From: Dan Fabulich (daniel.fabulich@yale.edu)
Date: Tue Aug 17 1999 - 14:45:33 MDT
On Tue, 17 Aug 1999 hal@finney.org wrote:
> John Clark, <jonkc@worldnet.att.net>, writes:
> > hal@finney.org <hal@finney.org> On Tuesday, August 17, 1999 Wrote:
> >
> > >This points up an ambiguity in the MWI, which is, when do other universes
> > >exist? That is, when does the universe split? You can give two answers.
> > >One is that it splits whenever there is an alternative which is explored
> > >in the quantum realm. The other is that it splits whenever there is
> > >a measurement which causes what would conventionally be called wave
> > >function collapse.
> >
> > I've never heard of that second version of the MWI before, I always
> > thought it's entire advantage was that it didn't have to explain what
> > a measurement is.
>
> As an example of the second interpretation, see the Many-Worlds FAQ,
> http://www.cs.mu.oz.au/~fjh/many-worlds-faq.html:
>
> : Q7 When do worlds split?
> : ---------------------
> : Worlds irrevocably "split" at the sites of measurement-like interactions
> : associated with thermodynamically irreversible processes. (See "What
> : is a measurement?") An irreversible process will always produce
> : decoherence which splits worlds. (See "Why do worlds split?", "What is
> : decoherence?" and "When does Schrodinger's cat split?" for a concrete
> : example.)
> : [...]
> : The advantage of linking the definition of worlds and the splitting
> : process with thermodynamics is the splitting process becomes
> : irreversible and only permits forward-time-branching, following the
> : increase with entropy. (See "Why don't worlds fuse, as well as split?")
>
> John's version is the second one above, Mike Price's (author of the FAQ)
> is the first. Both versions are fairly widely used.
As usual, it's a dessert topping AND a floor wax.
Clark stated it wrongly: it's not that MWI doesn't have to define a
measurement, it's that it CAN define a measurement in a physically
rigorous way. Rather, it doesn't have to define what an "observer" is,
which the Copenhagen interpretation does need to define, since Copenhagen
requires an observer to collapse the waveform. Taking a cue from the FAQ,
let's look up what IT says a measurement is:
---
Q5 What is a measurement?
A measurement is an interaction, usually irreversible, between subsystems
that correlates the value of a quantity in one subsystem with the value of
a quantity in the other subsystem. The interaction may trigger an
amplification process within one object or subsystem with many internal
degrees of freedom, leading to an irreversible high-level change in the
same object. If the course of the amplification is sensitive to the
initial interaction then we can designate the system containing the
amplified process as the "measuring apparatus", since the trigger is
sensitive to some (often microphysical) quantity or parameter of the one
of the other subsystems, which we designate the "object" system. Eg the
detection of a charged particle (the object) by a Geiger counter (the
measuring apparatus) leads to the generation of a "click" (high-level
change). The absence of a charged particle does not generate a click. The
interaction is with those elements of the charged particle's wavefunction
that passes between the charged detector plates, triggering the
amplification process (an irreversible electron cascade or avalanche),
which is ultimately converted to a click.
A measurement, by this definition, does not require the presence of an
conscious observer, only of irreversible processes.
---
The worlds are splitting when we measure them because measurement is
an irreversible process. It has thus been postulated that were a
reversible mind to take the measurement, a difference between MWI and
Copenhagen cauld be observed. This is also discussed in the FAQ, though
the FAQ suggests the use of nanotechnology to perform the measurement,
rather than Clark's Quantum computer.
---
Q36 What unique predictions does many-worlds make?
A prediction occurs when a theory suggests new phenomena. Many-worlds
makes at least three predictions, two of them unique: about linearity,
(See "Is linearity exact?"), quantum gravity (See "Why quantum gravity?")
and reversible quantum computers (See "Could we detect other
Everett-worlds?").
Q37 Could we detect other Everett-worlds?
Many-Worlds predicts that the Everett-worlds do not interact with each
other because of the presumed linearity of the wave equation. However
worlds do interfere with each other, and this enables the theory to be
tested. (Interfere and interact mean different things in quantum
mechanics. Pictorially: Interactions occur at the vertices within Feynman
diagrams. Interference occurs when you add together different Feynman
diagrams with the same external lines.)
