In favour of this de-bugging. One of the other glaring omissions from the sequence is discussion of modal interpretations of quantum mechanics. These are formally very similar to MWI (there is a wave function for the universe, there is no collapse) but the “many worlds” are interpreted as possible worlds (or universes), only one of which is actual. This approach has a lot going for it, common-sense wise.
Modalism has its place in a discussion of the options. But in fact my call for “debugging” was not aimed at reforming the account of QM provided by the Sequence. The arguments about QM serve to illustrate various general points—e.g. “think like reality”—and I’m saying that a functional substitute for all that should be constructed, or at least outlined. We should at least have an idea of what could take the Sequence’s place in the flow of argument, if one were to remove it.
Some thoughts on modal interpretations:
The concept of a modal interpretation is even vaguer in its implications than many-worlds and retrocausal interpretations. The only unifying concept seems to be that other worlds exist in the discourse, but they are purely counterfactual and play no role in explaining anything that happens in the one actual world.
There are various theorems (“Hardy theorems”) proving that an ontological theory can’t assign definite values to all observables in all quantum states, such that all QM expectations are satisfied simultaneously. “Antirealists” like to use this as evidence that you can’t make an objective theory that accounts for QM. But you never perform all possible measurements simultaneously; all that matters is that what the theory says about position when position is measured matches what QM says, and the same for other observables. At other times, position can be doing whatever is required by the logic of the new theory, it can even be absent ontologically.
The modalists have brought all this to the fore and they even have a few technical insights about the construction of a full proper theory, but so far as I can see, these insights aren’t comprehensive enough to single out an ontologically distinctive class of theory, compared to many-worlds or retrocausality. Bohmian mechanics, especially in its wavefunction-less “nomological” form, is a modal interpretation in the sense that, e.g. Bohmian momentum behaves like quantum momentum only when a momentum measurement is occurring. (The Bohmian mechanics of the measurement interaction forces it to behave appropriately.)
You could even argue that many worlds is modal! - in the technical sense that a “world” or “branch” which is an eigenstate of some observable will not provide an associated eigenvalue for a complementary observable.
The concept of a modal interpretation is even vaguer in its implications than many-worlds and retrocausal interpretations. The only unifying concept seems to be that other worlds exist in the discourse, but they are purely counterfactual and play no role in explaining anything that happens in the one actual world.
I don’t agree that the concept of a modal interpretation is vague. The basic concept is that a quantum system can have a physical property with a definite value without its wavefunction necessarily having to be in an eigenstate of the corresponding operator. So the eigenstate-eigenvalue link is not bidirectional. That’s basically it.
The only vagueness is that there are then multiple interpretations, each of which assigns different properties as the ones which have the definite values. So which properties does the system have then, and how can we tell?
There are various theorems (“Hardy theorems”) proving that an ontological theory can’t assign definite values to all observables in all quantum states, such that all QM expectations are satisfied simultaneously.
I think you mean Kochen-Specker theorem here (and similar results going back to Gleason’s theorem)? The system can’t have definite (non-contextual) values of all operators at once, because the operators don’t commute. Particular interpretations build a maximal set of properties which the system can have at once. Hardy’s theorem seems to be related to whether the properties can be Lorentz invariant or not.
As you say, Bohmian mechanics is one of the interpretations (based on assigning definite position states to all particles at all times), but perhaps is not the most plausible one, since the choice of the position operator as the “preferred” operator is “put in” by hand. Other interpretations try to allow the preferred operators to “drop out” of the wave function (via measurement events or other decoherence events) rather than being “put in” and are in that sense simpler (fewer assumptions) and more plausible.
You seem then to be left with the problem that the “real” world can be affected by the “imaginary” ones, otherwise you don’t get interference. The sense in which this makes sense does not seem to me to be ‘common’.
Did you read the link? Most of the recent modal interpretations are based heavily on decoherence (between different branches of the wave function). So, no, the possible worlds don’t “interfere” with each other.
There are different ways of splitting the wave function into “worlds”—this is why there are several modal interpretations, not just one of them. This ambiguity is a more powerful criticism by the way (exactly what are the worlds, and why should we believe one particular split rather than the others?)
