Re: Rovelli on EPR
- From: Oh No <NotI@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>
- Date: Fri, 2 Jun 2006 10:44:31 +0000 (UTC)
Thus spake rof@xxxxxxxxxxxx
Oh No <NotI@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> writes:
Thus spake rof@xxxxxxxxxxxx
Oh No <NotI@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> writes:
The fundamental principle is that we can only say where something is if
we say where it is relative to other matter.
It will not be easy
to build it into a mathematical stucture.
I don't think it is.
Perhaps I was being facetious; in fact I believe it will be
impossible.
I find that unnecessarily defeatist. Einstein already built a fair bit
of the principle into special and general relativity. People other than
Rovelli have thought that quantum uncertainty had something to do with
the principle (starting with Heisenberg). Clearly the principle is
restrictive. The problem is with formalising it. I don't believe the
universe can be inconsistent with itself, so I think it natural that it
must be describable by a formal mathematical structure.
And yet to
me, the principle enters into every part of the paper. Certainly I
discuss it in the introduction, and the whole purpose of introducing
quantum logic is to have a formal language in which we can discuss
matter and measurement in the absence of background.
You mention it in various places, but it seems to me to
have no relation to quantum logic or any of the other
formalism.
I think the problem is with measurement in general. Quantum logic, as
you understand it (probably correctly) incorporates the projection
postulate, and with that the measurement problem, as you have outlined.
The resolution of the problem would be to drop the projection postulate
and to prove it (ultimately) as a theorem.
I must regard a principle which attempts
to place restrictions on what I can say as belonging to the field
of linguistics, and not physics.
I don't think you would really. Actually the opposite. The only
restriction I wish to place on language is to ensure that it is used to
discuss physics rather than fantasy. Language can describe a land of
wizards and dragons, but such a land does not exist. Likewise language
can discuss absolute space, and yet with a careful analysis of
measurement, we may recognise that absolute space has no empirical
justification.
If I were to put a restriction on language, I would insist that
when talking about physics we should speak literally. In my ideal
world, people would not say that quantum mechanics involves a change
in the rules of logic,
I agree with you completely on that. I think this is this misconception
about quantum logic which has held up its development as a tool for
understanding nature.
You claim that the introduction of the Hilbert space does
nothing more than provide a "formal language in which we can discuss
matter and measurement in the absence of background." But
my point is that the Hilbert space structure puts many
nontrivial constraints on the statistics of the results
of measurements. So you are not merely introducing a
language, but you are also introducing assumptions about
the statistics of the results of experiments. The reason
that the steps which you use to justify the Hilbert space
formalism don't seem adequate to me is that you never
say "Here I'm assuming in advance that the statistics
of the results of experiments will satisfy certain constraints
and these are the constraints and these are the reasons
why it's reasonable for me to suppose that actual
experimental results will satisfy those constraints."
Again, I think the issue is the measurement problem. If the projection
postulate were dropped, would you still have a problem?
If you said that, and gave good reasons, I'd be delighted.
But instead you make a brief mention that phase has something
to do with motion and say it will all be explained in
section 3, but in section 3 you assume that no more
justification is needed for the use of complex Hilbert
spaces. You seem to assume that it was all settled
earlier.
At that stage of the paper, all I have considered is measurement results
of position for a single particle at time t. At that point phase is an
irrelevance. I don't see need for justification of something which has
no effect. Later I want to be able to do Lorentz transforms, since I
also know that they are part and parcel of the fundamental principle.
When covariance is brought in, phase starts to play a role, and with it
equations of motion appear for the phase relationships. This places
restrictions on phase, but I see no problem with that because in the
first instance phase was completely arbitrary.
But even in the form in which I agree with it, the principle
does not provide us with any "positive knowledge". It only
tells us what is not the case, without giving us any clearer
idea of what might actually be the case.
True, but that changes the question. Having answered the question "what
can we not say?" the question becomes "what can we say?". The objective
now is to write down postulates for what we can say, in accordance with
observation and without contradicting the fundamental principle. The
development of a formal language is just a tool for doing that.
But it places nontrivial constraints on the statistics of the
results of experiments, so it's not just a choice of notation.
Will allow that these constraint come from two sources, 1) covariance,
which is legitimate, and 2) the projection postulate, which I have
suggested we drop (along with its implications).
my central problems seems to be that
the use of quantum logic seems to be unjustified and the
relationalism doesn't seem to have anything to do with
quantum logic.
