That is, if a quantum world is something whose existence is fuzzy and which doesn’t even have a definite multiplicity—that is, we can’t even say if there’s one, two, or many of them—if those are the properties of a quantum world, then is it possible for the real world to be one of those?
The real world is a single point in configuration space (there are uncountably many such points). So what’s the point of keeping track of the blobs? It’s because the Hilbert space is so vast that it’s very unlikely that two blobs will ever interact again. We care about which blob we’re in because it comprises all the amplitude that can actually affect us. Furthermore, the blobs often split into chunks that we care about (achieving this is the point of experiment?), for instance one blob with the cat alive, one blob with it dead.
As for the question about frequencies, I have no idea.
The real world is a single point in configuration space
That can’t be what they think in Oxford, or else they would agree with argumzio, who says there are uncountably many worlds. In the Oxford version of MWI, the real world is one of those “blobs”, therefore it’s partly a matter of definition, and that’s why there’s no exact number of worlds.
Yes they call the blobs “worlds” but that doesn’t mean that they think the “real world” or “individually observed world” is a exactly one of the blobs.
The “real world”, in the Oxford MWI, is the entire wavefunction, not just one branch. That is the fundamental ontology of the interpretation. There’s no sense in which one blob is more “real” than any other.
But the individually observed portion of reality is just part of the wavefunction, yes? So, what sort of part?
Why does it need a special name? There’s a wavefunction. Part of that wavefunction represents a Mitchell_Porter observing stuff. It’s that part of the wavefunction.
That’s no good if I’m trying to evaluate MWI as a physical theory. Those are just words. You can try to extract a “branch” from a wavefunction or a state vector in a variety of ways. You might focus on a specific classical configuration (then we might have to quibble about whether you mean the point in configuration space that is labeled by that configuration, or whether you mean the delta function peaked at that point in configuration space). Or we might be talking about some other sort of basis function in terms of which a wavefunction might be decomposed (momentum eigenfunctions, wavelets, eigenfunctions of other observables). We might be talking about reduced density matrices rather than pure states…
If someone wants to insist that, in their version of MWI, there is a locally specific reality only for the region of the observer’s brain corresponding to conscious observation, they can dodge some of the details by saying we don’t know enough neuroscience yet. But they should be able to make precise statements about what sort of mathematical vivisection is going to be performed on the local wavefunction in order to get the “part of the wavefunction… observing stuff”. Otherwise, they don’t yet have a physical theory, just a vague hope that some version of Many Minds will work out.
And by the way, if we are not saying that branches correspond to universe-wide configurations, but rather just to local configurations, what’s responsible for tying together a million different information-processing events into a single mind-state? Every neighboring molecule in the brain ought to be locally branching, constantly, and independently of branchings on the other side of the skull. How could you ever justify speaking about “the” state of someone’s brain, even just as one branch of an Everett multiverse? The cognitive state will have to “supervene” on something which, from an atomic and subatomic level, is already a very intricate superposition.
If you tell me that reality is one big wavefunction, and that observable reality is made of states of neurons, then you need to tell me how to get “state of neuron” from “wavefunction”. Which set of numbers do I use?
Is it the coefficients of the wavefunction, expressed in a global configuration basis? Is it the coefficients of the wavefunction, expressed in some other basis? Or should I be looking at the matrix elements of reduced density matrices?
Also, if we talk about the configuration basis, should I regard the numbers specifying a particular configuration as part of reality? From a Hilbert-space geometric perspective, a “wavefunction” is actually a state vector, so it’s just a ray in Hilbert space, and the associated configuration is just a label for that ray, like the “x” attached to a coordinate axis.
A basis function is a different object to a density matrix, and the coefficient of a basis vector is a different sort of quantity to the quantities appearing in the label of the basis vector (that is, the eigenvalues associated with the vector).
I need to know which of the various types of number that can be associated with a quantum state, are supposed to be related to observable reality.
I’ll copy my comment from the other thread:
The real world is a single point in configuration space (there are uncountably many such points). So what’s the point of keeping track of the blobs? It’s because the Hilbert space is so vast that it’s very unlikely that two blobs will ever interact again. We care about which blob we’re in because it comprises all the amplitude that can actually affect us. Furthermore, the blobs often split into chunks that we care about (achieving this is the point of experiment?), for instance one blob with the cat alive, one blob with it dead.
As for the question about frequencies, I have no idea.
That can’t be what they think in Oxford, or else they would agree with argumzio, who says there are uncountably many worlds. In the Oxford version of MWI, the real world is one of those “blobs”, therefore it’s partly a matter of definition, and that’s why there’s no exact number of worlds.
Yes they call the blobs “worlds” but that doesn’t mean that they think the “real world” or “individually observed world” is a exactly one of the blobs.
The “real world”, in the Oxford MWI, is the entire wavefunction, not just one branch. That is the fundamental ontology of the interpretation. There’s no sense in which one blob is more “real” than any other.
But the individually observed portion of reality is just part of the wavefunction, yes? So, what sort of part?
Why does it need a special name? There’s a wavefunction. Part of that wavefunction represents a Mitchell_Porter observing stuff. It’s that part of the wavefunction.
That’s no good if I’m trying to evaluate MWI as a physical theory. Those are just words. You can try to extract a “branch” from a wavefunction or a state vector in a variety of ways. You might focus on a specific classical configuration (then we might have to quibble about whether you mean the point in configuration space that is labeled by that configuration, or whether you mean the delta function peaked at that point in configuration space). Or we might be talking about some other sort of basis function in terms of which a wavefunction might be decomposed (momentum eigenfunctions, wavelets, eigenfunctions of other observables). We might be talking about reduced density matrices rather than pure states…
If someone wants to insist that, in their version of MWI, there is a locally specific reality only for the region of the observer’s brain corresponding to conscious observation, they can dodge some of the details by saying we don’t know enough neuroscience yet. But they should be able to make precise statements about what sort of mathematical vivisection is going to be performed on the local wavefunction in order to get the “part of the wavefunction… observing stuff”. Otherwise, they don’t yet have a physical theory, just a vague hope that some version of Many Minds will work out.
And by the way, if we are not saying that branches correspond to universe-wide configurations, but rather just to local configurations, what’s responsible for tying together a million different information-processing events into a single mind-state? Every neighboring molecule in the brain ought to be locally branching, constantly, and independently of branchings on the other side of the skull. How could you ever justify speaking about “the” state of someone’s brain, even just as one branch of an Everett multiverse? The cognitive state will have to “supervene” on something which, from an atomic and subatomic level, is already a very intricate superposition.
No, you have this backwards. You’re looking for some words. I’m telling you there are just numbers. The numbers are all we need to be evaluating here.
Fine, let’s talk about numbers.
If you tell me that reality is one big wavefunction, and that observable reality is made of states of neurons, then you need to tell me how to get “state of neuron” from “wavefunction”. Which set of numbers do I use?
Is it the coefficients of the wavefunction, expressed in a global configuration basis? Is it the coefficients of the wavefunction, expressed in some other basis? Or should I be looking at the matrix elements of reduced density matrices?
Also, if we talk about the configuration basis, should I regard the numbers specifying a particular configuration as part of reality? From a Hilbert-space geometric perspective, a “wavefunction” is actually a state vector, so it’s just a ray in Hilbert space, and the associated configuration is just a label for that ray, like the “x” attached to a coordinate axis.
A basis function is a different object to a density matrix, and the coefficient of a basis vector is a different sort of quantity to the quantities appearing in the label of the basis vector (that is, the eigenvalues associated with the vector).
I need to know which of the various types of number that can be associated with a quantum state, are supposed to be related to observable reality.