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The weirdness of quantum mechanics with respect to bases is very counterintuitive but makes perfect sense internal to the logic of the quantum world. It is a so

The weirdness of quantum mechanics with respect to bases is very counterintuitive but makes perfect sense internal to the logic of the quantum world. It is a sort of relativity where there can be incompatible viewpoints. Namely, a hermitian operator is some view of the world, its eigenbasis tells you what you can see from that viewpoint. Two hermitian operators can be incompatible in that they can't be simultaneously diagnolized. Entanglement is another weirdness that makes perfect sense internally. The tensor product of projective hilbert spaces is not the same as the cartesian product. The segre embedding captures this. Theres more to the geometry of quantum phenomena than naively expected. The outcome of measurements collapsing to the eigenbasis of a hermitian operator has a beautiful an elegant geometric interpretation. It makes perfect sense really, just not classical sense. Decoherence explains why we see collapse to this set very well. What is utterly baffling and puzzling is that we only ever see one particular outcome. Decoherence cannot explain that and nothing in quantum mechanics explains that.

cjfd 6y ago
"What is utterly baffling and puzzling is that we only ever see one particular outcome." Actually, there is an answer to this. See e.g. https://arxiv.org/abs/quant-ph/0503009 https://arxiv.org/abs/quant-ph/0503009 tldr: if information is transferred from a microscopic quantum state to a macroscopic one, one always gets a collapse of the wave function.
- prox 6y ago
  So it is a bit like a wave crashing at a beachhead?
  - ben_w 6y ago
    Any analogy we can build from everyday experience to try to explain quantum mechanics is as incorrect as any analogy a 17th century alchemist could use to explain a smartphone. The maths is what it is and does what it does, and if you play with things at that scale you can build a new intuition, but it just isn’t like the macroscopic world.
    - ctdonath 6y ago
      Question then is: why does scaling up from quantum become like the macroscopic world? Just as scaling up from bits and NAND gates can become like virtual reality.
      - ben_w 6y ago
        It takes a degree (or equivalent effort) to understand everything on the path from NAND to VR; It looks like a similar amount of effort is needed to fully understand going from QM to macroscopic — though even that much is a guess on my part, as my QM knowledge is PBS Space Time videos on YouTube and some of the Brilliant.org courses.
      - OkayPhysicist 6y ago
        Bell curves. When you look at the distributions, it becomes pretty clear that as you add lots of particles you approach classical physics pretty quickly, because the likelyhood of the average behavior to differ from the expected behavior falls towards zero very fast.
- Enginerrrd 6y ago
  Honestly, assuming the linearity of QM, the many worlds interpretation also provides an answer to this IMO. Your observations, thoughts, etc, exist in the domain of eigenvalues of measurement operators applied to a quantum state and the universe itself is a massively entangled state vector in hilbert space. There is no decoherence at all. Instead, anything you can conceive of doing or measuring is actually a linear quantum operation taking a well described state in hilbert space from one state to another. What we actually see, and observe, and perceive is all just computation in the domain of the eigenvalues rather than the underlying true state of the universe as a vector in hilbert space. The fact that you remember a consistent history is because your 'remembering' is itself one such eigenvalue of a measurement operator applied to a massively entangled set of histories and you only think you get one result because that thinking itself occurs in the domain of the eigenvalues rather than the true state.
CuriouslyC 6y ago
I can't help but feel that the accuracy of the mathematics misleads us as to our degree of understanding of the system. Perhaps at the scale we're considering, the observer is coupled to the outcome.
- ncallaway 6y ago
  > the observer is coupled to the outcome. Maybe I've misunderstood something, but isn't that the explanation of an Everettian many worlds interpretation? That the observed "collapse" is really just the entangling of the observer with the system?
bopbeepboop 6y ago
> What is utterly baffling and puzzling is that we only ever see one particular outcome. Why is this baffling? I legitimately don’t understand: we’ve never seen anything else. If we’re “baffled” by reality, the naive interpretation would be our models have become faulty. Reading QM, and particularly after we learned assuming non-determinism was purely extraneous, I can’t escape the feeling it’s simply muddled thought — particularly in regards to confusing estimation and reality.
jules 6y ago
I don't understand what's so surprising about only ever seeing one particular outcome. Suppose you have a robot that can observe some spin. We put the robot in a box together with a spin and make it measure the spin. Now the robot's mind plus the spin is a superposition of ("I measured up", spin is actually up) and ("I measured down", spin is actually down), but in no case is the robot's mind in a state "I measured both up and down". To me, the weird part is that there are phenomena (like the EPR paradox) where the final result cannot be explained by adding up the probabilities of the individual possibilities, but has to be explained by adding up of probability amplitudes of the individual possibilities and then taking the probability of that.
- lisper 6y ago
  > ("I measured up", spin is actually up) IMHO this is the fundamental mistake people make: conflating "I measured spin up" with "spin is actually up". Think about it: what is the evidence that there is actually a correspondence between a measurement and some external reality? There is only one possible answer to that: you can correlate this measurement with the outcomes of other measurements. For example, if you measure the same particle in the same basis twice in a row you will get the same result. But there is a problem with that: if you actually look at the details you will find that it is actually not possible to measure the same particle in the same basis twice in a row because actually making a measurement requires entangling the particle with a macroscopic system, and you can only do that once. The best you can do is run a particle through a series of filters and look at where it ended up. You can then retrodict that the particle went one way or went another way, but you cannot actually measure its trajectory. In fact, you cannot even know that there even is a particle in your apparatus until the end when you actually measure it. So the only thing you are left with at the end is a single actual measurement, and a macroscopic arrangement of some experimental setup about which you can tell a consistent story retroactively, but where you do not and cannot possibly have any direct evidence that your story is actually true, i.e. that the particle "actually" was spin up. And this is exactly what QM predicts: the consistent outcomes of measurements is not the result of the particle "actually" being spin up or spin down, but because the macroscopic systems (like humans) which compare the outcomes of their measurements are mutually entangled with each other and so decohere into classically consistent states. So if I ask you what you see as the outcome of the experiment, QM predicts that my perception of your answer will match my perception of the outcome. But it emphatically does NOT say that this outcome is actually real.
wnoise 6y ago
> What is utterly baffling and puzzling is that we only ever see one particular outcome. Decoherence cannot explain that and nothing in quantum mechanics explains that. The blog post has a link to a transcript of Sidney Coleman's lecture "Quantum Mechanics in Your Face". https://arxiv.org/abs/2011.12671 https://arxiv.org/abs/2011.12671 The section on the cloud chamber through to the end does assert a reasonable answer this. (pp 9-12).

