5 ms·

You can't test if quantum uses complex numbers

61 points by EvgeniyZh 1y ago

trhway 1y ago
>Not allowing the players to come into the game with entangled states is really, really strange. I think i saw such a warning on a casino door in LV.
- amelius 1y ago
  How did they check?
  - rdtsc 1y ago
    They just observe you, then you're good to come in.
  - TheOtherHobbes 1y ago
    They asked a friend.
moktonar 1y ago
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!
- catigula 1y ago
  Quantum computing research feels like one of those things whose greatest effort would likely be classified research. In fact, you could argue the article in the OP looks like well-poisoning based on the author's conclusions.
- terminalbraid 1y ago
  What was wrong with the proof in this case? The paper explicitly states and acknowledges the issue raised by this article before the author was aware of it. The author of the article just contends that it is an experimental issue to set up unentangled initial states which are required for the experiment, and indeed someone who was going to perform the experiment needs to convincing demonstrate the assumptions are met. The author even admits this "is better than doing no test at all".
  - moi2388 1y ago
    Nothing, except the perception of what was said and what was actually said. (The same happend to Bells inequality actually) “ (…) you can just mimic the behavior of complex numbers using pairs of real numbers (and appropriately tweaked definitions of operations). (…) What Renou et al are actually claiming is that if you start with quantum mechanics, and then remove all operations and states involving non-real numbers, and then try to emulate what was lost using what remains, you will fail in an experimentally detectable way” Meaning it’s actually totally possible to only use reals to encode the complex Numbers, but not to also remove all operators which do the same things as the complex numbers would.
    - j16sdiz 1y ago
      "the math breaks if you just remove the math" "actually you can replace with something equivalent" "i said just remove the math, not replacing it" so, what's the news?
- gus_massa 1y ago
  Nobody takes what is published at face value [1], the researchers read and reproduce the result. The reproduction is never published. If it's a positive result, the idea is to add a tweak and get a free paper, or combine with another technique and get a free paper, or copy the same idea to another area and get a free paper, or ... For negative results, it's more difficult, but if someone is getting a promising results, they will not just drop whatever they are doing because some random said it's impossible. It's also a matter of reputation. Everyone knows everyone and have read a few of the previous papers (or papers of the advisor/coworker/whatever). If the previous papers were good, it's a good signal to take a look at the new result. If the previous papers were dubious, you skim it in case there is something interesting, but may just ignore it. [1] Perhaps the exception are medical trials, but they have a lot of rules and paperwork to avoid lying, error, misrepresentations and other nasty stuff. Anyway, after reading a lot of ivermectin preprints during peak pandemic, I'm not so sure.
  - moktonar 1y ago
    Sure, but if the result is convincing enough, it might linger for a long time before someone finds a corner case where it doesn’t hold. For these reasons I think it would be better to have a different approach.
    - gus_massa 1y ago
      That's a hard problem. There is finite amount of money, so it's better to use it for promising research instead of potencial crackpots. Researchers have a finite amount of time, so it's better to focus on promising research lines instead of potencial dead ends. I'm not sure how to solve it, that avoids wasting money and time on flat earth research. (I think the researcher time is more critical. If 10% of the money is wasted, nobody would care, some research flops anyway. If someone wasted 5 years doing flat earth research, it's difficult to get back. (I'd ask x5 of the money in exchange of the reputation damage.))
      - moktonar 1y ago
        You solve it by staying skeptic! :)
prof-dr-ir 1y ago
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. /rant, with apologies
- jjk166 1y ago
  The "i" is there because it is a convenient way in our system of mathematics to write out such an equation, but that really comes from the fact that complex numbers have two dimensionality. Our best understanding of the universe demands that higher dimensionality, not necessarily the imaginary-ness. Yes a different mathematical formulation may be rewritten into this imaginary form, and thus is mathematically equivalent. But by the same logic a heliocentric system of elliptical orbits is mathematically equivalent to a geocentric system of epicycles. From one perspective there is a certain deeper meaning there - the universe has no absolute reference frame; but if you view your cosmos in terms of epicycles its very difficult to develop an understanding of what drives those epicycles, namely gravity. Likewise thinking about quantum mechanics in terms of of imaginary numbers may allow for accurate calculations, but nevertheless be an intellectual stumbling block for understanding why the universe is this way. I personally have no issue with "imaginary" numbers having real physical meaning. Our inability to process the square root of negative 1 seems more like a limitation of our ape brains than the universe, and likewise for the majority of quantum weirdness. But in throwing up my hands saying the question can not be answered, I have guaranteed that I will never find the answer even if it does indeed exist.
rhdunn 1y ago
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.
- taeric 1y ago
  My mental model is that complex numbers are the first of the basic number systems that no longer has a total ordering. That alone is super useful for it. Quantum is an odd one, as the name indicates that it deals in quantums. Minimum values that can't be divided. The difficult parts seems more to be in systems that have a probability space more than an analytical model that describes them. Which, fair, it is not a number system.
  - CGMthrowaway 1y ago
    The loss of ordering is what makes complex numbers unique and useful for describing systems like rotations and probabilities. Classical probability works with real numbers (probabilities between 0 and 1). Quantum probability involves amplitudes represented by complex numbers. These amplitudes can wave-interfere with each other, leading to superposition and entanglement
    - ogogmad 1y ago
      The phase space formulation of QM still only uses REAL-valued probabilities, but outside the interval [0,1]. I'm not sure I agree with the rest of your comment either.
hyghjiyhu 1y ago
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?
- Strilanc 1y ago
  No, the pre-shared states are never consumed. They are catalysts, not fuel.
WhitneyLand 1y ago
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.
- gsf_emergency_2 1y ago
  The paper is a non-sequitur. Charitably. 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
- naasking 1y ago
  > 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.
Talinx 1y ago
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.

