GRW Theory Research Articles

What is It Like to be a Relativistic GRW Theory? Or: Quantum Mechanics and Relativity, Still in Conflict After All These Years

The violation of Bell’s inequality has shown that quantum theory and relativity are in tension: reality is nonlocal. Nonetheless, many have argued that GRW-type theories are to be preferred to pilot-wave theories as they are more compatible with relativity: while relativistic pilot-wave theories require a preferred slicing of space-time, foliation-free relativistic GRW-type theories have been proposed. In this paper I discuss various meanings of ‘relativistic invariance,’ and I show how GRW-type theories, while being more relativistic in one sense, are less relativistic in another. If so, the initial claim that GRW-type theories have a greater compatibility with relativity is unwarranted: both type of theories violate relativity, one way or another.

Ontology of a Wavefunction from the Perspective of an Invariant Proper Time

All the arguments of a wavefunction are defined at the same instant, implying the notion of simultaneity. In a somewhat related matter, certain phenomena in quantum mechanics seem to have non-local causal relations. Both concepts contradict the special relativity. We propose defining the wavefunction with respect to the invariant proper time of special relativity instead of the standard time. Moreover, we shall adopt the original idea of Schrodinger, suggesting that the wavefunction represents an ontological cloud-like object that we shall call “individual fabric” that has a finite density amplitude vanishing at infinity. Consequently, the action of measurement can be assimilated to the introduction of a confining potential that triggers an inherent nonlocal mechanism within the individual fabric. This mechanism is formalised by multiplying the wavefunction with a localising Gaussian, as in the GRW theory, but in a deterministic manner.

Master equations for Wigner functions with spontaneous collapse and their relation to thermodynamic irreversibility

Wigner functions, allowing for a reformulation of quantum mechanics in phase space, are of central importance for the study of the quantum-classical transition. A full understanding of the quantum-classical transition, however, also requires an explanation for the absence of macroscopic superpositions to solve the quantum measurement problem. Stochastic reformulations of quantum mechanics based on spontaneous collapses of the wavefunction are a popular approach to this issue. In this article, we derive the dynamic equations for the four most important spontaneous collapse models—Ghirardi–Rimini–Weber (GRW) theory, continuous spontaneous localization (CSL) model, Diósi-Penrose model, and dissipative GRW model—in the Wigner framework. The resulting master equations are approximated by Fokker–Planck equations. Moreover, we use the phase-space form of GRW theory to test, via molecular dynamics simulations, David Albert’s suggestion that the stochasticity induced by spontaneous collapses is responsible for the emergence of thermodynamic irreversibility. The simulations show that, for initial conditions leading to anti-thermodynamic behavior in the classical case, GRW-type perturbations do not lead to thermodynamic behavior. Consequently, the GRW-based equilibration mechanism proposed by Albert is not observed.

A Refined Propensity Account for GRW Theory

Spontaneous collapse theories of quantum mechanics turn the usual Schrödinger equation into a stochastic dynamical law. In particular, in this paper I will focus on the GRW theory. Two philosophical issues that can be raised about GRW concern (a) the ontology of the theory, in particular the nature of the wave function and its role within the theory, and (b) the interpretation of the objective probabilities involved in the dynamics of the theory. During the last years, it has been claimed that we can take advantage of dispositional properties in order to develop an ontology for GRW theory, and also in order to ground the objective probabilities which are postulated by it. However, in this paper I will argue that the dispositional interpretations which have been discussed in the literature so far are either flawed or—at best—incomplete. If we want to endorse a dispositional interpretation of GRW theory we thus need an extended account which specifies the precise nature of those properties and which makes also clear how they can correctly ground all the probabilities postulated by the theory. Thus, after having introduced several different kinds of probabilistic dispositions, I will try to fill the gap in the literature by proposing a novel and complete dispositional account of GRW, based on what I call spontaneous weighted multi-track propensities. I claim that such an account can satisfy both of our desiderata.

The physical salience of non-fundamental local beables

I defend the idea that objects and events in three-dimensional space (so-called local beables) are part of the derivative ontology of quantum mechanics, rather than its fundamental ontology. The main objection to this idea stems from the question of how it can endow local beables with physical salience, as opposed to mere mathematical definability. I show that the responses to this objection in the previous literature are insufficient, and I provide the necessary arguments to render them successful. This includes demonstrating the legitimacy of dynamical considerations in the derivation of local beables and responding to the threat stemming from the availability of different sets of local beables in the context of the GRW theory.

Killer collapse: empirically probing the philosophically unsatisfactory region of GRW

GRW theory offers precise laws for the collapse of the wave function. These collapses are characterized by two new constants, \(\lambda \) and \(\sigma \). Recent work has put experimental upper bounds on the collapse rate, \(\lambda \). Lower bounds on \(\lambda \) have been more controversial since GRW begins to take on a many-worlds character for small values of \(\lambda \). Here I examine GRW in this odd region of parameter space where collapse events act as natural disasters that destroy branches of the wave function along with their occupants. Our continued survival provides evidence that we don’t live in a universe like that. I offer a quantitative analysis of how such evidence can be used to assess versions of GRW with small collapse rates in an effort to move towards more principled and experimentally-informed lower bounds for \(\lambda \).

Hidden variable interpretation of spontaneous localization theory

The spontaneous localization theory of Ghirardi, Rimini, and Weber (GRW) is a theory in which wavepacket reduction is treated as a genuine physical process. Here it is shown that the mathematical formalism of GRW can be given an interpretation in terms of an evolving distribution of particles on configuration space similar to Bohmian mechanics (BM). The GRW wavefunction acts as a pilot wave for the set of particles. In addition, a continuous stream of noisy information concerning the precise whereabouts of the particles must be specified. Nonlinear filtering techniques are used to determine the dynamics of the distribution of particles conditional on this noisy information and consistency with the GRW wavefunction dynamics is demonstrated. Viewing this development as a hybrid BM–GRW theory, it is argued that, besides helping to clarify the relationship between the GRW theory and BM, its merits make it worth considering in its own right.

