# [time 708] Re: [time 706] Re: [time 702] Time operator?

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

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
> > 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?
> I see the "dynamical law" as defining a pattern of behavior of a system
> as it evolves in its time. When we say that we localize it in time, we
> are refering, to be consistent, to the time of the localizing agent, not
> the system in question's time. There is no "time" for all unless we are
> merely considering the trivial case when all systems are synchronized...
>
> Hitoshi, are the QM orbits constructed in a Hilbert space such that
> they are strictly orthogonal to each other? This, to me, says that the
> LS are independent and thus have independent space-time framings of
> 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

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