Those talks are interesting and make some valuable points but I don't think they really address the elephant in the room. For a no collapse interpretation of QM to be correct the importance of macroscopic superposition states to empirical validity must be derived not assumed and the theory on its own can't explain why these states should play any special role in predictions.
And it's not enough merely to just identify some special mathematical property these states have with respect to the dynamics but -- unless it wants to add that as an extra physical principle undermining the claimed simplicity of no-collapse views -- you need to explain why that property is the one that should be relevant to making predictions.
To sharpen the problem note that given some complete wave-function in some Hilbert space describing the universe I can decompose the wavefunction into an infinitary sum in a whole lots of ways. Indeed, it's relatively trivial to decompose a function under an L^2 (and I suspect L^p for any p \geq 1) metric into a sum of functions which intuitively implement whatever Turing machine I want*. And it's not a priori obvious that the decomposition into something like semi-classical histories is the one you should use to figure out what observations to predict rather than some jury rigged decomposition into Turing machines implementing whatever observer you feel like.
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*: Basically, we use translations, negations and scalings of a function which intuitively describes the operation of the Turing machine to sum to the desired function. The fact that it's possible is basically just the same result about the fact that Lebesque measure lets us approximate integrals with square functions. Just make sure that the level you use to encode a 1 decreases as both t and the square of the tape it's on increase so it's like integrating using square approximations. And with a linear dynamics if we converge to the overall solution in norm then the infinite sum is a solution and we can regard the partial sums as approximate solutions with everything behaving nicely.
In vN's proof of the quantum ergodic theorem he defines coarse grained operators that can be regarded as macroscopic observables (ie classical reality). Then one can show, under weak conditions on the Hamiltonian, etc., that systems evolve into (decohered) superpositions of the corresponding states.
IF you accept that decoherence accounts for measurement outcomes (the phenomenology perceived by the observer) and the emergence of a semiclassical reality, then the next question is why we need to impose vN's collapse postulate. If one eliminates this postulate, then you get MW.
Maybe a better way of putting the problem is that the logical form of the result you need isn't that there exists one decomposition which predicts some stuff about observers in the components of that decomposition but that ALL 'valid' decompositions that in some sense represent observers give rise to observers whose observations have the right form. So far you are only showing the existence of one decomposition.
So you either need an extra assumption which says that only the kind of decompositions that you are considering count as valid or a much stronger result that tries to give an a priori account of which functions in the Hilbert space represent appropriate observers and show that those all must be semi-classical.
And it's not enough to show that only semi-classical decompositions have something that resembles a classical history because you are still presupposing a preferred status for certain decompositions without justification.
It's not that you need the collapse postulate per se but you need something to explain why it's semi-classical reality which is what predicts observations.
If you are arguing that MW is superior because it makes less assumptions then you can't assume that the way you derive predictions from the theory is to look for a decomposition into semiclassical pieces. You need to derive the fact that this decomposition and not some other one is what predicts observations entirely from the theory and you need extra assumptions to do that.
You can't just assume that semiclassical descriptions have a privleges place in predicting observations.
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Now it's totally plausible to say ok; the complete theory is MW plus the extra assumption that what predicts observations is semi-classical descriptions. Fine that works but that's a bit more complicated and it's no longer obviously simpler than competitors. Also if you really have an infinite state space there are some complications about deriving the born rule but I presume that's what you were glossing over.
1. The emergence of a superposition of semiclassical states is a *dynamical* consequence, although it depends only weakly on choice of Hamiltonian. It's not an input to the theory, it's a consequence of the dynamics. That's why the vN quantum ergodic theorem is very important - although most people have just assumed the results without even knowing about the existence of the theorem. (It was forgotten and the paper only existed in German until translated into English in 2010!)
2. Why observers on these semiclassical branches observe the Born rule to be true (ie probabilistic QM outcomes) is a separate question, which I and others have worked on. Perhaps this is what you mean by QM predictions?
Sure that's great and all but why do we care about these semiclassical branches in the first place? If you just handed me the theory I could note that certain decompositions have mathematical property A with respect to the dynamics (the result you mention in 1) but so what? There are infinitely many mathematical properties so why should the decomposition that has property A have special status in predicting observations?
