From: paul@mtnmath.UUCP (Paul Budnik)
Newsgroups: sci.physics
Subject: Defining local, causal etc., was: Hidden variable theories
Date: 13 Sep 92 20:03:43 GMT
Organization: Mountain Math Software, P. O. Box 2124, Saratoga. CA 95070

In article <1992Sep13.060538.19628@galois.mit.edu>, jbaez@riesz.mit.edu (John C. Baez) writes:
> ... After all the purpose of the
> >experiment is to test the correctness of quantum mechanics and it is only
> >macroscopic observations (that classical theory deals well with)
> >that are relevant to the experiment. Within this model I believe
> >these terms have well defined and accepted meanings.
> 
> Which for some reason you are loath to tell us....

Because classical theory is deterministic these definitions are not
problematic. Basing these definitions on a deterministic model does
not make them inconsistent with quantum mechanical predictions, since
the predictions of quantum mechanics do not preclude this possibility. 
Any definition of these properties based on probabilistic models,
including the diamond property you described, *cannot* be mathematically
rigorous because there is no rigorous mathematical definition of a
random sequence. There is reason to believe that no such definition is
possible.

A theory is local iff the future state at a given point
is determined by the previous state in a local region surrounding this point.
In a continuous theory the size of this region must go to zero as
the time between states goes to zero. 

The *Dictionary of Scientific and Technical Terms* defines causality in
classical mechanics as follows:

	The principle that the specification of the dynamic variables of a
	system at a given time, and of the external forces acting on the
	system completely determines the value of dynamic variables at a
	later time.

Influence is defined by the Oxford English dictionary as:

	To affect the condition of; to have an effect on.

Violations of Bell's inequality violate either causality or Lorentz invariance
because future events in some coordinate systems affect current results.

Violations of Bell's inequality violate locality because distant events affect
instantaneously local results.

Violations of Bell's inequality show local actions instantaneously
influence distant events because local actions affect distant events
instantaneously.

Instantaneous means instantaneous in an inertial coordinate system in
which both observers are at rest.

Affect means that changing a parameter of the model changes the
value of a variable in the model.

> Now it is true in quantum field theory that if Sam repeatedly makes a 
> pair of photons, sends one on to me for experimentation and plays around with 
> the other himself, and later on Sam and I compare notes, we can get results 
> that aren't consistent with classical mechanics and causality.  To be precise, 
> they can violate Bell's inequality.  Of course, this is no big surprise,
> really, since classical mechanics is wrong!  :-)  We do NOT - at least,
> nobody ever has - get results that violate the diamond property.

And no one has gotten results that violate Bell's inequality either, because
no one has shown that the correlated events have a space-like separation.
Well it is not surprising that classical mechanics is wrong, it will be
extraordinary if Bell's inequality is violated. What the diamond property
leaves out and what would be so extraordinary is that the outcomes of
the observations are changed in an experimentally detectable way as
a result of distant manipulations. The probability distribution of the
results do not change but the *results do change*.

>...
> >So you *have* redefined influence! 
> 
> No, it would only count as REdefining it if you or someone else had
> already defined it!  In fact, when people started thinking about
> causality in relativity they rather quickly arrived at this notion.  
> Haag and Kastler merely stated in C*-algebraic language something that
> had been floating around for quite some time.  

Do you see any problem in applying the Oxford dictionary of influence
to classical mechanics in the way I just described? Do you not think that
in applying the word to quantum mechanics one should make the definition
consistent with how it is used in classical mechanics if this is possible?
It certainly seems possible to me and confusing and misleading to REdefine
it in the way you have.

>... 
> Naturally.  Life is short.  I work on the models I do because I
> consider them the most likely.  If I'm wrong, so be it.  It's a
> calculated risk.  

That's fine. My complaint is that you are taking excessive liberties
with language when you describe the models you are working on.

> I *certainly* don't believe in "instantaneous collapse of the wave
> function," and have inveighed against it repeatedly on the net.  Now
> is not the time for another round of *that*.  But briefly, A) I don't
> believe in "collapse of the wavefunction" and B) "instantaneous"
> collapse does not make sense in special relativity, since simultaneity
> of distant events is observer-dependent.  

But you believe in a model that has the same experimentally detectable
consequences. What are your objective reasons for preferring this model
to one in which collapse is an objective Lorentz invariant process?

> >I will be happy to bet you $50 that by the year 2005 there will be
> >substantial experimental evidence that that the correlated events
> >observed in tests of Bell's do not have a space-like separation.
>
> Why such a subtly phrased bet?  Why don't you come out and bet that there will
> be substantial experimental evidence that Bell's equality HOLDS
> whenever the events are spacelike separated?  
> I would be glad to bet $50 that the preponderance of tests of Bell's inequality 
> up to year X (you name it) will show that it is VIOLATED.  Name a year
> by which you think they will have done the experiment right, so that
> the events are really spacelike separated.

The problem with your wording is that I do not think any tests have shown
that it is violated. All the experimental evidence to date is that it holds.
Experimental results consistent with quantum mechanics are not the same
thing as experimental results against Bell's inequality, unless you have
more faith in existing formulations of quantum mechanics then you do in
locality. This is a matter of judgement or religion and not a good basis
for deciding a wager. You need to show the events are space-like separated
by direct measurement, if you want to claim you have evidence against Bell's
inequality. By your definition and my reasoning I could name the year 1992
and would almost certainly win the bet.

Why do you object to my wording?

Paul Budnik
Newsgroups: sci.physics,sci.math