From: lizi@ocf.berkeley.edu (Cosma R. Shalizi)
Newsgroups: sci.philosophy.tech
Subject: Re: Hidden Variables
Date: 29 Aug 1992 19:23:31 GMT
Organization: Vampire Research Group at Berkeley :)
NNTP-Posting-Host: headcrash.berkeley.edu
Summary: Snodgrass has problems

In article <snodgras.714198449@crash> snodgras@crash.cts.com writes:
>In <1992Aug16.203826.10685@galois.mit.edu> tycchow@riesz.mit.edu (Timothy Y. Chow) writes:
>>>1. How accurate is Peebles' claim?  To what extent can it be proved that
>>nobody will ever devise a local hidden variables theory?
>      The notion that it can be proved one way or another is itself a notion
>part-in-parcel with the current paradigm. One often reads that Heisenberg's
>uncertainty principle has been proved, or put another way that it is a fact
>of nature that was discovered. In truth it is merely a mathematical formulation
>based on a history of assumptions, a formulation which has been taken as
>literal truth. The layers of assumption start with the origins of quantum
>theory, i.e. that 'energy' (which was first considered a substance, then
>recognized as motion, then again viewed as 'packetized' and hence a substance
>for the second time) that energy is REAL, and that the mathematical formalisms
>used to describe quantum emission are actual -- a notion Planck himself
>disputed. From there we move into statistical description of e.g. orbits
>of electron (or shells) and based on properties of these highly abstract
>formalisms, we end up with Heisenberg's principle and the rejection of
>'determinism'. Now, when you talk about undermining such a notion, or bringing
>together evidence against it, you're talking about events which must take
>place for the overthrow of a paradigm, not about some little experiment
>someone does somewhere. A shift in belief systems is required.
   Ahem. This is all very entertaining to collectors of bad Kuhn, but...
You seem to know a fair amount of quantum mechanics; excellent.
It should, however, be pointed out that,
* "Packetization" of a quantity does not imply that it is a substance. Motion -
  by your own account _not_ a substance - is "packetized."
* The "mathematical formalisms used to describe quantum emission are actual"
  - well, now, what does _that_ mean? That they are actual mathematical
  formalisms? Hardly a point worth debating. You mean that they are _true_.
  Quite possibly there are other mathematical formalisms that would do just
  as well. In light of your comments below, I should say that no non-mathe-
  matical formalisms will give us the information we are asking for - who
  will emit what when? - since it is quantitative (i.e. mathematical) infor-
  mation we want. But they _do_ match the phenomena (to within the limits
  of experimental error, et cetera, et cetera), AND no better alternatives
  are "on the market" AND we can derive them from more general bits of math
  whose other testable predictions are also confirmed gives us some reason
  - but not, of course, proof - for accepting them as valid.
* The Uncertainty Principle does not just apply to energy and duration, but
  to _any_ two observables whose operators are non-commuting - e.g., position
  and momentum. It can be derived from some fairly simple theorems about
  vector spaces, the psi wave and operators - I've done so, and so's every-
  one else who passed undergraduate QM here. There are even more or less
  intuitive arguments for the UP, at least as regards position/momentum and
  energy/duration, e.g., "What do you mean this thing has _a_ momentum?
  It has values of k all over the place!"
* I have read (in the Macmillan _Encyclopedia of Philosophy_) that von Neumann
  was able to derive most if not all of QM _starting from_ the uncertainty
  principle. I cannot vouch for this myself, however. If so, given the
  very great success of QM, it seems unlikely that the uncertainty principle
  and its implications are so much moonshine swilled by the stubborn
  adherents of the nefarious dominant paradigm; though it is of course log-
  ically possible that this is so, and that pigs will fly out of your monitor
  as you read this sentence.
* Why do you think that the overthrow of a paradigm could not be accomplished
  on the evidence of "some little experiment someone does somewhere?" What
  if, say, someone repeatedly and accurately measures a velocity of
  400,000 km/s for an electron?

>>2. Are there any plausible non-local hidden variables theories around?
>      The very manner in which the question is phrased precludes a
>positive answer. A theory which obviates the uncertainty principle would
>have to be alot more than plausible to overthrow quantum theory.
   A theory would indeed have to be much more than plausible to overthrow
QM. That's not what he was asking. A plausible non-local hidden variable
theory (NLHV) might be much less plausible than QM; there could be absolutely
no empirical or logical grounds on which to favor an NLHV, and it might
still be plausible.

>>I frequently encounter technically naive philosophers who have a strong
>>feeling that nature is fundamentally deterministic, and so I'm interested
>>in seeing how strongly one can argue against hidden variable theories.
>      I frequently encounter philosophically (or historically) naive
>scientists, who seem to overlook the most obvious philosophical contradictions
>in favor of strict belief in the current paradigm. As far as your interest
>in arguing against hidden variables, you'll only be satisfied (I suspect)
>with an argument phrased in the terms of quantum theory itself, or at least
>within the geometrical paradigm of 'explanation by equation'. But how much
>interest do you have in an argument which rejects this notion that
>mathematics, whether statistical or geometric, can fill the role of cause
>in scientific explanation? Otherwise, you might as well read Einstein's
>arguments! Wasn't he just about the last official holdout against quantum
>physics?
   The "philosophically (or historically) naive" part is telling. The philo-
sophy and history of science have no necessary relation. Even assuming "para-
digm" is a useful & meaningful concept, the fact that scientists (or philo-
sophers, artists, brick-layers, et cetera) have "shifted" their paradigms
for such-and-such reasons does NOT imply that this is why they SHOULD have
shifted if they wanted to be rational. See David Stove's _Popper and After:
Four Modern Irrationalists_, Pergamon Press, 1982.
   What "obvious philosophical contradictions?" While you're at it, what _is_
a philosophical contradiction? I understand a _logical_ contradiction, and
an _empirical_ contradiction (e.g., between the proposition, "No ravens are
black" and "All reported ravens have been black"), but philosophical ones
are new to me, and I eagerly desire enlightenment.
   "The GEOMETRICAL paradigm of 'explanation by equation?'" Eh?
   Mathematics does not "fill the role of cause" in scientific explanation.
That would imply that _because_ we have written this equation, or drawn this
diagram, that empircal result would follow _and might not have if we hadn't_.
I doubt that even the most extreme worshipper of mathematics claims this. 
Math is a means of describing observations and measurements and the relations
between them. Einstein's arguements against QM were of the sort: Assume this
theory is true. Then, under the following circumstances, you would expect
this result, which is so bizarre as to imply that something is wrong with
this theory. This is not entirely valid, because the bizarre results could,
in fact, take place, at which point they become evidence _for_ QM, and not
against it. I know of at least one instance where the bizarre results have
been confirmed - the EPR experiment - and none where they have been looked
for and not found.
   Why not, for that matter, read _Hegel's_ arguments, e.g., for their being
only seven planets? Wasn't he one of the last official holdouts _with brains_
against merely empirical science, uninformed by the luminous truths of
Reason? 

   I confess that I am only an undergraduate, and not a particularly intel-
ligent one at that. I welcome correction on any errors I may have made about
QM, but doubt they are large enough to wreck my argument.

>      snodgras@crash.cts.com
Cosma Rohilla Shalizi
lizi@ocf.berkeley.edu to friends
larval physicist
"[In Bergon's view] Intellect is the misfortune of man, while instinct is
 seen at its best in ants, bees and Bergson."
 -Bertrand Russell, _A History of Western Philosophy_