From Aaron Sloman Fri May 10 08:38:48 BST 1996
To: adrienne@dvir.weizmann.ac.il
Subject: Classical physics and determinism
Dear Adrienne,
I've been having some inconclusive discussion with Henry Stapp about the
differences between classical physics and quantum physics, and one of
your recent comments seems to me to be relevant to the point I am
groping to make:
To me (working on turbulence) the behaviour of the cup of coffee is
complicated but not so very complex: we have its equation of motion,
and believe it to be fully specified by a few parameters and the
initial conditions, and in the stirred case the functional form of
the stirring.
The only problem is that the equation of motion is non-linear and so
the specification of the initial conditions to sufficient accuracy is
impossible.
I've been trying to extend that notion to show that classical mechanics
has two lives,
(a) one, the "official theory" which is deterministic and
(b) implicit actual theory that physicists and engineers use
which was not deterministic (because it was "obvious"(?) that
reality could not be, because of the nature of initial conditions.)
Here's the argument, which is part of a larger exercise attempting to
understand the role of ideas about possibility in our thoughts about
mechanisms of many kinds:
=======================================================================
Statistical mechanics has been important in classical physics
as I understand it (remember I'm very much an amateur) for at least
about 100 years. Now one way of looking at that is to say that that's
just because we don't know enough, and if we had truly exact measures of
everything then we could feed them into our equations and everything
would be completely deterministic (even if not all the equations could
be solved analytically....)
I'd like to offer an alternative view, namely that the very notion of
infinite precision of measurement is a sort of *metaphysical* ideal for
which there is no scientific basis and never has been.
In particular a complete specification of a point on the real continuum
in some sense requires (in general) an infinite amount of information
(except for the tiny subset of points that can be determined
algorithmically).
(E.g. there are infinitely many points in the real unit interval whose
infinite binary representation is non-computable, i.e. not definable by
a Turing machine. In fact, far more are non-computable than are
computable: only countably many are computable.)
Why should we assume that there is anything in the physical universe
that has an infinite amount of information embodied in it, such as the
size or position of a particle?
Of course classical mechanics uses equations such that *if* you had the
information then *in principle* you can feed it into the equations, and
get infinitely precise results. But since no classical physicist ever
had access to any measuring device with infinite precision, it is
arguable that in a sense they never really assumed or even needed the
availability of such information, except in their philosophical moments
(e.g. Pascal).
Moreover it was commonplace in physics labs to play with devices that
demonstrated the statistical nature of reality. One I remember first
seeing as an undergraduate in the 50's was an array of pins on a
vertical panel, above a row of vertical tubes, and a sort of funnel
above the pins through which a lot of ping-pong balls could be dropped
onto the pins. It's impossible to ensure that one drops a ball through
the funnel in such a way that it lands in a designated tube after
hitting various pins on the way down. And yet if you pour a lot of balls
through the funnel, without taking much care, they always form the same
shaped histogram in the tubes (corresponding to a certain probability
distribution).
Do you recognize this familiar teaching toy from my description?
I don't think I have heard ANY good argument in support of the claim
that, in a device like that, every individual ball has a set of
properties when it goes through the funnel that determines precisely
which tube it will end up in. (More precisely the claim would be that
the combination of ball and array of pins and tubes has an initial set
of properties that determines the precise outcome. I am saying there has
never been any justification for such a claim - only philosophical
prejudice.)
Admittedly, the array of pins through which the ball falls is such as to
enormously amplify slight differences in initial conditions, but why
should we believe that two balls that follow different paths really did
have different initial states if we have no hope of being able to
measure such differences?
(Similar comments can be made about chaotic systems, which can appear to
be indistinguishable at a particular time and yet behave very
differently a short time later.)
If the state of a ball coming down the funnel is not determined with
infinite precision, then instead of saying that the array of pins
determines the consequences of the initial state, we could say that the
ball has an *indeterminate* initial state, which is equally compatible
with ending up in a number of different tubes, and the geometry of the
array of pins together with gravity (along with thermal and other
motions that prevent a ball sitting forever on a pin or bouncing up and
down indefinitely on the same pin) "forces a selection".
What I am trying to do is suggest that the notion of infinitely precise
state may not have been an essential feature of classical physics,
just a philosophical interpretation favoured by deterministic
philosophers. Once the idea is abandoned, we have the alternative view
that mechanisms known long before quantum mechanics can force selections
between possibilities that are not predetermined. (I would claim that
gambling casinos contain many such devices.)
