🚀 go-pugleaf

In article <1992Sep28.214420.18300@galois.mit.edu>, jbaez@riesz.mit.edu (John C. Baez) writes:

> The thing about "interpretations of QM" is that for the most part
> they are not really physical theories.  QM is a physical theory and
> makes testable predictions which seem to work well.  One can
> think of this theory as consisting of two parts: the part that's pure
> mathematics, and the part that tells us how to use this math to
> calculate predictions from data we input.  One could call the latter
> part the "interpretation" of QM, but usually interpretations of QM
> do more.   "Interpretations" usually dress up this theory with a bunch
> of language to give us a "picture" of the world QM is describing; this 
> picture has the pragmatic effect of allowing us to match up the math of
> QM with things we observe, but one can't typically experimentally test
> all the elements of the picture.

Every physical theory has the problem of mapping the mathematics into
experimental predictions. Any theory using sophisticated mathematics
or referring to nonmacroscopic objects can have problems at visualizing
its content. Only quantum mechanics has interpretations.

Interpretations exist for quantum mechanics because the theory is not
formalizable. One cannot define a model for a quantum mechanical system
in ZFC. That is the standard criteria for whether a mathematical model
has a rigorous definition. If that were possible there would be no
ambiguitys about what quantum mechanics means in a mathematical sense
and there would be no need for interpretations. 

It is not simply a matter of being extremely difficult to define such
a model. It would take some major change to ZFC to allow one to rigorously
define a random sequence. A change that I do not think any mathematicians
foresee happening. It would also be difficult to rigorously define
what happens when an observation is made and make this consistent with
a rigorous definition of special relativity.

Paul Budnik