In the Many Worlds interpretation, the universal quantum state is a giant superposition of all objects in the universe:
There is no ‘wave function’ collapse in this interpretation, so everything remains entangled. How then does this universe ‘split’? The usual story says that a measurement process yields several possibilities, much like the different possible sizes of the triangle below:
And it is these different possible outcomes that define how the universe splits into separate worlds, each corresponding to one of the outcomes:
But the problem is that in order to define a measurement process that yielded the clearly defined triangle outcomes, we assumed that there were distinguishable objects in our universe. Specifically, here’s what we needed in order to get those well-defined outcomes:
(1) a system that can have ‘triangle’ properties
(2) a large number of other, distinguishable systems that can measure those properties
(3) a clearly defined, force-based interaction between the measuring systems and the system to be measured (i.e. an interaction based on a force such as electromagnetism)
(4) no other quantum correlations (‘entanglement’) among these systems and between these systems and the rest of the universe
Let’s return to the original, universal quantum state to see whether these requirements can really be met in an interpretation without collapse. The universe has many component objects, but if all of them were created at once in the Big Bang, they are all quantum-correlated. When we have quantum correlations among all pieces of the universe, we have no way of saying that specific kinds of measurements are taking place, or even what kinds of objects there are and what properties they have. That’s why the universal quantum state is pictured above as a ‘soup’ without clearly defined objects or properties.
In terms of Schrodinger’s Cat, the first problem is that we don’t have any way to identify an independently existing object like a cat. Even if we did, we would not have any reason to say that the two possible states of the cat are ‘alive’ and ‘dead,’ since another mathematically allowable situation is two possible states of the cat in which he is ‘alive + dead’ or ‘alive – dead.’ The first case (pictured on the left below) corresponds to the common sense observable, let’s call it ‘Cat Viability,’ while the second case (pictured on the right below) corresponds to a crazy but equally mathematically allowable observable – let’s call it the ‘Superposed Cat’ observable. The second one is crazy because in each outcome, the cat is still in a superposition of alive and dead!
Without collapse, we have no way to say that the world splits along sensible lines (as on the left hand side) rather than along crazy lines (as on the right hand side). We are in this predicament because of the assumption that the Universe has an overall quantum state that never has any kind of real ‘collapse’ that could separate its components into independent systems that are not quantum-correlated with each other. The Universal state does not allow us to say that some of its systems belong to a ‘radioactive atom,’ others to a Geiger counter, and other to a ‘cat’, where each of those systems is only interacting by a well-defined physical interaction that does not involve quantum correlations. It turns out that the inability to separate the mutually quantum-correlated components of the Universal quantum state leaves us with no reason to say why the relevant outcomes are ‘cat alive’ and ‘cat dead’ as opposed to ‘superposed cat 1’ and ‘superposed cat 2.’
The basic problem is that we don’t have a clearly defined, force-based interaction between the different components of our universe, because without collapse, there is ongoing entanglement among all its components. What we need to be able to say is that we have a bunch of separated pieces of the universe that have no quantum correlations amongst each other, but that do have well-defined interactions that can be understood in terms of specific forces such as electromagnetism. But we cannot say this in the Many-Worlds picture, which has no collapse that could truly distinguish the pieces from each other as independent objects that only interact via well-defined forces.
Presentations that attempt to argue that the macroscopic world of ordinary experience naturally ‘emerges’ from a universal quantum state in a Many Worlds interpretation all rely on smuggling in an assumption that the universe can be divided into pieces that do not have quantum correlations. But this assumption is not legitimate under the basic Many Worlds assumption that there is no “collapse.” Therefore, there is no way to say why the universe ‘splits’ in the right way. Without a coherent account of splitting, the universe cannot really split, and the “Many Worlds” picture cannot get off the ground. The conclusion is that even though the Many Worlds picture makes for some fun science fiction stories, it is probably not the right approach to interpreting quantum theory.
For the technical version of this discussion, see http://philsci-archive.pitt.edu/10757/, which argues that the mistake in the Many Worlds picture is similar to one made by Ludwig Boltzmann when he tried to ‘derive’ the irreversible second law of thermodynamics from reversible laws of motion.
 Even if we allow for particle creation at a later time, the deterministic evolution presumed by the Everettian picture does not allow for any phase randomness (distinguishability) of those newly created particles.
3 thoughts on “Why the World Cannot Really Split in the Many-Worlds Interpretation”
Reblogged this on rekastner and commented:
I updated this post to be easier to access, and clarified some of language.