Does that make any sense?
I wonder if it is possible to start from a view of classical physics
which is like the one I've sketched (i.e. objects have states whose
precision is limited, so that in some experimental situations their
future possibilities are not determined, and yet physical apparatus can
force a selection to be made, but only in a statistical fashion, not a
deterministic fashion), and then go on to say exactly what quantum
mechanics adds to that? (Maybe that would enable me to understand
quantum mechanics at last?)
Or is my picture of classical physics already inherently quantum
mechanical? I suspect not, since, for example, it has no notion of
quanta: it says precision is not unlimited, but it does not specify any
bounds to the precision. The lack of definite bounds might be another
example of something that has no precise measure. However, in quantum
mechanics there are precise laws regarding uncertainty of measurement.
So that might be a difference: i.e. QM adds some determinism to
classical mechanics conceived my way ????
Henry's answer is that I am just wrong about classical physics. But even
if that is the case, then it still leaves open the question whether
there is a view of physics which is intermediate between classical and
quantum physics. My suspicion is that many people working with classical
physics must implicitly have had such a view. I think it was implicit in
the way I was taught physics many years ago.
Aaron
=======================================================================
From Aaron Sloman Fri May 10 09:56:30 BST 1996
To: adrienne@dvir.weizmann.ac.il
Subject: Re: Classical physics and determinism
Dear Adrienne,
Isn't email amazing? Thanks for such a rapid response.
Just one further comment to feed your weekend ponderings:
> ....there IS
> inherent imprecision at the smallest scales due to thermal vibrations,
This assumes that there is a perfectly precise value for relevant
physical variables (e.g. position, velocity, mass, diameter, etc. of
particles) but that these are changing too fast or too irregularly to be
capable of precise measurement. I want to consider an alternative,
namely that there's nothing precise to be blurred by motion.
I am wondering about the implications of giving up the idea of perfect
precision. So even if we ignore thermal vibrations and the like is there
any reason to believe in these infinitely precise values? One answer is
that the equations of classical physics presuppose their existence. But
I wonder whether that's actually so. The equations can propagate ranges
of imprecision as well as perfect values, and that's how they have to be
used in practice, which works very well for engineering desing, and much
useful prediction till you get non-linear feedback loops and chaos, etc.
On this view we get various kinds of small scale and large scale
indeterminism out of something close to classical physics, but without
any of the mysteries of quantum mechanics, no consciousness making
choices, etc., just things like the geometry of a configuration allowing
only N possible outcomes with nothing in between, etc.
I guess if there is a residual mystery it's where the regularities in
the distributions of outcomes come from. Why don't you ever get 100
balls falling into one column and none in the rest? Or do you believe
that if you try often enough you eventually will? Could it be a brute
physical fact that that's just impossible given the way decision-forcing
mechanisms interact with inherently imprecise values? (I have to confess
that I don't know whether I'm talking complete nonsense!)
Cheers.
Aaron
=======================================================================
From Aaron Sloman Thu May 9 19:30:19 BST 1996
To: STAPP@theorm.lbl.gov
Subject: Re: Comments on your paper.
Henry,
Thanks for the comments.
> The idea that possibilities are actualities in classical mechanics
> sounds odd, but may be sensible in some way: it brings us closer.
that's what I felt -- but I wasn't sure whether it was illusory,
for the reasons you mention.
> But choices seem to have no ontological status: everything just
> automatically unfolds, and the possibilities, considered as things like
> elasticity, just feed into this automatic continuous process. The
> experiential qualities still seem to be a superfluous add-on.
I think that's an "official theory" of classical physics. The reality
may be different, for the following (possibly weak??) reasons.
Statistical mechanics has been important in classical physics
as I understand it (remember I'm very much an amateur) for at least
about 100 years. Now one way of looking at that is to say that that's
just because we don't know enough, and if we had truly exact measures of
everything then we could feed them into our equations and everything
would be completely deterministic (even if not all the equations could
be solved analytically....)
I'd like to offer an alternative view, namely that the very notion of
infinite precision of measurement is a sort of *metaphysical* ideal for
which there is no scientific basis and never has been.
In particular a complete specification of a point on the real continuum
in some sense requires (in general) an infinite amount of information
(except for the tiny subset of points that can be determined
algorithmically).
(E.g. there are infinitely many points in the real unit interval whose
infinite binary representation is non-computable, i.e. not definable by
a Turing machine. In fact, far more are non-computable than are
computable: only countably many are computable.)
