465 Cohen Hall
Office Hours: MWF: 12-1
First reading: Frame of the Universe- Ch. 4,5
Universe, Space and Time
Universe as a whole is spherical. There is a part within it that is observable- handled by
Geocentric, with circular orbits. Center of the universe is the central fire, and the
counter-Earth blocks the Earth from the central fire.
This is true because a world created by God must be perfect, intentional, harmonious and
Prof. Zoltan Domotor
Prof. Zoltan Domotor
Galileo and the Church
In 1632, Galileo Galilei published his lifes masterpiece, Dialogue Concerning
the Two Chief World Systems , in which he
Term paper: 15 pages double spaced, on anything that is covered this semester.
Minkowski spacetime and its light cone structure.
With time on the y-axis, and space coordinate on the x-axis, the light
Confirmation of Relativity Theories
Definition: An event (phenomenon) E is said to confirm a hypothesis H in theory T just in
case the following conditions are satisfied:
Event E is observed out there.
Reading: Today: Frame, ch. 13- General Relativity. Next week: Frame, ch. 14Relativistic cosmological models.
General Relativity (Einstein 1915)
Inertial force arises in the presence of acceleration (fo
P1- Geometric cosmological models (Frame, Ch. 4,5,6)- Pythagoras-Philolaus, Aristotle,
Pythagoras-Philolaus (580 BC)
Underlying metaphysics: Triangle with numbers at one angle (top), music at an
Consequences of Special Relativity (cont.)
1. Relativistic composition of velocities
2. Minkowski light cone structure of spacetime
3. Nonexistence of absolute simultaneity- Time has sense only in reference to its
Consequences of the Two Principles of Special Relativity
1. Nonlinear relativistic composition of velocities: V 1 V2=(V1+V2)/(1+(V1V2/c2) c.
V c=(V+c)/(1+(v/c) x c/c=(v+c)c)/(c+v)=c.
2. Minkowski light cone structure
MIDTERM: Wednesday 11/3
Consequences of Newtons Laws
1. Keplers laws follow as theorems from Newtons laws.
2. Galileos Earth-bound laws (freefall, trajectories of projectiles, periods of pendulums)
also follow as the
Newtons Laws of Motion
L1 Law of inertia- All bodies move in a straight line with constant velocity (or remain in a
state of rest) if no forces act upon them (Descartes).
Symbolically: Force(b,t)=0 velocity (b,t)=con
Next reading: Frame, ch. 12 Special Relativity
Newtons 4 Fundamental Theoretical Concepts
1. The notion of absolute space (infinite container conception). This notion also includes
the notion of absolute rest.
Johannes Kepler (1571-1630)
Keplers laws (empirical rather than theoretical, meaning Kepler simply put down a
summary statement of his observations, he does not give explanations).
Law of ellipses- All planets move i
Galileo and the Church
The conflict started with a letter addressed to Grand Duchess Christine. In 1616, Pope
V issues a decree that puts Copernicus on the Index. Cardinal Bellarmine notifies
Galileo about his letter
Nicholas Copernicus (Conclusion)
Osiander edited/published Copernicuss book. Osiander wrote an unsigned preface,
changed the name of the book (without Copernicuss permission) to something that
sounded more Aristoteli
Copernican Heliocentric Cosmological Model
The static sun is the center of the universe, with the planets (up to Saturn had been
discovered) orbiting around the sun, and the moon orbiting around the Earth, with an
Ptolemaic Geocentric Cosmological Model (Conclusion)
The problem: Phenomena (data) indicate complex motions of the following kind:
Mercurys heart-like orbit from the vantage point of Earth.
1. Ptolemy saved the phenom
Reading: Frame of the Universe, ch. 8 (Copernican Revolution)
Ptolemaic Geocentric Cosmological Model (that saved all of the phenomena, 160
Trouble in the Aristotelian paradise
Variable distances of planets from t
Reading: Frame of the Universe, Chapter 6
Aristotelian 2-Sphere Cosmological Model
Static Earth in the center of the universe. There is one sphere, on whichs surface is the
moon (so the first sphere is basically the m
Aristotelian Strictly Geocentric 2-Sphere Model of the Universe (350 BC)
Earth is in the center of the universe (static, spherical Earth in center)
Arguments: If the Earth moved, then when you jump, you woul
Ancient Cosmological Paradigms
Mini-paradigm shifts in the ancient geocentric tradition:
Pre-scientific cosmology Pythagoras-Philolaus cosm. paradigm Aristotelian strictly
geocentric cosmological paradigm Ptolemaic ge
I. Roots of Relativity
A world created by God.
Prominent cosmologists and philosophers of the ancient tradition:
900700 BC: Homeric period (pre-philosophy); 600 BC: Thales (starting point for
philosophy); 580 BC: *Pyt