From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Re: Hidden variable theories, was: Uncertainty Princi
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Fri, 11 Sep 92 01:56:14 GMT

In article <268@mtnmath.UUCP> paul@mtnmath.UUCP (Paul Budnik) writes:
>In article <1992Sep9.223637.24769@newshost.lanl.gov>, jlg@cochiti.lanl.gov (Jim Giles) writes:
>> 
>> It is not information either in Shannon's sense or anyone else's.  It 
>> _would_ be information if it permitted something known only at the other
>> end to be *transmitted* to us.
>
>But of course it does. It tells us something about what *combinations* of
>polarizer angles and detections that happened at the other end.

In a down-to-earth vein, I would only say information was being
transmitted by such a device if I could use it tell my grandma what I
was having for dinner, or at least do so with some statistically
significant chance (i.e., I'll accept a noisy channel as long as it's
not 100% noise).  It would only be if someone did THIS with quantum
trickery that I would get nervous.  But of course one can't.

>To test Bell's inequality you must determine if certain bit streams are
>correlated. The information that produced that correlation was transmitted
>instantly at the time an observation was made. If no information was
>transmitted the bit streams would not be correlated. If the information
>was not transmitted at the time an observation was made, but was contained
>in the photons when they were created, a local hidden variables theory could
>account for the results and Bell's inequality would not be violated.

We will sink into idle semantics here but I would not say the
correlation was "transmitted".  Quantum mechanics simply allows
different sorts of correlations than classical mechanics.  That's why a
local hidden variables theory can't account for violations of Bell's
inequality.  I would speak of transmission only if I could use the
device to send a message to my grandma - NOT just produce some
correlation that we can only verify when I go visit her later.

>It is a fact that a distant manipulation instantly produces a local affect
>according to the instantaneous collapse postulate.
>That you cannot detect the effect *at the time it occurs*
>does not make it any less real. You are able to verify experimentally that
>it did occur and you can measure the exact time that it happened.
>This violates either Lorentz invariance or causality. Several physicists
>writing in this area have made this point.

Yeah, and several more have made the opposite point.  Namely, that you
are using the word "causality" in a certain way, which I think is the
"wrong" way, but in any case, that there's another sensible usage of it
such that causality is not violated.

I would say causality was violated if I could decide to eat a bacon
cheeseburger and then pull out my Bell Labs quantum transmitter and let
my grandma know that fact at some point along her worldline that is
outside my lightcone.  Regardless of the definition of "causality",
let's agree that that CANNOT be done according to standard quantum mechanics.
If it could be done, by Lorentz invariance my grandma could send a
message back into my past to tell me not to eat the bacon cheeseburger:

        \             /
         \           /
          \         /
           \       /
            \     /
             \   /
              \*/
     G        / \
             / @ \
            /     \       
           /       \

In this spacetime diagram, at the event marked * I send a message to my
grandma that I am going to eat a bacon cheeseburger.  She receives it at
the event marked G and sends a message telling "Don't do it!  It's bad
for you!" which I receive in the past at the event marked @.  

This would be a nasty paradoxical causal loop, which I call a violation
of causality.  This cannot occur in the usual theory of quantum
mechanics + special relativity, even though Bell's inequality is violated.