On 10-08-2019 10:20, Bruce Kellett wrote:
On Sat, Aug 10, 2019 at 6:16 PM smitra <[email protected]> wrote:
On 10-08-2019 09:49, Bruce Kellett wrote:
But when you cannot reach, or ignore, some of this larger number
of
degrees of freedom, you end up with a mixed state. That is how
decoherence reduces the pure state to a mixture on measurement --
there are always degrees of freedom that are not recoverable --
those
infamous IR photons, for example. The brain does not take all
this
entanglement with the environment into account, so it is a
classical
object.
And that step of tracing out the environmental degrees of freedom
is
where we make a mathematical approximation in order to be able to
do
practical calculations. But as you have said in this thread, the
mathematics we use to describe a system is not necessarily a good
physical representation of the system. It's not up to the brain to
decide to not take entanglement into account.
No, the brain has no choice. It simply cannot take these environmental
dof into account. So on its own reckoning, it is a classical object.
It cannot be "classical" in the way we conventionally define it, as
that's a concept that cannot exist in the known universe. What we want
to do is extract an object out of an entangled state in a physically
correct way, instead of a way that yields negligible errors when
computing expectation values of generic macroscopic observables, but is
physically incorrect.
We may describe the brain
as a classical object, but that doesn't make it so.
Tell me one practical way in which this makes a difference.
There is no practical difference between a collapse interpretation and
the MWI, neither is there a practical difference between a theory that
says that all planets that are beyond the cosmological horizon are made
out of green cheese and the standard astrophysical models.
I do think that sticking to the relevant physics one can learn a great
deal more than by invoking irrelevant models. E.g. in thermodynamics we
ignore the correlations between the molecules that makes the physical
state a specially prepared state w.r.t. inverse time evolution. So,
ignoring the correlations and pretending that everything is random is
good enough if we focus on being able to predict measurement outcomes,
but the fact that the state isn't just any random state follows from the
fact that entropy would go down under time reversal while it would
increase if the state were truly random.
So, the well known paradoxes in statistical physics go away when we take
into account the way we've oversimplified the physics. In the case of QM
exactly the same thing happens when using the density matrix formalism
and tracing out the environment. You lose the information needed to
describe the inverse time evolution correctly. But unlike ion
statistical physics, that's not the topic under discussion. The ignored
correlations between the degrees of freedom in the brain and the
environment do however solve a lot of other paradoxes invoked by people
who argue that AI can never generate consciousness.
Let's consider a robot with an electronic brain that runs a well defined
algorithm. Then there exists a notion about what algorithm the brain is
running, and we may call this a classical description of the electronic
brain. We include in the algorithm the exact computational state. The
exact description of the physical state involves all the entanglements
of all the atoms in the electronic brain and all the other local degrees
of freedom in the environment. If we then extract the computational
state represented as a bitstring out of this state, then the exact
physical state can be written as:
|psi> = |b1>|e1> + |b2>|e2> + |b3>|e3>
where the |bj> are normalized computational states and the |ej> are the
unnormalized "environmental" state that include everything except the
computational state. Then <ej|ej> is the probability for the system to
be in the state |bj>|ej>. So, it also includes the state of the atoms in
the brain given whatever computational state the brain is in. Now
suppose that the robot is conscious, then what it will know/feel about
itself and its local environment will be contained in the bistring
describing its computational state, but the mapping from computational
states to awareness cannot be one to one. Whatever we are aware of,
won't precisely specify the exact computational state defined by what
all the neurons are doing at some time. This means that there exists a
large number of different |bj>'s that generate the exact same awareness
for the robot.
Suppose that the robot is subjectively aware that it prepared the spin
of an electron to be polarized in the positive in the x-direction and
knows that I measured the spin then before I let the robot know the
result of the measurement, the robot will find itself in the state:
|psi> = |up> + |down>]
where
|up> = sum over states where |ej> contains Saibal finding spin up of
|bj>|ej>,
|down> = sum over states where |ej> contains Saibal finding spin down of
|bj>|ej>.
The robot will thus be in a superposition of two classes of worlds where
the result of the spin measurement is different.
Saibal
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