe, we can

show that the EP is modified by our thinking.

I need some time to go over my Category theory books to formulate my

thinking better. Lately, I have had little sleep and am making serious

mistakes in my thinking. I apologize... :)

Onward to the Unknown,

Stephen

**Next message:**Ben Goertzel: "[time 198] local systems, measurement, etc."**Previous message:**Hitoshi Kitada: "[time 196] Re: [time 193] Re: [time 192] one more addition to Re: Prugovecki's time"**In reply to:**Stephen P. King: "[time 187] Re: one more addition to Re: Prugovecki's time"

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