Jesse,
Rather than making a detailed response to your points -- which would
take us rather too far off the track -- I will make a short argument.
I think you may have missed a salient feature of my little story about
mismatching. The point to which I wish to draw attention is that Alice
and Bob do not know that they are in an impossible world until after
they have compared their experimental notes. In general, in order to do
the matching in a way that will preserve the quantum correlations, you
have to know the probabilities of the combined worlds in advance. But
these probabilities can be calculated only after Alice and Bob exchange
notes.
So you need to know the relative orientations and results in order to
calculate the probabilities required to get consistent matchings, but
these probabilities become available only after the matching is
complete. In other words, the model as proposed is incoherent.
You might try to get around this by saying that you can garner the
results from both Alice and Bob before they meet up. You can't do this
by asking them -- who does the asking? And they might refuse to
cooperate. Individuals can't stymie quantum mechanics simply be being
uncooperative! Alternatively, you might argue that the experiments
performed by Alice and Bob have completely decohered, and the coherence
phases have been distributed through the environment. Maybe the relevant
information can be recovered from the effects of decoherence into the
environment? I don't fancy your chances here either.
Again, Alice and Bob might try to thwart such a scenario by careful
shielding of their apparatus and not communicating with anyone. Once
more, I don't think quantum mechanics can be stymied by silence and lead
shielding.
The real problem is that any theory which enables the gathering of such
information from the results of environmental decoherence would have to
involve radically new physics, of a kind that has never been seen
before. This would have to be universal physics -- we can't just dream
up an ad hoc theory that applies only to the correlations of entangled
particles! Whatever the nature of this new theory, it would by in
addition to quantum mechanics, so you will not have solved the problem
of non-locality in quantum mechanics, you will have abandoned quantum
mechanics in favour of your new theory.
Bruce
On 23/04/2016 3:21 am, Jesse Mazer wrote:
On Fri, Apr 22, 2016 at 2:35 AM, Bruce Kellett
<bhkell...@optusnet.com.au <mailto:bhkell...@optusnet.com.au>> wrote:
On 22/04/2016 2:46 pm, Jesse Mazer wrote:
On Thu, Apr 21, 2016 at 11:25 PM, Bruce Kellett
<bhkell...@optusnet.com.au <mailto:bhkell...@optusnet.com.au>> wrote:
On 22/04/2016 12:53 pm, Jesse Mazer wrote:
On Thu, Apr 21, 2016 at 9:49 PM, Bruce Kellett
<bhkell...@optusnet.com.au
<mailto:bhkell...@optusnet.com.au>> wrote:
The point here is that some combinations of results are
forbidden. How can this happen?
By the appropriate matching rules for locally-generated
copies in different locations, as in my toy model. There's
no reason you can't have something similar in a more general
model, which I think is exactly what people like Rubin are
presenting.
The best I can make of this is that you have some theory that
is not quantum mechanics. Quantum mechanics does not give any
such "matching rules"
It's important to distinguish between theories of physics and the
mathematical models used to express them--a physical theory is
defined entirely by the predictions about observable outcomes,
not any elements of the model that are not directly measurable
even in principle. For example, curved spacetime is not essential
to general relativity as a theory, though it is a feature of the
most commonly-used mathematical model (there is an alternate
formulation that only uses flat spacetime, but has a field
defined on this spacetime which varies the length of rulers and
the ticking rate of clocks at different points in the spacetime,
and physicists would still call this 'general relativity').
Likewise, a state vector in Hilbert space is not essential to
quantum mechanics as a theory. And if one *could* come up with a
model involving "matching rules" that would be equivalent in its
predictions about observable measurement results as the existing
mathematical models, this would merely be a new mathematical
model for the same physical theory.
It would seem that you are not a physicist! What you claim here
about physics is actually quite contentious. It seems to
constitute an extreme form of instrumentalism.
I don't think that's the case, I'm basically just talking about how
physicists *define* the physical content of a theory. But it would
help if you would define what you mean by "instrumentalism". For
example, some articles I found googling the term seem to say that it
suggests we should not assign any "reality" to elements of the theory
beyond the predictions about empirical measurements; I would say any
talk of "reality" beyond measurements is more of a philosophical issue
than a scientific one, but I don't see anything wrong with having
opinions on such philosophical issues. In particular, if there is an
element that seems to show up in *all* our mathematical models, like
the notion of an "electron" which isn't absent from any formulation of
quantum electrodynamics, it certainly makes sense to me to call it
"real". Likewise, although we can't ever get evidence that space and
matter continue beyond the boundary of the observable universe, it
would require a very contrived model to avoid it (one which treated us
as being at the exact center of real space, for example), so
disbelieving it would to me seem like a ridiculous philosophical view,
akin to solipsism (speaking of which, I could also potentially come up
with a solipsistic interpretation of quantum physics in which I and
only I am capable of collapsing the wavefunction with my observations,
but this would seem equally ridiculous despite the fact that I can't
come up with any experiment that would falsify it for me).
