Abstract Some physicists but many philosophers believe that standard Hilbert space quantum mechanics faces a serious measurement problem, whose solution requires a new theory or at least a novel interpretation of standard quantum mechanics. Itamar Pitowsky did not. Instead, he argued in a major essay (Pitowsky 2006) that quantum mechanics offers a new theory of probability. In these and other respects, his views paralleled those of QBists (quantum Bayesians): but their views on the objectivity of measurement outcomes diverged radically. Indeed, Itamar’s view of quantum probability depended on his subtle treatment of the objectivity of outcomes as events whose collective structure underlay this new theory of probability. His thesis is puzzling—that quantum mechanics requires a new theory of probability, as distinct from new ways of calculating probabilities that play the same role as other probabilities in physics and daily life. This essay articulates sources of puzzlement.
Abstract Some physicists but many philosophers believe that standard Hilbert space quantum mechanics faces a serious measurement problem, whose solution requires a new theory or at least a novel interpretation of standard quantum mechanics. Itamar Pitowsky did not. Instead, he argued in a major essay (Pitowsky 2006) that quantum mechanics offers a new theory of probability. In these and other respects, his views paralleled those of QBists (quantum Bayesians): but their views on the objectivity of measurement outcomes diverged radically. Indeed, Itamar’s view of quantum probability depended on his subtle treatment of the objectivity of outcomes as events whose collective structure underlay this new theory of probability. His thesis is puzzling—that quantum mechanics requires a new theory of probability, as distinct from new ways of calculating probabilities that play the same role as other probabilities in physics and daily life. This essay articulates sources of puzzlement.
Quantum mechanics is the most useful and powerful theory physicists have ever devised. Yet today, nearly 90 years after its formulation, disagreement about the meaning of the theory is stronger than ever. New interpretations appear every year. None ever disappear. Probability theory is considerably older than quantum mechanics and has also been plagued from the beginning by questions about its meaning. And quantum mechanics is inherently and famously probabilistic. For the past decade, Carl Caves, Chris Fuchs, and Rüdiger Schack have been arguing that the confusion at the foundations of quantum mechanics arises out of a confusion, prevalent among physicists, about the nature of probability [1]. They maintain that if probability is properly understood, the notorious quantum paradoxes either vanish or assume less vexing forms. Most physicists have a frequentist view of probability: Probabilities describe objective properties of ensembles of “identically prepared” systems. Caves, Fuchs, and Schack take a personalist Bayesian view: An agent assigns a probability p to a single event as a measure of her belief that the event will take place [2]. Such an agent is willing to pay less than $ p for a coupon that will pay her $1 if the event happens, and she is willing to underwrite and sell such a coupon for more than $ p . Surprisingly, the standard rules for probability follow from the requirement that an agent should never face certain loss in a single event. (For example, if p exceeded 1, she would pay more than $1 for a coupon that returned at most $1; if p were negative, she would pay somebody to take a coupon from her that might cost her another $1.) Avoiding certain loss is the only constraint on an agent's probability assignments. The probability of an event is not inherent in that event. Different agents, with different beliefs, will in general assign different probabilities to the same event. The personalist Bayesian view of probability is widely held [3], though not by many physicists. It has profound implications for the meaning of quantum mechanics, which Fuchs and Schack call quantum Bayesianism—QBism for short. Since quantum states determine probabilities, if probabilities are indeed assigned by an agent to express her degree of belief, then the quantum state of a physical system is not inherent in that system but assigned by an agent to encapsulate her beliefs about it. State assignments, like probabilities, are relative to an agent.
I review the role of probability in contemporary physics and the origin of probabilistic time asymmetry, beginning with the pre-quantum case (both stochastic mechanics and classical statistical mechanics) but concentrating on quantum theory. I argue that quantum mechanics radically changes the pre-quantum situation and that the philosophical nature of objective probability in physics, and of probabilistic asymmetry in time, is dependent on the correct resolution of the quantum measurement problem.
The main difficulty facing no-collapse theories of quantum mechanics in the Everettian tradition concerns the role of probability within a theory in which every possible outcome of a measurement actually occurs. The problem is two-fold: First, what do probability claims mean within such a theory? Second, what ensures that the probabilities attached to measurement outcomes match those of standard quantum mechanics? Deutsch has recently proposed a decision-theoretic solution to the second problem, according to which agents are rationally required to weight the outcomes of measurements according to the standard quantum-mechanical probability measure. I show that this argument admits counterexamples, and hence fails to establish the standard probability weighting as a rational requirement.
Quantum mechanics is a fundamentally probabilistic theory (at least so far as the empirical predictions are concerned). It follows that, if one wants to properly understand quantum mechanics, it is essential to clearly understand the meaning of probability statements. The interpretation of probability has excited nearly as much philosophical controversy as the interpretation of quantum mechanics. 20th century physicists have mostly adopted a frequentist conception. In this paper it is argued that we ought, instead, to adopt a logical or Bayesian conception. The paper includes a comparison of the orthodox and Bayesian theories of statistical inference. It concludes with a few remarks concerning the implications for the concept of physical reality.
Abstract Until recently Jeffrey Bub and Itamar Pitowsky, in the framework of an information-theoretic view of quantum mechanics, claimed first that to the measurement problem in its ordinary formulation there correspond in effect two measurement problems (simply called the big and the small measurement problems), with a different degree of relevance and, second, that the analysis of a quantum measurement is a problem only if other assumptions – taken by Pitowsky and Bub to be unnecessary ‘dogmas’ – are assumed. Here I critically discuss this unconventional stance on the measurement problem and argue that the Bub-Pitowsky arguments are inconclusive, mainly because they rely on an unwarranted extension to the quantum realm of a distinction concerning the foundations of special relativity which is in itself rather controversial.
Applications of quantum mechanics have led to many successful predictions and explanations of puzzling phenomena, and we now apply quantum mechanics to gain, process, and communicate information in novel ways. We can understand quantum mechanics by understanding how we have applied it. We should not seek agreement on the nature of the world it represents, because this theory does not itself represent the physical world (though its applications do help us to represent it better). When applied to a quantum state, quantum mechanics yields probabiities for physical events: both state and probability are objective--not because they represent elements of phyiscal reality, but because each exerts norrmative authority over the beliefs of anyone who accepts quantum mechanics and applies it relative to a physical situation they may (but need not) occupy. These events may be described by statements that are meaningful in an appropriate environmental context, and quantum mechanics can help one to say when that is. Measurement creates an appropriate context, so here the Born rule indirectly yields probabilities of measurement outcomes. The quantum state of a system does not "collapse" on measurement: a new state must be assigned relative to a physical situation in which information about the outcome is accessible. Understood this way, there is no measurement problem, and violations of Bell inequalities does not demonstrate "spooky" non-local action. Quantum field theories have no physical ontology of their own: a quantum field is a mathematical object in a model whose application helps us to improve and extend our descriptions of the world in other terms. We cannot realise the scenario of Wigner's friend and its recent extensions: but the data that provide overwhelming evidence for quantum mechanics are objective in the same sense as the relative measurement outcomes described in those scenarios.