This article nearly pegs my bogometer. It reads more like numerology than science. Yes, it is true that quantum bounds "arise naturally" from quantum theory, but what matters is not that they arise but how they arise, and on this the article is completely mute. The mere fact that you can coax the same numbers out of a classical experiment is completely meaningless. What matters is how you coax those numbers out, and in particular, whether the manner in which you coaxed those numbers out involved a quantum effect or simply manipulating unconstrained degrees of freedom to get the result you want. There may be something interesting going on here, but there is no way to tell from reading this article. If you really could get a quantum bound out of a classical system in a non-bogus way, that would be big news, the biggest breakthrough in physics in decades. I'll give you long odds against.
Indeed. From the discussion section of their paper:
"This shows that quantum correlations can be universally recreated with classical systems at the expense of some extra resources" (Emphasis added)
I might be wrong, but judging from Fig. 1 in the paper, it seems these "extra resources" involved are exponential, which is exactly what we would expect since we already know arbitrary quantum circuits can be simulated classically with exponential slowdown! But I guess the setup is interesting in of itself --from an experimentalist point of view at least.
PRL does a fine job of checking scientific soundness, but their assessment of importance/notability is unimpressive, like most processes involving a handful of humans. (I've published there, and it was far from my most notable result.) Lots of boring stuff passes the filter.
I quit after the abstract. No one ever said something was quantum because the number 2 * sqrt(2) appeared, kind of like no one really thinks that something is a circle just because you can coax pi out of it.
Now, if they actually violated Bell's inequality in a non-quantum experiment in which Bell's inequality were actually applicable, that would be huge news (and grounds to try to confirm the results). But finding a number that violates it out of context isn't news at all.
tl:dr 2.78 3.14. Hence this post is quantum and circular.
Apparently for a 2d convex hull, the perimeter of it is pi times the mead width of it.
Does that count as a circle being involved?
I guess if you showed that the perimeter was proportional to the mean width, then circles would prove that the constant of proportion would be pi, because pi is (often? by definition) the perimeter of the circle divided by the (constant) width.
I don't know if you count that as a circle being involved.
I would. Pi is (indeed always) the circumference of a circle divided by its diameter. To calculate the perimeter of a 2d convex hull, my impulse would be to model the shape in polar coordinates and integrate over theta. The fact that this calculation relies on polar coordinates strongly implies a relationship to circles -- specifically, L = 2 * pi * r_mean turns out to be unsurprising, since you're basically treating each slice of the hull as a slice of a circle, and calculation based on that circle's radius.
by usually I meant that is usually how it is defined. Of course it is always true that it is that value, I just meant, like, what description of the value is used to define what value we mean. I was unclear on that part. I meant that I think that in most cases, pi = circumference / diameter is the definition of pi, rather than pi being defined in some other way, and it being proven as a theorem that pi = circumference / diameter.
Like, suppose I defined pi as sqrt(6*Zeta(2)) , this would still be the same value, so it would work as a definition of pi, but I don't think it is often defined in a way like this.
I think I mostly wrote ^ because I felt like the way I worded my previous comment could be misinterpreted in a way that I feel would make me look dumb, so I wanted to clarify what I actually meant.
Your point about considering it in polar coordinates seems like a good explanation. I hadn't thought of that, I like it, thank you for that. I don't yet see how to make that rigorous, but it sounds like it makes sense in a nice way. Thank you.
There are many ways to arrive at Pi which themselves are quite divorced from "a circle", since you could arrive at the conclusion in a one dimensional Universe.
It's true that if you were to graph these equations you would see circles, but that is besides the point - a one dimensional being wouldn't be able to understand your graph, but could still read you the digits of pi.
The first one there is derived from a definition of a circle: x^2 + y^2 = c. Most of the rest use an arctangent. Only the last one is not obviously related to a circle.
We are in 3 dimensions but we use higher dimensional math all the time, so I don't know why a 1D creature would be so constrained.
I've once heard a statement that polarization can only have a quantum explanation. The effect is that when you have two polarizers at right angles, no light gets through, but when you insert another polarizer at, say, 45 degrees to the others, some light gets through all the polarizers. The thing is, classical EM wave theory predicts the exact same result.
You raise an interesting point, and you're right that quantum treatment is not necessary in the regime where many light particles pass through the circuit, in which case we can talk about light as a continuous thing, that can be infinitely subdivided. A quantum treatment of polarization is only required in the single-photon regime.
Specifically consider an experiment where a light beam passes through three polarizing filters: first a horizontally-polarizing lens H, then a diagonally polarizing lens D, and finally a vertically polarizing lens V.
photons ------> H ----> D --> V ->
The result of this "triple filtering" for a beam of light (consisting of gazillions of photons, modelled as a continuous wave) can be explained as the wave amplitude being "projected" along the polarization axis of each lens. At each polarization step the projection angle is 45 degrees, so the wave intensity is reduced by cos(45)=1/sqrt(2) which is equivalent to a reduction in optical power of 1/2. The power of the beam that passes through all three lenses is 1/4 of the power leaving the first lens. No need for quantum, since we model the beam of light as a continuous quantity that can be infinitely subdivided.
If we repeat the same experiment sending one photon at a time however, we can't say "the photon divides" since by definition a photon is the smallest possible quantum of light. There is not such thing as 1/sqrt(2) of a photon. Basically, when a H-polarized photon reaches a D-polarizing lens, a classical physicists is forced to pick whether the photon goes through, or is reflected—the option "partially goes through" is not allowed. It's only in this regime that the "photon is a wave" explanation fails.
