On Fri, 26 Jun 1998, Bill Unruh wrote:
> Well, I guess we have finally come to the knub of the disagreement. I
> contend that your willingness to separate the truth of the proposition
> from the evidence (which once upon a time you agreed was not valid in
> QM) is an assumption about reality.
Dear Bill,
It does appear that we have isolated our point of disagreement. Let me
summarize the situation as I see it.
You claim that I am inserting a reality assumption that is alien to
quantum thinking. You have admitted that my framework does satisfy some of the
reality assumptions that quantum thinking normally requires:
1. I have no ``hidden variable'' assumption: no assumption that outcomes of
unperformed measurements have definite (or predetermined) values.
It is completely allowed, within the framework I employ,
that the values of the outcomes of the actually performed experiments are not
defined or specified in nature until that experiment is actually
performed; and no outcome is assumed to be defined in nature for an
experiment that is not performed.
2. My formalism is such that no outcome appears to any observer unless
the associated experiment is actually performed, and no two incompatible
experiments can both be performed.
3. There are no presumed realities except for the performed experiments
and the outcomes that appear to the observers of the actually performed
experiments: e.g., There is no Einstein Reality Assumption that some other
kind of reality exists if some value `could be measured' but is not actually
measured.
4. I define the issue that I am considering as a theoretical one of whether
the actual world can be considered to be imbedded in a set of hypothetical
worlds that satisfy certain conditions. This is intended to be useful as a
condition that limits the ways that we may consistently and coherently
think about (e.g., model) nature.
5. These conditions are closely connected to the microcausality conditions
that are basic conditions on local relativistic quantum field theory.
There one can imagine the quantum world to be imbedded in a classically
describable world that allows certain `external parameters' to be manipulated.
These changes can alter, relative to the actual world, which experiments
are performed. In relativistic local quantum field theory one can, and does,
impose the demand that the changes in expectation values induced by a
hypothetical change in which experiment is performed in a spacetime region
be confined to the forward light cone of that region.
6. In quantum field theory the dynamical laws of quantum theory are
exactly the same in the actual and hypothetical worlds, apart from the
small localized perturbation in the hypothetical world that alters the
choice of which experiment is performed.
7, This restriction is something we want to retain. Indeed, the whole idea of
`what would happen' in a hypothetical world becomes ill-defined if one allows
the laws of nature to fail in the hypothetical world: the notion that the laws
of nature apply equally to the actual and hypothetical worlds is the
*sine qua non* of scientific discussions of such matters.
8. I explicitly specify the pertinent QM law/prediction that holds in case
L2 and R1 are performed in the actual world: L2^c^R1-> L2^R1^f. And
I explicitly specify that THIS is the law/prediction that is assumed to
holds also in the hypothetical world.
9. You admit that *if* THIS assumption is made then my proof is OK.
10. So you are, in that sense, admitting that my proof of line 5 is OK:
L2->SR, does follow from my explicity stated assumptions.
11. You are not objecting to my locality assumption, LOC1, which is the
only locality assumption that goes into the proof of line 5.
12. And you accept that the problem I address makes sense only if the
laws/prediction of QM are assumed to carry over to hypothetical world.
I explicitly state the pertinent law/prediction that would hold if L2 and R1
were actually performed, and you agree that if I assume that this
law holds also if that world is hypothetical then my proof goes through.
So what is the problem?
You say:
> R1 is not, by explicit assumption,
> actually measured independently of L2. R1 is a counterfactual. As such
> it is not actaully measured, but the value of R1 is infered from the
> actual measurement on L2. Such inference is a form of measurement (a la
> von Neumann) but it is not an independent measurement. If R1 were
> as I discussed above
> actaully measured and L2 were actaully measured and found to have value
> c then your statement would be justified. However, by explicit
> hypothesis, R1 is not actually measured. R2 is actually measured by
> hypothesis.
Correct.
> Under that condition, the best you can say is that
> L1^c^R1->L1^c^R1^f and not L1^c^R1->L1^R1^f.
I assume that you have made the same misprint again, writing L1
in place of L2: I wonder whether that persisting confusion of symbols
is a manifestation of some problem in your thinking when you come to make
this odd claim, which requires abandoning the basic rule of logic that A^B->A,
which is essentially a definition of what the logical terms are supposed to
mean.