Do you accept that without the projection postulate, and without time
evolution, all I have done is make simple (almost trivial) statements
about probabilistic results of measurement of position at given time
without an assumption of background space, and created a slightly
elaborate mathematical structure with which to discuss them?
Also, the idea of assigning weird "truth values" to statements
about counterfactuals seems to me to be unnecessary and
confusing. Why can't everything be expressed with statements which
are actually true?
If you don't feel comfortable with the notion of "truth value", I am
happy to ignore it. However I do not think the situation is
fundamentally different from probability theory. The statement "Next
time I throw a die, it will be a 6" cannot be actually true. But
presumably you accept the truth of the statement "The probability that I
throw a six is 1/6"? and that if one creates a formal language in which
1/6 is said to be the truth value for the former statement, then the
statements of that language can be true? In fact, I believe you already
reduced quantum logic to Boolean logic much in this manner in another
post.
The principle of relativity which Eugene was referring to was the
principle of the constant speed of propagation of information.
The principle of relativity which is contained (let us say,
for the sake of the argument) in the fundamental principle
of relationism is the principle that one cannot say how
fast something is moving unless we specify an object
to which that motion is relative.
Those are two different principles of relativity.
The main point is that both principles are necessary. I would argue,
however, that, according to the fundamental principle of relationism, to
talk of speed or even of space-time coordinates we have first to
propagate information.
It seems that you would have to appeal to some principles other
than "absolute space does not exist" to deduce that "to talk of
speed or even of space-time coordinates we have first to propagate
information". The first doesn't say anything about information,
so some principle about information would need to be used as well.
I only see two options. Either there is
instantaneous propagation which is empirically false, or there exists a
maximal speed for the propagation of information.
Why not a variable maximum speed, or a probability distribution
of speeds which is vanishingly small at very high speeds?
I don't know that a variable maximum speed makes sense. Since all speeds
are determined relative to the maximum (or we have no empirical
definition of speed) the maximum speed can only be 1 relative to itself.
Strictly, since relativity is a classical theory, I think we should
assume that there may be a probability distribution of speeds in the
quantum domain, and that the maximum speed is either a theoretical
maximum or a mean. I don't think either of those suppositions changes
the validity of special relativity as a theory, however.
I would argue further,
that the principle requires that the properties of matter have no
dependency on time or position, and that this is expressed in the
cosmological principle, from which we may infer the principle of general
relativity.
Have these arguments been expressed rigorously?
I do not see how it is possible to argue rigorously prior to creating a
formal mathematical structure. What one can do is examine the arguments
one has for choosing axioms, and make them more and more solid, or
alternatively find fault with them and discard or modify them as
appropriate. In this way one seeks to find more fundamental axioms with
which to define a mathematical structure.
In any case, your argument seems to be that quantum
logic on its own places no restrictions on the results
of measurements.
I don't say no restriction; just that on its own it doesn't get us very
far.
It can reduce the number of measurements we need to make from
81 to 18. That seems to me to get us quite far. In fact, this
seems to me to be the principal issue in need of explanation.
Yes. But in the interests of proceeding formally, I am suggesting we
drop the projection postulate, and lose all these other measurements in
the process, at least for the time being. I have said that other
measurement must be reduced to measurement of position, or a combination
of measurements of position of particles in a more complex system. We
have a lot more material to cover, concerning what more complex systems
are possible in principle, before we can start to think about a proper
treatment of measurement in general.
You say: "We cannot usefully determine anything much from that
unless we also have a time evolution equation." I don't know
what you mean by "determine anything much from that". What
we can do, without a time evolution operator, is observe,
for each preparation, the probability of observing each
result to each measurement. Measurements performed at
different times after the preparation of the system simply
count as different measurements. After we have collected
the statistics of the measurement results, we then
go about constructing a time evolution operator to describe
the statistical relationships we have empirically discovered.
I don't do things in that order at all. I create a mathematical
structure then define time evolution as dictated by covariance
considerations. That leads me to qed, plus some variants which appear to
include theories of weak and strong interactions. The time evolution for
any given situation must be an application of these fundamental
theories. I have just put a paper on this on arxiv, gr-qc/0605127
I think I won't be able to understand anything later in
the paper unless the foundations make sense to me.
Is there anything that does not make sense about the treatment of
Hilbert space built on the discrete measurement results for measurement
of position of a single particle at given time, ignoring both the
possibility of another type of measurement, and that of a second
measurement at later time?
