On Sat, Jan 30, 2021 at 2:29 PM smitra <[email protected]> wrote:
On 30-01-2021 01:41, Bruce Kellett wrote:
On Sat, Jan 30, 2021 at 11:20 AM smitra <[email protected]> wrote:
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.
The usual meaning is what we require in these circumstances.
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 argument that I have presented does not depend on MWI. What you do
in MWI is not really relevant because MWI still does not allow for the
reversibility of processes involving the escape of IR photons to outer
space. I am considering a particular case in order to show that
universal unitary evolution does not capture an essential element of
the physics. If you start by insisting that evolution is necessarily
always unitary, then you have begged the question. For these reasons
MWI does not get you off the hook here.
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 on earth is "the whole reality of the physical state"? We are
looking at the physics of a particular situation in which the physical
state is such that reversibility is impossible in principle, because
reversibility would violate the known laws of physics. The point is
that unitary evolution does not capture the reality of this situation
-- the probability of reversing is known to be exactly zero, so the
off-diagonal elements of the density matrix must vanish. This is a
non-unitary requirement. Therefore, unitary evolution does not capture
the physics of this situation. MWI does not help you here.
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.
No. I agree that this is inconsistent with MWI, since MWI insists on
universal unitary evolution. If such unitary evolution cannot capture
essential elements of the physical situation, then it must be wrong.
You simply beg the question if you insist that MWI must be correct. It
is under test, so you cannot logically assume it is true from the
start. However, I have not made any appeal to Copenhagen or any other
particular interpretation. I am simply pointing to a physical result
that must be explainable by whatever interpretation or theory you
adopt.
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.
I am pointing out that some collapse is a necessary consequence of the
physics -- I am not prejudging the issue as you seem to be doing.
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.
How do you make out that physics does not make a distinction between
Alice making a measurement and Bob making a measurement? If one can
only discuss things on the list by assuming from the start that
computationalism and MWI is necessarily correct, then the email list
is pretty useless. I thought the idea was to allow free and open
discussion of the strengths and weaknesses of this type of theory.
Begging the question is not a characteristic of free and open
discussion of the merits of any theory.
Bruce
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.
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