I ALLOW *also* the prediction L2^c^R1-> L2^c^R1^f.
What this assertion means in logic, and normal language, is that under the
condition that the conditions for L2 and for c and for R1 are all
satisfied, it is true that the conditions for L2 and for c and for R1
and for f are all satisfied. This meaning is a matter of how logical
words/symbols are to be used. They are to be used in this way no matter
whether we are speaking about abstract mathematical propositions,
about properties of graphs or topological structures, about properties
of languages, or sociological constructs, or whatever. They are just
conventions about how the words are to be used.
The fact that the sufficient conditions for L2 and for c and for R1 and
for f are all satisfied entails that any subset of these conditions are
satisfied: A^B->A. Your method of expressing your objection to my argument
is not a satisfactory method because your substantive objection. whatever
it might be, is obscured by your violation of the conventions of rational
discourse.
I do believe that your inability to express your objections
within the normal linguistic framework is a reflection of some basic
confusion.
This particular statement, L2^c^R1-> L2^c^R1^f-/-> L2^R1^f pertains
explicitly to a hypothetical world, not to the real world. So it is certainly
not a reality assumption: it is a theoretical assumption about what sort of
logical conditions are going to be placed on the allowed hypothetical worlds.
You are saying that the laws of logic breakdown in the the allowed
hypothetical worlds, even though they hold in the real world. What sort of
``reality'' condition is that?
> Just as in the vonNeumann analysis of STern Gerlach, you cannot say that
> the electron has spin up independent
> of the direction of deflection of the electron beam in the magnet.
The analogy to the Stern-Gerlach experiment does not support your position.
Rather it undermines it.
There is no breakdown of the rules of logic in that case. The
analog of L2^c^R1->L2^R1^f is normally taken to hold: if L2^c^R1
*were to be true* then L2^R1^f *would be true*. That certainly does not
entail or mean that f holds in the actual world where R2 is performed
and g appears: f cannot appear in that actual world because it is a possible
outcome of R1, which is not performed in the actual world. It does help always
to speak only of `outcome appearing to observers of anexperiment', in
order to keep thinking straight.
It is the whole statement that is true in the Stern-Gerlach case, not just
the free-floating conclusion. The statement specifies some particular
conditions that are sufficient to ensure *the validity of the defining
conditions for the conclusion*. One does not need to squeeze the
meaning of the whole statement into the conclusion: i.e., to conflate these
particular sufficient conditions with the defining conditions. The whole
true statement is the correct way to specify specify the connection between
these two logically separate conditions.
Similarly, it is the whole statement L2->SR that is claimed to be true
under some conditions. These include the theoretical condition that
L2^c^R1->L2^c^R1^f. This condition would be a prediction of quantum theory
if R1 were real, and it is assumed to hold also in the
theoretical/hypothetical world.
The need for c to hold is an aspect of the whole statement: it need not,
and cannot, be made part of the definition of what it means for SR
to be true. What it means for SR to be true needs to be defined before one
proves it: its meaning does not change once it is prove.
Everything is perfectly taken care of without disrupting the rules of
rational discourse. If one pursues the rational course, then one takes
careful account of the full statement of the particular sufficient
conditions under which the defining conditions for the conclusion is
derived, rather that trying make these particular sufficient conditions
part of a new definition of the conclusion.
> Counterfactual reasoning is very tricky, again because such reasoning
> asserts a falsehood. The reasoning allowed in those situations is
> crucially dependent on the theoretical framework within which the
> reasoning is applied. Not all logical steps are allowable (otherwise the
> well known attribute of logic, namely that from a false premise, any
> statement can be proven true, would also apply).
>
I have carefully specified the logical framework that I use. As regards
the problem of logical coherence and self-consistency, I am
protected from any problem of that sort by the fact that I follow
the rules of a consistent modal logic. Logicians have been very concerned
about this question of consistency, and by staying within a consistent modal
logic I am protected against the kind of problem you mention.
I agree that the quantum physicist cannot take over a modal logic without
question. I do not accept it blindly. I have carefully tailored what I
accept in order both to retain fully the logical structure that ensures
consistency, yet to restrict the real to what is essential to quantum
theory, as I discussed at the beginning.
