History and Philosophy Of Science | The History & Philosophy of Special Relativity
X790 | 28392 | Amit Hagar

In our thinking about the world, especially in physics, infinities
play a crucial role; the continuum of the real numbers as a
representation of spacetime is the best known example.  Throughout
the history of science, however, many have felt that the continuum
model is an unphysical idealization, and that there are in fact only
a finite number of degrees of freedom in any finite volume. This
tension between the discrete and the continuous has its roots in the
philosophy of mathematics, and goes back to the early days of Zeno.
Penetrating modern theoretical physics, it has fuelled the
development of our theories of matter. But while ideas about atomism
and discreteness have proven instrumental in the inception of
statistical mechanics and the quantum theory, the attempts to
incorporate them into the space-time arena and to apply them in
field theories have met with strong resistance. Trying to overcome
theoretical inconsistencies in the context of the unification of
quantum theory with the special theory of relativity, that arise
from the tension between a point particle and a continuous field, or
from the attempts to quantize fields with infinite degrees of
freedom, many physicists had entertained the notion of a fundamental
length, but had eventually abandoned it, as it became difficult to
reconcile the hypothesis of discrete space with local Lorentz
invariance and with unitary quantum theory. Remarkably, in recent
years theoretical physics has witnessed a revival of the notion of
fundamental length, and many candidates to the future theory of
quantum gravity incorporate it in their theoretical structure.
This course will investigate the inter-relations between mathematics
and physics as they are manifest in the development of the ideas
surrounding the notion of fundamental length. Possible research
questions: Zenoís argument against the continuum; Non-standard
analyses and the alternative to the real line segment; Argument
against discrete spacetime; Discreteness in Statistical Mechanics;
Non local field theories; Heisenberg and March on fundamental
length; Fundamental length in quantum gravity; Violations of Lorenz
invariance in HEP

All the physics/math necessary for the course will be taught in
class; the class will definitely be accessible to humanities
students and conceptually challenging to both humanities and science
majors. Each participant in the seminar will be required to make at
least one presentation to the seminar, on a the research topic to be
chosen in consultation with the instructor, that would result in a
research paper (minimum 20 pp). Grading will given according to
studentís presentation and final term paper. The extra credit
reflects the fact this course is a research seminar, which requires
substantial research and writing skills.