Quantum theory cannot consistently describe the use of itself | Hacker News Reader

Quantum theory cannot consistently describe the use of itself

nature.com

61 pointslisper22 comments

"Quantum theory" does not contain any instructions for how to give "quantum behavior" to observers. Either you imagine there being observers outside of the system (in which case there are some rules for calculating the probability distributions of what they see), or you imagine one big system with no special role of observer (in which case you can "count" the dominance of some states over others in the great big universal superposition).

In the first case there is such a thing as an observer but they aren't quantum, in the second case there is no distinguished role of observer.

Very good point!

Is it non-controversial to assume a randomness generator in a fundamental thought experiment? Also macro state. It is hard to see how the deterministic part of QM could be inconsistent. However the interpretation of its application to accommodate classical concepts had never seemed self-consistent even before this.

Scott Aaronson discussed this on his blog,

https://www.scottaaronson.com/blog/?p=3975

The discussion there suggests there might be some semantic disagreement over exactly what is meant by certain measurements and observer states in the paradox, and so Aaronson at least does not agree that the paper creates the trilemma situation that it primarily focuses on.

This discussion also breaks down the paradox into terms that describe it as a combination of both the previously known thought experiments for Wigner’s friend and Hardy’s paradox.

The first requirement of their no-go theorem ("an agent can be certain that a given proposition holds whenever the quantum-mechanical Born rule assigns probability-1 to it") is interesting, considering the fact that "happens with probability one" is no longer synonymous with "always happens" when you have a probability space with infinite cardinality. Hence the distinction between the technical terms "almost always" and "always" in probability theory.

I haven't finished reading the paper, but does anyone who has already encountered it know if this objection is covered (either in the paper itself or in later discussion)?

I don’t believe it was raised anywhere, also just one harp on what you said: it’s not just having infinite cardinality but also having an appropriate probability measure on the space. For example, the positive integers have infinite cardinality, but you can put probability distributions on that space for which there are no non-empty subspaces with probability zero, like (1/2)^k.

However I don’t think this issue would actually matter, because from the observer’s point of view in such a situation the probability of discovering you are in one of the Everett branches where the probability-1 event did not occur is exactly 0, so in terms of forming beliefs, you’d assign zero probability to that outcome.

Think of it this way, if I create a random continuous function on [0, 1], the probability that it is also differentiable is 0, even though there are tons of familiar examples like x^2 or sin(x).

So if I offer you a wager of whether the randomly generated function is differentiable, your belief ought to be that it always is not, even though the technical term would be “almost always” in formal measure theoretic probability theory.

This is four months old and much heralded when it was published. Has there been any response to it since then?

Just found this refutation:

https://dustinlazarovici.com/wp-content/uploads/comment_renn...

Too bad it uses Bohmian Mechanics.

Why is that bad?

Bohmian mecahnics isn't identical to Quantum mechanics empirically. I used to think that but there are counterexamples. Additionally, the metaphysical strains it takes are philosophically appealing but not experimentally productive.

Discussed a few months ago via a couple of popular articles: https://news.ycombinator.com/item?id=18023452

Could the conclusion of this paper point towards a useful quantum computer being an impossible result?

It's purely an opinion and interpretation.

The other interpretation is that the experiment shows that collapse of potential fields into manifest reality is individual for each observer.

> The other interpretation is that the experiment shows that collapse of potential fields into manifest reality is individual for each observer

General Relativity makes sense because our interpretation of a phenomenon is distorted in a mathematically reversible way which is localized to the observer.

If it were to be proven that a given wave function could collapse into two distinct quantum states simultaneously depending on the state of the observer, it would basically throw a wrench into the entire system.

Nothing is capable of describing itself and the system in which it exists. It’s a much more complicated version of a file that contains its own hashsum

I'd say that it's more about the ability to manipulate its own hash (aka Gödel number). But that's probably what you meant.

I have high expectations that it will be proven that Perl can describe itself, and that only Perl can describe itself. :)

It would be like a super-quine: a program capable of printing out it's own source code as well as the code needed to compile itself.

It's more subtle than that, for example:

https://en.wikipedia.org/wiki/Self-verifying_theories

An inconsistent theory can prove its own consistency, so in what sense does a system proving its own consistency provide evidence that it is consistent?

This issue is addressed informally in the introduction to the authors paper available here [1]. The pivotal move that addresses your complaint head on is Theorem 4.3.

[1] https://www.jstor.org/stable/2695030

It's mind-boggling that they don't cite Gödel.

Edit: This is a Quora gem: https://www.quora.com/Did-Russell-understand-Godels-incomple...

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