I see the issue as similar to chaos theory or statistical mechanics. The
superposition of states in a system shifts to entanglements with states in
an apparatus, which evolve through many states. We can think of the
superposition of photons passing through a double slit, where if we place
spin states at one slit we convert that superposition into the entanglement
with spins. If we then have a general needle state this entanglement is
spread into more states which is associated with the einselected state of a
classical outcome. This evolution is a sort of diffusion that because of
its complexity is extremely difficult to track. As a result we have
decoherent sets that are in effect coarse grained sets of states.
Even if an observer could observe all possible states of the apparatus or
the general needle state, this leads to the difficulty that the observer
herself is also a complex of quantum states. This means that a fine grained
description may be simply impossible. This leads to a situation where a set
of quantum states are encoding quantum states, which can't be completely
described in a closed system. Measurements tend to involve a classical
system that in some ways is an open system, not closed. There is a sort of
Universal Turing Machine or Godel numbering involved with attempting to
describe this in a completely axiomatic manner.
I was going to write more on this, but I am very tied up with other work.
This is usually a very active time of the year.
Cheers LC
On Sunday, December 17, 2017 at 11:30:10 AM UTC-6, Bruno Marchal wrote:
>
>
> On 16 Dec 2017, at 13:47, Lawrence Crowell wrote:
>
> On Friday, December 15, 2017 at 1:17:09 PM UTC-6, Bruno Marchal wrote:
>>
>>
>> On 15 Dec 2017, at 06:20, Brent Meeker wrote:
>>
>>
>>
>> On 12/14/2017 6:27 PM, Jason Resch wrote:
>>
>>
>>> *I don't see how Wigner's friend presents a problem for Copenhagen.
>>> According to the CI, the wf collapses when the system measured, which is
>>> when the box is opened. What am I missing? The issue of the cat's memory is
>>> a different matter, problematic IMO. AG *
>>>
>>>
>>
>> The problem is according to the CI, an isolated system evolves according
>> to the Shrodinger equation, and therefore does not collapse. But it also
>> says observation causes collapse.
>>
>>
>> That is not CI. CI always supposed there is a classical realm in which
>> measurements and observations were made by classical devices. Wigner toyed
>> with the idea that consciousness was required, but that was never Bohr's
>> idea of CI. In a sense, decoherence filled in CI by providing the
>> mechanism of collapse.
>>
>>
>> I would say that decoherence explains the illusion of a collapse in the
>> mind of the machine keeping a diary of the results of measurement.
>> Decoherence is relative entanglement, and the tracing-out by the relative
>> observers.
>>
>> The decoherence theory explains that the universe differentiation is
>> quite speedy, and why macroscopic coherence is hard to be maintained,
>> although possible for some material, and quantum topology promises
>> theoretically possible "solid" qubit, etc. Like you said; it is only a
>> matter or isolation. Now, the lack of isolation makes coherence easy lost,
>> but that means only the quasi-irreversible lack of interference with some
>> terms of the universal wave, not their genuine disappearance, which would
>> contradict linearity, unitarity, well, the SWE-or DIRAC-or Feynman.
>>
>> Bruno
>>
>
> You wrote a part on this with respect to Godel's theorem a few weeks ago,
> which I lost in the huge sea of posts on this thread. I was going to
> respond but lost the post.
>
> Quantum mechanics is independent of measurement.
>
>
> OK.
>
>
>
> Quantum amplitudes evolve by unitarity or Schrodinger type of evolution
> and this is perfectly deterministic.
>
>
> OK.
>
>
> Once one throws a measurement or decoherence into picture things become
> less clear.
>
>
>
> Decoherence is only relative entanglement. It is explicitly how Everett
> explains the "illusion of collapse" in the mind of the observer-machine.
> Things become less clear, but only because it is psychologically hard to
> apply QM to oneself, as it involves our counterparts.