> To repeat myself, in quantum mechanics the truth of a proposition cannot
> be separated from the evidence used to demonstrate its truth.
To repeat myself, this statement is ambiguous, and your argument rests on that
ambiguity.
The statement ``the outcome appearing to observers in L in the actual
world where L2 and R2 are performed is d'' might be true and might be
false: it is true or false depending on what the facts of the matter are.
Thus the `defining condition for the statement to be true' IS SEPARABLE
from the facts that determine whether or not that condition is
satisfied: otherwise there would be no way to distinguish the condition
for the statement to be true from the condition that it be false.
> The truth of a
> propostion in a situation is not in attribute simply of the proposition
> but of the complete situation.
In rational thought *the defining conditions for a proposition to be true*
must be specified by the words/symbols in the proposition. In a situation
described by a statement in which the proposition appears that statement
may describe conditions that are sufficient to ensure that the defining
condition for the proposition to be true are met. Thus *the fact that
a proposition true* in a certain situation described by a statement that
contains that proposition certain can depend (and normally does depend)
on the conditions specified in the statement. But the *defining conditions
for the proposition to be true* do not.
The phrase `The truth of a proposition' is ambiguous: one should always replace
it by either `The *fact* that a proposition is true' or `The
*defining condition* for a proposition to be true."
> In this case, the truth of the
> counterfactual proposition R1^c is not independent of the evidence, L2^c
> which is used to deduce the truth of that proposition.
The fact that outcome c *would appear* to the observers of the earlier
L2 if R1 were to be performed later rather than R2 follows from LOC1 and the fact
that outcome c appear to the observers of this same L2 in the real situation
in which R2 was freely chosen in the later region R.
> In the
> counterfactual case, the only evidence for the truth of R1^f is L2^c
> (Not L2, but L2^c),
The fact that R1^f is true under the specified condition depends on the fact that
L2^c holds under those conditions.
But the *defining conditions* for R1^f to be true *could hold* also
under some other conditions.
> and the truth of R1^c cannot be seperated from the
> truth of L2^c.
The symbol c stand for the condition that `outcome c appears to the observers
of the outcome of L2'. The symbol c has no meaning unless L2 is performed.
> To do so is to adopt an attitude of realism to R1^f
To do what? I never separate the truth of c from L2! It is unthinkable
within the severely restricted realm of allowed possibilities.
Moreover, R1 is very explicitly identified as being hypothetical, not real.
So any conditions pertaining to R1 are not condition on the nature
of reality: they are NOT reality condition. They are theoretical
restrictions on worlds that are explicitly proclaimed to be purely
theoretical.
> (Realism for me is precisely the claim that the truth of a proposition
> is independent of the evidence for that truth- that once you have proven
> a proposition true, then you can accept it as true independent of that
> proof-- in this case that the value of R1 is f even if you deny the only
> evidence therefor, namely that L2 is c.)
>
The condition R1^f is not free-floating: it is not claimed to be true.
In fact, it cannot be true, since R2 is actually performed. What is true, under
certain specified theoretical assumptions, is *the whole statement* L2->SR.
The condition L2^c is part of what has gone into the proof that L2->SR.
But the defining condition for the statement L2->SR to be true does not
involve condition any on c. Nor do the defining conditions for SR to be true.
In summary, your argument:
1. Demands abandoning a basic principle of rational discourse, the
rule that A^B->A.
2. Demands abandoning the basic principle of rational discourse that
the defining condition for a proposition to be true should be defined
by the words/symbols in that proposition.
3. Is not supported by the example of the Stern-Gerloch experiment that you
cite for support.
4. Is not about a `reality' condition. You claim that I ought to allow
laws of logic to fail in the *hypothetical* worlds that are being
contemplated, even though they do not fail in the real world.
[You accept that L2^R2^g-> L2^c^R2^g-> L2^c^R2, but insist that I
reject L2^c^R1->L2^c^R1^f->L2^R1^f]
5. Is based on an ambiguity in the meaning of the phrase
`The truth of a proposition': you confound the meaning `The *fact*
that a proposition is true under certain conditions' with
`The *defining conditions* for the proposition to be true.'
In view of these glaring difficulties I really think you ought to
admit that you have not made a rational case.
Sincerely yours, Henry