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Quantum trajectories more or less have the usual Copenhagen interpretation built in, so they don't really solve the old interpretation problems any more than de

Quantum trajectories more or less have the usual Copenhagen interpretation built in, so they don't really solve the old interpretation problems any more than decoherence does. Although they can be a nice way to understand some experiments, in particular how conditional probabilities of a set of measurement results obtained in sequence occur, I'm not sure if it's good to present it as some fundamental insight in popular articles.

jeremyjh 7y ago
This seems to be the opposite of what the article is saying, or implying. I read it as saying that there is no need for an interpretation, because there is no wave function collapse; the particle can be described in precise terms.
- chrischen 7y ago
  It was buried way deep in the article, but: > But what exactly is this trajectory? One thing is clear: It’s not like a classical trajectory, meaning a path taken in space. It’s more like the path taken through the abstract space of possible states the system might have, which is called Hilbert space. QTT is not a definite prediction of classical physical trajectory.
  - simonh 7y ago
    Although classical physical trajectory is one if the possible states QTT helps us predict. It’s more than that, not less.
- n4r9 7y ago
  To be fair in both everettian and de broglie bohm interpretations there is no physical wave function collapse. Even in neo-Copenhagen interpretations like QBism the apparent collapse is merely a reflection of an agent's belief update process.
  - kgwgk 7y ago
    QBism has a cool name, but I think it's not as revolutionary as it may seem at first sight. There are two kinds of uncertainty about a quantum system: the "classical" ignorance about what is the true quantum state and the non-determinism of the outcome of measurements even if the quantum state is perfectly known (note that only in this case the system can be described using a wave function). "Up to an overall unitary ‘readjustment’ of one’s final probabilistic beliefs [...] quantum collapse is precisely Bayesian conditionalization." I'd say that this 'readjustment' is the collapse with another name. "Quantum measurement is nothing more, and nothing less, than a refinement and a readjustment of one’s initial state of belief. [...] Let us look at two limiting cases of efficient measurements. In the first, we imagine an observer whose initial belief structure ρ = |ψ⟩⟨ψ| is a maximally sharp state of belief. By this account, no measurement whatsoever can refine it. [...] The only state change that can come about from a measurement must be purely of the mental-readjustment sort: We learn nothing new; we just change what we can predict as a consequence of the side effects of our experimental intervention. That is to say, there is a sense in which the measurement is solely disturbance." Ok, so when you do a measurement on a pure state (i.e. when the knowledge about the quantum state is maximal and cannot be refined by Bayesian updating): instead of the "wave function collapse" of “standard” QM (the wave function changes to the eigenstate corresponding to the outcome of the measurement) you have a "mental-readjustment" (because as a side effect of the measurement now you describe the system using the same wave function as in standard QM). What are the problems with the "wave function collapse" that are solved by calling it "mental readjustment"? https://www.perimeterinstitute.ca/personal/cfuchs/Oviedo.pdf https://www.perimeterinstitute.ca/personal/cfuchs/Oviedo.pdf
    - n4r9 7y ago
      I think the first thing to say is that the mathematics of quantum theory is the same no matter what interpretation you adhere to (with a small caveat for things like gravity-induced collapse). So, yes, collapse is unavoidable as a mathematical operation which we apply when making predictions about future events. Where interpretations differ is in the physical content they assign to mathematical objects and operations. In some interpretations the wave function is "really objectively out there", but in others the wave function is "just a good way to store my beliefs about the future". If you adhere to the former case, then either collapse is merely apparent (ie. many-worlds) or it's a real mechanical thing that is going on in the outside world. If you adhere to the latter case then the collapse process is merely an act of updating beliefs. Now, if collapse is a real physical process then you run into the measurement problem and "Wigner's friend" style problems. At what point does collapse occur and what induces it? Why is quantum evolution reversible right up until the point of collapse? Is there a combined wave function describing both the observer and the system, and does that wave function collapse? etc... In QBism these issues do not arise because it makes perfect classical sense for, say, an observer of an observer to have beliefs about what that other observer believes.

jeremyjh 7y ago

This seems to be the opposite of what the article is saying, or implying. I read it as saying that there is no need for an interpretation, because there is no wave function collapse; the particle can be described in precise terms.

chrischen 7y ago
It was buried way deep in the article, but: > But what exactly is this trajectory? One thing is clear: It’s not like a classical trajectory, meaning a path taken in space. It’s more like the path taken through the abstract space of possible states the system might have, which is called Hilbert space. QTT is not a definite prediction of classical physical trajectory.
- simonh 7y ago
  Although classical physical trajectory is one if the possible states QTT helps us predict. It’s more than that, not less.
n4r9 7y ago
To be fair in both everettian and de broglie bohm interpretations there is no physical wave function collapse. Even in neo-Copenhagen interpretations like QBism the apparent collapse is merely a reflection of an agent's belief update process.
- kgwgk 7y ago
  QBism has a cool name, but I think it's not as revolutionary as it may seem at first sight. There are two kinds of uncertainty about a quantum system: the "classical" ignorance about what is the true quantum state and the non-determinism of the outcome of measurements even if the quantum state is perfectly known (note that only in this case the system can be described using a wave function). "Up to an overall unitary ‘readjustment’ of one’s final probabilistic beliefs [...] quantum collapse is precisely Bayesian conditionalization." I'd say that this 'readjustment' is the collapse with another name. "Quantum measurement is nothing more, and nothing less, than a refinement and a readjustment of one’s initial state of belief. [...] Let us look at two limiting cases of efficient measurements. In the first, we imagine an observer whose initial belief structure ρ = |ψ⟩⟨ψ| is a maximally sharp state of belief. By this account, no measurement whatsoever can refine it. [...] The only state change that can come about from a measurement must be purely of the mental-readjustment sort: We learn nothing new; we just change what we can predict as a consequence of the side effects of our experimental intervention. That is to say, there is a sense in which the measurement is solely disturbance." Ok, so when you do a measurement on a pure state (i.e. when the knowledge about the quantum state is maximal and cannot be refined by Bayesian updating): instead of the "wave function collapse" of “standard” QM (the wave function changes to the eigenstate corresponding to the outcome of the measurement) you have a "mental-readjustment" (because as a side effect of the measurement now you describe the system using the same wave function as in standard QM). What are the problems with the "wave function collapse" that are solved by calling it "mental readjustment"? https://www.perimeterinstitute.ca/personal/cfuchs/Oviedo.pdf https://www.perimeterinstitute.ca/personal/cfuchs/Oviedo.pdf
  - n4r9 7y ago
    I think the first thing to say is that the mathematics of quantum theory is the same no matter what interpretation you adhere to (with a small caveat for things like gravity-induced collapse). So, yes, collapse is unavoidable as a mathematical operation which we apply when making predictions about future events. Where interpretations differ is in the physical content they assign to mathematical objects and operations. In some interpretations the wave function is "really objectively out there", but in others the wave function is "just a good way to store my beliefs about the future". If you adhere to the former case, then either collapse is merely apparent (ie. many-worlds) or it's a real mechanical thing that is going on in the outside world. If you adhere to the latter case then the collapse process is merely an act of updating beliefs. Now, if collapse is a real physical process then you run into the measurement problem and "Wigner's friend" style problems. At what point does collapse occur and what induces it? Why is quantum evolution reversible right up until the point of collapse? Is there a combined wave function describing both the observer and the system, and does that wave function collapse? etc... In QBism these issues do not arise because it makes perfect classical sense for, say, an observer of an observer to have beliefs about what that other observer believes.