The theoey needs to predict observations without starting from the assumption that observations come from descriptions that are semiclassical. That can either be an extra assumption or must be derived.
These semiclassical branches exhibit the phenomenology that we observe in the real world. We detect objects that are localized in space, have well-defined energies (within some narrow band), etc. It's good that a no-collapse formulation produces outcomes that resemble our observations, without positing a priori a "classical reality" (cf Copenhagen).
Now suppose you conduct a quantum experiment (eg Stern-Gerlach spin measurement). Does the no-collapse version of QM explain the Born rule probabilities? If yes, then you've shown that the no-collapse theory reproduces the phenomenology of QM.
But the theory needs to predict that most observers see something like the real world not just that some do.
I mean if I just gave a theory that said everything mathematically possible happens it wouldn't be a good theory because it includes in all those possibilities ones which agree with observation. A theory is tested by what it excludes as much as what it includes.
I'm a physics experimentalist and have never worried (thought much) about QM interpretations. Use which ever model makes it easier for you to do a calculation. (whatever works for you.) As far as measurement and wave function collapse; The simplest process for me to think about is starting with a photon and an electron, and then ending with no photon and the electron in a higher energy state.* And as far as I know we have no model for that process.... how the heck do you cram a big photon into an electron state? Or am I somehow misunderstanding the wavefunction collapse?
*Isn't there also a wave function creation problem? Where there is first no photon and then an electron in a lower energy state and one more photon. A new wavefunction.
>“Many Worlds follows trivially if we require that quantum mechanics applies to every object in the universe.”
*Decoherence* follows trivially if we apply QM uniformly to everything. MWI is another matter entirely. Certainly it's the most straightforward extrapolation of Schrodinger, but history generally shows that naive extrapolations of models beyond what's directly supported by experiment frequently run into trouble. A naive extrapolation of the Standard Model implies matter-antimatter parity, for example, and a naive extrapolation of classical E&M led to infinite self-energy of the electron. From an epistemic perspective, don't you think it's more likely that some undiscovered symmetry-breaking principle selects a single decoherent reality than that we live in an infinite-computational-complexity ensemble of everything happening? Symmetry breaking has a healthy track record, after all. If I was a researcher I'd spend a lot more time looking for that than trying to understand the dynamics of the multiverse.
If decoherence accounts for measurement outcomes (the phenomenology perceived by the observer) and the emergence of a semiclassical reality, then the next question is why we need to impose vN's collapse postulate. If one eliminates this postulate (which was never well-defined, see Wigner's friend arguments, etc.), then you get MW. The remaining problem is to account for the Born rule (apparent probabilisitic outcomes). Some of the links above lead to papers about how the Born rule (probability) emerges in MW.
Yes, MW is a direct extrapolation but it's really only appealing because we otherwise can't answer "well what happens to the unobserved branches" or "where exactly does unitarity break down". I consider that a God-of-the-gaps argument. It might well be right (and of course God might really exist too) and I appreciate that I'm positing a non-parsimonious symmetry-breaking principle, but MWI has conceptual difficulties as well (consistent probability measure, anyone? How low a probability is it physically possible to keep on the books? Does the multiverse have infinite floating-point precision? If not, can't you imagine some kind of probabilistic version of how quantization solved the ultraviolet catastrophe?). I think that epistemic humility dictates a measured shoulder-shrug and a reminder that we only have direct evidence for a single decoherent reality.
How are you defining decoherence? Most formalizations I've seen require you to assume a semi-classical environment to derive the result about decoherence.
“Many Worlds follows trivially if we require that quantum mechanics applies to every object in the universe.”
Are you saying you favor the many worlds interpretation as opposed to the Copenhagen? To a layman like me that sounds like either absurd nonsense (violates the conservation of matter and energy) or else a distinction without a difference. Why not just stick with the phenomenology and admit we don't understand it? [Answer: because it is against human nature.]
Those talks are interesting and make some valuable points but I don't think they really address the elephant in the room. For a no collapse interpretation of QM to be correct the importance of macroscopic superposition states to empirical validity must be derived not assumed and the theory on its own can't explain why these states should play any special role in predictions.
