Comment by AlexCoventry
11 hours ago
In the Scott Aaronson talk he links at the bottom[1], Prof. Aaronson says
> A fourth reason why people didn’t take QC seriously is that, a century after the discovery of QM, some people still harbor doubts about quantum mechanics itself... Or they say things like, “complex Hilbert space in 2^n dimensions is a nice mathematical formalism, but mathematical formalism is not reality”—the kind of thing you say when you want to doubt, but not take full intellectual responsibility for your doubts.
How is that a failure to take intellectual responsibility? (Asking because it's basically what I think[2], but I promise not to argue with any explanation given here. :-)
One should investigate closely the connection between (well-supported) theories of physics and "reality", which, I gather, in this case means something like "the ontology of the universe".
Is the universe "actually made of" a flexible substance that moves according to the equations of GR? In one sense, it doesn't matter. It acts like it does, and so well that we can make very precise predictions about what will happen.
Suppose a naysayer in 2010 said "Well, GR is a nice mathematical formalism, but mathematical formalism isn't reality. It's preposterous to think space is actually made of this mysterious flexible substance. You'll never see gravitational waves. It's a fiction of the math."
The naysayer has conflated the claim "GR is ontologically true" with the claim "GR makes accurate predictions." The first is irrelevant, and may be freely denied without casting meaningful doubt on the second, which has been well-tested for a century. It would be a great surprise to conduct an experiment and learn that GR mispredicted the result.
QM predicts QC. To doubt QC is to doubt that QM accurately predicts experiments we can conduct. In this case, once again, a century of experiments cuts the other direction. The failure of QC would be the surprise, not its success.
So the GR guy would have been wrong, but how would he be failing to take intellectual responsibility?
I don't think what Aaronson says is fair and it's very easy (and kinda rude) way to dismiss an opinion you don't agree with, but also I don't think it applies to your post. You are questioning the implementation, it seems, he says that there are people who doubt the theory is correct in the first place. 17th century physics didn't predict the existence of that sphere of yours, and it's a very practical question if such sphere could be manufactured or not (and it could've turned out either way with given priors).
Instead, what Aaronson refers to is probably more like people saying "planets moving in epicycles are a nice mathematical formalism, but mathematical formalism is not reality" — you know, the kind of thing you say when you want to doubt, but not take full intellectual responsibility for your doubts...
I am not Scott Aaronson, but probably because that statement is not making any effort to analyze how Hilbert is connected to reality and how where why that connection breaks down.
> complex Hilbert space in 2^n dimensions
A very simple argument is that there's strong reasons to believe that energy is required to represent all information in the physical universe. You can't have "states" without mass/energy storing that state somewhere.
2^n is clearly super-linear in 'n', so as you scale to many particles, the equations suggest that you'd need a ludicrously huge state space, which requires a matching amount of energy to store. Clearly, this is not what happens, increasing the mass/energy of a system 10x doesn't result in 2^10 = 1024x as much mass/energy. You get 10x, plus or minus a correction for binding energy, GR, or whatever.
Quantum Computing is firmly based on pretending that this isn't how it is, that somehow you can squeeze 2^n bits of information out of a system with 'n' parts to it.
The ever increasing difficulties with noise, etc... indicate that no, there's no free lunch here, no matter how long we stand in the queue with an empty tray.
> How is that a failure to take intellectual responsibility?
The argument is metaphysical, it doesn't pose any concrete questions about the validity of QM, which would go like "does QM predicts reality correctly". All the physics is built upon a nice mathematical formalism of real numbers, and it doesn't make physics invalid, it can be used to build planes and computers, despite those pesky real numbers, that are unreal.
Intellectual responsibility means that you filled your metaphysics with some substance. I don't really know, how to do it for quantum mechanics, but if I wanted to, I might start with the inability of QM to explain gravity, I'd dig this topic to the point when I would be able to propose a specific way how research on quantum gravity could overturn QM and make it wrong. Or at least I'd try to make an argument that QM predictions about QC might become false.
But I cannot make such arguments, because I don't know QM, and I'm not going to dive into it, because I know better ways to spend my time, so I'll keep my mouth shut and will not voice vague statements about QM being not reality.
In any case from metaphysical standpoint, I'm sure that physics is not reality, physics is a mathematical description of reality. It doesn't matter if this description is incomplete or even wrong if it works for our case. Like Newton's gravity still works, while being proved wrong. We just need to bear in mind the limits of applicability. So I see the argument Scott Aaronson discusses as a very general truth "a map is not territory" which is used in an incorrect way. The correct (intellectually responsible) way is to point to the limits of applicability and to build an argument that they can bite.
> Asking because it's basically what I think[2]
I had followed your link after I wrote the first part, and I was delighted to see that you targeted the limits of applicability. Your argument is different from just saying "mathematical formalism is not reality".
I cannot verify your thoughts, because I don't know QM or how QC are supposed to work, but you are talking about the limits of applicability: "a theoretically-capable Quantum Computer will be testing the predictions of Quantum Mechanics to a degree of precision hundreds of orders of magnitude greater than any physics experiment to date". It doesn't seem to me as intellectual irresponsibility, it is not intellectual irresponsibility if you really know what you a talking about and can defend your statement when talking with PhD in QM.
> but I promise not to argue with any explanation given here.
Feel free to argue, I have nothing against it. :)
BTW, do you don't take QC seriously because of that? Do you expect QM (as a theory) to fail as a result or R&D work that is done on QC? I agree that there is a probability of QM failing, but my uneducated guess that the probability is low enough (maybe 0.1?) to take QC seriously.
Thanks for your thoughtful and kind reply.
> BTW, do you don't take QC seriously because of that?
Not as a threat to real-world cryptography, but I do take it seriously as a scientific endeavor.
> Do you expect QM (as a theory) to fail as a result
Yes, similar to how Newtonian Mechanics fails at high precision or in extreme circumstances.
Isn’t that kind of like saying “complex numbers are a nice formalism, but only the reals actually exist”?
What does “reality” mean, in this context?
"Reality" in this case would be a cryptographically relevant Quantum Computer, as predicted by current Quantum Mechanical calculations which use these 2^n-dimensional Hilbert Spaces he mentions.