Günther, I am aware of that argument, but it has very little to do with favoring many worlds in the sense of Everett. See Tegmark’s distinction between Level III and Level IV. The worlds of an Everett multiverse are supposed to be connected facets of a single entity, not disjoint Level IV entities.
This allows me to highlight another aspect of many worlds, which is the thorough confusion regarding causality. What are the basic cause-and-effect relationships, according to many worlds? What are the entities that enter into them? Do worlds have causal power, or are they purely epiphenomenal? Remember, that-which-exists at any moment does not just consist of a set of worlds, but a set of worlds each with a complex number attached. And that-which-exists in the next moment is—the same set of worlds, but now with different complex numbers attached. The more I think about it, the less sense it makes, but people have been seduced by the simple-sounding rhetoric of worlds splitting and recombining.
To say it all again: what are we being offered by this account? On the one hand, a qualitative picture: the reality we see is just one sheet in a sheaf of worlds, which split and merge as they become dissimilar and then become similar again. On the other hand, a quantitative promise: the picture isn’t quite complete, but we hope to get the exact probabilities back somehow.
Now what is the reality of quantum mechanics, applied to the whole universe? (If we adopt the configuration-centric approach.) There is a space of classical-looking “configurations”—each an arrangement of particles in space, or a frozen sea of waves in fundamental fields. Then, there is a complex number, a “probability amplitude”, associated with each configuration. Finally, we have an equation, the Schrödinger equation, which describes how the complex numbers change with time. That’s it.
If we just look at the configuration space, and ignore the complex numbers, there is no splitting and merging, nothing changes. We have a set of instantaneous world-states, just sitting there.
If we try to bring the complex numbers into the picture, there are two obvious options. One is to identify a world with a particular static configuration. Then nothing ever actually moves in any world, all that changes is the mysterious complex number globally associated with it. That’s one way to break down a universal wavefunction into “many worlds”, but it seems meaningless.
The other way is to break down the wavefunction at any moment in that fashion, but to deny any relationship between the worlds of one moment and the world of the next, as I described it up in my second paragraph. So once again, reality ends up consisting of a set of static spatial configurations, each with a complex number magically attached, but there is no continuity of existence.
There is actually a third option, however—an alternative way to assert continuity of existence, between the worlds of one moment and the world of the next. Basically, you go against the gradient in configuration space of the angles of the complex numbers, in order to decide which world-moments later continue the world-moments of now. That defines a family of nonintersecting trajectories, each of which resembles a perturbed version of a classical history. In fact, we’ve just reinvented a form of Bohmian mechanics.
But enough. I hope someone grasps that we have simply not been given a picture which can sustain the rhetoric of worlds splitting. Either the worlds sit there unchanging, or they only exist for a moment, or they are self-sufficient Bohmian worlds which neither split nor join. If I try to understand mangled worlds in this way, it seems to say, “ignore those configurations where the amplitude is very small”. But they’re either there or not; and if they are literally not, we’re no longer using the Schrödinger equation.
Günther, I am aware of that argument, but it has very little to do with favoring many worlds in the sense of Everett. See Tegmark’s distinction between Level III and Level IV. The worlds of an Everett multiverse are supposed to be connected facets of a single entity, not disjoint Level IV entities.
This allows me to highlight another aspect of many worlds, which is the thorough confusion regarding causality. What are the basic cause-and-effect relationships, according to many worlds? What are the entities that enter into them? Do worlds have causal power, or are they purely epiphenomenal? Remember, that-which-exists at any moment does not just consist of a set of worlds, but a set of worlds each with a complex number attached. And that-which-exists in the next moment is—the same set of worlds, but now with different complex numbers attached. The more I think about it, the less sense it makes, but people have been seduced by the simple-sounding rhetoric of worlds splitting and recombining.
To say it all again: what are we being offered by this account? On the one hand, a qualitative picture: the reality we see is just one sheet in a sheaf of worlds, which split and merge as they become dissimilar and then become similar again. On the other hand, a quantitative promise: the picture isn’t quite complete, but we hope to get the exact probabilities back somehow.
Now what is the reality of quantum mechanics, applied to the whole universe? (If we adopt the configuration-centric approach.) There is a space of classical-looking “configurations”—each an arrangement of particles in space, or a frozen sea of waves in fundamental fields. Then, there is a complex number, a “probability amplitude”, associated with each configuration. Finally, we have an equation, the Schrödinger equation, which describes how the complex numbers change with time. That’s it.
If we just look at the configuration space, and ignore the complex numbers, there is no splitting and merging, nothing changes. We have a set of instantaneous world-states, just sitting there.
If we try to bring the complex numbers into the picture, there are two obvious options. One is to identify a world with a particular static configuration. Then nothing ever actually moves in any world, all that changes is the mysterious complex number globally associated with it. That’s one way to break down a universal wavefunction into “many worlds”, but it seems meaningless.
The other way is to break down the wavefunction at any moment in that fashion, but to deny any relationship between the worlds of one moment and the world of the next, as I described it up in my second paragraph. So once again, reality ends up consisting of a set of static spatial configurations, each with a complex number magically attached, but there is no continuity of existence.
There is actually a third option, however—an alternative way to assert continuity of existence, between the worlds of one moment and the world of the next. Basically, you go against the gradient in configuration space of the angles of the complex numbers, in order to decide which world-moments later continue the world-moments of now. That defines a family of nonintersecting trajectories, each of which resembles a perturbed version of a classical history. In fact, we’ve just reinvented a form of Bohmian mechanics.
But enough. I hope someone grasps that we have simply not been given a picture which can sustain the rhetoric of worlds splitting. Either the worlds sit there unchanging, or they only exist for a moment, or they are self-sufficient Bohmian worlds which neither split nor join. If I try to understand mangled worlds in this way, it seems to say, “ignore those configurations where the amplitude is very small”. But they’re either there or not; and if they are literally not, we’re no longer using the Schrödinger equation.