Andrew Elby

Why “modal” interpretations of quantum mechanics don't solve the measurement problem

According to “modal” interpretations of quantum mechanics, an observable Q can possess a definite value even when the quantum state is not an eigenstate of Q. In this paper, I discuss some interpretive difficulties faced by modal theorists. First, expanding upon Albert and Loewer, I identify two reasons why real-life measurements are never ideal, and I discuss why these considerations bode ill for modal interpretations. Second, I show that modal interpretations provide a less satisfactory explanation of “interference” effects than is provided by pilot-wave interpretations.

Nonlocality and Gleason's lemma. Part 2. Stochastic theories

I derive a Gleason-type contradiction from assumptions weaker than those needed to reach a Bell inequality. By establishing the inconsistency between local realism and QMs perfect EPR-type anticorrelations, the proof fills in a gap left open by Bell arguments.

A SQUID no-go theorem without macrorealism : what SQUID's really tell us about nature

Without invoking macrorealism, we derive a contradiction between the quantum mechanical predictions forsquids and two intuitive conditions. First, we assume that asquid can be measured without significantly disturbing its subsequent macroscopic behavior. Second, we assume a trivial realism condition much weaker than Leggetts macrorealism. Quantum mechanics itself obeys our realism assumption. This proof suggests that althoughsquid experiments cannot rule out macrorealism, they can rule out most theories that allow noninvasive measurements.

What makes a theory physically “complete”?

Three claims about what makes a theory “physically complete” are (1) Shimonys assertion that a complete theory says “all there is to say” about nature; (2) EPRs requirement that a complete theory describe all “elements of reality”; and (3) Ballentine and Jarretts claim that a “predictively complete” theory must obey a condition used in Bell deviations. After introducing “statistical completeness” as a partial formalization of (1), we explore the logical and motivational relationships connecting these completeness conditions. We find that statistical completeness motivates but does not imply Jarretts completeness condition, because Jarretts condition encodes further intuitions about locality and causality. We also dispute Ballentine and Jarretts claim that EPR-completeness implies Jarretts completeness condition.

Why SQUID experiments can rule out non-invasive measurability

Abstract From macrorealism and non-invasive measurability (NIM), Leggett and Garg derive inequalities that contradict QMs predictions for SQUIDs. We derive those inequalities from NIM and a “realism” assumption weaker than macrorealism. If Tesches null-result measurements violate those inequalities, our derivation suggests that NIM is the “culprit” and must be renounced.

Weakening the locality conditions in algebraic nonlocality proofs

Abstract Using the Kochen-Specker theorem, we derive a simple algebraic contradiction between various locality assumptions and the predictions of quantum mechanics. Unlike previous algebraic nonlocality proofs, this proof invokes locality conditions uniformly weaker than those needed to derive Bells inequality. Consequently, our proof rules out a broader class of hidden variable theories.

Contentious Contents: For Inductive Probability

According to Popper and Miller [1983 and 1987], the part of a hypothesis that transcends the evidence is probablistically countersupported by the evidence. Therefore, inductive support is not probabilistic support. Their argument hinges on imposing the following necessary condition on ‘the part of a hypothesis h that goes beyond the evidence e’: that transcendent part, called k, must share no nontrivial consequences with e. I propose a new condition on k that is incompatible with Popper and Millers condition. I then show why the new condition is a viable alternative to Popper and Millers. By doing so, I refute their argument that probabilistic support cannot be inductive.

Why Local Realistic Theories Violate, Nontrivially, the Quantum Mechanical EPR Perfect Correlations

Using the Kochen–Specker contradiction, I prove that ‘local realistic’ theories predict nontrivial violations of the quantum mechanical EPR-type perfect anticorrelations. The proof invokes the same stochastic local realism conditions used in Bell arguments. For a class of theories called ‘orthodox spin theories’, the perfect anticorrelations used in the proof emerge from rotational symmetry. Therefore, an orthodox spin theorist must abandon either the spirit of relativity, as encoded by local realism, or the letter of relativity, which demands rotational invariance.

Critique of Home and Sengupta's derivation of a Bell inequality

Home and Sengupta claim to derive a Bell-type inequality without assuming locality. I show that their derivation implicitly assumes determinism and a weak locality condition. Their derivation also relies upon further, highly implausible conditions that severely limit the physical implications of their argument.

On the physical interpretation of Heywood and Redhead's algebraic impossibility theorem

Heywood and Redheads 1983 algebraic (Kochen-Specker type) impossibility proof, which establishes the inconsistency of a broad class of contextualized local realistic theories, assumes two locality conditions and two auxiliary assumptions. One of those auxiliary conditions, FUNC*, has been called a physically unmotivated,ad hoc formal constraint.In this paper, we derive Heywood and Redheads auxiliary conditions from physical assumptions. This allows us to analyze which classes of hidden-variables theories escape the Heywood-Redhead contradiction. By doing so, we hope to clarify the physical and philosophical ramifications of the Heywood-Redhead proof. Most current hidden-variables theories, it turns out, violate Heywood and Redheads auxiliary conditions.