And it's not enough merely to just identify some special mathematical property these states have with respect to the dynamics but -- unless it wants to add that as an extra physical principle undermining the claimed simplicity of no-collapse views -- you need to explain why that property is the one that should be relevant to making predictions.
To sharpen the problem note that given some complete wave-function in some Hilbert space describing the universe I can decompose the wavefunction into an infinitary sum in a whole lots of ways. Indeed, it's relatively trivial to decompose a function under an L^2 (and I suspect L^p for any p \geq 1) metric into a sum of functions which intuitively implement whatever Turing machine I want*. And it's not a priori obvious that the decomposition into something like semi-classical histories is the one you should use to figure out what observations to predict rather than some jury rigged decomposition into Turing machines implementing whatever observer you feel like.
---
*: Basically, we use translations, negations and scalings of a function which intuitively describes the operation of the Turing machine to sum to the desired function. The fact that it's possible is basically just the same result about the fact that Lebesque measure lets us approximate integrals with square functions. Just make sure that the level you use to encode a 1 decreases as both t and the square of the tape it's on increase so it's like integrating using square approximations. And with a linear dynamics if we converge to the overall solution in norm then the infinite sum is a solution and we can regard the partial sums as approximate solutions with everything behaving nicely.
Not sure I understand your point.
In vN's proof of the quantum ergodic theorem he defines coarse grained operators that can be regarded as macroscopic observables (ie classical reality). Then one can show, under weak conditions on the Hamiltonian, etc., that systems evolve into (decohered) superpositions of the corresponding states.
IF you accept that decoherence accounts for measurement outcomes (the phenomenology perceived by the observer) and the emergence of a semiclassical reality, then the next question is why we need to impose vN's collapse postulate. If one eliminates this postulate, then you get MW.
Maybe a better way of putting the problem is that the logical form of the result you need isn't that there exists one decomposition which predicts some stuff about observers in the components of that decomposition but that ALL 'valid' decompositions that in some sense represent observers give rise to observers whose observations have the right form. So far you are only showing the existence of one decomposition.
So you either need an extra assumption which says that only the kind of decompositions that you are considering count as valid or a much stronger result that tries to give an a priori account of which functions in the Hilbert space represent appropriate observers and show that those all must be semi-classical.
And it's not enough to show that only semi-classical decompositions have something that resembles a classical history because you are still presupposing a preferred status for certain decompositions without justification.
It's not that you need the collapse postulate per se but you need something to explain why it's semi-classical reality which is what predicts observations.
If you are arguing that MW is superior because it makes less assumptions then you can't assume that the way you derive predictions from the theory is to look for a decomposition into semiclassical pieces. You need to derive the fact that this decomposition and not some other one is what predicts observations entirely from the theory and you need extra assumptions to do that.
You can't just assume that semiclassical descriptions have a privleges place in predicting observations.
--
Now it's totally plausible to say ok; the complete theory is MW plus the extra assumption that what predicts observations is semi-classical descriptions. Fine that works but that's a bit more complicated and it's no longer obviously simpler than competitors. Also if you really have an infinite state space there are some complications about deriving the born rule but I presume that's what you were glossing over.
We might be talking past each other a bit here.
1. The emergence of a superposition of semiclassical states is a *dynamical* consequence, although it depends only weakly on choice of Hamiltonian. It's not an input to the theory, it's a consequence of the dynamics. That's why the vN quantum ergodic theorem is very important - although most people have just assumed the results without even knowing about the existence of the theorem. (It was forgotten and the paper only existed in German until translated into English in 2010!)
2. Why observers on these semiclassical branches observe the Born rule to be true (ie probabilistic QM outcomes) is a separate question, which I and others have worked on. Perhaps this is what you mean by QM predictions?
https://arxiv.org/abs/1110.0549
https://drive.google.com/file/d/0ByYDxaP-OyVjQTlGQ1lrUjNtbkE/view?usp=sharing&resourcekey=0-o18cDgg_hDAGop2zMimZfw
https://infoproc.blogspot.com/2020/07/discrete-hilbert-space-born-rule-and.html
Sure that's great and all but why do we care about these semiclassical branches in the first place? If you just handed me the theory I could note that certain decompositions have mathematical property A with respect to the dynamics (the result you mention in 1) but so what? There are infinitely many mathematical properties so why should the decomposition that has property A have special status in predicting observations?