cjfd 6y ago

"What is utterly baffling and puzzling is that we only ever see one particular outcome." Actually, there is an answer to this. See e.g. https://arxiv.org/abs/quant-ph/0503009 https://arxiv.org/abs/quant-ph/0503009 tldr: if information is transferred from a microscopic quantum state to a macroscopic one, one always gets a collapse of the wave function.

prox 6y ago
So it is a bit like a wave crashing at a beachhead?
- ben_w 6y ago
  Any analogy we can build from everyday experience to try to explain quantum mechanics is as incorrect as any analogy a 17th century alchemist could use to explain a smartphone. The maths is what it is and does what it does, and if you play with things at that scale you can build a new intuition, but it just isn’t like the macroscopic world.
  - ctdonath 6y ago
    Question then is: why does scaling up from quantum become like the macroscopic world? Just as scaling up from bits and NAND gates can become like virtual reality.
    - ben_w 6y ago
      It takes a degree (or equivalent effort) to understand everything on the path from NAND to VR; It looks like a similar amount of effort is needed to fully understand going from QM to macroscopic — though even that much is a guess on my part, as my QM knowledge is PBS Space Time videos on YouTube and some of the Brilliant.org courses.
    - OkayPhysicist 6y ago
      Bell curves. When you look at the distributions, it becomes pretty clear that as you add lots of particles you approach classical physics pretty quickly, because the likelyhood of the average behavior to differ from the expected behavior falls towards zero very fast.
Enginerrrd 6y ago
Honestly, assuming the linearity of QM, the many worlds interpretation also provides an answer to this IMO. Your observations, thoughts, etc, exist in the domain of eigenvalues of measurement operators applied to a quantum state and the universe itself is a massively entangled state vector in hilbert space. There is no decoherence at all. Instead, anything you can conceive of doing or measuring is actually a linear quantum operation taking a well described state in hilbert space from one state to another. What we actually see, and observe, and perceive is all just computation in the domain of the eigenvalues rather than the underlying true state of the universe as a vector in hilbert space. The fact that you remember a consistent history is because your 'remembering' is itself one such eigenvalue of a measurement operator applied to a massively entangled set of histories and you only think you get one result because that thinking itself occurs in the domain of the eigenvalues rather than the true state.

