One person’s “occam’s razor” may be description length, another’s may be elegance, and a third person’s may be “avoiding having too much info inside your system” (as some anti-MW people argue). I think discussions like “what’s real” need to be done thoughtfully, otherwise people tend to argue past each other, and come off overconfident/ underinformed.
To be fair, I did use language like this so I shouldn’t be talking—but I used it tongue-in-cheek, and the real motivation given in the above is not “the DM is a more fundamental notion” but “DM lets you make concrete the very suggestive analogy between quantum phase and probability”, which you would probably agree with.
For what it’s worth, there are “different layers of theory” (often scale-dependent), like classical vs. quantum vs. relativity, etc., where there I think it’s silly to talk about “ontological truth”. But these theories are local conceptual optima among a graveyard of “outdated” theories, that are strictly conceptually inferior to new ones: examples are heliocentrism (and Ptolemy’s epycycles), the ether, etc.
Interestingly, I would agree with you (with somewhat low confidence) that in this question there is a consensus among physicists that one picture is simply “more correct” in the sense of giving theoretically and conceptually more elegant/ precise explanations. Except your sign is wrong: this is the density matrix picture (the wavefunction picture is genuinely understood as “not the right theory”, but still taught and still used in many contexts where it doesn’t cause issues).
I also think that there are two separate things that you can discuss.
Should you think of thermodynamics, probability, and things like thermal baths as fundamental to your theory or incidental epistemological crutches to model the world at limited information?
Assuming you are studying a “non-thermodynamic system with complete information”, where all dynamics is invertible over long timescales, should you use wave functions or density matrices?
Note that for #1, you should not think of a density function as a probability distribution on quantum states (see the discussion with Optimization Process in the comments), and this is a bad intuition pump. Instead, the thing that replaces probability distributions in quantum mechanics is a density matrix.
I think a charitable interpertation of your criticism would be a criticism of #1 (putting limited-info dynamics—i.e., quantum thermodynamics) as primary to “invertible dynamics”. Here there is a debate to be had.
I think there is not really a debate in #2: even in invertible QM (no probability), you need to use density matrices if you want to study different subsystems (e.g. when modeling systems existing in an infinite, but not thermodynamic universe you need this language, since restricting a wavefunction to a subsystem makes it mixed). There’s also a transposed discussion, that I don’t really understand, of all of this in field theory: when do you have fields vs. operators vs. other more complicated stuff, and there is some interesting relationship to how you conceptualize “boundaries”—but this is not what we’re discussing. So you really can’t get away from using density matrices even in a nice invertible universe, as soon as you want to relate systems to subsystems.
For question #1 is reasonable (though I don’t know how productive) to discuss what is “primary”. I think (but here I am really out of my depth) that people who study very “fundamental” quantum phenomena increasingly use a picture with a thermal bath (e.g. I vaguely remember this happening in some lectures here). At the same time, it’s reasonable to say that “invertible” QM phenomena are primary and statistical phenomena are ontological epiphenomena on top of this. While this may be a philosophical debate, I don’t think it’s a physical one, since the two pictures are theoretically interchangeable (as I mentioned, there is a canonical way to get thermodynamics from unitary QM as a certain “optimal lower bound on information dynamics”, appropriately understood).
Still, as soon as you introduce the notion of measurement, you cannot get away from thermodynamics. Measurement is an inherently information-destroying operation, and iiuc can only be put “into theory” (rather than being an arbitrary add-on that professors tell you about) using the thermodynamic picture with nonunitary operators on density matrices.
people who study very “fundamental” quantum phenomena increasingly use a picture with a thermal bath
Maybe talking about the construction of pointer states? That linked paper does it just as you might prefer, putting the Boltzmann distribution into a density matrix. But of course you could rephrase it as a probability distribution over states and the math goes through the same, you’ve just shifted the vibe from “the Boltzmann distribution is in the territory” to “the Boltzmann distribution is in the map.”
Still, as soon as you introduce the notion of measurement, you cannot get away from thermodynamics. Measurement is an inherently information-destroying operation, and iiuc can only be put “into theory” (rather than being an arbitrary add-on that professors tell you about) using the thermodynamic picture with nonunitary operators on density matrices.