Why should we assume that there is anything in the physical universe
that has an infinite amount of information embodied in it, such as the
size or position of a particle?
Of course classical mechanics uses equations such that *if* you had the
information then *in principle* you can feed it into the equations, and
get infinitely precise results. But since no classical physicist ever
had access to any measuring device with infinite precision, it is
arguable that in a sense they never really assumed or even needed the
availability of such information, except in their philosophical moments
(e.g. Pascal).
Moreover it was commonplace in physics labs to play with devices that
demonstrated the statistical nature of reality. One I remember first
seeing as an undergraduate in the 50's was an array of pins on a
vertical panel, above a row of vertical tubes, and a sort of funnel
above the pins through which a lot of ping-pong balls could be dropped
onto the pins. It's impossible to ensure that one drops a ball through
the funnel in such a way that it lands in a designated tube after
hitting various pins on the way down. And yet if you pour a lot of balls
through the funnel, without taking much care, they always form the same
shaped histogram in the tubes (corresponding to a certain probability
distribution).
Do you recognize this familiar teaching toy from my description?
I don't think I have heard ANY good argument in support of the claim
that, in a device like that, every individual ball has a set of
properties when it goes through the funnel that determines precisely
which tube it will end up in. (More precisely the claim would be that
the combination of ball and array of pins and tubes has an initial set
of properties that determines the precise outcome. I am saying there has
never been any justification for such a claim - only philosophical
prejudice.)
Admittedly, the array of pins through which the ball falls is such as to
enormously amplify slight differences in initial conditions, but why
should we believe that two balls that follow different paths really did
have different initial states if we have no hope of being able to
measure such differences?
(Similar comments can be made about chaotic systems, which can appear to
be indistinguishable at a particular time and yet behave very
differently a short time later.)
If the state of a ball coming down the funnel is not determined with
infinite precision, then instead of saying that the array of pins
determines the consequences of the initial state, we could say that the
ball has an *indeterminate* initial state, which is equally compatible
with ending up in a number of different tubes, and the geometry of the
array of pins together with gravity (along with thermal and other
motions that prevent a ball sitting forever on a pin or bouncing up and
down indefinitely on the same pin) "forces a selection".
What I am trying to do is suggest that the notion of infinitely precise
state may not have been an essential feature of classical physics,
just a philosophical interpretation favoured by deterministic
philosophers. Once the idea is abandoned, we have the alternative view
that mechanisms known long before quantum mechanics can force selections
between possibilities that are not predetermined. (I would claim that
gambling casinos contain many such devices.)
Does that make any sense?
I wonder if it is possible to start from a view of classical physics
which is like the one I've sketched (i.e. objects have states whose
precision is limited, so that in some experimental situations their
future possibilities are not determined, and yet physical apparatus can
force a selection to be made, but only in a statistical fashion, not a
deterministic fashion), and then go on to say exactly what quantum
mechanics adds to that? (Maybe that would enable me to understand
quantum mechanics at last?)
Or is my picture of classical physics already inherently quantum
mechanical? I suspect not, since, for example, it has no notion of
quanta: it says precision is not unlimited, but it does not specify any
bounds to the precision. The lack of definite bounds might be another
example of something that has no precise measure. However, in quantum
mechanics there are precise laws regarding uncertainty of measurement.
So that might be a difference: i.e. QM adds some determinism to
classical mechanics conceived my way ????
> Yes, in my picture conscious experiences are a very high-level form of a
> general type of beingness that is associated with the reduction of wave
> function, generally.
I would like to see that notion explained without making any assumptions
about our ordinary notion of consciousness, experience, perception,
thinking, etc. being brought in, i.e. it should be explained at a level
at which the dynamics could operate in the physical world without any
human beings or other experiencers like them.
Then, when the two different notions have been separately defined, it
might be possible to show how there's some deep affinity. Otherwise it
looks like sleight of hand, importing a familiar concept into territory
where it's application is totally unjustified.
>....
If it is agreed that states are not infinitely precise, then there can
be differences not entailed by the actual.
>....
=======================================================================
From Aaron Sloman Thu May 16 00:15:27 BST 1996
To: STAPP@theorm.lbl.gov
Subject: Re: Comments on your paper.
Dear Henry,
Thanks for your comments received a few days ago.
> I think we must realize that we cannot speak with much precision or authority
> or knowledge about the world itself: we can debate endlessly. But we can speak
> of our theories about nature in precise terms.
