Many of the interpretations of quantum mechanics are nondeterministic.
Relational quantum mechanics interprets particles as taking on discrete states at random whenever they interact with another particle, but only in relation to what they interact with and not in relation to anything else. That means particles don’t have absolute properties, like, if you measure its spin to be +1/2, this is not an absolute property, but a property that exists only relative to you/your measuring device. Each interaction leads to particles taking on definite states randomly according to the statistics predicted by quantum theory, but only in relation to things participating in those interactions.
Time-symmetric interpretations explain violations of Bell inequalities through rejecting a fundamental arrow of time. Without it, there’s no reason to evolve the state vector in a single time-direction. It thus adopts the Two-State Vector Formalism which evolves it in both directions simultaneously. When you do this, you find it places enough constructs on the particles give you absolutely deterministic values called weak values, but these weak values are not what you directly measure. What you directly measure are the “strong” values. You can interpret it such that every time two particles interact, they take on “strong” values randomly according to a rule called the Aharonov-Bergmann-Lebowitz rule. This makes time-symmetric interpretations local realist but not local deterministic, as it can explain violations of Bell inequalities through local information stored in the particles, but that local information still only statistically determines what you observe.
Objective collapse models are not really interpretations but new models because they can’t universally reproduce the mathematics of quantum theory, but some serious physicists have explored them as possibilities and they are also fundamentally random. You assume that particles literally spread out as waves until some threshold is met then they collapse down randomly into classical particles. The reason this can’t reproduce the mathematics of quantum theory is because this implies quantum effects cannot be scaled beyond whatever that threshold is, but no such threshold exists in traditional quantum mechanics, so such a theory must necessarily deviate from its predictions at that threshold. However, it is very hard to scale quantum effects to large scales, so if you place the threshold high enough, you can’t practically distinguish it from traditional quantum mechanics.
I think a lot of proponents of objective collapse would pick a bone with that, haha, although it’s really just semantics. They are proposing extra dynamics that we don’t understand and can’t yet measure.
Relational quantum mechanics interprets particles as taking on discrete states at random whenever they interact with another particle, but only in relation to what they interact with and not in relation to anything else
What’s the definition of interact here? Does it have an arbitrary cutoff like in objective collapse? You can make a non-separable state as big as you want.
This is also the first I’ve heard anything about time-symmetric interpretations. That sounds pretty fascinating. Does it not have experimenter “free will”, or do they sidestep the no-go theorems some other way?
So saying we stick with objective collapse or multiple worlds, what I mean is, could you define a non-Lipschitz continuous potential well (for example) that leads to multiple solutions to a wave equation given the same boundary?
Many of the interpretations of quantum mechanics are nondeterministic.
Relational quantum mechanics interprets particles as taking on discrete states at random whenever they interact with another particle, but only in relation to what they interact with and not in relation to anything else. That means particles don’t have absolute properties, like, if you measure its spin to be +1/2, this is not an absolute property, but a property that exists only relative to you/your measuring device. Each interaction leads to particles taking on definite states randomly according to the statistics predicted by quantum theory, but only in relation to things participating in those interactions.
Time-symmetric interpretations explain violations of Bell inequalities through rejecting a fundamental arrow of time. Without it, there’s no reason to evolve the state vector in a single time-direction. It thus adopts the Two-State Vector Formalism which evolves it in both directions simultaneously. When you do this, you find it places enough constructs on the particles give you absolutely deterministic values called weak values, but these weak values are not what you directly measure. What you directly measure are the “strong” values. You can interpret it such that every time two particles interact, they take on “strong” values randomly according to a rule called the Aharonov-Bergmann-Lebowitz rule. This makes time-symmetric interpretations local realist but not local deterministic, as it can explain violations of Bell inequalities through local information stored in the particles, but that local information still only statistically determines what you observe.
Objective collapse models are not really interpretations but new models because they can’t universally reproduce the mathematics of quantum theory, but some serious physicists have explored them as possibilities and they are also fundamentally random. You assume that particles literally spread out as waves until some threshold is met then they collapse down randomly into classical particles. The reason this can’t reproduce the mathematics of quantum theory is because this implies quantum effects cannot be scaled beyond whatever that threshold is, but no such threshold exists in traditional quantum mechanics, so such a theory must necessarily deviate from its predictions at that threshold. However, it is very hard to scale quantum effects to large scales, so if you place the threshold high enough, you can’t practically distinguish it from traditional quantum mechanics.
I think a lot of proponents of objective collapse would pick a bone with that, haha, although it’s really just semantics. They are proposing extra dynamics that we don’t understand and can’t yet measure.
What’s the definition of interact here? Does it have an arbitrary cutoff like in objective collapse? You can make a non-separable state as big as you want.
This is also the first I’ve heard anything about time-symmetric interpretations. That sounds pretty fascinating. Does it not have experimenter “free will”, or do they sidestep the no-go theorems some other way?
So saying we stick with objective collapse or multiple worlds, what I mean is, could you define a non-Lipschitz continuous potential well (for example) that leads to multiple solutions to a wave equation given the same boundary?