Also, it seems from my googling that many instrumentalists would
define the validity of scientific theories solely in terms of what we
humans can actually verify in principle, giving up the notion of any
objective truth about nature independent of what humans know. If so, I
am not taking this position either. I'm saying the physical content of
a theory is defined in terms of the complete set of predictions about
things that could *in principle* be measured by some arbitrarily
advanced physical being at the right place and time (so the fact that
we may have no way of verifying most of the predictions of string
theory at any time in the forseeable theory does not disqualify it as
a scientific theory, for example), and I personally believe there is
some objective truth about what mathematical relationship describes
the complete set of in-principle-measurable facts about our physical
universe.
The basic point I was making with my point about physics theories vs.
mathematical models is that I'm pretty sure the vast majority of the
modern physics community would define a physics theory in terms of its
predictions about in-principle-measurable facts, and if two
mathematical models can be proved to be identical in *all* their
predictions about such facts, then they are defined to be different
models of the "same theory", not different theories. Do you disagree
with this narrow claim? I can point to plenty of examples of
physicists who do treat different models with identical predictions as
the same theory. For example, earlier I mentioned the alternate
formulation of general relativity which gets rid of any notion of
curved spacetime, replacing it with a field that shrinks rulers and
slows down clocks differently in different regions of spacetime. I
learned about this formulation from Kip Thorne's book "Black Holes and
Time Warps" where after discussing this alternate form he writes on p.
400: "What is the real, genuine truth? Is spacetime really flat, as
the above paragraphs suggest, or is it really curved? To a physicist
like me this is an uninteresting question because it has no physical
consequences. Both viewpoints, curved spacetime and flat, give
precisely the same predictions for any measurements performed with
perfect rulers and clocks, and also (it turns out) the same
predictions for any measurements performed with any kind of physical
apparatus whatsoever. ... They disagree as to whether that measured
distance is the 'real' distance, but such a disagreement is a matter
of philosophy, not physics. Since the two viewpoints agree on the
results of all experiments, they are physically equivalent. ...
Moreover, physicists can and do use the two viewpoints interchangeably
when trying to deduce the predictions of general relativity."
I think that pretty unambiguously supports the point of view I
described, don't you? And Kip Thorne is one of the leading researchers
in general relativity (see
https://cosmolearning.org/courses/overview-of-gravitational-wave-science-400/about-the-professor/
for an overview of his contributions), so I think he has pretty good
authority to speak for how the physics community in general thinks
about these matters. But if you're not convinced by that, let me know
if you want me to look for more quotes, I'm sure I could find similar
comments in the context of other theories--for example, are you aware
that quantum physics has multiple mathematical models for generating
predictions, like the "Schroedinger picture" (which deals with a
quantum state vector that changes with time while measurement
operators stay constant), the "Heisenberg picture" (which deals with a
quantum state vector that remains fixed forever, while the measurement
operators change with time), and the Feynman path integral (based on
summing amplitudes to all possible paths a particle could take to get
to a given location, to find the total amplitude of finding it there)?
But physicists definitely view them all as formulations of the same
theory, "quantum mechanics", not different theories. Likewise, when
discussing different interpretations of QM like the MWI and Bohmian
mechanics, physicists will regularly point out that these are not
really distinct physical theories, which is the whole reason they use
the alternate term "interpretation".
If you do disagree with this point of view on what constitutes a
theory of physics, can you point to *any* modern (mainstream)
physicists who clearly say something different, pointing to examples
of models that they acknowledge make identical predictions but which
they still argue should be considered distinct theories of physics?
If a physical theory is determined only by the predictions it
gives for the results of experiments, I am puzzled by why you
should have such a strong reaction against the notion of
non-locality. The non-local calculations of standard QM give a
completely straightforward mathematical model for calculating
probabilities; a model that is, in the terms of of other physical
theories, phenomenally successful. If your only concern is to get
an instrument to predict experimental results (probabilities), why
should you worry whether the theory is non-local or not? According
to you, the mathematical model has nothing to do with physical
reality (whatever that is). The anti-realist would have no worries
about such trivia.
