[ExI] QT and SR

[Lee Corbin]

Serafino asks a lot of good questions. Fortunately I am not
in a state of mind to waver on anything, or to resist answering.
Or unfortunately. Wha'ever.

> Subtle questions. And the possible answers depend
> on the specific points of view, or interpretations.
> What are these states?

Actually existing configurations of matter and energy!

> Are they physical?

Yes.

> Are they mathematical?

Our descriptions of them are mathematical.

> Are they statistical?

No.

> Do they represent information carried by a quantum system?

Yes.

> Do they represent observer's information?

Not only that.

> Rather, do they represent the 'image' of the information carried by 
> a quantum system?

Yes, that too.

> Do they represent experimental contexts? 

Yes.

> Do they represent statistical ensembles?

No.

> Or do they represent single systems?

Yes.

> Are they subjective?

Certainly not!

> Are they objective?

Yes!

> Are they tendencies, propensities, potentialities? 

No!

> Are they actualities?

Yes! Yes!

> Should we give up the possibility of treating the wave function as
> an isomorphic image of what is actually processed in the laboratory?

Never! Never give up!

> In QM the outcome of a measurement - repeated many
> times - of an observable, isn't in general the same. 
> So QM gives the expectation value of the observable 
> to be measured. (In special cases it gives the actual 
> outcome of the measurement, non just the expectation 
> value).

Right.

> While it is possible to say that QM does not care of
> unperformed measurements, what can we say about the
> value of an observable between two measurements?
> Is it undefined? Is it unknowable? 

It is a superposition before the measurements, it is a
superposition between the measurements, and it will
be a superposition after the measurements. Superposition
now, superposition tomorrow, and superposition forever!
(If I cain't get segregation, I'll jist settle for superposition, me.)

Aren't you lucky I am in such a decisive state of mind 
tonight?   DON'T  ANSWER!

Lee

> In QM the total information of a system, represented 
> by the state vector, is never complete. Information
> is limited. The total information of a system suffices 
> to specify the eigenstate of one observable only, 
> at choice. Thus, all possible future measurement results 
> cannot be precisely defined.
> 
> The state vector can be said to represent our knowledge 
> about the recent history of a system which is necessary 
> to arrive at the set of probabilistic predictions
> for all possible future observations of the system.
> The set of future probabilistic predictions specified 
> by the recent history of the system is indifferent 
> to the knowledge collected from all the previous measurements 
> in the whole history of the system. As Pauli once wrote: 
> "In the case of indefiniteness of a property of a system 
> for a certain experimental arrangement (for a certain
> state of the system) any attempt to measure that property 
> destroys (at least partially) the influence of earlier 
> knowledge of the system on (possibly statistical) statements 
> about later possible measurement results."
> 
> Can we say that the observable has a *definite* value between 
> two measurements? No, in general we cannot say that. 
> If the state is a pure state (and not a mixture) we cannot 
> say there is any definite value [1].
> 
> Can we say the value of the observable is *unknowable* between
> two measurements? No, we cannot say that, because QM in general
> provides a sort of information, a sort of knowledge, whose nature
> is probabilistic though.  
> 
> [1]
> Imagine a spin-1/2 particle. Imagine its state described by 
> the superposition psi = sqrt(1/2)[(s+)_z +(s-)_z].
> There are two possibilities.
>    A) That psi above is a pure state. Since we know that
> (s+)_z = sqrt(1/2)[(s+)_x +(s-)_x]
> (s-)_z = sqrt(1/2)[(s+)_x -(s-)_x]
> (where _z, _x, are the z-component and the x-component of spin) 
> we can write that psi = sqrt(1/2)[(s+)_z +(s-)_z] = (s+)_x.
> Now, if the x-component of spin is measured by passing 
> the spin-1/2 particle through a Stern-Gerlach with its field 
> oriented along the x-axis, the particle will *always* emerge 'up' 
> (that is, as (s+)_x). The experiment confirms that.
>    B) But if by sqrt(1/2)[(s+)_z +(s-)_z] we mean
> a *mixture* of sqrt(1/2)[(s+)_z] and sqrt(1/2)[(s-)_z],
> we might also think that -before measurement- the particle 
> has a *definite* value of the z-projection of spin,
> say [(s+)_z] or [(s-)_z]. But in this case, measuring the 
> x-component of the spin, we would find 'up' with the
> probability 0,5 and 'down' with the same probability.
> Experiments does not confirm that! 
> 
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