X-Message-Number: 8613
Date: Fri, 19 Sep 1997 21:29:27 -0700 (PDT)
From: John K Clark <>
Subject: QM

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In #8608 Andre Robatino <> On Thu, 18 Sep 97 Wrote:


        >the (slight) arbitrariness in the way one represents |psi> is not
        
        >unique to QM: in classical mechanics, the coordinates one uses to
        
        >describe a system are known only up to an arbitrary translation,
                >rotation, and uniform velocity.
              

I can't really argue with that because "slight" is a subjective measure, 
personally I would rate it somewhat greater than slight and somewhat less 
than enormous. Let me give an example.

A photon passes through a polarizing filter set in the vertical position, 
the photon can be described by the state vector |psi v>. Linearly polarized  
light can be synthesized by equal mixtures of left and right circularly 
polarized light, so our photon must also have a state vector associated with 
its left polarized state, we'll call it |psi L> and |<psi v/psi L>|^2 =1/2. 
The photon then encounters a second polarizer set at angel Q to the vertical. 
This changes the photon, it's new vertical and left state vectors are 
|psi' v> and |psi' L>.

We always assume in all further calculations that 
<psi v/psi L><psi L/psi' v> = 1/2 *e^iQ   
but there is no physical reason why that must be true only that it could be, 
it's a purely arbitrary convention, a Martian might assume that  
<psi v/psi L><psi L/psi' v> =(1/squareroot 2) *e^-iQ 
and his physics would work just as well and give the same answers as ours.


                                            John K Clark     

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