Re: Two EPR questions
From: Ilja Schmelzer (Ilja.Schmelzer_at_FernUni-Hagen.de)
Date: 11/19/04
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Date: Fri, 19 Nov 2004 19:29:50 +0000 (UTC)
<rof@maths.tcd.ie> schrieb
> "Ilja Schmelzer" <Ilja.Schmelzer@FernUni-Hagen.de> writes:
> ><rof@maths.tcd.ie> schrieb
> >> "Ilja Schmelzer" <Ilja.Schmelzer@FernUni-Hagen.de> writes:
> >Moreover, it is not given that the construction M_n is spatial.
> >If we construct following Bohmian mechanics we construct
> >some Psi(q) which is not spatial but defined on the configuration
> >space.
>
> Sure, but the reason that it's an explanation that one feels
> comfortable with is because it's easy to visualise. One imagines
> a wave moving in some space (here, it's configuration space),
> and that is something that we're used to. The state of affairs (the
> wavefunction, Psi, ignoring for a moment the particle positions)
> is represented as being composed of several mini-states of affairs,
> Psi(x), each at a different position.
> One becomes a lot less comfortable
> with it once one reflects on the fact that the place where the
> wavefunction lives is not real space at all, but an abstract
> construction called configuration space whose dimension is 3N.
I know. That's my point - the Psi(q) isn't spatial.
> We can make it make a little more sense by noticing that the
> space over which the wavefunction is defined is the same as
> the space over which probability distributions (of generic
> states of affairs of the system, or configurations) are
> naturally defined. Information that we have might have about
> the configuration of the system at a given time would naturally
> be expressed as a real function on this space, and a description
> which included the instantaneous rate of change of this
> probability distribution would naturally be expressed as
> two real functions (or one complex function) on this space.
This is the base of the QM interpretation that the wave function
does not describe some state of reality but our knowledge about
reality. But I think there is no necessity for such a non-realistic
interpretation.
I feel uncomfortable with this space too. But I have another
idea: There is simply our universe, q in Q, and something else,
unknown. But whatever this unknown thing is, once it interacts
with our universe, its action somehow depends on the state
of our universe and, therefore, it may be described by some
function on all possible states of the universe too.
> >I would not argue that there is some strong urge to develop ontological
> >theories. Ontological theories have been successful, there is no reason
> >to give them up.
> There is no success of any theory which can be ascribed to its
> ontological character.
I disagree, but acknowledge that it's hard to prove that
the ontological character of certain theories has been
important for their success.
> > With Bohmian mechanics they are successful today
> > too.
> Only insofar as Bohmian mechanics has been able to reproduce
> the predictions of a theory (Copenhagen-style quantum mechanics) which
> wasn't ontological. In so far as Bohmian mechanics has not been
> able to follow quantum mechanics (pair creation, for example),
> it has not been successful, although I recognise that there has
> been progress in this direction.
Sorry, I don't see why you think pair creation is problematic.
Of course, in field theory you have to use an appropriate
configuration space - a space of functions - and a formulation
of QFT with an appropriate wave function - which is a wave
functional on this function space.
To define everything accurately, a discretization or other
type of regularization is necessary in QFT as well.
But, in general, once you have managed to make the
quantum part mathematically consistent, to add the
guiding equation is not really problematic.
All you need is a probability current operator J.
Then you have
d/dt Q = <Psi J Psi>/<Psi Psi>
> >> A may think it's on ontological theory, but A is confusing himself.
> >> Imagine there is a digital machine, which takes 1's and 0's as
> >> input. You feed in some sequence of 1's and 0's, generated by
> >> some algorithm. The machine proceeds to construct a Markov model
> >> to predict the sequence. It is successful to some degree - most
> >> of the time it correctly predicts the next input. Has it discovered
> >> reality? Is its Markov model an ontological theory?
>
> >Once it predicts successfully, there is some probability that the
> >algorithm has been guessed correctly. In other words, that
> >the algorithm used to create the input sequence and the
> >algorithm used by the machine to predict the input sequence are
> >in some sense equivalent.
>
> But this doesn't answer either of the above questions.
And there is no necessity to answer the first. Of course,
if we have a realistic theory of everything, we also cannot
be sure that the theory is true. And we never will be sure.
