On 30-01-2021 00:37, Bruce Kellett wrote:
On Sat, Jan 30, 2021 at 1:41 AM Bruno Marchal <[email protected]>
wrote:
On 28 Jan 2021, at 06:58, Bruce Kellett <[email protected]>
wrote:
This is certainly a problem for Deutsch's interpretation of
'world'. Because there are an infinite number of equivalent sets
of basis vectors available for every Hilbert space, it makes
little sense to claim that an observer is uncertain as to which
basis he is in. He could choose any basis whatsoever. But if he
wants his choice to make sense in his lived life, he would be wise
to choose the basis that is singled out by decoherence as stable
against environmental degradation. In other words, he has to rely
on decoherence to solve the basis problem. Deutsch has no way of
resolving the preferred basis problem in his approach since, to
him, all bases correspond to equivalent 'worlds’.
That is why it is preferable to abandon the idea of “world” (an
idea which BTW belongs more to metaphysics than physics) and use the
“relative state”, or the “history” notions instead.
Decoherence is irreversible from inside the multiverse for the same
reason that statistical physics is reversible, in Everett. The whole
“universe” remains “in principle” reversible, bit not from
inside, unless amnesia and ultra-sophisiticated technology (which
doubtfully could ever exist).
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.
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.
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.
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. 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. 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. 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.
Saibal
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