Everything is weighted by squared-norm of the amplitude. And, y’know, quantum mechanics is unitary. What needs to be preserved, is preserved.
More generally, we might imagine that we lived in a world where physics was just probabilistic in the ordinary way, rather than quantum (in the sense of based on amplitudes); MWI might also be a natural way to think if we lived in that world (though not as natural as it is in the world of actual QM, as in that world we wouldn’t have any real need for MWI); then, well, everything would be weighted by probability, and everything would be stochastic rather than unitary. Of course if you don’t require preservation of whatever the appropriate weighting is, you’ll get an absurd result.
You do seem to be pretty confused about what MWI says; it does not, as you seem to suggest, posit a finite number of universes, which split at discrete points, and where the probability of an event is the proportion of universes it occurs in. “Universes” here are just identified with the states that we’re looking at a wave function over, or perhaps trajectories through such, so there are infinitely many. And having the universes split and not interfere with each other, would work with ordinary probability, but it won’t work with quantum amplitudes—if that were the case we’d just see probabilistic effects, not quantum effects. The many worlds of MWI do interfere with each other. When decoherence occurs the result is to effectively split collections of universes off from each other so they don’t interfere anymore, but in a coherent quantum system the notion of splitting doesn’t make much sense.
Remember, the key suppositions of MWI are just that A. the equations of quantum mechanics are literally true all the time—there is no magical waveform collapse; and B. the wavefunction is a complete description of reality; it’s not guiding any hidden variables. (And I suppose, C., decoherence is responsible for the appearance of collapse, etc., but that’s more of a conclusion than a suppostion.) Hence why it’s claimed here that MWI wins by Occam’s Razor. It really is the minimal interpretation of QM!
If there is an actual problem with MWI, I’d say it’s the one Scott Aaronson points out here (I doubt this observation is original to him, but not being too familiar of the history of this, it’s the first place I’d seen it; does anyone know the history of this?); the virtue of MWI is its minimality, but unfortunately it seems to be too minimal to answer this question! Assuming the question is meaningful, anyway. But the alternatives still seem distinctly unsatisfactory...
Remember, the key suppositions of MWI are just that [...] Hence why it’s claimed here that MWI wins by Occam’s Razor.
You can’t get the probabilities from those suppositions. And without the probabilities, MWI has no predictive power; it’s just a metaphysics which says “Everything that can happen does happen”, and which then gives wrong predictions if you count the worlds the way you would count anything else.
But even if you can justify the required probability measure, there is another problem. John Bell once wrote of Bohmian theories (see last paragraph here):
As with relativity before Einstein, there is a preferred reference frame in the formulation of the theory…but it is experimentally indistinguishable.
In a Bohmian theory, you take the classical theory that is to be quantized, and add to the classical equations of motion a nonlocal term, dependent on the wavefunction, which adds an extra wiggle to the motion, giving you quantum behavior. The nonlocality means that you need a notion of objective simultaneity in order to define that term. So when you construct the Bohmian counterpart of a relativistic quantum theory (i.e. of a quantum field theory), you will still see relativistic effects like length contraction and time dilation (since they are in the classical counterpart of the quantum field theory), but you have to pick a reference frame in order to make the Bohmian construction—which might be seen as an indication of its artificiality.
The same thing happens in MWI. In MWI you reify the wavefunction—you assume it is a real thing—and then you divide it up into worlds. To perform this division, you need a universal time coordinate, so relativity disappears at the fundamental level. Furthermore, since there is no particular connection between the worlds of the wavefunction in one moment, and the worlds of the wavefunction in the next moment, you don’t even have persistence of a world in time, so you can’t even think about performing a Lorentz transformation. Instead, you have a set of disconnected world-moments, with mysterious nonstandard probabilities attached to them in order to make predictions turn out right.
All of that says to me that the MWI construction is just as artificial as the Bohmian one.
You can’t get the probabilities from those suppositions. And without the probabilities, MWI has no predictive power; it’s just a metaphysics which says “Everything that can happen does happen”, and which then gives wrong predictions if you count the worlds the way you would count anything else.
Sorry, yes. I took weighting things by squared-norm of amplitude as implicit, seeing as we’re discussing QM in the first place.
The weighting quantity is conserved. So far as I can tell, that entirely answers the objection you raised. I’m really not seeing where it fails. Could you explain?
If I understand you correctly, there is an equal number of world splits every second in every branch. They are all weighted, so that no branch can explode?
Worlds are weighted by squared-norm of amplitude, a quantity that is conserved. If two worlds are really not interfering with each other any more, then amplitude will not somehow vanish from the future of one and appear in the future in the other.
