On 14/12/2017 9:23 pm, smitra wrote:
On 14-12-2017 02:35, Bruce Kellett wrote:
On 14/12/2017 11:52 am, smitra wrote:
On 13-12-2017 22:55, Bruce Kellett wrote:
On 14/12/2017 8:23 am, smitra wrote:
So, let's examine this more closely. We start with a state that is
a superposition of branches that each undergo classical evolution,
so I'm not now appealing to the arguments in the paper by
Albrecht. Then we end up with a state of the form:
Sum over j [|heads(j)>|env(heads,j)> +
Sum over j |tails(j)>|env(tails,j)>]
where j enumerates microstates of the coin and the state of the
environment in each sector where the coin is heads or tails
depends on the microstate of the coin. The coin states are not
normalized, the norms are chosen to yield the correct
probabilities. E.g. if tails has zero probability then all the
|tail(j)> are given a norm of zero. So, the above expression is
completely general.
Now, I'm part of the environment, so we can write:
|env(X,j)> = Sum over k of |me(X,Y,j,k)>|env'(X,Y,j,k)>
where X is heads or tails, Y, denotes my macrostate that I'll
define below, j denotes the microstate of the coin and k sums over
microstates corresponding to macrostate Y.
This splitting of my state into a macrostate Y and microstate k is
in principle arbitrary, we can choose this splitting such that Y
keep tracts of what I'm aware of and then k takes into account all
the other degrees of freedom in my body and brain that I'm not
aware of. E.g. if I were a digital computer then Y would
correspond to some bitstring defined by the computational state of
the computer and we then sum over all the possible microstates
that correspond to some fixed macrostate.
Then when I'm not yet aware of the result of the coin throw, we have:
|me(X,Y,j,k)> = |Awareness(Y)>|body(X,Y,j,k)>
where Y contains all the information that I am aware of, and that
doesn't include the result if the coin throw nor information
contained only at the microscopic scale. So, Awareness (Y) for a
given Y defines who I am, where I am , and what I'm experiencing.
It should be clear that despite decoherence, |Awareness(Y)> will
factor out of the global superposition as it doesn't depend on X,
k and j.
So, given what I know, I cannot tell in which branch I am.
Therefore unless all the branches corresponding to one outcome
have zero norm, I will have copies in both branches.
There is just no way that all the information describing what I'm
aware of at some moment is going to constrain how someone else can
throw a coin to such a degree that the outcome will be fixed.
So the end point of your analysis is that you can't see how it could
be possible that you are not right? The outcome is fixed -- and the
same -- in all worlds in which you participate!
But it is quite easy to see what is going on. Since it is all
independent of your awareness, we can factor that out of the
summations. And you still do not get a coherent superposition from a
decoherent mixture. What goes on in the world is independent of
whether or not the rock on the floor is aware of it or not. You are
not in a position any different from that of said rock. Look at the
expansion for Schrödinger's cat:
|nucleus>|box>|cat>you>|environment> -->
{|decayed>|poison spilt>|cat dead>|You>|environment records dead cat>
+ |undecayed>|poison intact>|cat alive>|You>|environment records
live cat>}
You can see that your state does not change (is irrelevant) until you
interact with the environment in such a way that your consciousness
becomes entangled with the state of the cat. This is not mysterious,
and it is not changed just because you claim there is some magic
associated with consciousness that makes a difference. You are just
reverting to Copenhagen or many minds where consciousness is necessary
for the understanding of QM.
The lack of coherence is not relevant unless it affects the two
states denoted by |you>.
That is not true.
If you have a coherent superposition then it's clear that the two
|you>'s are identical.
No, it is not. In the above expansion of the cat scenario, I have a
coherent superposition of live and dead cats -- in different branches
of course, but until decoherence separates the worlds, the
superposition is intact. And Bruno would claim that it is never
broken. So your awareness (or not) of the facts about the world or not
does not affect anything.
If it isn't then it's not clear if that's the case or not and one
needs to take a deeper look. However, it's then also a philosophical
issue as probabilities are not going to be different from a
classical analysis.
There is nothing wrong to invoke consciousness, walking away from
that just because that's the popular thing to do, doesn't make it
right. What I'm arguing for is to define conscious experience as the
computational state of the relevant machine (or brain), which is
then given by some bistring. This can then be included in the
quantum state and that makes everything well defined.
You can invoke consciousness if you wish. But unless that actually
gives you a rational path between the initial mixed state and the
desired coherent state, then invoking consciousness is of no value.
You have not answered the question asked -- how do you propose to get
from the non-coherent mixture to the pure state? Your problem is that
you are trying to bulldoze quantum mechanics into you bitstring world,
and it is refusing to go.
As I said earlier, it is provably the case that your bitstring plenum
is incompatible with quantum mechanics. The reason is essentially seen
in this coin toss case -- QM says that the decohered mixture can never
give a coherent pure state; your bitstrings, since they contain all
logical possibilities, not just the subset of nomological
possibilities, say that the world with heads and the world with tails
both exist. This is demonstrably false given the stated example
because the laws of physics are obeyed.
You're basically arguing on the basis of straw man arguments by
invoking coherence as a fundamental thing when what matters is whether
or not the state the observer finds himself in exists in both sectors.
You are clearly begging the question here because you are assuming that
there are two sectors. But that has not been demonstrated: shaking the
coin involves non-coherent interactions, and it has not been shown that
this can lead to a coherent superposition of different coin states. To
get two worlds, one with heads showing and one with tails showing, the
coin has to be put into such a state. And you can't do that according to
standard quantum mechanics.
"QM says that the decohered mixture can never give a coherent pure
state;"
QM in the MWI cannot possibly say that, because unitary QM as used in
the MWI is manifestly invariant under time inversion. Now, we're not
considering coins as isolated objects here, so of course the
environment does get entangled with the coin. But you cannot use mixed
states in your analysis, because then you're moving in the FAPP area
that's not valid for the particular questions we're addressing here.
I do not have to invoke FAPP after some unitary evolution: the coin
starts off decoherent, and shaking or whatever is also non-coherent.
There is nothing FAPP here. Time reversal invariance is of no use to you
either, because the non-coherent coin state was not the product of
unitary evolution of some prior coherent pure state.
Mixed states are not fundamental, they're only an approximate tool
that FAPP yield the correct answers, which is why we use them in
calculations.
Mixed states are a fundamental part of QM -- we use them all the time in
state preparation where we make non-coherent mixtures of different pure
states. Again, nothing FAPP about this process.
And it is not provably the case that my analysis is incompatible with
standard QM, I used nothing else that standard QM (but without any
FAPP assumptions) to derive my result.
You assume the result you want to prove, and that is not a procedure of
standard quantum mechanics.
Now, I've shown some time ago that you get exactly the same results
for certain nontrivial processes as you would when using classical
reasoning, see e.g. here:
https://arxiv.org/abs/0902.3825
But the interpretation of how the probabilities of the outcomes are
reached are in general going to be radically different.
I have had a quick look at this paper, and at first sight it appears
deeply flawed because you are using tensor products of states, then
summing over one of the components. Since the initial product state is
entangled, that necessarily leads to mixed states, which you then assume
are pure. Also, your assumption 3 is generally false.
So I don't think that that paper is going to help you in the current
discussion.
Bruce
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