Proper relativistic position operators in 1+1 and 2+1 dimensions

We have revisited the Dirac theory in [Formula: see text] and [Formula: see text] dimensions by using the covariant representation of the parity-extended Poincaré group in their native dimensions. The parity operator plays a crucial role in deriving wave equations in both theories. We studied two position operators, a canonical one and a covariant one that becomes the particle position operator projected onto the particle subspace. In [Formula: see text] dimensions the particle position operator, not the canonical position operator, provides the conserved Lorentz generator. The mass moment defined by the canonical position operator needs an additional unphysical spin-like operator to become the conserved Lorentz generator in [Formula: see text] dimensions. In [Formula: see text] dimensions, the sum of the orbital angular momentum given by the canonical position operator and the spin angular momentum becomes a constant of motion. However, orbital and spin angular momentum do not conserve separately. On the other hand the orbital angular momentum given by the particle position operator and its corresponding spin angular momentum become a constant of motion separately.

How to Be Antiscientific

This article is a response to the science wars that broke out in the mid-1990s. It focuses on an analysis of pragmatics and the nature of the use of statements about science by scientists. What triggered the science wars were the relativistic and constructivist claims of sociologists and historians of science about their field, but the author demonstrates that scientists themselves indulge in similar judgments. As an interested observer, he shows through a series of examples that the metascientific claims of scientists about the nature of science and the scientific method are diverse and often contradict each other. Possible conclusions to be drawn from this variability are then analyzed. The first one is that some metascientific statements by scientists are true and others are false. The second one suggests that all metascientific statements made by working scientists should be ignored. The author shows that both these conclusions are unsatisfactory. The main thrust of the article pertains to the variability of metascientific statements and their relationship with science itself. According to the author, metascientific statements, which often oppose each other, do not describe a single essence of science or a universal scientific method, but they highlight instead specific aspects of scientific practices localized in space, time and cultural context. This makes the relationship between metascience and science contingent, and the question of how to be antiscientific becomes problematic. The author outlines invalid ways to be antiscientific and shows how a relativistic position could be not antiscientific. One can have confidence in the sciences and yet be skeptical about the metascientific statements which offer a single essence of science. The author finds that being for or against a certain essence of science in general means being against nothing very much in particular. What matters is local criticism within a science itself or in the separate parts of it which are associated with specific research or institutional issues.

Relativism: A demon roaming through science

The advocates of the so-called "hard science" view relativism as an extreme undesirable standpoint. The ill fame of relativism is most frequently explained by the opinion that relativism is striving, in general, for the position where "everything is possible", thus hindering the progress of science and leading to its destruction in the long run. Those opposing relativism, consider relativistic position, in the best of cases, depressing and solipsistic, and, in the worst of cases, extremely destructive. Regarding the fact that such an attitude most often results from the ignorance (sometimes from profound ignorance) of the basic principles of relativistic doctrine, a more elaborate consideration was given herein to the relativistic doctrine: its definitions, opposing other doctrines and diverse orientations. In short, relativism is founded neither upon a view that everything is possible, nor is its application impossible in science nor are its implications so destructive for science as stated by the opponents of this attitude. In addition, the article considers the issue of harmonizing relativism with multiperspectivism of science. Therefore, the presentation to follow should be taken as an attempt to define relativism more closely and to point out its potentials and the road science can take in the time to come.