What Sniffnoy’s remark resolves this?
Everything is weighted by squared-norm of the amplitude. And, y’know, quantum mechanics is unitary. What needs to be preserved, is preserved.
More generally, we might imagine that we lived in a world where physics was just probabilistic in the ordinary way, rather than quantum (in the sense of based on amplitudes); MWI might also be a natural way to think if we lived in that world (though not as natural as it is in the world of actual QM, as in that world we wouldn’t have any real need for MWI); then, well, everything would be weighted by probability, and everything would be stochastic rather than unitary. Of course if you don’t require preservation of whatever the appropriate weighting is, you’ll get an absurd result.
You do seem to be pretty confused about what MWI says; it does not, as you seem to suggest, posit a finite number of universes, which split at discrete points, and where the probability of an event is the proportion of universes it occurs in. “Universes” here are just identified with the states that we’re looking at a wave function over, or perhaps trajectories through such, so there are infinitely many. And having the universes split and not interfere with each other, would work with ordinary probability, but it won’t work with quantum amplitudes—if that were the case we’d just see probabilistic effects, not quantum effects. The many worlds of MWI do interfere with each other. When decoherence occurs the result is to effectively split collections of universes off from each other so they don’t interfere anymore, but in a coherent quantum system the notion of splitting doesn’t make much sense.
Remember, the key suppositions of MWI are just that A. the equations of quantum mechanics are literally true all the time—there is no magical waveform collapse; and B. the wavefunction is a complete description of reality; it’s not guiding any hidden variables. (And I suppose, C., decoherence is responsible for the appearance of collapse, etc., but that’s more of a conclusion than a suppostion.) Hence why it’s claimed here that MWI wins by Occam’s Razor. It really is the minimal interpretation of QM!
If there is an actual problem with MWI, I’d say it’s the one Scott Aaronson points out here (I doubt this observation is original to him, but not being too familiar of the history of this, it’s the first place I’d seen it; does anyone know the history of this?); the virtue of MWI is its minimality, but unfortunately it seems to be too minimal to answer this question! Assuming the question is meaningful, anyway. But the alternatives still seem distinctly unsatisfactory...
You can’t get the probabilities from those suppositions. And without the probabilities, MWI has no predictive power; it’s just a metaphysics which says “Everything that can happen does happen”, and which then gives wrong predictions if you count the worlds the way you would count anything else.
But even if you can justify the required probability measure, there is another problem. John Bell once wrote of Bohmian theories (see last paragraph here):
In a Bohmian theory, you take the classical theory that is to be quantized, and add to the classical equations of motion a nonlocal term, dependent on the wavefunction, which adds an extra wiggle to the motion, giving you quantum behavior. The nonlocality means that you need a notion of objective simultaneity in order to define that term. So when you construct the Bohmian counterpart of a relativistic quantum theory (i.e. of a quantum field theory), you will still see relativistic effects like length contraction and time dilation (since they are in the classical counterpart of the quantum field theory), but you have to pick a reference frame in order to make the Bohmian construction—which might be seen as an indication of its artificiality.
The same thing happens in MWI. In MWI you reify the wavefunction—you assume it is a real thing—and then you divide it up into worlds. To perform this division, you need a universal time coordinate, so relativity disappears at the fundamental level. Furthermore, since there is no particular connection between the worlds of the wavefunction in one moment, and the worlds of the wavefunction in the next moment, you don’t even have persistence of a world in time, so you can’t even think about performing a Lorentz transformation. Instead, you have a set of disconnected world-moments, with mysterious nonstandard probabilities attached to them in order to make predictions turn out right.
All of that says to me that the MWI construction is just as artificial as the Bohmian one.
Sorry, yes. I took weighting things by squared-norm of amplitude as implicit, seeing as we’re discussing QM in the first place.
That doesn’t excuse the MWI at all. Could very well be, that something else is needed to resolve the dilemmas.
And you haven’t answer my question, maybe something else.
The weighting quantity is conserved. So far as I can tell, that entirely answers the objection you raised. I’m really not seeing where it fails. Could you explain?
Edit: s/preserved/conserved/
If I understand you correctly, there is an equal number of world splits every second in every branch. They are all weighted, so that no branch can explode?
Is that correct?
Worlds are weighted by squared-norm of amplitude, a quantity that is conserved. If two worlds are really not interfering with each other any more, then amplitude will not somehow vanish from the future of one and appear in the future in the other.
In this remark. His expansion below should make it clear what the relevant points are.