On 19 Oct 2013, at 09:42, Jason Resch wrote:




On Fri, Oct 18, 2013 at 6:09 PM, meekerdb <meeke...@verizon.net> wrote:
On 10/18/2013 1:45 PM, Jason Resch wrote:



On Fri, Oct 18, 2013 at 11:37 AM, meekerdb <meeke...@verizon.net> wrote:
On 10/18/2013 12:42 AM, Jason Resch wrote:
But that's not compatible with Bruno's idea of eliminating the physical - at least not unless he can solve the basis problem.


Could you do me a favor and explain what the basis problem is in a way that a 6th grader could understand? I've found all kinds of things said on it, and they all seem to be asking different things.

For physicists, it's part of the problem of explaining the emergence of the classical world from the quantum world. Decoherence can diagonalize (approximately) a reduced density matrix IN SOME BASIS.

Is this the same basis as in "momentum basis" and "position basis", or is it some other usage of the term?

Forgive my ignorance, but what does it mean to "diagonalize a reduced density matrix"?

It means to take an average over all the other variables except those of interest (i.e. the ones you measure). If you do this in a particular basis we think it makes the submatrix corresponding to those variables diagonal. Then it can be interpreted as the probabilities of the different values. Note that it is a mathematical operation that depends on choosing a basis, not a physical process.

Is this a process to recover the probabilities of some observation from some point of view? I so will different probabilities be calculated if one takes a different basis?

The MWI view is that this is a physical process - which it could be IF the basis was not an arbitrary choice but was somehow dictated by the physics. But so far there are only hand waving arguments that "it must be that way".



Can you provide an example of how using a different basis leads to different conclusions? I very much appreciate your helping me to understand this problem.

Let me try a short attempt.
May be you are more familiar with vectors than with "density matrices" used by Brent.

Definite states (like definite position) define a base in a vector space. QM associates such a base to anything you can observe, and reciprocally, having a base, you can find the corresponding measuring apparatus. (forgetting annoying selection rules for some observable, like charge).

The most typical example is position. A system having a definite position will be the same as a system having all possible impulsion in the parallel "universes", and reciprocally. So a superposition correspond to well defined state for a different measuring apparatus. Likewise a state like 1/sqrt(2)(up + down) is a well defined state in the base {1/sqrt(2)(up + down) , 1/sqrt(2)(up - down) }. When you measure 1/sqrt(2)(up + down) in the base {1/sqrt(2)(up + down) , 1/sqrt(2)(up - down) }, you get 1/sqrt(2)(up + down) with probability one. But in the base {up, down}, you will get up or down with probability 1/2, and the local system state will seemingly undergo a projection on up or down state. (That projection is the vector equivalent of the wave packet reduction, and in the MW, there is no reduction, as you have seen. It is only a subjective selection). But now, it looks like the choice of the measuring apparatus determine the possible type of parallel universes you can access, so that the notion of parallel universe seems to be non intrinsic, but depending on the choice of the base, or equivalently, the choice of the observable measured (or the corresponding apparatus).

Everett was well aware of that problem, and when you do the math, the entire picture does not depend on the choice of the base, despite locally, the choice of the base will determine the type of parallel universe you can access.

There is a problem only if we believe in some naive boolean type of universe. It is just that in some terms of the universal Everett superposition, machines can develop, and then they will indeed continue to work in the same bases (if they are classical machines). But the whole quantum state will not depend on that base at all.

I thought that this was the reason to use the label "relative states" instead of parallel universes, but apparently Everett has been asked to avoid the label "parallel universe" as it looks too much like sc. fic. IMO: relative states is better, by preventing the belief that some base plays a crucial role right at the start, which is not the case, as the role will be indexical and relative.

The base problem disappears when you take 1) the universal wave, and 2) accept the idea that all states of the subsystem are relative indexical defined by the base in which some self-aware subparts (local universal machine) can develop and remember personal memories.

Hope this can help a little bit. Normally this is explained in Albert's book, which I think you have.

Bruno







Being diagonal in one basis means it's superposition in some other basis. So for physicists the problem is saying what privileges or picks out the particular bases we see in experiments. Why do our instruments have needles that are in eigen states of position, while some other things (e.g. atoms) are in eigen states of energy or eigen states of momentum. For physicists there are some suggestive, but not fully worked out answers to these questions, e.g. you get position eigenstates because the interaction term of the Hamiltonian is a function of position. But those answers assume the physics. If you want to reconstruct physics from experiences, you can't borrow the physical explanation to say why your experiences are classical.


I think the assumption that experiences are classical comes from the classicality of Turing machines (which are the supposed mechanism by which experiences are manifest).

I don't think there's anything either classical or quantum about Turing machines. They are just mathematical abstractions. And assuming they read and write qubits instead of bits doesn't change the range of things they can compute.

But qubits don't exist in normal definitions of information or Turing machines. Sure, they can be modeled, but only by splitting the entire tape and Turing machine and having one of them read a 1 and the other read a 0. When you do this, you are talking about two different computational states, (you might as well model them as separate Turing machines/programs at this point) and hence you are talking about two different minds, not one mind that is conscious of a superpositional state.

Jason


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