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UNL2201
SPACE, TIME AND MATTER
2013/2014, Semester 2
University Scholars Programme (University Scholars Programme)
Modular Credits: 4
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Teaching Modes
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Twice weekly meetings for seminars and discussion (2 hours each)
Synopsis
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Our common-sense conception of space, time and matter posits that everything is made up of tiny indivisible, unchangeable particles (called atoms) that move in a vast void or empty space. Advocated by Greek philosophers, Democritus and Leucippus in 5th century BCE, this simplistic notion has survived major revisions of our world view and is still held by the lay, but educated masses . Likened to an empty stage, space is sometime regarded as the arena for matter to stage its play; in the form of motion. How accurate and complete is this view? Is space a passive entity that behaves as a place holder for matter to make it presence? Or does it have physical reality, the sort that we usually ascribe to matter? Can space, if it exists in the physical sense, be independent from matter that populates it? What, then, are the attributes of space and time that would allow one to measure and hence ascribe physical reality?
In this module we retrace key developments that led Einstein to his theory of General Relativity. This module introduces students to some of the assumptions and ideas that underlie our current conception of space and time. The three strands, namely the philosophical, mathematical and physical aspects, are used as frameworks for examining the issues related to the subject matter.
Syllabus
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Tentative Outline
Early conceptions of space, time and matter.
ideas of Descartes, Leibniz, Kant and Galileo with emphasis on rationalism and empiricism;
The axiomatic and the scientific methods;
Kant’s concept of space and time.
The mathematization of science in the 17
^{th}
Century.
Descartes’ coordinate geometry (the marriage of algebra and geometry);
Galileo’s Principle of Inertia and the mathematics of motion;
Newton’s laws of motion and the concept of absolute space.
The mathematical foundations of geometry.
Euclid’s axiomatic approach to geometry;
Topological spaces leading up to manifolds and Riemannian spaces;
The notion of symmetries and its relation to geometry.
The relativity of space and time
Galilean Relativity and its implication for space and time;
Einstein’s theory of Special Relativity – its emergence and its implications;
Space and Time as a four-dimensional continuum – Minkowski space;
Einstein’s theory of General Relativity.
Einstein’s Equivalence Principle and its implications;
Riemannian geometry as the framework for space and time in the presence of matter;
Validation of Einstein’s theory of General Relativity and its cosmological implications.
Assessment
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Class Participation and Individual Assignments 20%
Group Assignments 20%
Term Paper 30%
Final Exam 30%
Workload
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2-2-0-3-3
Workload Components : A-B-C-D-E
A: no. of lecture hours per week
B: no. of tutorial hours per week
C: no. of lab hours per week
D: no. of hours for projects, assignments, fieldwork etc per week
E: no. of hours for preparatory work by a student per week