You want too much certainty.
If I was not clear enough about the second: A Marcov model is
an ontological theory (or can be formulated in such a way).
> There's also the problem of the vagueness of the "in some
> sense" which is inevitably reached by proponents of realism
> in this situation.
Such is life.
> The grand project of ontology is not to guess an algorithm which
> predicts future observations (which is, in fact, the only thing
> we can do), but to determine what it is that really exists.
This project has been given up long time ago. At least if you
mean "determine" as giving certainty. The current (not that grand)
project of ontology is to guess what it is that really is, and to
test this guess using its testable consequences.
> If a machine develops an algorithm to correctly predict whether
> the next input will be a 1 or a 0, the most one can say about
> it is that that is what it has achieved. To say that it has
> discovered the ontological basis of reality, one has to radically
> change what one means by "discovered the ontological basis of
> reality."
Its you who wants to say this. I'm quite satisfied by giving
a reasonable guess which allows to derive predictions
which survive tests.
> One who, observing traffic lights, eventually says "A repeating
> pattern of green, then yellow and then red," has hardly reached the
> ultimate goal that realists aspire to.
You postulate some utopic ultimate goals for realists and
then argue that these goals are utopic. So what? These are
not my goals.
> Alan Sokal, in his "Defense of a Modest Scientific Realism",
> examines these issues a little bit, but, since he too is
> wedded to realism, doesn't quite reach the correct answer,
> but instead ends with:
> "Since no existing theory purports to be a final theory, there
> is no reason to consider it as literally true or to worry too
> much about whether the entities it postulates `really exist'.
> Or rather, when worrying about whether the unobservable entities
> of a given theory `really exist', it is important to distinguish
> existence _as a fundamental constituent of the universe_ from
> existence _in some coarse-grained sense_. It is a reasonable guess
> that _none_ of the theoretical entities in our present-day
> theories are truly fundamental, and that _all_ of the theoretical
> entities in our present-day well-confirmed theories will maintain
> some status as derived entities in future theories." (His italics)
Quite reasonable.
> In the end, he opts for saying that things exist "in some coarse-grained
> sense", which means that he wants to ascribe to them some property
> which he feels is related to existence or reality, but which is so
> vague that he cannot tell us what it is, and, lacking any concrete
> or even specific thing to say, must instead appeal to our sympathy
> to his realist position in order to convince us to accept what he
> is saying as a valid defense of realism.
Why do you think this is too vague? We have lot's of examples
where one theory appears as a limit of some more fundamental
theory. And in all these cases the objects which "exist" in the
approximation are somehow constructed from the objects
which "exist" in the more fundamental theory. In every such case
we can consider this connection in detail, as detailed as we like.
Thus, the "vague" notion is not an appeal to sympathy, but
an appeal to the large body of experience with such derived,
non-fundamental objects.
And, of course, a consequence of the fact that the most
fundamental theory is unknown.
> Notice that he also explicitly subscribes to the view that,
> if an entity from one theory appears as a derived or emergent
> thing in a more mature theory, then that entity cannot be a
> "fundamental constituent of the universe." What he leaves open,
> but implicitly suggests, is that, in a final theory, which
> makes perfect predictions and has no further refinement, we
> might actually consider the entities with which it deals to
> be fundamental constituents of the universe which really exist.
> This is, of course, what the whole exercise was intended to
> deduce, and which it has failed to deduce, so he ends by
> surreptitiously implying it.
The idea to _deduce_ the most fundamental theory has been
given up long ago. But there is no reason to give up the
modern realism which does not propose such utopic
nonsense.
> It is very important in these matters not to decide that we like
> realism and then accept as valid an otherwise insufficient
> argument in favour of it.
Ok. So what?
> Thus, if we find that the arguments with which
> we convince ourselves that realism is necessary amount to
> "In my opinion, realism should be considered a part of logic,"
> then we must go in search of the reason why that opinion
> was adopted, and reject it unless there is a rigorous basis
> for it.
I have adopted it because I have found the arguments
in favour of this position convincing.
I do not believe in such things as "rigorous basis" in
general and in the most fundamental philosophy especially.
Logic may not be justified on a rigorous basis. Because
any possible "rigorous basis" is, itself, based on logic.
