On 10/11/2013 4:09 AM, Pierz wrote:



On Friday, October 11, 2013 12:25:45 PM UTC+11, Brent wrote:

    So there are infinitely many identical universes preceding a measurement.  
How are
    these universes distinct from one another?

They aren't 'distinct'. The hypothesis is that every universe branch contains an *uncountable* infinity of fungible (identical and interchangeable) universes. While this seems extravagant, it actually kind of makes more sense than the idea of a universe "splitting" into two (where did the second universe come from?). Instead, uncountable infinities of universes are differentiated from one another. Quantum interference patterns arise because of the possibility of universes merging back into one another again.

    Do they divide into two infinite subsets on a binary measurement, or do 
infinitely
    many come into existence in order that some branch-counting measure 
produces the
    right proportion?  Do you not see any problems with assigning a measure to 
infinite
    countable subsets (are there more even numbers that square numbers?).

The former. Deutsch goes into the problem of infinite countable sets in great detail and shows how this is *not* a problem for these uncountable infinities (as Russell points out)), whereas it may be a problem for Bruno's computations - a point I've tried to argue with Bruno, but he bamboozles my sophomoric maths with his replies. To me it seems you can't count computations that go through a state, because for every function f that computes a certain function, there is also some function f1 that also computes f such that f1 = f + 1 - 1. But maybe that can be solved by counting only the functions with the least number of steps (?).

    And why should we prefer this model to simply saying the Born rule derives 
from a
    Bayesian epistemic view of QM as argued by, for example, Chris Fuchs?

I don't know about Chris Fuchs, although isn't that just Copenhagen?

No, it's an interpretation of QM as personal probabilities, i.e. quantum Bayesianism. It reifies information, not quantum states, c.f. http://arxiv.org/pdf/1207.2141.pdf or http://arxiv.org/pdf/1301.3274.pdf It's might be compatible with Bruno's ideas where Copenhagen certainly isn't.

It's clear that one would need strong reasons to favour MWI with its crazy proliferation of entities, which at first blush seems to run against Occam's razor. However Deutsch makes a damn good fist of explaining why we in fact have those reasons. For instance, when a quantum computer calculates a function based on a superposition of states, MWI can explain where these calculations are occurring - in other universes. The computer is exploiting the possibility of massive parallelism inherent in that infinity of universes. It is entirely unclear how these calculations occur in the standard interpretation. MWI also solves the problem of what happens to non-realized measurement states once a system decoheres. And of course it gets around the intractable difficulties of non-computable wave "collapse". So it's a case of choose your poison: infinite universes or conceptual incoherence. I'll take the former, even though in some ways I'd "like" the universe (or the multiverse) better if it wasn't that way.

If you just read this list you have the impression that MWI is the consensus "true" interpretation of QM; but it's still controversial (as are all other intepretations). I highly recommend reading Scott Aaronson's arXiv:1108.1791v3 "Why Philosophers Should Care About Computational Complexity". Section 8 is his discussion of Deutsch's argument based on computation. He gives several reasons why Deutsch's argument, if not actually wrong, may not mean what people think it means. Here's the concluding part:


=============================

One can sharpen the point as follows: if one took the parallel-universes 
explanation of how a
quantum computer works too seriously (as many popular writers do!), then it would be natural to
make further inferences about quantum computing that are flat-out wrong. For 
example:

“Using only a thousand quantum bits (or qubits), a quantum computer could store 
21000
classical bits.”

This is true only for a bizarre definition of the word “store”! The fundamental problem is that,
when you measure a quantum computer’s state, you see only one of the possible 
outcomes; the
rest disappear. Indeed, a celebrated result called Holevo’s Theorem [74] says that, using n qubits, there is no way to store more than n classical bits so that the bits can be reliably retrieved later. In other words: for at least one natural definition of “information-carrying capacity,” qubits have
exactly the same capacity as bits.

To take another example:

“Unlike a classical computer, which can only factor numbers by trying the 
divisors one
by one, a quantum computer could try all possible divisors in parallel.”

If quantum computers can harness vast numbers of parallel worlds, then the 
above seems like a
reasonable guess as to how Shor’s algorithm works. But it’s not how it works at all. Notice that, if Shor’s algorithm did work that way, then it could be used not only for factoring integers, but also for the much larger task of solving NP-complete problems in polynomial time. (As mentioned in footnote 12, the factoring problem is strongly believed not to be NP-complete.) But contrary to
a common misconception, quantum computers are neither known nor believed to be 
able to solve
NP-complete problems efficiently.52 As usual, the fundamental problem is that measuring reveals just a single random outcome |xi. To get around that problem, and ensure that the right outcome is observed with high probability, a quantum algorithm needs to generate an interference pattern,
in which the computational paths leading to a given wrong outcome cancel each 
other out, while
the paths leading to a given right outcome reinforce each other. This is a delicate requirement, and as far as anyone knows, it can only be achieved for a few problems, most of which (like the
factoring problem) have special structure arising from algebra or number 
theory.53

A Many-Worlder might retort: “sure, I agree that quantum computing involves 
harnessing the
parallel universes in subtle and non-obvious ways, but it’s still harnessing parallel universes!” But even here, there’s a fascinating irony. Suppose we choose to think of a quantum algorithm in terms of parallel universes. Then to put it crudely, not only must many universes interfere to give a large final amplitude to the right answer; they must also, by interfering, lose their identities as parallel
universes! In other words, to whatever extent a collection of universes is 
useful for quantum
computation, to that extent it is arguable whether we ought to call them 
“parallel universes”
at all (as opposed to parts of one exponentially-large, self-interfering, quantum-mechanical blob). Conversely, to whatever extent the universes have unambiguously separate identities, to that extent
they’re now “decohered” and out of causal contact with each other. Thus we can 
explain the
outputs of any future computations by invoking only one of the universes, and treating the others
as unrealized hypotheticals.

To clarify, I don’t regard either of the above objections to Deutsch’s argument as decisive, and
am unsure what I think about the matter. My purpose, in setting out the 
objections, was simply
to illustrate the potential of quantum computing theory to inform debates about the Many-Worlds
Interpretation.

================================================



Max Born was my great grandfather. I wonder what he would have made of Everett if he'd been a bit younger. When he died in 1970, it was still probably too out there for him to have seriously considered.

A lineage to be proud of! My grandfather was Isaac Newton, Isaac Newton Hart, a Texas farmer and rancher. :-) Everett proposed the relative state interpretation in 1957, just three years after Born got the Nobel prize. But it wasn't very popular until years later, so Born may not have heard of it.

Brent

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