On 30-01-2021 01:41, Bruce Kellett wrote:
On Sat, Jan 30, 2021 at 11:20 AM smitra <[email protected]> wrote:
On 30-01-2021 00:37, Bruce Kellett wrote:
It is difficult to give any sensible meaning to a statement like
this.
The idea behind the universality of unitary evolution in
Everettian
QM is that the initially pure state always remains pure. In an
interaction with decoherence, the off-diagonal elements of the
density
matrix remain finite, albeit arbitrarily small. This means that
there
always remains a non-zero probability that the state will
recohere.
But this picture is, in fact, wrong. As has been pointed out, the
irreversibility introduced by decoherence is actually an 'in
principle' irreversibility, induced by the laws of physics, such
as
the speed of light being an upper limit on possible speeds, and
the
laws of thermodynamics limiting local decreases in entropy. Once
decoherence entangles the results of any interaction with the
wider
thermal environment, it is not possible to avoid the loss of
information to outer space via the emission of IR photons. This
process is in principle irreversible, because these photons can
never
be captured and returned. What is more, decoherence is general and
will always result in entanglement with the wider thermal
environment.
And this entanglement will generally happen very quickly -- in
fractions of a second. So the loss of thermal photons is
essentially
instantaneous. Given this, the probability that the initial state
will
eventually recohere is exactly zero. If the density matrix is to
reflect this physical reality, then the off-diagonal elements will
have to be set to precisely zero, the pure state has to reduce to
a
mixture. This cannot happen by unitary evolution, true, so unitary
evolution itself cannot reflect the whole of physical reality. The
limit as the off-diagonal elements of the density matrix become
small
via decoherence, and approach zero, is a singular limit -- the
progression from infinitesimal to zero is not continuous. The
Schrodinger equation cannot capture this singular limit so it
cannot
capture the whole of the physical reality. The "collapse
postulate"
has a sound physical basis! Decoherence does, indeed, lead the
initially pure state to become mixed. That is physically
unavoidable.
Claiming that the coherence is not lost to the "whole universe" is
just an empty rhetorical flourish, with no operational content.
Bruce
This argument is wrong for two reasons. First, your definition of
irreversibility is wrong, it has nothing to do with the practical
impossibility to reverse the evolution of the state. Time evolution
is
said to be reversible if two different initial state will evolve to
two
different final state, which is true for unitary time evolution.
You are making exactly the same mistake as was made earlier with
Deutsch's definition of 'world'. You are using a technical definition
that does not always relate to the usual meaning of the term.
'Reversible' means that the situation can be reversed. In this
context, it means that coherence can be restored. If you want to mean
something different, then you should use a different term, and your
objection collapses.
The usual meaning is wrong, the technical definition is what it is for a
good reason. That no physical process exists to get the initial state
back e.g. because time reversibility is not possible due to CP violation
can be the case, but that does not capture the aspect of reversibility
that one needs. Also in the example you raise with photons escaping and
whether or not you can then get interference, as that's also not a
relevant issue in the MWI when we focus on a the state of a local
observer.
The second mistake that leads to the wrong conclusion that a pure
state
evolves to a mixed state is that this requires entanglement with an
infinite number of physical degrees of freedom when, precisely due
to
locality (finite c), only a finite number of degrees of freedom get
entangled at any given time.
This is technically incorrect. There is no requirement for an infinite
number of degrees of freedom. Escape of just one IR photon to outer
space is sufficient to destroy reversibility. Then, in order to
reflect this irreversibility, the off-diagonal elements of the density
matrix should be exactly zero (reducing the pure state to a mixture).
Unitary evolution cannot give this, so unitary evolution, by itself,
is unable to capture that whole reality about the physical state.
You are then replacing the density matrix by the reduced density matrix
and then claiming that the reduced density matrix describes a mixed
state. That's true but irrelevant if you want to capture the whole
reality of the physical state.
What this shows is that the notion of a World is only approximate,
and
therefore cannot play any role in defining what observation is,
because
we obviously do observe things and that must then have a
mathematically
exact formulation, not an approximate one, no matter how accurate
that
approximation is.
The definition of 'world' in the context of QM is made exact precisely
because of this irreversibility. Worlds are well-defined and distinct
precisely because they can no longer interact or recohere. The laws of
physics ensure this.
Your argument is based on replacing the exact physical state by the
reduced density matrix, so you are smuggling in the Copenhagen
interpetation in by hand, you are not really considering the MWI.
A definition of observation should involve defining the algorithm
that
defines the observer and the content of the observation in terms of
the
relevant local physical degrees of freedom.
Bullshit.
You make arbitrary appeals to algorithms that do not exist. Besides,
nothing that I have said is unique to the process of conscious
observation. It is true for any interaction whatsoever in the quantum
domain.
If you disagree, you could define observers and observations in the
context of the MWI in a different way and discuss that, but what you are
doing is setting up an argument that is incompatible with the MWI by
invoking collapse.
There is no need to define a
"World" which is a meaningless concept, observer's are in principle
only
aware of their own physical state.
And that physical state is part of a unique world. The word 'world' is
useful, and has clear operational content.
That state can contain information
about the environment, but what matters is not the environment but
the
computational state of the algorithm that defines the observer.
Forget algorithms. We are talking about physics, here, not
computationalism.
This can be done rigorously in the MWI by invoking entanglement to
get to
correlations between slightly different inputs and outputs of the
algorithm such that the spread in the inputs and outputs is below
the
resolution the observer can detect.
So what?
To get to a meaningful definition of observers and observations. If your
model cannot distinguish Alice from making a measurement or Bob from
making measurement, it's no good for the sort of discussions in this
email list. Of course, you need to simplify things, but one can then
work in a simplified model where Alice and Bob are similar programs that
have a different memory content while they can do the same sort of
measurements and store the information from those measurements in their
memories. The state Bob finds himself in is then always some bitstring
that is then in some entangled superposition with the environment, with
the terms in that superposition referring to slightly different physical
states that fall within Bob's detection resolution. So, Bob's subjective
states are then coarse grained versions of the bit string, which allows
for small counterfactual differences to physically exist (counterfactual
w.r.t. a hypothetical superobserver that can observe the exact
bitstring). These counterfactual inputs and outputs then define the
algorithm. The lack of existence of counterfactuals in a classical
determinsitc setting makes the movie graph argument possible with leads
to a paradox for computationalism.
Saibal
Bruce
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