The theoey needs to predict observations without starting from the assumption that observations come from descriptions that are semiclassical. That can either be an extra assumption or must be derived.
These semiclassical branches exhibit the phenomenology that we observe in the real world. We detect objects that are localized in space, have well-defined energies (within some narrow band), etc. It's good that a no-collapse formulation produces outcomes that resemble our observations, without positing a priori a "classical reality" (cf Copenhagen).
Now suppose you conduct a quantum experiment (eg Stern-Gerlach spin measurement). Does the no-collapse version of QM explain the Born rule probabilities? If yes, then you've shown that the no-collapse theory reproduces the phenomenology of QM.
But the theory needs to predict that most observers see something like the real world not just that some do.
I mean if I just gave a theory that said everything mathematically possible happens it wouldn't be a good theory because it includes in all those possibilities ones which agree with observation. A theory is tested by what it excludes as much as what it includes.
I'm a physics experimentalist and have never worried (thought much) about QM interpretations. Use which ever model makes it easier for you to do a calculation. (whatever works for you.) As far as measurement and wave function collapse; The simplest process for me to think about is starting with a photon and an electron, and then ending with no photon and the electron in a higher energy state.* And as far as I know we have no model for that process.... how the heck do you cram a big photon into an electron state? Or am I somehow misunderstanding the wavefunction collapse?
*Isn't there also a wave function creation problem? Where there is first no photon and then an electron in a lower energy state and one more photon. A new wavefunction.
>“Many Worlds follows trivially if we require that quantum mechanics applies to every object in the universe.”
*Decoherence* follows trivially if we apply QM uniformly to everything. MWI is another matter entirely. Certainly it's the most straightforward extrapolation of Schrodinger, but history generally shows that naive extrapolations of models beyond what's directly supported by experiment frequently run into trouble. A naive extrapolation of the Standard Model implies matter-antimatter parity, for example, and a naive extrapolation of classical E&M led to infinite self-energy of the electron. From an epistemic perspective, don't you think it's more likely that some undiscovered symmetry-breaking principle selects a single decoherent reality than that we live in an infinite-computational-complexity ensemble of everything happening? Symmetry breaking has a healthy track record, after all. If I was a researcher I'd spend a lot more time looking for that than trying to understand the dynamics of the multiverse.
If decoherence accounts for measurement outcomes (the phenomenology perceived by the observer) and the emergence of a semiclassical reality, then the next question is why we need to impose vN's collapse postulate. If one eliminates this postulate (which was never well-defined, see Wigner's friend arguments, etc.), then you get MW. The remaining problem is to account for the Born rule (apparent probabilisitic outcomes). Some of the links above lead to papers about how the Born rule (probability) emerges in MW.
Yes, MW is a direct extrapolation but it's really only appealing because we otherwise can't answer "well what happens to the unobserved branches" or "where exactly does unitarity break down". I consider that a God-of-the-gaps argument. It might well be right (and of course God might really exist too) and I appreciate that I'm positing a non-parsimonious symmetry-breaking principle, but MWI has conceptual difficulties as well (consistent probability measure, anyone? How low a probability is it physically possible to keep on the books? Does the multiverse have infinite floating-point precision? If not, can't you imagine some kind of probabilistic version of how quantization solved the ultraviolet catastrophe?). I think that epistemic humility dictates a measured shoulder-shrug and a reminder that we only have direct evidence for a single decoherent reality.
How are you defining decoherence? Most formalizations I've seen require you to assume a semi-classical environment to derive the result about decoherence.
“Many Worlds follows trivially if we require that quantum mechanics applies to every object in the universe.”
Are you saying you favor the many worlds interpretation as opposed to the Copenhagen? To a layman like me that sounds like either absurd nonsense (violates the conservation of matter and energy) or else a distinction without a difference. Why not just stick with the phenomenology and admit we don't understand it? [Answer: because it is against human nature.]
So, is many worlds your preferred interpretation of quantum mechanics?