I find that cases like this represent one of the biggest problems in today’s research: once someone falsifies something, an entire branch of research gets cut off completely as nobody wants to pursue that path anymore, understandably. But if the “proof” is in fact wrong, then you actually just hid a big part of the research surface to everybody. And usually that’s also where progress is made: when, despite proof, research is pursued because of a gut feeling. Stay skeptic!
Frankly I am so tired of this whole branch of research where people try to be foundational about "quantum theory" but at the same time boil it down to qubits, gates, bell tests and, well, two-by-two matrices.
Here is my viewpoint, which somehow some people find controversial: quantum theory is first and foremost a description of individual particles. To describe their time evolution, we use the Schrodinger equation:
i d_t Psi = H Psi
What is that "i" there? Oh right, the imaginary unit. So... quantum theory uses complex numbers.
Now you are free to search for another theory without the "i", and perhaps even find something that is somehow mathematically consistent. But that theory either describes experiments just as well as ordinary quantum theory, in which case it is physically equivalent and of no advantage (except to those with strong allergies to complex numbers), or it does not, and then it is wrong.
Of course the last logical possibility is that your theory might do better than quantum theory... but that is the dream only of those who do not known quantum field theory.
IIUC, complex numbers are a number system that supports rotations -- one representation is as an angle and a magnitude. As such they work well at describing systems that have rotational components. This makes them useful for working with waves like in QM (light, etc.) and Fourier transformations/analysis (sine waves) which is why they are used in QM.
If you exclude non-real operations and states you are removing part of the system such that it becomes impossible to work with certain cases -- like handling non-real roots of ax^2 + bx + c polynomials.
It is possible to represent complex numbers as 2x2 matrices as those can encode 2D rotations. With the matrix formulation you are not dealing with imaginary numbers -- or you are, but they are not encoded with i = sqrt(-1) but as a 45deg rotation. IIRC, there is a formulation of Dirac's QED (Quantum ElectroDynamics) using matrices.
So this is obviously an incredibly technical post. And I can't claim to understand half of it. But I do have one question that may or may not be intelligent. Given that preexisting entanglement is the issue, does that entanglement get "used up" or not? Will it be possible to drain it all by testing for long enough?
So, the point of the entire article is that he didn’t like the title of paper he’s criticizing?
The post implies flaws in the original paper, then at the very end seems to concede it was technically fine just should’ve been up front about entanglement.
The post should be edited to be more upfront about what he realized after writing it.
By assuming no entanglement, it's also not a paper about quantum. (Entanglement <=> quantum)
It should not be in Nature. It is... a homework problem, at best? To teach students not to get too excited about publishing.
Without the technical footnote, it could still have been an interesting paper. But wrong
As for homework problems, the blogpost is a better starting point for one. Maybe the blog author should be a prof, and the paper authors should become adjuncts
> So, the point of the entire article is that he didn’t like the title of paper he’s criticizing?
I think the article makes a good point when it says that nobody else he spoke to about it had noticed this qualifier either. There is a long history of papers in physics making grand claims that lead to decades of mistaken beliefs. For instance, von Neumann's mistaken proof ruling out any kind of hidden variable theory from reproducing QM. Some people still cite this incorrect proof to this day to dismiss hidden variables, 70 years later.
And once you make the caveat obvious, the paper is kind of a nothingburger that got published in Nature.
I don't get why we talk about using complex numbers when doing quantum physics. What's really important is that we use numbers from an algebraically closed field (complex numbers being just a simple example). This makes it clearer what's happening under the hood.
10 comments
[ 5.0 ms ] story [ 39.0 ms ] threadI think i saw such a warning on a casino door in LV.
Here is my viewpoint, which somehow some people find controversial: quantum theory is first and foremost a description of individual particles. To describe their time evolution, we use the Schrodinger equation:
i d_t Psi = H Psi
What is that "i" there? Oh right, the imaginary unit. So... quantum theory uses complex numbers.
Now you are free to search for another theory without the "i", and perhaps even find something that is somehow mathematically consistent. But that theory either describes experiments just as well as ordinary quantum theory, in which case it is physically equivalent and of no advantage (except to those with strong allergies to complex numbers), or it does not, and then it is wrong.
Of course the last logical possibility is that your theory might do better than quantum theory... but that is the dream only of those who do not known quantum field theory.
/rant, with apologies
If you exclude non-real operations and states you are removing part of the system such that it becomes impossible to work with certain cases -- like handling non-real roots of ax^2 + bx + c polynomials.
It is possible to represent complex numbers as 2x2 matrices as those can encode 2D rotations. With the matrix formulation you are not dealing with imaginary numbers -- or you are, but they are not encoded with i = sqrt(-1) but as a 45deg rotation. IIRC, there is a formulation of Dirac's QED (Quantum ElectroDynamics) using matrices.
The post implies flaws in the original paper, then at the very end seems to concede it was technically fine just should’ve been up front about entanglement.
The post should be edited to be more upfront about what he realized after writing it.
By assuming no entanglement, it's also not a paper about quantum. (Entanglement <=> quantum)
It should not be in Nature. It is... a homework problem, at best? To teach students not to get too excited about publishing.
Without the technical footnote, it could still have been an interesting paper. But wrong
As for homework problems, the blogpost is a better starting point for one. Maybe the blog author should be a prof, and the paper authors should become adjuncts
I think the article makes a good point when it says that nobody else he spoke to about it had noticed this qualifier either. There is a long history of papers in physics making grand claims that lead to decades of mistaken beliefs. For instance, von Neumann's mistaken proof ruling out any kind of hidden variable theory from reproducing QM. Some people still cite this incorrect proof to this day to dismiss hidden variables, 70 years later.
And once you make the caveat obvious, the paper is kind of a nothingburger that got published in Nature.