On Monday, October 14, 2019 at 4:44:42 PM UTC-5, Bruce wrote:
>
> On Tue, Oct 15, 2019 at 5:38 AM Philip Thrift <[email protected]
> <javascript:>> wrote:
>
>> On Monday, October 14, 2019 at 1:20:39 PM UTC-5, Brent wrote:
>>>
>>> Part of the dislike of the MWI is that its proponents assume a purity
>>> that is not an evident virtue of the intepretation. For example,
>>> interpreting the squared amplitudes as probabilities seems to be assumed,
>>> along with the existence of the preferred basis in which the amplitudes are
>>> defined. Together these are almost the same as CI. If you ask
>>> "probabilities of what?" in MWI the answer can't be probability of existing
>>> because MWI has committed to all solutions, however improbable, existing.
>>> So it becomes probability of finding yourself in a particular world...which
>>> depends on a theory of consciousness and seems to regress to von Neumann
>>> and Wigner.
>>>
>>> Zurek's envariance attempts to answer these questions and provide a
>>> justification for preferred bases and what probability refers to. But
>>> notice that to the extent he succeeds he is justifying taking a simple
>>> probabilistic view and saying one of those preferred states happens and the
>>> others don't.
>>>
>>> Brent
>>>
>>>
>>>
>> In the single-particle double-slit experiment*, an observer could see a
>> dot appear anywhere on a screen where path interference does not reduce the
>> probability to zero. So with the literal many-world-branching theory, how
>> many different worlds are produced, each on with its own observer seeing a
>> dot on the screen?
>>
>
> According to MWI, an infinite number. Each world will have the dot at a
> different place on the screen.
>
> Bruce
>
What you say may open up a bit of a hole or snag in MWI. This is something
I have been pondering some since Carroll's popularization. If MWI
fundamentally preserves unitarity by splitting off worlds then localization
of a measurement is an illusion.Consider a particle measured somewhere on a
path from x and x'. The path integral and the nonlocality of paths is a
sum over all possible measurements in all space containing x and x', then
there must be a continuum of possible worlds splitting off. If the operator
has a continuum of eigenvalues *x*|x> = x|x> there must then be a continuum
of possible worlds if there is indeed no fundamental localization with a
measurement. This is not just infinite, but uncountably infinite.
This is different from how decoherence maintains unitarity and conserves
qubits. There a local interaction occurs that induces quantum phase to
enter into a set of ancillary states or reservoir of states. Then we can
consider quantum states as finite, but unbounded from above, so that local
observations and measurements are possible.
This does seem to run into some oddities that either need to be worked out
or that might indicate some gap in MWI. The persistence of nonlocality in
MWI is interesting for possible quantum gravitation work. In that case I
can think of maybe a way around this, where this uncountably infinite set
of g_{ij} configurations, or Ψ[g_{ij}], can be identified with "exotic"
manifolds that are removed. It is less clear how this can happen with
ordinary quantum fields that have local realizations.
LC
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