CuriouslyC 6y ago

I can't help but feel that the accuracy of the mathematics misleads us as to our degree of understanding of the system. Perhaps at the scale we're considering, the observer is coupled to the outcome.

ncallaway 6y ago
> the observer is coupled to the outcome. Maybe I've misunderstood something, but isn't that the explanation of an Everettian many worlds interpretation? That the observed "collapse" is really just the entangling of the observer with the system?

bopbeepboop 6y ago

> What is utterly baffling and puzzling is that we only ever see one particular outcome. Why is this baffling? I legitimately don’t understand: we’ve never seen anything else. If we’re “baffled” by reality, the naive interpretation would be our models have become faulty. Reading QM, and particularly after we learned assuming non-determinism was purely extraneous, I can’t escape the feeling it’s simply muddled thought — particularly in regards to confusing estimation and reality.

jules 6y ago

I don't understand what's so surprising about only ever seeing one particular outcome. Suppose you have a robot that can observe some spin. We put the robot in a box together with a spin and make it measure the spin. Now the robot's mind plus the spin is a superposition of ("I measured up", spin is actually up) and ("I measured down", spin is actually down), but in no case is the robot's mind in a state "I measured both up and down". To me, the weird part is that there are phenomena (like the EPR paradox) where the final result cannot be explained by adding up the probabilities of the individual possibilities, but has to be explained by adding up of probability amplitudes of the individual possibilities and then taking the probability of that.

lisper 6y ago
> ("I measured up", spin is actually up) IMHO this is the fundamental mistake people make: conflating "I measured spin up" with "spin is actually up". Think about it: what is the evidence that there is actually a correspondence between a measurement and some external reality? There is only one possible answer to that: you can correlate this measurement with the outcomes of other measurements. For example, if you measure the same particle in the same basis twice in a row you will get the same result. But there is a problem with that: if you actually look at the details you will find that it is actually not possible to measure the same particle in the same basis twice in a row because actually making a measurement requires entangling the particle with a macroscopic system, and you can only do that once. The best you can do is run a particle through a series of filters and look at where it ended up. You can then retrodict that the particle went one way or went another way, but you cannot actually measure its trajectory. In fact, you cannot even know that there even is a particle in your apparatus until the end when you actually measure it. So the only thing you are left with at the end is a single actual measurement, and a macroscopic arrangement of some experimental setup about which you can tell a consistent story retroactively, but where you do not and cannot possibly have any direct evidence that your story is actually true, i.e. that the particle "actually" was spin up. And this is exactly what QM predicts: the consistent outcomes of measurements is not the result of the particle "actually" being spin up or spin down, but because the macroscopic systems (like humans) which compare the outcomes of their measurements are mutually entangled with each other and so decohere into classically consistent states. So if I ask you what you see as the outcome of the experiment, QM predicts that my perception of your answer will match my perception of the outcome. But it emphatically does NOT say that this outcome is actually real.

wnoise 6y ago

> What is utterly baffling and puzzling is that we only ever see one particular outcome. Decoherence cannot explain that and nothing in quantum mechanics explains that. The blog post has a link to a transcript of Sidney Coleman's lecture "Quantum Mechanics in Your Face". https://arxiv.org/abs/2011.12671 https://arxiv.org/abs/2011.12671 The section on the cloud chamber through to the end does assert a reasonable answer this. (pp 9-12).