Are GRW Tails as Bad as They Say?

Abstract

GRW models of the physical world are criticized in the literature for involving wave function “tails” that allegedly create fatal interpretive problems and even compromise standard arithmetic. I find such objections both unfair and misguided. But not all is well with the GRW approach. One complaint I articulate in this paper does not have to do with tails as such but with the specific way in which past physical structures linger forever in the total GRW wave function. By pushing the total proposal towards either the “Many Worlds” approach or the Bohmian approach, this feature diminishes extant GRW claims to preferability. I suggest, however, that the problem here is just an artifact of the particular and ultimately optional genre of collapse mechanism chosen by GRW.

Quantum theory and determinism

“…The GRW provides similar, but not exactly the same evolution: (10) where d = 10 −5 cm is the GHZ parameter and l 5cm is the distance between the atom in the pointer which was "hit" by the GRW collapse mechanism in the READY and YES positions. This is the GRW tail problem [95][96][97]. The wave function after the measurement according to the GRW is a superposition of the state corresponding to one outcome with an amplitude close to 1 and the state corresponding to the other outcome with an exponentially small amplitude.…”

The Quantum Measurement Problem: State of Play

“…Taken to its logical conclusion, this seems to suggest that the GRW theory with a functionalist reading of the link principles is just as much a 'many-worlds' theory as is the Everett interpretation (a point made by (Cordero 1999)). But the matter has received rather little critical discussion, and it may well be that the problem is solvable either via identifying a conceptual error in the argument, or by modification of the GRW dynamics so as to suppress the structure in the low-weight branches.…”

“…The main locus of purely philosophical work on the GRW theory in the past decade has been the so-called "problem of tails". As I shall argue (following Cordero (1999) to some extent) there are actually two "problems of tails", only one of which is a particular problem of dynamical-collapse theories, but both are concerned with the stubborn resistance of the wavefunction to remain decently confined in a finite-volume region of space.…”

Paradoxes and Primitive Ontology in Collapse Theories of Quantum Mechanics

“…Thus, it seems not justified to say that, when ψ is close to |dead , the cat is really dead. This paradox is another version of the "tail problem" (Shimony, 1990;Albert and Loewer, 1990;Lewis, 1995;Albert and Loewer, 1996;Cordero, 1999).…”

“…Paradox: A variant of the previous paradox was formulated by Lewis (1997) in terms of counting marbles; the discussion continued in (Cordero, 1999;Monton, 1999, 2000;Ghirardi, 1999a,b, 2001;Frigg, 2003;Lewis, 2003Lewis, , 2005Lewis, , 2006Monton, 2004;Wallace, 2008;Pearle, 2009;McQueen, 2015). Let ψ 1 be the state "the marble is inside the box" and ψ 2 the state "the marble is outside the box"; these wave functions have disjoint supports S 1 , S 2 in configuration space (i.e., wherever one is nonzero the other is zero).…”