>
>
>
>
>
>
> We might then invoke Kant's *noumena* and *phenomena* as a way of
> thinking about this. Decoherence is just a way of looking at what happens
> to a quantum wave that is disturbed by the environment, which can include a
> laboratory measurement.
>
>
> Even Bohr admitted, in his reply to EPR, that such a disturbance cannot be
> entirely mechanical. I don't think there are disturbance, only
> entanglement. The laws of big numbers justifies the appearance of
> irreversibility and collapse, but that never happens. Eventually, the wave
> itself arises from number's incompleteness self-reflected (you need yo
> study my papers to get this).
>
>
>
>
>
>
> Given that an optical photon is about .1eV in energy a 100 light source
> produces then around 10^{22} photons every second, which in the Fermi
> golden rule are emitted by spontaneous emission and thus their wave
> functions are decoherent. This is a numerically massive process in the
> universe at large. We have these various interpretations of what happens
> with these decoherent events, which are described phenomenologically. These
> various interpretations are putative noumena for the processes of
> decoherence or measurement.
>
>
> I do not assume a physical universe. It can't work with any reasonable
> solution of the computationalist mind-body problem. I assume mechanism, and
> enough of arithmetic to define what are the universal turing machines.
>
>
>
>
> If we think of a measurement as a large system with many quantum states,
> say a mole ~ 6x10^{23} of states, that couples to a system with a small
> number of states. In a measurement the large number of states produce a
> classical(like) outcome for the occurrence of the small number of states.
> The process appears to involve a type of self reference as well as the
> necessity for einselected quantum states (Zurek etc) that define a
> classically stable needle state and its outcome.
>
>
> I am OK with Zurek (and he cited Everett for the basic idea).
>
>
>
> The process appears to require that states involved with the needle state
> encode quantum numbers as Godel numbers, which in general leads to a
> breakdown of computability.
>
>
>
> That would be interesting. Mechanism, paradoxically enough, entails a
> breakdown of computability for two among five nuances of the 3p machine
> provability.
>
> Mechanism implies that "we live in arithmetic", and since Gödel we know
> that most of arithmetic breakdown computability. Most attribute of machines
> are already non computable, for example. In fact, the mystery is how much
> the physical reality seem to be computable!
>
>
>
>
>
> The quantum classical dichotomy here may reflect a sort of axiomatic
> incompleteness; the physical axioms of quantum mechanics are unable to
> compute how a macroscopic outcome, such as a needle state or a particular
> state in a decoherent set occurs.
>
>
> That form of indeterminacy concerns the long run of a machine. But the
> self-duplication (amoeba) illustrates how indeterminacy is implied
> phenomenologically by third person determinacy. That gives an abrupt form
> of indeterminacy similar to the observation of a quantum superposition.
> Then the math confirms, up to now, that we find a quantum formalism for
> the first person plural views in arithmetic.
>
>
>
>
> I proposed something of this sort a long time ago, around the same time I
> illustrated how the Schild's ladder in general relativity and quantum spins
> had the same Galois field representation.
>
>
> Very interesting.
>
>
>
> In the latter case I got a muted response, and of course now the idea
> general relativity and quantum mechanics are categorically equivalent is a
> hot topic. The idea that quantum outcomes are not computed by quantum
> evolution, say the quantum computer executing operations on qubits, was met
> by horror. "Oh the humanity" and so forth was sounded. However, it seems
> plausible to me to this day that all we can ever have is phenomenology on
> this, but we will never understand the noumena according to some set of
> postulates or physical axioms that are complete and consistent in QM. If GR
> = QM in quantum gravity this has an impact there as well, in particular
> with the problem of the firewall.
>
>
> I am agnostic on a primary ontological physical universe. What can be
> proved (in elementary arithmetic) is the existence of a complex highly
> structured web of digital-machines dreams, and of some coherent sharable
> phenomenological reality stabilizing first person plural relative
> "realities". Aristotle's WYSIWYG metaphysics might be false, time to reread
> Plato , and Pythagorus.
>
> Bruno
>
>
>
> LC
>
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