Thus, the "rigorous basis" is only circular reasoning.
> As it stands, it looks quite like a demand that
> realism be adopted as an axiom; that is, it looks like
> a dogmatic assertion of a statement which cannot be deduced
> by reason.
It cannot be deduced, indeed. As well as logic cannot
be deduced. It does not mean that there is no justification.
> >That's not really a problem. Once we don't know the complete
> >input data used by the algorithm we cannot predict everything.
> >Nonetheless it is possible that the algorithms we guess and the
> >algorithms used in the "fabric of reality" are equivalent.
>
> The implicit assertion here is that the fabric of reality
> is implementing some kind of algorithm (recall that an algorithm
> is a list of instructions for computing one thing from another).
Yep. As a realist, I use implicit assertions about reality.
> The equivalence here is again, "in some sense", and has the particular
> difficulty that one algorithm (the one used by a human) has, as its
> output, patterns of sensations (as a prediction of future input).
> I doubt that an algorithm which has sensations as output is one
> that most realists would accept as an example of something which
> could qualify as a fundamental constituent of reality, since the
> things with which it deals (sensations) are purely mental.
Here several things are mingled. The algorithm which is assumed
to be used by the fabric of reality is one which computes
X_n+1 = f(X_n).
To derive testable predictions from this we have to solve some
other problems. Namely to connect the X_n with the E_n.
> >> Whether or not a particle even exists can depend on the motion of
> >> the observer (cf. the Unruh effect), so it seems strange to put that
> >> sticky reality label onto the particles and their positions in space.
>
> >I don't.
>
> But Bohmian mechanics does, and that is the context in which I made
> the remark above.
Bohmian theories supposed to handle the Unruh effect don't.
> In this case,
> are you asserting that "reality" is something which can be
> defined, or that its definition can change from theory to theory?
The definition of reality is part of the realistic theory. It
changes from theory to theory.
In NT reality consists of point particles attracted by forces,
in GR it consists of a manifold with a metric and some
matter fields on it, in field theory of fields
(psi(x),A_i(x),g_ij(x)), in Bohmian theories of
some q in Q and some Psi: Q-->C, where Q is
the configuration space which is very different in
different Bohmian theories.
Especially, a BT which handles the Unruh effect
may have, as the configuration space,
some fields q=(psi(x),A_i(x),g_mn(x)), or
some regularization, as, for example, some
lattice theory q=(psi(n),A_i(n),g_mn(n)), n in Z^3.
Realism is the preference for theories which
make clear definitions about what is real. And fulfill
some consistency conditions about these real objects.
(for example, we can apply probability theory and
logic if we work with real objects, "counterfactual
existence").
> I am always completely in favour of using classical logic and
> probability theory.
Fine.
> >Sorry, but we use physical theories to predict things which do not
> >happen in our mind, but in reality. (Except you are a pure solipsist.)
> >Of course, I feel free to say that there is a law of gravity out there.
>
> >I may be wrong about the details of the law of gravity. But it is
> >a hypothesis (in my mind) about what is out there.
>
> So you begin to understand; the law of gravity, as you
> know it, is not something which exists independently of you, but a
> hypothesis which relies on you for its existence.
No. Apples fall down even if I don't have any theory about this.
The particular law of gravity is a model of this in my mind. But
its purpose is to describe something which exists really, outside
of my mind, independent of my existence.
> The real difficulty here is (as I mentioned before) the manifold
> use of the word "real".
Not that difficult IMHO.
Of course, I'm sometimes sloppy too, especially in usenet
postings. But usually I try to label different concepts with
different labels.
For example, "realistic theory" is always a theory. Realism
I use not for a particular theory about reality but a definition
of a class of theories, namely "realistic theories". Reality
I use for all this stuff outside, which is not in our minds.
Sometimes we have equivalent things denoted by the same
label. For example, the definition of a class of theories,
namely the class of realistic theories, is in some sense
equivalent to a (meta)theory (about reality) that the correct
theory is an element of this class. Or to a methodological
decision to restrict yourself (or the community which follows
your argumentation) to this subclass of theories, rejecting
other theories from the start. All these conceptually different
but equivalent things I name "realism".
> To add further to this confusion is the additional confusion caused
> by the inappropriate use of the notion of "outside." The relations
> of outside and inside are properly ascribed only to objects which
> are in space.