61 points by EvgeniyZh 1y ago

>Not allowing the players to come into the game with entangled states is really, really strange. I think i saw such a warning on a casino door in LV.

amelius 1y ago
How did they check?
- rdtsc 1y ago
  They just observe you, then you're good to come in.
- TheOtherHobbes 1y ago
  They asked a friend.

moktonar 1y ago

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!

catigula 1y ago
Quantum computing research feels like one of those things whose greatest effort would likely be classified research. In fact, you could argue the article in the OP looks like well-poisoning based on the author's conclusions.
terminalbraid 1y ago
What was wrong with the proof in this case? The paper explicitly states and acknowledges the issue raised by this article before the author was aware of it. The author of the article just contends that it is an experimental issue to set up unentangled initial states which are required for the experiment, and indeed someone who was going to perform the experiment needs to convincing demonstrate the assumptions are met. The author even admits this "is better than doing no test at all".
- moi2388 1y ago
  Nothing, except the perception of what was said and what was actually said. (The same happend to Bells inequality actually) “ (…) you can just mimic the behavior of complex numbers using pairs of real numbers (and appropriately tweaked definitions of operations). (…) What Renou et al are actually claiming is that if you start with quantum mechanics, and then remove all operations and states involving non-real numbers, and then try to emulate what was lost using what remains, you will fail in an experimentally detectable way” Meaning it’s actually totally possible to only use reals to encode the complex Numbers, but not to also remove all operators which do the same things as the complex numbers would.
  - j16sdiz 1y ago
    "the math breaks if you just remove the math" "actually you can replace with something equivalent" "i said just remove the math, not replacing it" so, what's the news?
gus_massa 1y ago
Nobody takes what is published at face value [1], the researchers read and reproduce the result. The reproduction is never published. If it's a positive result, the idea is to add a tweak and get a free paper, or combine with another technique and get a free paper, or copy the same idea to another area and get a free paper, or ... For negative results, it's more difficult, but if someone is getting a promising results, they will not just drop whatever they are doing because some random said it's impossible. It's also a matter of reputation. Everyone knows everyone and have read a few of the previous papers (or papers of the advisor/coworker/whatever). If the previous papers were good, it's a good signal to take a look at the new result. If the previous papers were dubious, you skim it in case there is something interesting, but may just ignore it. [1] Perhaps the exception are medical trials, but they have a lot of rules and paperwork to avoid lying, error, misrepresentations and other nasty stuff. Anyway, after reading a lot of ivermectin preprints during peak pandemic, I'm not so sure.
- moktonar 1y ago
  Sure, but if the result is convincing enough, it might linger for a long time before someone finds a corner case where it doesn’t hold. For these reasons I think it would be better to have a different approach.
  - gus_massa 1y ago
    That's a hard problem. There is finite amount of money, so it's better to use it for promising research instead of potencial crackpots. Researchers have a finite amount of time, so it's better to focus on promising research lines instead of potencial dead ends. I'm not sure how to solve it, that avoids wasting money and time on flat earth research. (I think the researcher time is more critical. If 10% of the money is wasted, nobody would care, some research flops anyway. If someone wasted 5 years doing flat earth research, it's difficult to get back. (I'd ask x5 of the money in exchange of the reputation damage.))
    - moktonar 1y ago
      You solve it by staying skeptic! :)

prof-dr-ir 1y ago

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. /rant, with apologies

jjk166 1y ago
The "i" is there because it is a convenient way in our system of mathematics to write out such an equation, but that really comes from the fact that complex numbers have two dimensionality. Our best understanding of the universe demands that higher dimensionality, not necessarily the imaginary-ness. Yes a different mathematical formulation may be rewritten into this imaginary form, and thus is mathematically equivalent. But by the same logic a heliocentric system of elliptical orbits is mathematically equivalent to a geocentric system of epicycles. From one perspective there is a certain deeper meaning there - the universe has no absolute reference frame; but if you view your cosmos in terms of epicycles its very difficult to develop an understanding of what drives those epicycles, namely gravity. Likewise thinking about quantum mechanics in terms of of imaginary numbers may allow for accurate calculations, but nevertheless be an intellectual stumbling block for understanding why the universe is this way. I personally have no issue with "imaginary" numbers having real physical meaning. Our inability to process the square root of negative 1 seems more like a limitation of our ape brains than the universe, and likewise for the majority of quantum weirdness. But in throwing up my hands saying the question can not be answered, I have guaranteed that I will never find the answer even if it does indeed exist.

rhdunn 1y ago

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.

taeric 1y ago
My mental model is that complex numbers are the first of the basic number systems that no longer has a total ordering. That alone is super useful for it. Quantum is an odd one, as the name indicates that it deals in quantums. Minimum values that can't be divided. The difficult parts seems more to be in systems that have a probability space more than an analytical model that describes them. Which, fair, it is not a number system.
- CGMthrowaway 1y ago
  The loss of ordering is what makes complex numbers unique and useful for describing systems like rotations and probabilities. Classical probability works with real numbers (probabilities between 0 and 1). Quantum probability involves amplitudes represented by complex numbers. These amplitudes can wave-interfere with each other, leading to superposition and entanglement
  - ogogmad 1y ago
    The phase space formulation of QM still only uses REAL-valued probabilities, but outside the interval [0,1]. I'm not sure I agree with the rest of your comment either.

hyghjiyhu 1y ago

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?

Strilanc 1y ago
No, the pre-shared states are never consumed. They are catalysts, not fuel.

WhitneyLand 1y ago

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.

gsf_emergency_2 1y ago
The paper is a non-sequitur. Charitably. 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
naasking 1y ago
> 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.

Talinx 1y ago

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.