Again, I never said I was an anti-realist, it's just that I
distinguish between questions of philosophy and questions of physics,
as Kip Thorne did in the comment of his I quoted. It's only as a
philosophical matter that I find the many-worlds picture more
plausible, but I certainly don't think there are any knockdown
arguments against the idea that the reality underlying the
observations involves some genuine non-locality, it's a totally
plausible perspective. I'm curious though, what gave you the
impression I have a "strong reaction" against non-locality? I have
been trying to argue one point and one point only, that there is no
knockdown argument *against* the possibility of a local model which
reproduces all the predictions of existing models of QM, akin to
Bell's theorem which does provide a rigorous proof that you can't have
a "local realist" model (involving unique measurement) that reproduces
those predictions. *You* seemed to be arguing that there was such a
definitive argument against a local version of QM, and that was
basically the only reason I decided jumped into the discussion--did I
misunderstand you on this point, or was it just a matter of your
defining "QM" to include aspects of existing models which go beyond
the predictions about in-principle-measurable facts? If you are in
fact arguing that there is good reason to be 100% sure no local model
can even reproduce the empirical predictions of QM, then please give
your argument, since I already showed that Bell's argument isn't
sufficient to establish this if you allow for a
multiple-local-copies-with-matching model.
But you are clearly deeply worried about non-locality, which says
to me that you are not a thorough-going instrumentalist after all.
So that you say above about mathematical models being the only
concern is all all just so much hogwash -- you are actually
concerned that your physical theories conform to your own
particular set of philosophical prejudices.
That is your concern, but you cannot expect me to share it. I take
an instrumental (or epistemic) view of the wave function of QM.
That is to say, I view it as a mathematical object that can be
used to claculate the probabilities for experimental outcomes, but
it is not a real physical thing in the same sense as chairs and
tables, the earth and the moon, are real physical things. If the
wave function is not physical, then there is no physical collapse
when a measurement is made, there is only a change in our
knowledge, and the wave function changes instantaneously to
reflect this change. In just the same way, our probability
function for the outcome of a horse race, or of a lottery, changes
instantaneously once we learn the actual outcome. From this
perspective, MWI is just a ridiculously baroque construction
designed to preserve some persons' realist prejudices that the
wave function is a real physical object, like a chair or a table.
I don't assume the wave function is a real physical object--both
Deutsch/Hayden and Rubin seem to say that to formulate the MWI in a
local way you have to use some version of the Heisenberg picture,
where all the dynamics are described by changes in the local
operators, not a changing global wavefunction (a static wavefunction
is still used, but this seems more like a calculational tool than
anything else, and perhaps it would be possible to modify things so
that the same static wavefunction was used for all systems, and one
simply adjusted the initial states of the operators to get the right
predictions for initial measurements on the system). My philosophical
preference for the MWI basically just stems from the fact that it
gives an objective description of the physical state of every region
of spacetime (not just the ones we humans observe), and a single set
of equations for the time-evolution, without any hidden variables that
break some of the nice symmetries seen in the basic equations (Bohmian
mechanics seems to require breaking Lorentz-symmetry, and also seems
to require putting the position operator on a special footing). As for
what is "real", my opinion is that if the MWI is true, all the
"copies" of a system that arise in the model should be treated as
having equal physical reality, in particular I think other copies of
human beings or other intelligent beings that would arise in the
formalism should be assumed to be just as conscious as the ones we see
(this is similar to the belief that if the universe continues on
beyond the observable region we can measure, any intelligent life
which arises outside our observable bubble should be assumed to be
just as conscious as ourselves). Beyond this I don't see a need to
assume other more abstract aspects of the model, like operators or a
wavefunction, would be "real".
But these are just my personal philosophical opinions, I am not trying
to convince you that you should adopt them. Again, the only reason I
jumped in on this discussion was because you seemed to be making the
argument that there was some definitive proof that a many-worlds-type
model cannot possibly reproduce all the predicted observations of QM
in a local way (and in any arbitrary patch of spacetime, as I
clarified later), so please tell me whether you in fact believe this
is impossible, or if you're just skeptical but can't say for sure that
it can't be done.
Of course, modern developments in black hole theory and cosmology
render the whole debate about locality otiose. The currently
popular theory of holography is necessarily completely non-local;
and in a way that makes EPR correlations look tame.
If you have an argument as to why holography is absolutely
incompatible with any local model involving multiple copies of the
physical facts at each point in spacetime, please present it. String
theory in its current form is formulated in the framework of quantum
field theory, although things like dualities hint at an (unknown)
background-independent formulation (some string theorists do think
that things like holography indicate the background-independent form
will be more explicitly nonlocal, but you can find plenty of other
string theorists who disagree, it's a speculative question at
present). And if you leave out any notion of "collapse" from quantum
field theory it is said to be a theory that does respect locality, I
don't understand the details but apparently it has to do with the fact
that measurement operators with a spacelike separation always commute,
see http://www.scholarpedia.org/article/Local_operator for example.
So I don't think I will waste more time trying to convince you
that the standard non-local quantum theory is perfectly adequate
for the explanation of all observed phenomena in its domain.
Of course I agree with that statement 100%, but it has nothing to do
with the seeming claims of yours that I've been disputing.
Jesse
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