In any case, I think you missed the point here. Whether the modal interpretations are right or not, the problem is that they are just not discussed in the sequence. Instead, the sequence contains a colossal non-sequitur from “wave function collapse is a silly theory” to “so all these many worlds really exist”.
In favour of this de-bugging. One of the other glaring omissions from the sequence is discussion of modal interpretations of quantum mechanics. These are formally very similar to MWI (there is a wave function for the universe, there is no collapse) but the “many worlds” are interpreted as possible worlds (or universes), only one of which is actual. This approach has a lot going for it, common-sense wise.
Modalism has its place in a discussion of the options. But in fact my call for “debugging” was not aimed at reforming the account of QM provided by the Sequence. The arguments about QM serve to illustrate various general points—e.g. “think like reality”—and I’m saying that a functional substitute for all that should be constructed, or at least outlined. We should at least have an idea of what could take the Sequence’s place in the flow of argument, if one were to remove it.
Some thoughts on modal interpretations:
The concept of a modal interpretation is even vaguer in its implications than many-worlds and retrocausal interpretations. The only unifying concept seems to be that other worlds exist in the discourse, but they are purely counterfactual and play no role in explaining anything that happens in the one actual world.
There are various theorems (“Hardy theorems”) proving that an ontological theory can’t assign definite values to all observables in all quantum states, such that all QM expectations are satisfied simultaneously. “Antirealists” like to use this as evidence that you can’t make an objective theory that accounts for QM. But you never perform all possible measurements simultaneously; all that matters is that what the theory says about position when position is measured matches what QM says, and the same for other observables. At other times, position can be doing whatever is required by the logic of the new theory, it can even be absent ontologically.
The modalists have brought all this to the fore and they even have a few technical insights about the construction of a full proper theory, but so far as I can see, these insights aren’t comprehensive enough to single out an ontologically distinctive class of theory, compared to many-worlds or retrocausality. Bohmian mechanics, especially in its wavefunction-less “nomological” form, is a modal interpretation in the sense that, e.g. Bohmian momentum behaves like quantum momentum only when a momentum measurement is occurring. (The Bohmian mechanics of the measurement interaction forces it to behave appropriately.)
You could even argue that many worlds is modal! - in the technical sense that a “world” or “branch” which is an eigenstate of some observable will not provide an associated eigenvalue for a complementary observable.
I don’t agree that the concept of a modal interpretation is vague. The basic concept is that a quantum system can have a physical property with a definite value without its wavefunction necessarily having to be in an eigenstate of the corresponding operator. So the eigenstate-eigenvalue link is not bidirectional. That’s basically it.
The only vagueness is that there are then multiple interpretations, each of which assigns different properties as the ones which have the definite values. So which properties does the system have then, and how can we tell?
I think you mean Kochen-Specker theorem here (and similar results going back to Gleason’s theorem)? The system can’t have definite (non-contextual) values of all operators at once, because the operators don’t commute. Particular interpretations build a maximal set of properties which the system can have at once. Hardy’s theorem seems to be related to whether the properties can be Lorentz invariant or not.
As you say, Bohmian mechanics is one of the interpretations (based on assigning definite position states to all particles at all times), but perhaps is not the most plausible one, since the choice of the position operator as the “preferred” operator is “put in” by hand. Other interpretations try to allow the preferred operators to “drop out” of the wave function (via measurement events or other decoherence events) rather than being “put in” and are in that sense simpler (fewer assumptions) and more plausible.
You seem then to be left with the problem that the “real” world can be affected by the “imaginary” ones, otherwise you don’t get interference. The sense in which this makes sense does not seem to me to be ‘common’.
Did you read the link? Most of the recent modal interpretations are based heavily on decoherence (between different branches of the wave function). So, no, the possible worlds don’t “interfere” with each other.
There are different ways of splitting the wave function into “worlds”—this is why there are several modal interpretations, not just one of them. This ambiguity is a more powerful criticism by the way (exactly what are the worlds, and why should we believe one particular split rather than the others?)
In any case, I think you missed the point here. Whether the modal interpretations are right or not, the problem is that they are just not discussed in the sequence. Instead, the sequence contains a colossal non-sequitur from “wave function collapse is a silly theory” to “so all these many worlds really exist”.