Note that Scott Aaronson is one of the world’s leading experts in quantum computation and he’s roughly agnostic about MWI.
The whole idea that quantum computation is evidence for Many Worlds seems dodgy to me given that one then has to ask why quantum computation seems to be able to do so little. It looks like BQP is a proper subset of PSPACE and likely doesn’t include all of NP. If one takes that seriously and believes in Many Worlds one then has to ask why quantum computers are so weak.
It’s funny you bring this up, because I am in this course with Scott right now.
Note that the issue is whether quantum states are physically real, in which case the fact that you exploit canceling amplitude of quantum states in Shor’s algorithm would be evidence of many worlds in the sense of many neatly factorizing amplitude blobs. None of this cares whatsoever whether quantum computing is more powerful than classical computing, only about how it is doing the computation. Also, bounded error quantum algorithms pose another issue, since the outcome can be viewed statistically (which the linked paper casts into doubt).
We just had a sequence of classes on quantum computation and posted several interesting debates to our course blog. In particular, the paper I linked above was posted in the comments thread for our discussion about whether quantum computing can or cannot offer insight in the debate over interpretations.
Look here for the blog post about Many Worlds and look here for the new posts about quantum computing and closed timelike curves.
My username in those discussions is ‘bobthebayesian’ and I would welcome criticism of my ideas if it is constructive and helps me update to better understanding. However, I think Scott wants us to keep the blog mostly for students in the class and with few or no posts from outsiders.
For what it’s worth, Scott presents great challenges for Many Worlds that do not suffer from the usual shock level paranoia that most people have when the hear about it. He has no problem believing the trippy / weird consequences of Many Worlds. He said it well as follows on that class blog:
As I see it, the question then is whether we should be satisfied with MWI’s clear advantages in simplicity and elegance, or whether we should continue to search for a less “trippy” explanation. (After all, there are many simple, elegant theories whose “only” flaw is their failure to account for various aspects of our experience!)
I think the paper linked in the OP gives more reason to be satisfied with the simplicity of Many Worlds, beyond Bell’s theorem.
Also, if we want an argument from authority, Hawking, Feynman, Deutsch, and Weinberg all side with Many-Worlds. Yes, they have some nuanced beliefs.. Weinberg said it interestingly when he said Many Worlds is “like democracy… terrible except for the alternatives.” I don’t think that this (nor Aaronson’s agnosticism towards MWI) “proves” anything other than that it is a difficult problem. I, for one, do not share Deutsch’s view that MWI is straightforwardly obvious, especially not when you consider all the issues in trying to understand why we see the Born probabilities instead of something else (see here).
I do think that it is straightforward that we should not postulate “measurement” as an ontologically basic thing, though. And this is why MWI is the best theory we have so far. (Bohmian mechanics would be worth consideration if it weren’t for predictions that don’t agree with experiment and the inherent underdetermination problem that it suffers.)
I think the paper linked in the OP gives more reason to be satisfied with the simplicity of Many Worlds, beyond Bell’s theorem.
This seems right. Moreover, if I’m reading it correctly (although this is far from my area of expertise) it suggests that any consistent interpretation other than MWI will likely have the same weird aspects as MWI or others of equivalent weirdness. This makes MWI both stronger and it means that people who are holding out because they think that something else will come along are more likely out of luck.
If one takes that seriously and believes in Many Worlds one then has to ask why quantum computers are so weak.
No interpretation of quantum mechanics says anything at all about the extent of BQP, which is (as you well know) a purely mathematical question that has nothing to do with the laws of physics.
MWI implies that quantum computers compute BQP, and depending on how you specify Copenhagen, it implies either that quantum computers compute P or that they compute some mystical complexity class whose definition depends on the notion of “observer.” This is the sense in which quantum computation provides evidence for MWI. Your comment is unrelated to the reasons for Scott Aaronson’s agnosticism.
I think we’re discussing different aspects. The essential argument for MWI based on computational issues I’m addressing is that in the second to last paragraph of the above post:
On a related note, in one of David Deutsch’s original arguments for why Many Worlds was straightforwardly obvious from quantum theory, he mentions Shor’s quantum factoring algorithm. Essentially he asks any opponent of Many Worlds to give a real account, not just a parochial calculational account, of why the algorithm works when it is using exponentially more resources than could possibly be classically available to it.
The problem with that sort of argument is that it proves too much since one would then have to explain why one in fact only gets a bit more computational power over classical systems.
The problem with that sort of argument is that it proves too much since one would then have to explain why one in fact only gets a bit more computational power over classical systems.
I don’t see what you mean. Quantum computers seem to use this additional resource which is not available classically, as the existence of any classically impossible quantum algorithm shows. This argument doesn’t show that quantum computers get arbitrary access to this additional resource.
If I claim to have access to non-classical physics and show you one classically impossible feat, you should probably accept my argument. It is not compelling if you say “but what about this other classically impossible feat which you cannot achieve” and then ignore the explanation.
Well, but no one is disagreeing that quantum computers have access to non-classical resources. The problem is that explaining that by saying one has access to resources in other parts of the wavefunction creates the question “why do you only have a tiny bit of access” which about as large a question. It isn’t at all clear that that’s at all more satisfactory than simply saying that the actual laws of physics don’t work as our intuition would expect them to.
Because the effect of the waveform drops off quickly with distance.
MWI predicts that it should be difficult to use these resources. Classical physics predicts that it should be impossible. Ergo, the fact that they’re difficult to access is evidence for MWI.
Exactly. It makes no difference how powerful quantum computers are for Deutsch’s argument. If we had waited exponential time for a classical computer to do it, we would not wonder “where the number was factored.” Waiting only polynomial time for it to be factored then begs the question.