I hope my use of "outside" does not cause confusion.
It means "not in my mind or my soul". My mind,
(at least the material part of it) is sufficiently located in
space. If there is something non-material connected with
consciousness and so on (soul), it is not part of "outside".
> Now, taken together, these two confusions lead to the realist
> position, where the physicist believes that he is examining
> that which "really" exists, "outside" of his mind. In fact,
> what he is doing is examining things which are actual (in
> my sense of the term) and outside of his head. Perhaps I
> should emphasise that this is worth thinking about; many
> lives have been wasted chasing ghosts because of this
> misunderstanding.
I see not much advantage in your specification. I propose
theories about actual things outside of my head? Fine.
No problem. But also no advantage.
> >> ... but nobody tries to understand starting from
> >> the facts which are right in front of them. That's not what they
> >> were trained to do.
>
> >The point is that this is impossible. It is the old ideal of positivism
> >to derive theories from observable facts. Science works differently.
> >There is no derivation E_n ->X_n, there is guesswork. We guess
> >theories, derive the consequences, and reject the falsified guesses.
> >This is what we are trained to, and this is how science works.
>
> This is what we are trained to do, but it is only a small part of
> how science works, namely the part that Popper, with what talent
> he had, was able to identify. Since you are here invoking an argument
> from authority (Science),
My argument is not from authority (Science or Popper) but
I have described my theory of science, which agrees in its
most essential parts with Popper's theory about science.
> The problem that modern theoretical physics finds itself in is
> that people are only trained in what Newton calls the synthetic
> method, principally because it's the easiest thing to test
> in examinations. It would be rather an interesting experiment
> to take a young physicist-to-be and show him all of the phenomena
> of electromagnetism, and assign to him the project of finding
> equations which describe all the observed results.
> A physicist with this training would be better equipped for real
> investigation than his colleagues, who have merely been trained to
> do homework assignments in which the axioms are given and the
> theorems are to be deduced.
May be, but I don't argue about pedagogics.
There are more serious faults in modern science than this.
Scientists should be independent. At least as independent
as judges. Even more. Because a judge which makes obvious
nonsense harms other people, a scientist which makes
obvious nonsense doesn't.
But current scientific organization is the reverse. If you
have a grant for a few years, you have to care about your
future, the next grant. The decisions are made by
beaurocrats and other scientists (these two often unified
in a single person). The predictable result is conformity.
Another pressure into conformity is "publish or perish".
Publishing and being cited is easier in a large community
with lots of journals to publish and lots of readers.
The prediction agrees with observation. In the highly
speculative domain of modern fundamental physics,
where free science would lead to lot's of very different
directions (because they are not guided by experiments,
purely speculative, therefore its extremely hard to reject
a research proposal as false) we observe de facto only
two research directions - strings and LQG.
> I should add that it is not the case that the analytic method has
> been exhausted due to a lack of performable experiments whose
> results we do not know in advance. The confusion about realism
> and the many disagreements about quantum mechanics (among those
> who actually do think about it) are evidence enough that there
> is an opportunity, for one who is prepared to suspend judgment
> and avoid opinion, to discern something previously overlooked.
The second sentence does not prove the first. The last two
points are discussions not about the results of possible
experiments.
> >> In order to formulate the questions which relativity
> >> addresses in my language, which is to some extent solipsistic,
> >> one first has to address the question of what relationship
> >> exists between one observer's X_n and another's X'_n, which
> >> involves how one observer manifests himself within the X_n
> >> of another, and that is a difficult question.
>
> >In a realistic theory, the answer is simple: The X_n should be
> >equivalent, or at least one of the observers follows a wrong theory.
>
> There are several problem with that. One is, as you said yourself,
> that the X_n are not complete.
The M_n (perceptions) are not complete. The X_n are complete.
> That is, I perceive a room, with walls
> here and there, and you perceive a different room (presumably),
> and there is no simple matching of what I perceive to what you
> perceive.
This is about the M_n. My X_n contains also complete
information about the inside of your room. I don't perceive
the X_n. But the laws of physics, the rule which allows
to compute X_n+1=f(X_n), need the whole information,
my room as well as your room.
Ilja
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