Steven Weinstein

Is the Brain a Quantum Computer

We argue that computation via quantum mechanical processes is irrelevant to explaining how brains produce thought, contrary to the ongoing speculations of many theorists. First, quantum effects do not have the temporal properties required for neural information processing. Second, there are substantial physical obstacles to any organic instantiation of quantum computation. Third, there is no psychological evidence that such mental phenomena as consciousness and mathematical thinking require explanation via quantum theory. We conclude that understanding brain function is unlikely to require quantum computation or similar mechanisms.

On determinism and well-posedness in multiple time dimensions

We study the initial value problem for the wave equation and the ultrahyperbolic equation for data posed on initial hypersurfaces surface of arbitrary space–time signature. We show that, under a non-local constraint, the initial value problem posed on codimension-one hypersurfaces—the Cauchy problem—has global unique solutions in the Sobolev spaces Hm. Thus, it is well-posed. However, we show that the initial value problem on higher codimension hypersurfaces is ill-posed due to failure of uniqueness, at least when specifying a finite number of derivatives of the data. This failure is in contrast to a uniqueness result for data given in an arbitrary neighbourhood of such initial hypersurfaces, which Courant deduces from Asgeirsson’s mean value theorem. We give a generalization of Courant’s theorem that extends to a broader class of equations. The proofs use Fourier synthesis and the Holmgren–John uniqueness theorem.

Superluminal Signaling and Relativity

Special relativity is said to prohibit faster-than-light (superluminal) signaling, yet controversy regularly arises as to whether this or that physical phenomenon violates the prohibition. I argue that the controversy is a result of a lack of clarity as to what it means to ‘signal’, and I propose a criterion. I show that according to this criterion, superluminal signaling is not prohibited by special relativity.

Absolute Quantum Mechanics

Whereas one can conceive of a relational classical mechanics in which absolute space and time do not play a fundamental role, quantum mechanics does not readily admit any such relational formulation.

Nonlocality Without Nonlocality

Bell’s theorem is purported to demonstrate the impossibility of a local “hidden variable” theory underpinning quantum mechanics. It relies on the well-known assumption of ‘locality’, and also on a little-examined assumption called ‘statistical independence’ (SI). Violations of this assumption have variously been thought to suggest “backward causation”, a “conspiracy” on the part of nature, or the denial of “free will”. It will be shown here that these are spurious worries, and that denial of SI simply implies nonlocal correlation between spacelike degrees of freedom. Lorentz-invariant theories in which SI does not hold are easily constructed: two are exhibited here. It is conjectured, on this basis, that quantum-mechanical phenomena may be modeled by a local theory after all.

Strange Couplings and Space-Time Structure

General relativity is commonly thought to imply the existence of a unique metric structure for space-time. A simple example is presented of a general relativistic theory with ambiguous metric structure. Brans-Dicke theory is then presented as a further example of a space-time theory in which the metric structure is ambiguous. Other examples of theories with ambiguous metrical structure are mentioned. Finally, it is suggested that several new and interesting philosophical questions arise from the sorts of theories discussed.

Objectivity, Information, and Maxwell's Demon

This paper examines some common measures of complexity, structure, and information, with an eye toward understanding the extent to which complexity or information‐content may be regarded as objective properties of individual objects. A form of contextual objectivity is proposed which renders the measures objective, and which largely resolves the puzzle of Maxwells Demon.

Naive Quantum Gravity

In this paper we consider a naive conception of what a quantum theory of gravity might entail: a quantum-mechanically fluctuating gravitational field at each spacetime point. We argue that this idea is problematic both conceptually and technically.

Patterns in the Fabric of Nature

From classical mechanics to quantum field theory, the physical facts at one point in space are held to be independent of those at other points in space. I propose that we can usefully challenge this orthodoxy in order to explain otherwise puzzling correlations at both cosmological and microscopic scales.

ELECTROMAGNETISM AND TIME-ASYMMETRY

It is a commonplace to note that in a world governed by special or general relativity, an observer has access only to data within her past lightcone (if that). The significance of this for prediction, and thus for confirmation, does not however seem to have been appreciated. In this paper we show that what we regard as our most well-confirmed relativistic theory, Maxwells theory of electromagnetism, is not at all well-confirmed in the absence of an additional assumption, the assumption that all fields have sources in their past. We conclude that we have reason to believe that there is a lawlike time-asymmetry in the world.