Suppose you know no quantum mechanics. There are 10 different
measurements you perform, each of which can give 10 different
results. (Despite your protestations to the contrary, this is
quite possible. Consider a spin-9/2 particle and measurements
along any ten distinct axes in three-dimensional space as an
example.)
Trouble is, when I want to determine spin, I can't think of a way of
doing it which does not require an analysis of dynamics, like bending a
path in a Stern Gerlach experiment. In fact, the formulation of quantum
logic in A Relational Quantum Theory incorporating Gravity (RQG), gr-
qc/0508077 (revised from the version you read) makes no mention of spin.
It is introduced in a follow up paper "A Treatment of Quantum
Electrodynamics as a Model of Interactions between Sizeless Particles in
Relational Quantum Gravity" because it turns out that there is no
covariant formulation which does not require it.
These considerations are unnecessary. We can abstract from the
procedure involved in the measurement and from the
considerations involved in determining the final result.
All that you need to suppose is the case, in order for
my argument to work, is that the predictions of quantum
mechanics are actually correct.
Ok, so I am not going to suppose that. As I say, it is something which
should be proven, not assumed. In fact, for the purpose of
interpretation it does not even have to be proven, merely made sensible
and reasonable within the context of a physical model.
I think the complete answer to the issue you raise is not
simple.
I also think that it's not simple.
Then, will you accept, that for me to make my case, I have somehow to
lead you through to later parts of the papers?
As I formulate quantum theory I start with only one type of measurement,
specifically measurement of position. To put this in the context of your
example, let us call this measurement M9. I then construct labels for
other states artificially, by creating a Hilbert space which is, in
essence, determined by the probabilities for getting each of the results
r_9j. The claim that M9 is complete means to me that all physical states
can be represented by states of this Hilbert space. (in fact this
assumption has to be relaxed in qed, but I retain the Hilbert space even
though not all states in it necessarily correspond to real measurement
results - there will be so called "virtual" photons, which I treat as
real photons which cannot be directly measured).
But the Hilbert space is not "determined by the probabilities ...".
It is a set of linear sums of symbols like |x>, with complex
coefficients. The symbols |x> are associated with the possible
results of measurements of position. This introduces a
vector space whose dimensionality is twice the number of
possible measurement results. How do you know that this
is the right number of dimensions to encode the statistics
of the results of all other possible measurements?
At the present stage of the development, all we have actually done is
introduce free parameters. The next stage of the argument involves
bringing in covariance, justified from the fundamental principle, not
from statistics. We have to show that this restricts the free
parameters.
Introducing Luder's projection postulate at this stage does require an
additional assumption about the behaviour of matter. I don't think it is
quite fair to say it is a hidden assumption, but what is true is that it
constrains the theory in a non-trivial way, just as you suggest. As far
as the logical development of the model as a physical theory is
concerned, it is perhaps premature. Whether this is a legitimate
constraint, or even a necessary one, is an issue which I don't think can
be answered properly without first developing a complete account of time
evolution, including an account of the interactions of elementary
particles, namely a full and consistent qed.
Qed seems to me to be just a particular application of quantum
mechanics.
I agree with you in principle, but I assume you also know that this is
regarded by those most qualified to judge as an unsolved mathematical
problem. We have both agreed that resolving the issue of interpretation
will be difficult. The fact that we have first to construct qed is a
measure of how difficult. All the more so, because we will have to make
it compatible with general relativity (in appropriate approximations and
limits) at the same time. I say this, not to arbitrarily introduce new
fields, but because I hold that these apparently disparate problems are
all part and parcel of the same problem, and that there is no solution
to one which is not also a solution to the others.
Quantum mechanics seems to be a procedure for
assigning probabilities to the results of experiments, regardless
of what fields or particles we might suppose to be responsible
for the results.
Yes, but interpretation means that we also understand the physical
principles responsible for the results.
So, what I would say is, have I given a consistent interpretation of
quantum theory, I think I have: It is a model of interactions of between
sizeless particles in the absence of space-time background.
Well, I'm not sure what you mean by a consistent interpretation.
It is merely a conjecture of yours? Do you consider your own
arguments to be completely rigorous or merely plausible?
Many of them I consider rigorous. Certainly enough for me to be
convinced that there is essentially no other interpretation. I am not
going to claim to have made every aspect rigorous.
Regards
--
Charles Francis
substitute charles for NotI to email
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