🚀 go-pugleaf

>In article <1992Dec13.204233.10835@galois.mit.edu> jbaez@riesz.mit.edu (John C. Baez)
>totally misses the point in favor of a spelling flame:

On Usenet there is no such thing as "the" point, only my, your, his, and
her points.  I wasn't attempting to respond to your point.  I was
responding to Giles' points concerning applications of probability
theory to quantum mechanics.   

>If two events A and B are in isolated systems, isolated from the rest of
>the universe and each other, they will not be correlated. 

Since I don't know what "isolated from the rest of the universe" means,
I don't know what this means.  But it reminds me of an interesting fact.
In quantum field theory, say (to be simple) of a scalar field phi, in
the vacuum state the fields phi(x) and phi(y) at spacelike separated
points are not independent random variables but are correlated.  In
fact, the vacuum state can be shown to violate Bell's inequality:

Bell's inequality and quantum field theory II: Bell's inequalities are
maximally violated in the vacuum, Stephen Summers and Reinhard Werner,
J. Math. Phys..   (Sorry, I just have a preprint, so no more info.)

[A technical point: phi(x) should really be smeared with a test function
to obtain a random variable.]

I leave it to others to decide what "causes" this correlation.  

>I should further add that I have been a bit suspicious of Baez's definition
>of causality ever since I've noted he has had no problems with tachyons
>being non-causal while also believing in SR.

First of all, it's not "my" definition
of causality, it's a completely standard one; check out the references I
gave, e.g. p. 597 of Bogoliubov Logunov and Todorov's "Intro. to
Axiomatic QFT."   Second of all, the problem with the free tachyon field is not
that it's non-causal according to this definition (it's causal), the
problem is that it violates energy positivity.  That is, the Hamiltonian
is unbounded below.  "SR" is not a well-defined set of axioms, but it is
frequently taken to include Poincare-invariance, causality AND energy
positivity (and maybe other stuff too); all of these are independent
notions.  Thirdly, SR is not something I "believe in" -- general
relativity already shows that special relativity has its limitations --
it's just a model which appears to do quite well in a certain range of
circumstances.