X-Message-Number: 8601
From: Andre Robatino <>
Subject: Re: CryoNet #8596 - #8599
Date: Tue, 16 Sep 97 12:31:26 EDT

> Message #8599
> Date: Mon, 15 Sep 1997 21:27:41 -0700 (PDT)
> From: John K Clark <>
> Subject: Digital Shakespeare
> 
<snip>

> In #8592 Andre Robatino <> On Sat, 13 Sep 97 Wrote:
>                                  

>         > _Any_ state directly corresponds to a specific set of outcomes for
>         >some complete set of measurements. 
>                              
> 
> I don't dispute that a complete set of measurements  corresponds to a unique 
> quantum wave function, but we can never have a complete set of measurements 
> for reasons we both know.
>                              
  Maybe I'm not using the standard nomenclature, I mean a set of measurements
corresponding to commuting operators, such that assigning a value to each of
the measurements uniquely determines a state.  For example, for a hydrogen
atom, the measurements corresponding to the 3 integers (n, l, m) (I'm "lying"
in that the actual system is more complicated but the principle holds).  No
such set cannot contain both the position and momentum operator since they
don't commute.  For any state, such a set {M_i} together with associated
values {m_i} exist with the stated properties.

<snip>
> 

>         >if one starts from state |psi>, one is guaranteed to get value m_i

>         >for any measurement M_i in a particular complete set of measurements
>         >{M_i}
> 
> 

> You have it backward, in the real world you never start with the quantum wave
> function but with a measurement,

  If you insist, you can define the statement "the system is in state |psi>"
as shorthand for "the system has undergone measurement under one of the
aforementioned sets of measurements {M_i}, yielding values {m_i}, uniquely
determining this state (up to a phase factor) under the axioms of QM".

> and any set of measurements you make does 
> not correspond to a UNIQUE quantum wave function.

  One can determine it uniquely up to a phase factor.  See above.
>                              
> 

>         >if one starts from state |psi>, then the probability of finding the
>         >particle in volume dV near the point x is |psi(x)|^2 dV
> 
> 
> OK, You perform a measurement and find the particle in the volume (or maybe 
> you don't, after all you only have a probability). Yes, you can find a 
> quantum wave function that would satisfy the equations mathematically, 
> you can find lots and lots of them. My point is you would have no reason 
> to pick one over another.

  We've been through all this before.  Any change in the state other than by
an overall phase factor leads to changes in the probability of measuring
particular values associated with particular measurements.  These changes are
observable by the same procedure of creating the same state a large number of
times which is required for measuring a position PDF.  If you think
you can replace a state |psi> with another state |psi'> which differs from
|psi> by more than a phase factor, without observable consequences, please
specify |psi> and |psi'> and I will specify a measurement which has different
probabilities for its outcomes depending on which one you start with.

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