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).
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).