Sure, at some level of description it’s useful to say that measurement is irreversible, just like at some level of description it’s useful to say entropy always increases. Just like with entropy, it can be derived from boundary conditions + reversible dynamics + coarse-graining. Treating measurements as reversible probably has more applications than treating entropy as reversible, somewhere in quantum optics / quantum computing.
Thanks for the reference—I’ll check out the paper (though there are no pointer variables in this picture inherently).
I think there is a miscommunication in my messaging. Possibly through overcommitting to the “matrix” analogy, I may have given the impression that I’m doing something I’m not. In particular, the view here isn’t a controversial one—it has nothing to do with Everett or einselection or decoherence. Crucially, I am saying nothing at all about quantum branches.
I’m now realizing that when you say map or territory, you’re probably talking about a different picture where quantum interpretation (decoherence and branches) is foregrounded. I’m doing nothing of the sort, and as far as I can tell never making any “interpretive” claims.
All the statements in the post are essentially mathematically rigorous claims which say what happens when you
start with the usual QM picture, and posit that
your universe divides into at least two subsystems, one of which you’re studying
one of the subsystems your system is coupled to is a minimally informative infinite-dimensional environment (i.e., a bath).
Both of these are mathematically formalizable and aren’t saying anything about how to interpret quantum branches etc. And the Lindbladian is simply a useful formalism for tracking the evolution of a system that has these properties (subdivisions and baths). Note that (maybe this is the confusion?) subsystem does not mean quantum branch, or decoherence result. “Subsystem” means that we’re looking at these particles over here, but there are also those particles over there (i.e. in terms of math, your Hilbert space is a tensor product Sytem1⊗System2.
Also, I want to be clear that we can and should run this whole story without ever using the term “probability distribution” in any of the quantum-thermodynamics concepts. The language to describe a quantum system as above (system coupled with a bath) is from the start a language that only involves density matrices, and never uses the term “X is a probability distribution of Y”. Instead you can get classical probability distributions to map into this picture as a certain limit of these dynamics.
As to measurement, I think you’re once again talking about interpretation. I agree that in general, this may be tricky. But what is once again true mathematically is that if you model your system as coupled to a bath then you can set up behaviors that behave exactly as you would expect from an experiment from the point of view of studying the system (without asking questions about decoherence).
One person’s “occam’s razor” may be description length, another’s may be elegance, and a third person’s may be “avoiding having too much info inside your system” (as some anti-MW people argue). I think discussions like “what’s real” need to be done thoughtfully, otherwise people tend to argue past each other, and come off overconfident/ underinformed.
To be fair, I did use language like this so I shouldn’t be talking—but I used it tongue-in-cheek, and the real motivation given in the above is not “the DM is a more fundamental notion” but “DM lets you make concrete the very suggestive analogy between quantum phase and probability”, which you would probably agree with.
For what it’s worth, there are “different layers of theory” (often scale-dependent), like classical vs. quantum vs. relativity, etc., where there I think it’s silly to talk about “ontological truth”. But these theories are local conceptual optima among a graveyard of “outdated” theories, that are strictly conceptually inferior to new ones: examples are heliocentrism (and Ptolemy’s epycycles), the ether, etc.
Interestingly, I would agree with you (with somewhat low confidence) that in this question there is a consensus among physicists that one picture is simply “more correct” in the sense of giving theoretically and conceptually more elegant/ precise explanations. Except your sign is wrong: this is the density matrix picture (the wavefunction picture is genuinely understood as “not the right theory”, but still taught and still used in many contexts where it doesn’t cause issues).
I also think that there are two separate things that you can discuss.
Should you think of thermodynamics, probability, and things like thermal baths as fundamental to your theory or incidental epistemological crutches to model the world at limited information?
Assuming you are studying a “non-thermodynamic system with complete information”, where all dynamics is invertible over long timescales, should you use wave functions or density matrices?
Note that for #1, you should not think of a density function as a probability distribution on quantum states (see the discussion with Optimization Process in the comments), and this is a bad intuition pump. Instead, the thing that replaces probability distributions in quantum mechanics is a density matrix.
I think a charitable interpertation of your criticism would be a criticism of #1 (putting limited-info dynamics—i.e., quantum thermodynamics) as primary to “invertible dynamics”. Here there is a debate to be had.