I am well aware of the extremely interesting complexity limitations of quantum computing. It definitely only extends computational capability a little bit—and we still can’t even prove that P does not equal NP. But none of this is relevant to Deutsch’s “where was the number factored” argument. He is saying that if quantum states are physically real and not just a calculational tool, then you have to give a physical account of how Shor’s algorithm works and the orthodox views of wavefunction collapse could not do that.
Note that Scott Aaronson is one of the world’s leading experts in quantum computation and he’s roughly agnostic about MWI.
The whole idea that quantum computation is evidence for Many Worlds seems dodgy to me given that one then has to ask why quantum computation seems to be able to do so little. It looks like BQP is a proper subset of PSPACE and likely doesn’t include all of NP. If one takes that seriously and believes in Many Worlds one then has to ask why quantum computers are so weak.
It’s funny you bring this up, because I am in this course with Scott right now.
Note that the issue is whether quantum states are physically real, in which case the fact that you exploit canceling amplitude of quantum states in Shor’s algorithm would be evidence of many worlds in the sense of many neatly factorizing amplitude blobs. None of this cares whatsoever whether quantum computing is more powerful than classical computing, only about how it is doing the computation. Also, bounded error quantum algorithms pose another issue, since the outcome can be viewed statistically (which the linked paper casts into doubt).
We just had a sequence of classes on quantum computation and posted several interesting debates to our course blog. In particular, the paper I linked above was posted in the comments thread for our discussion about whether quantum computing can or cannot offer insight in the debate over interpretations.
Look here for the blog post about Many Worlds and look here for the new posts about quantum computing and closed timelike curves.
My username in those discussions is ‘bobthebayesian’ and I would welcome criticism of my ideas if it is constructive and helps me update to better understanding. However, I think Scott wants us to keep the blog mostly for students in the class and with few or no posts from outsiders.
For what it’s worth, Scott presents great challenges for Many Worlds that do not suffer from the usual shock level paranoia that most people have when the hear about it. He has no problem believing the trippy / weird consequences of Many Worlds. He said it well as follows on that class blog:
I think the paper linked in the OP gives more reason to be satisfied with the simplicity of Many Worlds, beyond Bell’s theorem.
Also, if we want an argument from authority, Hawking, Feynman, Deutsch, and Weinberg all side with Many-Worlds. Yes, they have some nuanced beliefs.. Weinberg said it interestingly when he said Many Worlds is “like democracy… terrible except for the alternatives.” I don’t think that this (nor Aaronson’s agnosticism towards MWI) “proves” anything other than that it is a difficult problem. I, for one, do not share Deutsch’s view that MWI is straightforwardly obvious, especially not when you consider all the issues in trying to understand why we see the Born probabilities instead of something else (see here).
I do think that it is straightforward that we should not postulate “measurement” as an ontologically basic thing, though. And this is why MWI is the best theory we have so far. (Bohmian mechanics would be worth consideration if it weren’t for predictions that don’t agree with experiment and the inherent underdetermination problem that it suffers.)
This seems right. Moreover, if I’m reading it correctly (although this is far from my area of expertise) it suggests that any consistent interpretation other than MWI will likely have the same weird aspects as MWI or others of equivalent weirdness. This makes MWI both stronger and it means that people who are holding out because they think that something else will come along are more likely out of luck.
No interpretation of quantum mechanics says anything at all about the extent of BQP, which is (as you well know) a purely mathematical question that has nothing to do with the laws of physics.
MWI implies that quantum computers compute BQP, and depending on how you specify Copenhagen, it implies either that quantum computers compute P or that they compute some mystical complexity class whose definition depends on the notion of “observer.” This is the sense in which quantum computation provides evidence for MWI. Your comment is unrelated to the reasons for Scott Aaronson’s agnosticism.
I think we’re discussing different aspects. The essential argument for MWI based on computational issues I’m addressing is that in the second to last paragraph of the above post:
The problem with that sort of argument is that it proves too much since one would then have to explain why one in fact only gets a bit more computational power over classical systems.
I don’t see what you mean. Quantum computers seem to use this additional resource which is not available classically, as the existence of any classically impossible quantum algorithm shows. This argument doesn’t show that quantum computers get arbitrary access to this additional resource.
If I claim to have access to non-classical physics and show you one classically impossible feat, you should probably accept my argument. It is not compelling if you say “but what about this other classically impossible feat which you cannot achieve” and then ignore the explanation.
Well, but no one is disagreeing that quantum computers have access to non-classical resources. The problem is that explaining that by saying one has access to resources in other parts of the wavefunction creates the question “why do you only have a tiny bit of access” which about as large a question. It isn’t at all clear that that’s at all more satisfactory than simply saying that the actual laws of physics don’t work as our intuition would expect them to.
Because the effect of the waveform drops off quickly with distance.
MWI predicts that it should be difficult to use these resources. Classical physics predicts that it should be impossible. Ergo, the fact that they’re difficult to access is evidence for MWI.
Exactly. It makes no difference how powerful quantum computers are for Deutsch’s argument. If we had waited exponential time for a classical computer to do it, we would not wonder “where the number was factored.” Waiting only polynomial time for it to be factored then begs the question.
I am well aware of the extremely interesting complexity limitations of quantum computing. It definitely only extends computational capability a little bit—and we still can’t even prove that P does not equal NP. But none of this is relevant to Deutsch’s “where was the number factored” argument. He is saying that if quantum states are physically real and not just a calculational tool, then you have to give a physical account of how Shor’s algorithm works and the orthodox views of wavefunction collapse could not do that.