The quantum explanation uses a probabilistic approach and explains the probability of a H-polarized photon going through the D-polarizing lens is 1/2 and subsequently the (now D-polarized photon) going through the third V-polarizing lens is also 1/2 so the overall probability of passing through all three lenses is 1/4.
When considering a single photon the classical explanation certainly fails. However, this is different from the claim that an effect perceived at macro levels cannot be explained by classical theory and only by quantum mechanics.
The paper's result sounds to be along similar lines - claiming that a certain number "could only have come from quantum theory" while classical physics perfectly well yields the same number.
By virtue of being a super-theory of classical mechanics, all phenomena are quantum phenomena with quantum explanations, so that's not what is being talked about here.
Well the single-photon quantum theory is just classical EM. So in a fairly stupid sense, it really is true that the only explanation of the polarisation is the quantum theory.
Skimmed the PDF, it seems like the point of this paper is just to show that yes, classical systems can (with memory, e.g. the reference https://arxiv.org/abs/1007.3650) simulate quantum ones, and thus finding "characteristic quantum numbers" shouldn't make one immediately suspect something quantum is going on. In the discussion it's like the ultimate nitpick: "The characteristic trait
of QT rely on the fact that the quantum bounds are
achieved without employing extra resources such as memory. Therefore, the principles needed to fully derive
QT (in the spirit of Refs. [33–37]) should account for that."
There are some people who find the concept of quantum physics philosophically displeasing and try however they can to ignore all the experimental evidence and say we're really in a classical universe. This isn't a case of one of those.
21 comments
[ 2.7 ms ] story [ 55.8 ms ] thread"This shows that quantum correlations can be universally recreated with classical systems at the expense of some extra resources" (Emphasis added)
I might be wrong, but judging from Fig. 1 in the paper, it seems these "extra resources" involved are exponential, which is exactly what we would expect since we already know arbitrary quantum circuits can be simulated classically with exponential slowdown! But I guess the setup is interesting in of itself --from an experimentalist point of view at least.
Preprint: http://arxiv.org/abs/1511.08144
Since this is published in PRL, it's been through some fairly stringent peer review. So I'll be mildly sceptical until someone wiser weighs in.
Paging Dr. Aaronson, Dr. Aaronson to the blogosphere.
Now, if they actually violated Bell's inequality in a non-quantum experiment in which Bell's inequality were actually applicable, that would be huge news (and grounds to try to confirm the results). But finding a number that violates it out of context isn't news at all.
tl:dr 2.78 3.14. Hence this post is quantum and circular.
Now that is a T-Shirt.
Where there's circle, there's a pi r two
Does that count as a circle being involved?
I guess if you showed that the perimeter was proportional to the mean width, then circles would prove that the constant of proportion would be pi, because pi is (often? by definition) the perimeter of the circle divided by the (constant) width.
I don't know if you count that as a circle being involved.
Like, suppose I defined pi as sqrt(6*Zeta(2)) , this would still be the same value, so it would work as a definition of pi, but I don't think it is often defined in a way like this.
I think I mostly wrote ^ because I felt like the way I worded my previous comment could be misinterpreted in a way that I feel would make me look dumb, so I wanted to clarify what I actually meant.
Your point about considering it in polar coordinates seems like a good explanation. I hadn't thought of that, I like it, thank you for that. I don't yet see how to make that rigorous, but it sounds like it makes sense in a nice way. Thank you.
It's true that if you were to graph these equations you would see circles, but that is besides the point - a one dimensional being wouldn't be able to understand your graph, but could still read you the digits of pi.
http://www.geom.uiuc.edu/~huberty/math5337/groupe/expresspi....
We are in 3 dimensions but we use higher dimensional math all the time, so I don't know why a 1D creature would be so constrained.
Specifically consider an experiment where a light beam passes through three polarizing filters: first a horizontally-polarizing lens H, then a diagonally polarizing lens D, and finally a vertically polarizing lens V.
The result of this "triple filtering" for a beam of light (consisting of gazillions of photons, modelled as a continuous wave) can be explained as the wave amplitude being "projected" along the polarization axis of each lens. At each polarization step the projection angle is 45 degrees, so the wave intensity is reduced by cos(45)=1/sqrt(2) which is equivalent to a reduction in optical power of 1/2. The power of the beam that passes through all three lenses is 1/4 of the power leaving the first lens. No need for quantum, since we model the beam of light as a continuous quantity that can be infinitely subdivided.If we repeat the same experiment sending one photon at a time however, we can't say "the photon divides" since by definition a photon is the smallest possible quantum of light. There is not such thing as 1/sqrt(2) of a photon. Basically, when a H-polarized photon reaches a D-polarizing lens, a classical physicists is forced to pick whether the photon goes through, or is reflected—the option "partially goes through" is not allowed. It's only in this regime that the "photon is a wave" explanation fails.
The quantum explanation uses a probabilistic approach and explains the probability of a H-polarized photon going through the D-polarizing lens is 1/2 and subsequently the (now D-polarized photon) going through the third V-polarizing lens is also 1/2 so the overall probability of passing through all three lenses is 1/4.
The paper's result sounds to be along similar lines - claiming that a certain number "could only have come from quantum theory" while classical physics perfectly well yields the same number.
By virtue of being a super-theory of classical mechanics, all phenomena are quantum phenomena with quantum explanations, so that's not what is being talked about here.
There are some people who find the concept of quantum physics philosophically displeasing and try however they can to ignore all the experimental evidence and say we're really in a classical universe. This isn't a case of one of those.