Empty Waves in Bohmian Quantum Mechanics

There is a recurring line of argument in the literature to the effect that Bohm's theory fails to solve the measurement problem. I show that this argument fails in all its variants. Hence Bohm's theory, whatever its drawbacks, at least succeeds in solving the measurement problem. I briefly discuss a similar argument that has been raised against the GRW theory. 1. Introduction2. Three Theories3. The Basic Argument4. Branches and Worlds5. Theory and Interpretation6. Size Matters7. Conclusion

Probability in GRW theory

GRW theory postulates a stochastic mechanism assuring that every so often the wave function of a quantum system is ‘hit’, which leaves it in a localised state. How are we to interpret the probabilities built into this mechanism? GRW theory is a firmly realist proposal and it is therefore clear that these probabilities are objective probabilities (i.e. chances). A discussion of the major theories of chance leads us to the conclusion that GRW probabilities can be understood only as either single case propensities or Humean objective chances. Although single case propensities have some intuitive appeal in the context of GRW theory, on balance it seems that Humean objective chances are preferable on conceptual grounds.

Completeness, supervenience and ontology

In 1935, Einstein, Podolsky and Rosen raised the issue of the completeness of the quantum description of a physical system. What they had in mind is whether or not the quantum description is informationally complete, in that all physical features of a system can be recovered from it. In a collapse theory such as the theory of Ghirardi, Rimini and Weber, the quantum wavefunction is informationally complete, and this has often been taken to suggest that according to that theory the wavefunction is all there is. If we distinguish the ontological completeness of a description from its informational completeness, we can see that the best interpretations of the GRW theory must postulate more physical ontology than just the wavefunction.

GRW: A Case Study in Quantum Ontology

AbstractThis article provides an overview of the philosophical literature on the GRW theory of quantum mechanics, and argues for a particular position regarding that literature. Much of the literature is ontological; it attempts to defend a conception of what the world is like according to the GRW theory against perceived competitors. I argue that there is no real debate here, since these supposedly conflicting positions are better regarded as alternative and compatible ways of describing the world of the GRW theory.

Losing Your Marbles in Wavefunction Collapse Theories

Peter Lewis ([1997]) has recently argued that the wavefunction collapse theory of GRW (Chirardi, Rimini and Weber [1986]) can only solve the problem of wavefunction tails at the expense of predicting that arithmetic does not apply to ordinary macroscopic objects. More specifically, Lewis argues that the GRW theory must violate the enumeration principle: that 'if marble 1 is in the box and marble 2 is in the box and so on through marble n, then all n marbles are in the box' ([1997], p. 321). Ghirardi and Bassi ([1999]) have replied that it is meaningless to say that the enumeration principle is violated because the wavefunction Lewis uses to exhibit the violation cannot persist, according to the GRW theory, for more than a split second ([1999], p. 709). On the contrary, we argue that Lewis's argument survives Ghirardi and Bassi's criticism unscathed. We then go on to show that, while the enumeration principle can fail in the GRW theory, the theory itself guarantees that the principle can never be empirically falsified, leaving the applicability of arithmetical reasoning to both micro- and macroscopic objects intact.

Do Dynamical Reduction Models Imply that Arithmetic Does Not Apply to Ordinary Macroscopic Objects?

We analyse a recent paper in which an alleged devastating criticism of the so called GRW proposal to account for the objectification of the properties of macroscopic systems has been presented and we show that the author has not taken into account the precise implications of the GRW theory. This fact makes his conclusions basically wrong. We also perform a survey of measurement theory aimed to focus better on the physical and the conceptual aspects of the so-called macro-objectification problem.

Quantum Mechanics, Orthogonality, and Counting

In quantum mechanics it is usually assumed that mutually exclusives states of affairs must be represented by orthogonal vectors. Recent attempts to solve the measurement problem, most notably the GRW theory, require the relaxation of this assumption. It is shown that a consequence of relaxing this assumption is that arithmatic does not apply to ordinary macroscopic objects. It is argued that such a radical move is unwarranted given the current state of understanding of the foundations of quantum mechanics.

GRW and the tails problem

The GRW theory is a recent attempt to solve the measurement problem in quantum mechanics, and the tails problem is a well-known and potentially fatal criticism of the GRW theory. The first half of the paper is an exposition of the measurement problem, the GRW theory, and the tails problem. In the remainder of the paper, two methods of dealing with the tails problem are considered: first, altering the GRW theory so as to avoid the tails problem; and second, denying that the tails problem is more than a novel aspect of a universal vagueness in the way scientific theories relate to everyday language.

On some speculations about the state reductions of photons

The spontaneous collapses of the wave functions of photons, within the framework of possible relativistic extensions of the theory of Ghirardi, Rimini, and Weber are discussed. It is shown that a recently published argument which claims that such collapses can account for the emergence of determinate outcomes of certain experiments involving fluorescent screens is inadequate, since it is based on an unreasonable speculation about the treatment of photons in the GRW theory.

Can GRW theory be tested by experiments on SQUIDS?

A recent theory shows that a collapse of the wavefunction representing a macroscopic pointer would result if one of its component particles were spontaneously localised. The consequences of such microscopic localisation for a SQUID operating in the macroscopic quantum regime is discussed.