Re: Superposed observers (was No new Einstein)

Charles Francis <charles@xxxxxxxxxxxxxxxx> writes:

>In message <1124861486.644970.9850@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
>I.Vecchi <vecchi@xxxxxxxxxxxxx> writes
>>
>>RQM brings to the forefront the issue of information exchange among
>>observers, which is barely mentioned in other approaches. Hence it
>>provided me with an effective (although incomplete) framework to tackle
>>conceptual questions such as the intersubjective rather than objective
>>nature of reality.
>>RQM has inspired others too (see e.g. [1] or/and ask Charles Francis).

Italo and Charles, I guess you can both provide answers to my
questions. As I understand it, quantum mechanics can be considered
as a general procedure for predicting future measurement
results based on past ones (and on the statistics that we have
empirically gathered about exactly that relationship between
past and future results, encoded in such things as the
Hamiltonian and so on). As such, I understand that the formalism
of quantum mechanics (with its Hilbert spaces and so on) makes
no reference to any physical object, except if one considers
a measurement result to be a physical object.

Now the relational interpretation, unless I'm mistaken,
attempts (like most interpretations of quantum mechanics),
to say that quantum mechanics is not a technique for
predicting the results of measurements, but is rather
a theory which asserts something about what exists
ontologically, namely interacting systems with various
relationships between them. It is presented as though
it were a great step forward in our understanding
of the world, but unless I'm mistaken, the great
insight is supposed to occur when somebody abandons
a different ontology (say, for example, the idea
of absolute space, or the idea that certain things
aren't observer-dependent, but exist absolutely)
and adopts this relational ontology instead.

>The fundamental idea that measurement is a relationship between matter
>and matter makes it natural that when no measurement is possible, nor is
>there a well defined value for the measured quantity. An observer in the
>box sees the cat alive or dead. An observer outside the box has no
>information, and is essentially just describing the probability of
>whether the cat is alive or dead. I see no deeper problem here than
>there is with classical probability theory. Two observers with different
>information correctly ascribe different probabilities to the same event.

Relationalism seems to advocate that we say that, when Nick
looks at the cat, then the cat becomes alive or dead "relative to"
Nick, but is not yet alive or dead relative to (for example) me.
When I look at the cat (or ask Nick), then the cat will become
alive or dead relative to me.

But the obvious question is: If the cat is dead relative to
Nick, can it be alive relative to me?

If not, then that means that, if the cat is dead relative to Nick,
then the cat is just dead (relative to everybody, that is, absolutely).
In that case, the expression "The cat is dead relative to Nick"
really just means "The cat is dead," and the "relative to Nick"
bit, which relationalism insists should be added to the end of the
sentence (in order to remove so-called conceptual problems),
is useless, except in so far as it might indicate that Nick
is aware that the cat is dead.

If yes, that is, if the cat can be dead relative to Nick and
alive relative to me, then the interpretation is just
many worlds.

The same question can be asked of the energy of a two-state
system. Can it have one well-defined energy relative to
me and a different well-defined energy relative to
somebody else? If no, it's not relational, and if yes,
it's many worlds.

Rovelli tries not to answer this question, but he hints
that the answer is "no", meaning that the cat can't be
dead relative to Nick and alive relative to me:
"In Everett, there is an ontological multiplicity of realities,
which is absent in the relational point of view, where physical
quantities are uniquely determined, once two systems are given."
(from the Stanford Encyclopaedia of philosophy)

>The problem moves on, and becomes one of explaining why there is a wave
>equation. As far as I can see the main reason that hasn't been solved is
>that people who study foundations fight shy of making it relativistic,
>whereas people who study relativistic field theories have no time or
>sympathy for foundations.

They have no understanding of foundations either.

>Plus of course, there are some really nasty
>mathematical problems which make them think qft can't be built on qm.

Do you mean Haag's theorem? Or do you mean the problems with
making path integrals rigorous? Or finding an actual example
of an interacting field theory? Or something to do with
renormalization?

>>I wonder whether one can dismiss the RQM framework and make sense of
>>Hawking's warning about the "trap of assuming that there is a single
>>metric for space-time, as there is in classical theory. In quantum
>>theory, on the other hand, one has to do a path integral over all
>>possible metrics. There will be different saddle points in the metric
>>for different questions. In particular the saddle point metrics for the
>>questions that outside observers ask will be different from the the
>>saddle point metric of an infalling observer". ([2])

>I hate when scientists talk like that. It seems as if they think you can
>make theoretical advances by making almost arbitrary changes to
>mathematical structure and just hoping that the answers come out right
>at the end of the day. Not quite as unlikely perhaps as an infinite load
>of monkeys writing a script for Hamlet, but still practically zero
>chance, in my view.

Which bit do you object to? Euclidean path integrals, in the form
of partition functions, are used successfully in various parts of
physics. Do you mean that you think it's nonsensical, or poorly
motivated, to integrate over metrics?

>It is necessary, IMV, to do like Einstein, and think
>really critically about how we measure things and the abstract
>mathematical structures required to describe it. (if no one does that,
>there will be no new Einstein)

Indeed; this is necessary. Unfortunately, it's not the kind of
thing which is done very frequently.

R.

.

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