I think there is not really a debate in #2: even in invertible QM (no probability), you need to use density matrices if you want to study different subsystems (e.g. when modeling systems existing in an infinite, but not thermodynamic universe you need this language, since restricting a wavefunction to a subsystem makes it mixed). There’s also a transposed discussion, that I don’t really understand, of all of this in field theory: when do you have fields vs. operators vs. other more complicated stuff, and there is some interesting relationship to how you conceptualize “boundaries”—but this is not what we’re discussing. So you really can’t get away from using density matrices even in a nice invertible universe, as soon as you want to relate systems to subsystems.
For question #1 is reasonable (though I don’t know how productive) to discuss what is “primary”. I think (but here I am really out of my depth) that people who study very “fundamental” quantum phenomena increasingly use a picture with a thermal bath (e.g. I vaguely remember this happening in some lectures here). At the same time, it’s reasonable to say that “invertible” QM phenomena are primary and statistical phenomena are ontological epiphenomena on top of this. While this may be a philosophical debate, I don’t think it’s a physical one, since the two pictures are theoretically interchangeable (as I mentioned, there is a canonical way to get thermodynamics from unitary QM as a certain “optimal lower bound on information dynamics”, appropriately understood).
Still, as soon as you introduce the notion of measurement, you cannot get away from thermodynamics. Measurement is an inherently information-destroying operation, and iiuc can only be put “into theory” (rather than being an arbitrary add-on that professors tell you about) using the thermodynamic picture with nonunitary operators on density matrices.
Maybe talking about the construction of pointer states? That linked paper does it just as you might prefer, putting the Boltzmann distribution into a density matrix. But of course you could rephrase it as a probability distribution over states and the math goes through the same, you’ve just shifted the vibe from “the Boltzmann distribution is in the territory” to “the Boltzmann distribution is in the map.”
Sure, at some level of description it’s useful to say that measurement is irreversible, just like at some level of description it’s useful to say entropy always increases. Just like with entropy, it can be derived from boundary conditions + reversible dynamics + coarse-graining. Treating measurements as reversible probably has more applications than treating entropy as reversible, somewhere in quantum optics / quantum computing.
Thanks for the reference—I’ll check out the paper (though there are no pointer variables in this picture inherently).
I think there is a miscommunication in my messaging. Possibly through overcommitting to the “matrix” analogy, I may have given the impression that I’m doing something I’m not. In particular, the view here isn’t a controversial one—it has nothing to do with Everett or einselection or decoherence. Crucially, I am saying nothing at all about quantum branches.
I’m now realizing that when you say map or territory, you’re probably talking about a different picture where quantum interpretation (decoherence and branches) is foregrounded. I’m doing nothing of the sort, and as far as I can tell never making any “interpretive” claims.
All the statements in the post are essentially mathematically rigorous claims which say what happens when you
start with the usual QM picture, and posit that
your universe divides into at least two subsystems, one of which you’re studying
one of the subsystems your system is coupled to is a minimally informative infinite-dimensional environment (i.e., a bath).
Both of these are mathematically formalizable and aren’t saying anything about how to interpret quantum branches etc. And the Lindbladian is simply a useful formalism for tracking the evolution of a system that has these properties (subdivisions and baths). Note that (maybe this is the confusion?) subsystem does not mean quantum branch, or decoherence result. “Subsystem” means that we’re looking at these particles over here, but there are also those particles over there (i.e. in terms of math, your Hilbert space is a tensor product Sytem1⊗System2.
Also, I want to be clear that we can and should run this whole story without ever using the term “probability distribution” in any of the quantum-thermodynamics concepts. The language to describe a quantum system as above (system coupled with a bath) is from the start a language that only involves density matrices, and never uses the term “X is a probability distribution of Y”. Instead you can get classical probability distributions to map into this picture as a certain limit of these dynamics.
As to measurement, I think you’re once again talking about interpretation. I agree that in general, this may be tricky. But what is once again true mathematically is that if you model your system as coupled to a bath then you can set up behaviors that behave exactly as you would expect from an experiment from the point of view of studying the system (without asking questions about decoherence).