What Splits in MWI? Toward a Complete Ansatz.
[Henry Stapp, from "The Basis Problem in Many-Worlds Theories", Sept. 18, 2001, LBNL-48917]
The second problem is that at each of these distinct "instants of splitting" the unified actual universe must be decomposed in a specified way into two systems, the 'observed system' and 'observing system'. Hence the rule that defines how the unified universe is to be split at that instant into these two special parts must be specified in terms solely of the state vector itself and its law of evolution.
Is it yourself or Stapp that has brought up Splitting? I would like to know what kind of Split you are referring to; is it Dewitt? Or do you differ from Stapp?
The following is the way Hegel defines infinity in the "Logic":
Somewhat comes to be an other, and the other generally comes to be an other. Thus essentially, relative to another, somewhat is virtually an other against it, and since what is passed into is quite the same as what passes over, since both have one and the same attribute, viz. to be an other, it follows that something in its passage into other only joins with itself. To be thus self-related in the passage and in the other is the genuine infinity.
The "somewhat" here is apparently that which breaks off from a total "something", which is more or less a quantum universe, in order to pursue its own coming to be, or becoming. The result of this is that "somewhat" first comes to be an "other" (phenomenal) quantum evolution. That then comes to be an actualized or classical-like "other" or "limit" to that quantum evolution. This second "other", which is "the other of the other" or "the negation of the negation", is like an object relative to "another" quantum system defined as a subject - hence, "relative to another, [the second other that] somewhat [has come to be] is virtually an other against it".
However, this object is a thing-in-itself or thing-in-its-idea divided into two distinct parts, the thing and its immanent idea, which are "what is passed into" and "what passes over". The thing is actually the eigenstate selected by the separated quantum process, which is still however thing-like or noumenal with respect to the original "something". The fact that "what is passed into" and "what passes over" are "quite the same" means, I believe, that they are fungible. So, when one universal something defines itself in terms of the "itself" or immanent idea of the object (rather than the "thing", which remains noumenal), it is implied that another universal something will define itself in terms of the fungible alternative.
So, essentially what has split is the object, into two parts, one thing-like and one immanent idea-like. It is the immanent idea-like part that is realized by the original something, which gains thereby a subjective and panpsychic character. But due to the sameness or fungibility of "what is passed into" and "what passes over", there must be another universal something that will realize the fungible alternative.