Re: Determinism

On Sep 16, 3:53 pm, "Flipper, the talking porpoise."
<plankenste...@xxxxxxxx> wrote:
If we lived in a deterministic universe would there be a test we could
perform that would reveal this?

Yes.

The double-slit experiment confirms that the universe is neither
strictly
determinate nor strictly indeterminate, but that the correct answer is
that
it's status as such is in fact indeterminately either one or the other.
It
may be regarded as one or the other interchangeably because the answer
itself is indeterminate.

To me, that's more a clever word play than a serious analysis.

A theory is indeterminate... hmm... maybe not the best choice of
words! An indeterminate theory might be an incompletely specified
one. What is meant is a theory containing random variables as opposed
to a theory containing no random variables. To say that the universe
is random would mean that it is faithfully modeled by a theory
containing random variables, and that this theory in turn cannot
itself be reproduced in distribution by a second theory without random
variables, with some one time distribution of initial conditions.

For reasons which may have more to do with human psychology than
physics, there has been a strong impetus since the inception of
quantum theory to regard that, besides being a theory containing
random variables, quantum theory must furthermore be the most complete
theory possible. This, as Sherlock Holmes might say, is theorizing in
advance of the facts.

There is no possible theory which cannot be modeled by a deterministic
theory, taking as the ultimate reductio ad absurdum a one time
"theory" which requires a sequence of quantities to be a particular
arbitrary sequence of quantities. What is wanted is some more
delicate test whether a random theory can be reduced to a non-random
theory with some specified degree of simplicity: when we can quantify
"degree of simplicity" we might be in a position to agree on what so-
called deterministic theories seem merely like legislation, and which
seem like theories, and to show whether or not a non-legislated theory
can cover the same ground as a given random theory.

"Legislated" corresponds roughly to "over-determined", in the art.

The closest reach to success in this line is Bell's theorem, which
shows with desired rigor that certain predictions of quantum mechanics
cannot be reproduced by certain kinds of deterministic theory. The
classes of deterministic theory left over would be no means seem
exclusively limited to legislation, however -- though possibly non-
local in the usual sense of locality -- and in my opinion it has not
even been shown with conviction that nature would have to resort to
such non-local theories to reproduce experiment: the "loophole"
pejorative attributed to the reservations arises from a needless
requirement that the unknown deterministic theory contain
conventionally used features, which nature may not in fact require.

In case anybody wanted to know. :-}

We can easily construct an algebraic example of a system which is
indeterminately either determined, or indetermined.

A single example should suffice.

You start with numbers of the form (a + ~b) where (a) is a nonrandom part,
and (~b) is the random part.

Let the position of a particle be given by y = f (a+ ~b) = sin (a + ~b)

Let ~b be chosen from the interval (-1,1) so that ~b = 0 is one possible
value of ~b.

Case A
if ~b = 0 then sin (a + ~b) = sin (a) and the situation is obviously
deterministic ,

but elswhere
Case B
~b =/= 0 and so sin (a + ~b) is at least partly indeterminate.

I don't agree with your analysis.

The function sin (a + ~b) is a random number. The fact that it
contains a random variable as an argument, one of whose possible
outcomes happens to be zero, doesn't change that. _After_ we've chosen
an outcome of the random variable, you could say the output was
subsequently determinate, but there is nothing special about zero in
that regard. If the realization of ~b was .3, then the outcome would
be equally determinate, in your sense.

You never know if you are looking at Case A or Case B because ~b is randomly
chosen, and so the indeterminacy of this equation may or may not be present
depending on ~b.

If the model contains a random element which has any effect on the
outcome, then the model is random. Saying that the universe is
indeterminate in your sense amounts to saying that a maximal model (we
can't do any better) has random elements. You are attaching some
significance to a particular outcome of a random variable (zero) which
somehow makes it less random than other outcomes. I can vaguely feel
your argument (zero doesn't affect the deterministic part -- aha!
_deterministic_ ... that's the word -- so in that case the system is
deterministic), but I think this is confused.

There is another element to "randomness" which comes up, sometimes in
explaining entropy, which concerns _our_ uncertainty about the state
of a system. We could be uncertain about the state of a determistic
system, and hence represent our knowledge with random variables; or,
we could be uncertain about the state of a random system! (That's
where the density matrix comes in, I believe.)

Anyway, to recast your argument, say we had a system with a random
part whose magnitude can be dialed in, from 0 - 9, where "0" means
deterministic. _Now_ we make the degree of randomness itself a random
variable. In this case, you want to say, the system is deterministic:
however, we can't tell if the system is deterministic!

There are a number of interesting issues here in disentangling the
randomness from the uncertainty in our knowledge, but in some way you
are referring to the uncertainty in the "randomness" variable, which
is a problem in statistics. Overall the model is random, however,
since it includes random variables.

I don't think this is what most people have in mind when they wonder
if the universe is "random", though.

Just like in the real world. : )- Hide quoted text -

- Show quoted text -


.

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