According to many-worlds model worlds split with the operation of every
thermodynamically irreversible process. The operation of our minds are
irreversible, carried along for the ride, so to speak, and divide with the
division of worlds. Normally this splitting is undetectable to us. To
detect the splitting we need to set an up experiment where a mind is split
but the world isn't. We need a reversible mind.
The general consensus in the literature [11], [16] is that the experiment
to detect other worlds, with reversible minds, will be doable by, perhaps,
about mid-21st century. That date is predicted from two trendlines, both
of which are widely accepted in their own respective fields. To detect the
other worlds you need a reversible machine intelligence. This requires two
things: reversible nanotechnology and AI.
1) Reversible nanoelectronics. This is an straight-line extrapolation
based upon the log(energy) / logic operation figures, which are projected
to drop below kT in about 2020. This trend has held good for 50 years. An
operation that thermally dissipates much less than kT of energy is
reversible. (This implies that frictive or dissipative forces are
insignificant by comparison with other processes.) If more than kT of
energy is released then, ultimately, new degrees of freedom are activated
in the environment and the change becomes irreversible.
2) AI. Complexity of human brain = approx 10^17 bits/sec, based on the
number of neurons (approx 10^10) per human brain, average number of
synapses per neuron (approx 10^4) and the average firing rate (approx 10^3
Hz). Straight line projection of log(cost) / logic operation says that
human level, self-aware machine intelligences will be commercially
available by about 2030-2040. Uncertainty due to present human-level
complexity, but the trend has held good for 40 years.
Assuming that we have a reversible machine intelligence to hand then the
experiment consists of the machine making three reversible measurements of
the spin of an electron (or polarisation of a photon). (1) First it
measures the spin along the z-axis. It records either spin "up" or spin
"down" and notes this in its memory. This measurement acts just to prepare
the electron in a definite state. (2) Second it measures the spin along
the x-axis and records either spin "left" or spin "right" and notes this
in its memory. The machine now reverses the entire x-axis measurement -
which must be possible, since physics is effectively reversible, if we can
describe the measuring process physically - including reversibly erasing
its memory of the second measurement. (3) Third the machine takes a spin
measurement along the z-axis. Again the machine makes a note of the
result.
According to the Copenhagen interpretation the original (1) and final (3)
z-axis spin measurements have only a 50% chance of agreeing because the
intervention of the x-axis measurement by the conscious observer (the
machine) caused the collapse of the electron's wavefunction. According to
many-worlds the first and third measurements will always agree, because
there was no intermediate wavefunction collapse. The machine was split
into two states or different worlds, by the second measurement; one where
it observed the electron with spin "left"; one where it observed the
electron with spin "right". Hence when the machine reversed the second
measurement these two worlds merged back together, restoring the original
state of the electron 100% of the time.
Only by accepting the existence of the other Everett-worlds is this 100%
restoration explicable.
---
I have to agree with Moss, however, who notes that the presence of
conventional detectors in Clark's quantum computer scenario would ruin the
test, since conventional detectors would fail to completely revert when
the quantum computer erased its memory.
As for the likelihood of this test ever occuring, the odds seem extremely
remote to me that we'll have reversible AI by 2040. Certainly we'll have
some kind of AI in the next 50 years, but I strongly doubt that it'll be
thermodynamically reversible.
Unfortunately, without reversible AI, the proponents of the Copenhagen
interpretation could plausibly argue that since there was no "real
observer," no real observation took place. Such a proponent would be hard
pressed to define what a "real observer" is, but no more so than today.
Hopefully such thinkers will be ignored: if the Copenhagen interpretation
breaks down in the face of reversible measurement, that is, if the
waveform for some reason fails to collapse whenever the measurement is
themodynamically reversible, the Copenhagen interpretation will be hard
pressed to explain it except by such "true consciousness" mumbo jumbo, and
the whole interpretation will then hopefully be rejected.
-Dan
-THAT THAT IS IS THAT THAT IS NOT IS NOT-
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