**Hitoshi Kitada** (*hitoshi@kitada.com*)

*Wed, 8 Sep 1999 07:02:16 +0900*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Hitoshi Kitada: "[time 709] Re: [time 705] FTL propagations"**Previous message:**Matti Pitkanen: "[time 707] Re: [time 706] Re: [time 702] Time operator?"**In reply to:**Stephen P. King: "[time 706] Re: [time 702] Time operator?"**Next in thread:**stephen p. king: "[time 711] Re: [time 708] Time operator => Ensembles of clocks?"

Dear Stephen,

Stephen P. King <stephenk1@home.com> wrote:

Subject: [time 706] Re: [time 702] Time operator?

[snip]

*> [HK]
*

*> > You are right again. I completely agree. This is the same problem if it is
*

*> > possible to construct a four dimensional version of the Hilbert space.
*

What I

*> > proposed is that if the space of states could be thought as the totality
*

of

*> > the QM orbits exp(-itH/h)Psi(x,t), then the conjugateness of t to H is
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*> > trivial. This is an identical propsoition by nature of positing the
*

problem.

*>
*

*> Matti, are you saying that the dynamical law is a priori to time? How?
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*> I see the "dynamical law" as defining a pattern of behavior of a system
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*> as it evolves in its time. When we say that we localize it in time, we
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*> are refering, to be consistent, to the time of the localizing agent, not
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*> the system in question's time. There is no "time" for all unless we are
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*> merely considering the trivial case when all systems are synchronized...
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*>
*

*> Hitoshi, are the QM orbits constructed in a Hilbert space such that
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*> they are strictly orthogonal to each other? This, to me, says that the
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*> LS are independent and thus have independent space-time framings of
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*> their observations. Does this affect your argument?
*

No. E.g., consider two orbits Psi(x,t) = exp(-itH/h)Psi(x,0) and Phi(x,t) =

exp(-itH/h)Phi(x,0) in the same LS. The inner product of these wrt the usual 3

dimensional Hilbert space is

(Psi(t), Phi(t)) = (Psi(0), Phi(0)).

This is not equalt to zero unless the initial states are orthogonal.

But two orbits in different LS's are of course orthogonal by definition.

*>
*

*> Later,
*

*>
*

*> Stephen
*

*>
*

*>
*

Best wishes,

Hitoshi

**Next message:**Hitoshi Kitada: "[time 709] Re: [time 705] FTL propagations"**Previous message:**Matti Pitkanen: "[time 707] Re: [time 706] Re: [time 702] Time operator?"**In reply to:**Stephen P. King: "[time 706] Re: [time 702] Time operator?"**Next in thread:**stephen p. king: "[time 711] Re: [time 708] Time operator => Ensembles of clocks?"

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