Up to a point I agree, though there are often degrees of imprecision in
the theories themselves (even in pure mathematical theorems and proofs,
as was shown very nicely by Imre Lakatos' work in the 1960s (Proofs and
Refuations -- including a detailed analysis of Euler's theorem regarding
relations between number of vertices, edges and faces of polyhedra).).
Scientific theories are subject to even more imprecision since they
refer to entities that cannot be fully defined in mathematical terms.
Of course I assume you are not claiming that scientists can talk only
about theories, for unless the theories referred to somthing there would
be nothing to disagree about, no point in observing reality to settle
disputes, and all theories would be equally good candidates for truth.
I have the impression that some of the people you quote in your paper
did not grasp this matter.(E.g. Bohr?)
> Classical theory, as a theory,
> has certain mathematical properties, and determinism etc. are among
> them.
The equations are deterministic, I agree. But what I was suggesting
was that the inputs (boundary conditions, measurements) etc. may never
have been sufficiently determinate for the equations to have fully
deterministic consequences.
Moreover, I suspect that that is exactly how physicists and engineers
applied and thought about classical physics whether they acknowledged
the fact explicity or not.
The discovery of chaotic systems, where the deterministic equations can
amplify indeterminacy of initial states to an extraordinary degree,
eventually forced the realisation on them.
....
My point was mainly about the nature of the classical theory.
I.e. it is normally presented as being fully deterministic when perhaps
it wasn't, and I think that was brought out in part by some of the
experiments with "toys" that amplified the indeterminacy.
Aaron
From Aaron Sloman Thu May 16 00:25:28 BST 1996
To: STAPP@theorm.lbl.gov,adrienne@dvir.weizmann.ac.il
Subject: Indeterminism in classical physics
Dear Henry and Adrienne,
By a strange coincidence I have recently stumbled across an article
pointing out that there's a history of attempts to bring out the
interminism in classical physics.
The article, in Mind Vo,105, no 417, Jan 1996 (pages 80--83) is by
Jon Perez Laraudogoitia,
He refers to earlier work by J. Earman, a book A Primer on Determinism,
Reidel 1986, which I have not read.
I am still trying to recall what it was that I was taught about this in
the 50s when I was a physics undergraduate in Cape Town, but the
memories are too vague, except that I have vague recollections that
statistical mechanics could not really work properly without an
assumption that at some level of detail reality was inherently
probabilistic rather than deterministic.
Maybe I should become a physics student again and try to catch up.
cheers.
Aaron
=======================================================================
From A.Sloman@cs.bham.ac.uk Thu May 16 08:15 BST 1996
Date: Thu, 16 May 1996 08:14:58 +0100
From: A.Sloman
To: STAPP@theorm.lbl.gov
Cc: A.Sloman
Subject: Re: Comments
Henry,
Quick greetings thanks an a short response before I have to
rush off
> It has always seemed to me that trying to make classical mechanics seem
> nondeterministic by talking about the fact that we cannot measure things
> accurately and hence cannot have exact knowledge about initial conditions
> is a muddying of the waters.
That could be so, though the heart of my argument was not just a point
about what we can measure but a suggestion that infinite precision is
something for which there may actually be no room in reality.
That's a very old idea and one of the roots of atomic theory, back in
ancient Greece I think.
So if some classical physicists had that idea then there could be
a variant of classical physics wthout one of the components
that make the other variants deterministic.
The important question then is whether that could be a coherent theory,
whether it is better or worse supported by evidence than the fully
deterministic classical physics, and how such a theory might cope with
the removal of indeterminism of end states in some of the experimental
situations like the balls and tubes experiment.
But I accept that such questions may be of little interest to someone
who believes that all forms of Co are false anyway.
I guess my interest in it is connected with trying to understand the
nature of the processes of science. What kinds of conceptual apparatus
are available physicists to build theories that have or might have had
in the past at least a prima facie case for being taken seriously
and what are the alternatives to full determinism outside the QM
context, and whether those alternatives have been fully considered in
the context of QM.
My recollections of a talk given by Roger Penrose a couple of years ago
suggests that he may be thinking along similar lines, in claiming that
it's the interaction of large scale and small scale phenomena that
causes the collapse.
Anyhow, ignore my ramblings I need to do more studying of physics,
though whether I'll ever find the time, is another matter
Thanks for your patience.
Aaron
See also
http://www.cs.bham.ac.uk/~axs/misc/real.possibility.html