A few more words on quantum theory. In effect, there is a prevailing myth and a rising heresy. The prevailing myth is the Copenhagen interpretation, the rising heresy is the many-worlds interpretation. They have this much in common, that both are full of fuzzy thinking but their acolytes believe them to be exact. Therefore, when you press the acolytes for details, you never get quite the same answers, because the belief that the interpretation does provide answers comes first, and then the details are invented in response to scrutiny, in faith that they are there already and the acolyte needs merely to think things through and rediscover them. One consequence of this situation is that it becomes very difficult to critique or rebut these interpretations, because the details are always different depending on one’s disputant, and if they can’t make it make sense, they will eventually appeal to authority and say that Bohr or Everett would have explained it better.
It is easier to see that Stuart is tying himself in knots. There is no such thing as position, but there is an observable called position, but it has no exact value, but it has an uncertainty in its value… (I had better observe in passing that whether physical continua are more like the reals or the rationals should make no difference to the illegitimacy of the idea that an entity can have a location without having a particular location. If anyone wants jargon with which to make this idea precise, see Armstrong on determinates and determinables. The illegitimate—because self-contradictory—idea is that of an objectively indeterminate determinable property.) The philosophical charisma of Bohr et al, while still strong, has declined a little, and so increasingly people are opting for the Everett approach. It sounds cleaner: there are many worlds, they all exist, that’s that! It sounds like a pleasing resolution to the problem of superposition.
But again, if you go into the details, you find discord among the acolytes, because the emperor, if not naked, is rather threadbare. For example: given that the state of the multiverse is described by some universal wavefunction, which part of the formalism corresponds to a “world”, an individual universe? One might try breaking down that wavefunction into linearly independent components, and saying that those are the worlds. But if they are linearly independent, then they evolve independently, which means that any one of them, alone, could have been the whole thing—so why would we need to postulate the other worlds? And anyway, aren’t the worlds supposed to be interacting? Double-slit diffraction is due to photons in the universes next door, for example… The problems in defining a world are so severe that one will find many-worlds advocates saying that the worlds aren’t really real, they only have an approximate existence. The seamless multiverse is the real reality, and a world is just an approximation and reification of a chunk of it. At this point the interpretation has declined from mathematics into rhetoric, i.e. handwaving. If one asks what part of the universal wavefunction correponds to the particular empirical realities which physical theory is ultimately supposed to account for, one is liable to get remarks about brain observables correlated with external-world observables—except it turns out that the existence of brains is no more objective than the existence of worlds… As I said, it is hard to rebut because it is so amorphous.
But if they are linearly independent, then they evolve independently, which means that any one of them, alone, could have been the whole thing—so why would we need to postulate the other worlds? And anyway, aren’t the worlds supposed to be interacting?
Can’t this be answered by an appeal to the fact that the initial state of the universe is supposed to be low-entropy? The wavefunction corresponding to one of the worlds, run back in time to the start of the universe, would have higher entropy than the wavefunction corresponding to all of them together, so it’s not as good a candidate for the starting wavefunction of the universe.
A few more words on quantum theory. In effect, there is a prevailing myth and a rising heresy. The prevailing myth is the Copenhagen interpretation, the rising heresy is the many-worlds interpretation. They have this much in common, that both are full of fuzzy thinking but their acolytes believe them to be exact. Therefore, when you press the acolytes for details, you never get quite the same answers, because the belief that the interpretation does provide answers comes first, and then the details are invented in response to scrutiny, in faith that they are there already and the acolyte needs merely to think things through and rediscover them. One consequence of this situation is that it becomes very difficult to critique or rebut these interpretations, because the details are always different depending on one’s disputant, and if they can’t make it make sense, they will eventually appeal to authority and say that Bohr or Everett would have explained it better.
It is easier to see that Stuart is tying himself in knots. There is no such thing as position, but there is an observable called position, but it has no exact value, but it has an uncertainty in its value… (I had better observe in passing that whether physical continua are more like the reals or the rationals should make no difference to the illegitimacy of the idea that an entity can have a location without having a particular location. If anyone wants jargon with which to make this idea precise, see Armstrong on determinates and determinables. The illegitimate—because self-contradictory—idea is that of an objectively indeterminate determinable property.) The philosophical charisma of Bohr et al, while still strong, has declined a little, and so increasingly people are opting for the Everett approach. It sounds cleaner: there are many worlds, they all exist, that’s that! It sounds like a pleasing resolution to the problem of superposition.
But again, if you go into the details, you find discord among the acolytes, because the emperor, if not naked, is rather threadbare. For example: given that the state of the multiverse is described by some universal wavefunction, which part of the formalism corresponds to a “world”, an individual universe? One might try breaking down that wavefunction into linearly independent components, and saying that those are the worlds. But if they are linearly independent, then they evolve independently, which means that any one of them, alone, could have been the whole thing—so why would we need to postulate the other worlds? And anyway, aren’t the worlds supposed to be interacting? Double-slit diffraction is due to photons in the universes next door, for example… The problems in defining a world are so severe that one will find many-worlds advocates saying that the worlds aren’t really real, they only have an approximate existence. The seamless multiverse is the real reality, and a world is just an approximation and reification of a chunk of it. At this point the interpretation has declined from mathematics into rhetoric, i.e. handwaving. If one asks what part of the universal wavefunction correponds to the particular empirical realities which physical theory is ultimately supposed to account for, one is liable to get remarks about brain observables correlated with external-world observables—except it turns out that the existence of brains is no more objective than the existence of worlds… As I said, it is hard to rebut because it is so amorphous.
Can’t this be answered by an appeal to the fact that the initial state of the universe is supposed to be low-entropy? The wavefunction corresponding to one of the worlds, run back in time to the start of the universe, would have higher entropy than the wavefunction corresponding to all of them together, so it’s not as good a candidate for the starting wavefunction of the universe.
My feeling is that Bohm escapes these problems, at the cost of requiring nonlocal information transfer (a high price, but one I’m willing to pay).